Full list of non-zero Kazhdan-Lusztig-Vogan polynomials:

   0:    0: 1

   1:    0: 1
         1: 1

   2:    0: 1
         2: 1

   3:    0: 1
         3: 1

   4:    0: 1
         4: 1

   5:    0: 1
         5: 1

   6:    0: 1
         1: 1
         2: 1
         6: 1

   7:    0: 1
         1: 1
         2: 1
         7: 1

   8:    0: 1
         2: 1
         3: 1
         8: 1

   9:    0: 1
         1: 1
         3: 1
         9: 1

  10:    0: 1
         2: 1
         3: 1
        10: 1

  11:    0: 1
         3: 1
         5: 1
        11: 1

  12:    0: 1
         3: 1
         4: 1
        12: 1

  13:    0: 1
         1: 1
         4: 1
        13: 1

  14:    0: 1
         2: 1
         4: 1
        14: 1

  15:    0: 1
         3: 1
         4: 1
        15: 1

  16:    0: 1
         1: 1
         5: 1
        16: 1

  17:    0: 1
         2: 1
         5: 1
        17: 1

  18:    0: 1
         3: 1
         5: 1
        18: 1

  19:    0: 1
         4: 1
         5: 1
        19: 1

  20:    0: 1
         1: 1
         2: 1
         3: 1
         6: 1
         8: 1
         9: 1
        20: 1

  21:    0: 1
         1: 1
         2: 1
         6: 1
         7: 1
        21: 1

  22:    0: 1
         1: 1
         2: 1
         3: 1
         7: 1
         8: 1
         9: 1
        22: 1

  23:    0: 1
         2: 1
         3: 1
         5: 1
         8: 1
        11: 1
        17: 1
        23: 1

  24:    0: 1
         2: 1
         3: 1
         4: 1
         8: 1
        12: 1
        14: 1
        24: 1

  25:    0: 1
         1: 1
         2: 1
         3: 1
         6: 1
         9: 1
        10: 1
        25: 1

  26:    0: 1
         1: 1
         2: 1
         3: 1
         7: 1
         9: 1
        10: 1
        26: 1

  27:    0: 1
         2: 1
         3: 1
         8: 1
        10: 1
        27: 1

  28:    0: 1
         1: 1
         3: 1
         5: 1
         9: 1
        11: 1
        16: 1
        28: 1

  29:    0: 1
         2: 1
         3: 1
         5: 1
        10: 1
        11: 1
        17: 1
        29: 1

  30:    0: 1
         1: 1
         3: 1
         4: 1
         9: 1
        12: 1
        13: 1
        30: 1

  31:    0: 1
         2: 1
         3: 1
         4: 1
        10: 1
        12: 1
        14: 1
        31: 1

  32:    0: 1
         3: 1
         4: 1
         5: 1
        11: 1
        12: 1
        19: 1
        32: 1

  33:    0: 1
         1: 1
         2: 1
         4: 1
         6: 1
        13: 1
        14: 1
        33: 1

  34:    0: 1
         1: 1
         2: 1
         4: 1
         7: 1
        13: 1
        14: 1
        34: 1

  35:    0: 1
         2: 1
         3: 1
         4: 1
         8: 1
        14: 1
        15: 1
        35: 1

  36:    0: 1
         1: 1
         3: 1
         4: 1
         9: 1
        13: 1
        15: 1
        36: 1

  37:    0: 1
         2: 1
         3: 1
         4: 1
        10: 1
        14: 1
        15: 1
        37: 1

  38:    0: 1
         3: 1
         4: 1
         5: 1
        11: 1
        15: 1
        19: 1
        38: 1

  39:    0: 1
         3: 1
         4: 1
        12: 1
        15: 1
        39: 1

  40:    0: 1
         1: 1
         2: 1
         5: 1
         6: 1
        16: 1
        17: 1
        40: 1

  41:    0: 1
         1: 1
         2: 1
         5: 1
         7: 1
        16: 1
        17: 1
        41: 1

  42:    0: 1
         2: 1
         3: 1
         5: 1
         8: 1
        17: 1
        18: 1
        42: 1

  43:    0: 1
         1: 1
         3: 1
         5: 1
         9: 1
        16: 1
        18: 1
        43: 1

  44:    0: 1
         2: 1
         3: 1
         5: 1
        10: 1
        17: 1
        18: 1
        44: 1

  45:    0: 1
         3: 1
         5: 1
        11: 1
        18: 1
        45: 1

  46:    0: 1
         3: 1
         4: 1
         5: 1
        12: 1
        18: 1
        19: 1
        46: 1

  47:    0: 1
         1: 1
         4: 1
         5: 1
        13: 1
        16: 1
        19: 1
        47: 1

  48:    0: 1
         2: 1
         4: 1
         5: 1
        14: 1
        17: 1
        19: 1
        48: 1

  49:    0: 1
         3: 1
         4: 1
         5: 1
        15: 1
        18: 1
        19: 1
        49: 1

  50:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         8: 1
         9: 1
        11: 1
        16: 1
        17: 1
        20: 1
        23: 1
        28: 1
        40: 1
        50: 1

  51:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         8: 1
         9: 1
        12: 1
        13: 1
        14: 1
        20: 1
        24: 1
        30: 1
        33: 1
        51: 1

  52:    0: 1
         1: 1
         2: 1
         3: 1
         6: 1
         7: 1
         8: 1
         9: 1
        20: 1
        21: 1
        22: 1
        52: 1

  53:    0: q+1
         1: 1
         2: q+1
         3: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        21: 1
        22: 1
        25: 1
        27: 1
        53: 1

  54:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         7: 1
         8: 1
         9: 1
        11: 1
        16: 1
        17: 1
        22: 1
        23: 1
        28: 1
        41: 1
        54: 1

  55:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         7: 1
         8: 1
         9: 1
        12: 1
        13: 1
        14: 1
        22: 1
        24: 1
        30: 1
        34: 1
        55: 1

  56:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        11: 1
        12: 1
        14: 1
        17: 1
        19: 1
        23: 1
        24: 1
        32: 1
        48: 1
        56: 1

  57:    0: 1
         1: 1
         2: 1
         3: 1
         6: 1
         8: 1
         9: 1
        10: 1
        20: 1
        25: 1
        27: 1
        57: 1

  58:    0: 1
         1: 1
         2: 1
         3: 1
         6: 1
         7: 1
         9: 1
        10: 1
        21: 1
        25: 1
        26: 1
        58: 1

  59:    0: 1
         1: 1
         2: 1
         3: 1
         7: 1
         8: 1
         9: 1
        10: 1
        22: 1
        26: 1
        27: 1
        59: 1

  60:    0: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        17: 1
        23: 1
        27: 1
        29: 1
        60: 1

  61:    0: 1
         2: 1
         3: 1
         4: 1
         8: 1
        10: 1
        12: 1
        14: 1
        24: 1
        27: 1
        31: 1
        61: 1

  62:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        25: 1
        28: 1
        29: 1
        40: 1
        62: 1

  63:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         7: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        26: 1
        28: 1
        29: 1
        41: 1
        63: 1

  64:    0: q+1
         2: 1
         3: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        17: 1
        18: 1
        27: 1
        29: 1
        42: 1
        45: 1
        64: 1

  65:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        25: 1
        30: 1
        31: 1
        33: 1
        65: 1

  66:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         7: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        26: 1
        30: 1
        31: 1
        34: 1
        66: 1

  67:    0: q+1
         2: 1
         3: q+1
         4: 1
         8: 1
        10: 1
        12: 1
        14: 1
        15: 1
        27: 1
        31: 1
        35: 1
        39: 1
        67: 1

  68:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        11: 1
        12: 1
        13: 1
        16: 1
        19: 1
        28: 1
        30: 1
        32: 1
        47: 1
        68: 1

  69:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        11: 1
        12: 1
        14: 1
        17: 1
        19: 1
        29: 1
        31: 1
        32: 1
        48: 1
        69: 1

  70:    0: q+1
         3: q+1
         4: 1
         5: 1
        11: 1
        12: 1
        15: 1
        18: 1
        19: 1
        32: 1
        39: 1
        45: 1
        49: 1
        70: 1

  71:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         8: 1
         9: 1
        13: 1
        14: 1
        15: 1
        20: 1
        33: 1
        35: 1
        36: 1
        71: 1

  72:    0: 1
         1: 1
         2: 1
         4: 1
         6: 1
         7: 1
        13: 1
        14: 1
        21: 1
        33: 1
        34: 1
        72: 1

  73:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         7: 1
         8: 1
         9: 1
        13: 1
        14: 1
        15: 1
        22: 1
        34: 1
        35: 1
        36: 1
        73: 1

  74:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        11: 1
        14: 1
        15: 1
        17: 1
        19: 1
        23: 1
        35: 1
        38: 1
        48: 1
        74: 1

  75:    0: 1
         2: 1
         3: 1
         4: 1
         8: 1
        12: 1
        14: 1
        15: 1
        24: 1
        35: 1
        39: 1
        75: 1

  76:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        25: 1
        33: 1
        36: 1
        37: 1
        76: 1

  77:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         7: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        26: 1
        34: 1
        36: 1
        37: 1
        77: 1

  78:    0: 1
         2: 1
         3: 1
         4: 1
         8: 1
        10: 1
        14: 1
        15: 1
        27: 1
        35: 1
        37: 1
        78: 1

  79:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        11: 1
        13: 1
        15: 1
        16: 1
        19: 1
        28: 1
        36: 1
        38: 1
        47: 1
        79: 1

  80:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        11: 1
        14: 1
        15: 1
        17: 1
        19: 1
        29: 1
        37: 1
        38: 1
        48: 1
        80: 1

  81:    0: 1
         1: 1
         3: 1
         4: 1
         9: 1
        12: 1
        13: 1
        15: 1
        30: 1
        36: 1
        39: 1
        81: 1

  82:    0: 1
         2: 1
         3: 1
         4: 1
        10: 1
        12: 1
        14: 1
        15: 1
        31: 1
        37: 1
        39: 1
        82: 1

  83:    0: 1
         3: 1
         4: 1
         5: 1
        11: 1
        12: 1
        15: 1
        19: 1
        32: 1
        38: 1
        39: 1
        83: 1

  84:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         8: 1
         9: 1
        16: 1
        17: 1
        18: 1
        20: 1
        40: 1
        42: 1
        43: 1
        84: 1

  85:    0: 1
         1: 1
         2: 1
         5: 1
         6: 1
         7: 1
        16: 1
        17: 1
        21: 1
        40: 1
        41: 1
        85: 1

  86:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         7: 1
         8: 1
         9: 1
        16: 1
        17: 1
        18: 1
        22: 1
        41: 1
        42: 1
        43: 1
        86: 1

  87:    0: 1
         2: 1
         3: 1
         5: 1
         8: 1
        11: 1
        17: 1
        18: 1
        23: 1
        42: 1
        45: 1
        87: 1

  88:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        12: 1
        14: 1
        17: 1
        18: 1
        19: 1
        24: 1
        42: 1
        46: 1
        48: 1
        88: 1

  89:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         9: 1
        10: 1
        16: 1
        17: 1
        18: 1
        25: 1
        40: 1
        43: 1
        44: 1
        89: 1

  90:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         7: 1
         9: 1
        10: 1
        16: 1
        17: 1
        18: 1
        26: 1
        41: 1
        43: 1
        44: 1
        90: 1

  91:    0: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        17: 1
        18: 1
        27: 1
        42: 1
        44: 1
        91: 1

  92:    0: 1
         1: 1
         3: 1
         5: 1
         9: 1
        11: 1
        16: 1
        18: 1
        28: 1
        43: 1
        45: 1
        92: 1

  93:    0: 1
         2: 1
         3: 1
         5: 1
        10: 1
        11: 1
        17: 1
        18: 1
        29: 1
        44: 1
        45: 1
        93: 1

  94:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        12: 1
        13: 1
        16: 1
        18: 1
        19: 1
        30: 1
        43: 1
        46: 1
        47: 1
        94: 1

  95:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        12: 1
        14: 1
        17: 1
        18: 1
        19: 1
        31: 1
        44: 1
        46: 1
        48: 1
        95: 1

  96:    0: 1
         3: 1
         4: 1
         5: 1
        11: 1
        12: 1
        18: 1
        19: 1
        32: 1
        45: 1
        46: 1
        96: 1

  97:    0: 1
         1: 1
         2: 1
         4: 1
         5: 1
         6: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        33: 1
        40: 1
        47: 1
        48: 1
        97: 1

  98:    0: 1
         1: 1
         2: 1
         4: 1
         5: 1
         7: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        34: 1
        41: 1
        47: 1
        48: 1
        98: 1

  99:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        35: 1
        42: 1
        48: 1
        49: 1
        99: 1

 100:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        13: 1
        15: 1
        16: 1
        18: 1
        19: 1
        36: 1
        43: 1
        47: 1
        49: 1
       100: 1

 101:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        37: 1
        44: 1
        48: 1
        49: 1
       101: 1

 102:    0: 1
         3: 1
         4: 1
         5: 1
        11: 1
        15: 1
        18: 1
        19: 1
        38: 1
        45: 1
        49: 1
       102: 1

 103:    0: 1
         3: 1
         4: 1
         5: 1
        12: 1
        15: 1
        18: 1
        19: 1
        39: 1
        46: 1
        49: 1
       103: 1

 104:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        20: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        40: 1
        47: 1
        48: 1
        50: 1
        51: 1
        56: 1
        68: 1
        97: 1
       104: 1

 105:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        16: 1
        17: 1
        20: 1
        21: 1
        22: 1
        23: 1
        28: 1
        40: 1
        41: 1
        50: 1
        52: 1
        54: 1
        85: 1
       105: 1

 106:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        12: 1
        13: 1
        14: 1
        20: 1
        21: 1
        22: 1
        24: 1
        30: 1
        33: 1
        34: 1
        51: 1
        52: 1
        55: 1
        72: 1
       106: 1

 107:    0: 1
         1: 1
         2: 1
         3: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        20: 1
        21: 1
        22: 1
        25: 1
        27: 1
        52: 1
        53: 1
        57: 1
       107: 1

 108:    0: q+1
         1: 1
         2: q+1
         3: 1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: q+1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        53: 1
        54: 1
        60: 1
        62: 1
        85: 1
       108: 1

 109:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: q+1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        53: 1
        55: 1
        61: 1
        65: 1
        72: 1
       109: 1

 110:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        34: 1
        41: 1
        47: 1
        48: 1
        54: 1
        55: 1
        56: 1
        68: 1
        98: 1
       110: 1

 111:    0: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         8: q+1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        32: 1
        35: 1
        39: 1
        42: 1
        45: 1
        48: 1
        49: 1
        56: 1
        70: 1
        75: 1
        87: 1
        99: 1
       111: 1

 112:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
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 113:    0: 1
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 114:    0: q+1
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 115:    0: 1
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 116:    0: 1
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 117:    0: 1
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 118:    0: 1
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 119:    0: q+1
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 120:    0: 1
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 121:    0: q+1
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 122:    0: 1
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 123:    0: q+1
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 124:    0: q+1
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 125:    0: 1
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 126:    0: q+1
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 127:    0: q+1
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 128:    0: 1
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 129:    0: 1
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 130:    0: 1
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 131:    0: q+1
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 132:    0: q+1
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 133:    0: q+1
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 134:    0: 1
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 135:    0: 1
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 136:    0: 1
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 137:    0: q+1
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 138:    0: 1
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 139:    0: 1
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         7: 1
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 140:    0: 1
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 141:    0: 1
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 142:    0: 1
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 143:    0: 1
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 144:    0: 1
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 145:    0: q+1
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 146:    0: 1
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        79: 1
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 147:    0: 1
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 148:    0: q+1
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        99: 1
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 149:    0: 1
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        39: 1
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 150:    0: 1
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 151:    0: 1
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        39: 1
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 152:    0: 1
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 153:    0: 1
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 154:    0: 1
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 155:    0: 1
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 156:    0: 1
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 157:    0: 1
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 158:    0: q+1
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 159:    0: 1
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        86: 1
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 160:    0: 1
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 161:    0: 1
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        32: 1
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        45: 1
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        56: 1
        87: 1
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 162:    0: 1
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         5: 1
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        43: 1
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 163:    0: 1
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        43: 1
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        58: 1
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        89: 1
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 164:    0: 1
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         5: 1
         7: 1
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        16: 1
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        22: 1
        26: 1
        27: 1
        41: 1
        42: 1
        43: 1
        44: 1
        59: 1
        86: 1
        90: 1
        91: 1
       164: 1

 165:    0: q+1
         2: q+1
         3: 1
         5: q+1
         8: 1
        10: 1
        11: 1
        17: q+1
        18: 1
        23: 1
        27: 1
        29: 1
        42: 1
        44: 1
        45: 1
        60: 1
        87: 1
        91: 1
        93: 1
       165: 1

 166:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        12: 1
        14: 1
        17: 1
        18: 1
        19: 1
        24: 1
        27: 1
        31: 1
        42: 1
        44: 1
        46: 1
        48: 1
        61: 1
        88: 1
        91: 1
        95: 1
       166: 1

 167:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        25: 1
        28: 1
        29: 1
        40: 1
        43: 1
        44: 1
        45: 1
        62: 1
        89: 1
        92: 1
        93: 1
       167: 1

 168:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         7: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        26: 1
        28: 1
        29: 1
        41: 1
        43: 1
        44: 1
        45: 1
        63: 1
        90: 1
        92: 1
        93: 1
       168: 1

 169:    0: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        17: 1
        18: 1
        27: 1
        29: 1
        42: 1
        44: 1
        45: 1
        64: 1
        91: 1
        93: 1
       169: 1

 170:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        25: 1
        30: 1
        31: 1
        33: 1
        40: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        65: 1
        89: 1
        94: 1
        95: 1
        97: 1
       170: 1

 171:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        26: 1
        30: 1
        31: 1
        34: 1
        41: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        66: 1
        90: 1
        94: 1
        95: 1
        98: 1
       171: 1

 172:    0: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         8: 1
        10: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: q+1
        19: 1
        27: 1
        31: 1
        35: 1
        39: 1
        42: 1
        44: 1
        46: 1
        48: 1
        49: 1
        67: 1
        91: 1
        95: 1
        99: 1
       103: 1
       172: 1

 173:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        11: 1
        12: 1
        13: 1
        16: 1
        18: 1
        19: 1
        28: 1
        30: 1
        32: 1
        43: 1
        45: 1
        46: 1
        47: 1
        68: 1
        92: 1
        94: 1
        96: 1
       173: 1

 174:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        11: 1
        12: 1
        14: 1
        17: 1
        18: 1
        19: 1
        29: 1
        31: 1
        32: 1
        44: 1
        45: 1
        46: 1
        48: 1
        69: 1
        93: 1
        95: 1
        96: 1
       174: 1

 175:    0: 1
         3: 1
         4: 1
         5: 1
        11: 1
        12: 1
        15: 1
        18: 1
        19: 1
        32: 1
        39: 1
        45: 1
        46: 1
        49: 1
        70: 1
        96: 1
       103: 1
       175: 1

 176:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        33: 1
        35: 1
        36: 1
        40: 1
        42: 1
        43: 1
        47: 1
        48: 1
        49: 1
        71: 1
        84: 1
        97: 1
        99: 1
       100: 1
       176: 1

 177:    0: 1
         1: 1
         2: 1
         4: 1
         5: 1
         6: 1
         7: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        21: 1
        33: 1
        34: 1
        40: 1
        41: 1
        47: 1
        48: 1
        72: 1
        85: 1
        97: 1
        98: 1
       177: 1

 178:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        34: 1
        35: 1
        36: 1
        41: 1
        42: 1
        43: 1
        47: 1
        48: 1
        49: 1
        73: 1
        86: 1
        98: 1
        99: 1
       100: 1
       178: 1

 179:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        11: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        35: 1
        38: 1
        42: 1
        45: 1
        48: 1
        49: 1
        74: 1
        87: 1
        99: 1
       102: 1
       179: 1

 180:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        24: 1
        35: 1
        39: 1
        42: 1
        46: 1
        48: 1
        49: 1
        75: 1
        88: 1
        99: 1
       103: 1
       180: 1

 181:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        25: 1
        33: 1
        36: 1
        37: 1
        40: 1
        43: 1
        44: 1
        47: 1
        48: 1
        49: 1
        76: 1
        89: 1
        97: 1
       100: 1
       101: 1
       181: 1

 182:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        26: 1
        34: 1
        36: 1
        37: 1
        41: 1
        43: 1
        44: 1
        47: 1
        48: 1
        49: 1
        77: 1
        90: 1
        98: 1
       100: 1
       101: 1
       182: 1

 183:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        27: 1
        35: 1
        37: 1
        42: 1
        44: 1
        48: 1
        49: 1
        78: 1
        91: 1
        99: 1
       101: 1
       183: 1

 184:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        11: 1
        13: 1
        15: 1
        16: 1
        18: 1
        19: 1
        28: 1
        36: 1
        38: 1
        43: 1
        45: 1
        47: 1
        49: 1
        79: 1
        92: 1
       100: 1
       102: 1
       184: 1

 185:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        11: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        29: 1
        37: 1
        38: 1
        44: 1
        45: 1
        48: 1
        49: 1
        80: 1
        93: 1
       101: 1
       102: 1
       185: 1

 186:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        12: 1
        13: 1
        15: 1
        16: 1
        18: 1
        19: 1
        30: 1
        36: 1
        39: 1
        43: 1
        46: 1
        47: 1
        49: 1
        81: 1
        94: 1
       100: 1
       103: 1
       186: 1

 187:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        31: 1
        37: 1
        39: 1
        44: 1
        46: 1
        48: 1
        49: 1
        82: 1
        95: 1
       101: 1
       103: 1
       187: 1

 188:    0: q+1
         3: 1
         4: q+1
         5: q+1
        11: 1
        12: 1
        15: 1
        18: 1
        19: q+1
        32: 1
        38: 1
        39: 1
        45: 1
        46: 1
        49: 1
        83: 1
        96: 1
       102: 1
       103: 1
       188: 1

 189:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         8: q+1
         9: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        68: 1
        70: 1
        71: 1
        75: 1
        81: 1
        84: 1
        87: 1
        92: 1
        97: 1
        99: 1
       100: 1
       104: 1
       111: 1
       132: 1
       135: 1
       155: 1
       176: 1
       189: 1

 190:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        68: 1
        72: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       110: 1
       177: 1
       190: 1

 191:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        85: 1
       105: 1
       107: 1
       108: 1
       112: 1
       191: 1

 192:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        72: 1
       106: 1
       107: 1
       109: 1
       113: 1
       192: 1

 193:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         5: q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 1
        16: 1
        17: q+1
        18: q+1
        20: 1
        21: 1
        22: q+1
        23: 1
        25: 1
        27: q+1
        28: 1
        29: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
       107: 1
       108: 1
       119: 1
       122: 1
       157: 1
       159: 1
       193: 1

 194:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        20: 1
        21: 1
        22: q+1
        24: 1
        25: 1
        27: q+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        39: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
       107: 1
       109: 1
       124: 1
       128: 1
       136: 1
       139: 1
       194: 1

 195:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: q+1
        16: 1
        17: q+1
        19: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        47: 1
        48: q+1
        53: 1
        54: 1
        55: 1
        56: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        72: 1
        85: 1
        97: 1
        98: 1
       108: 1
       109: 1
       110: 1
       118: 1
       129: 1
       177: 1
       195: 1

 196:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         7: q+1
         8: q+1
         9: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: q+1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        68: 1
        70: 1
        73: 1
        75: 1
        81: 1
        86: 1
        87: 1
        92: 1
        98: 1
        99: 1
       100: 1
       110: 1
       111: 1
       132: 1
       139: 1
       159: 1
       178: 1
       196: 1

 197:    0: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        45: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        69: 1
        70: 1
        75: 1
        78: 1
        82: 1
        87: 1
        91: 1
        93: 1
        99: 1
       101: 1
       111: 1
       118: 1
       133: 1
       145: 1
       165: 1
       183: 1
       197: 1

 198:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        40: 1
        47: 1
        48: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        97: 1
       104: 1
       112: 1
       113: 1
       118: 1
       129: 1
       198: 1

 199:    0: q+1
         1: q+1
         2: 1
         3: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        16: q+1
        17: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        40: 1
        41: 1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        85: 1
       105: 1
       112: 1
       114: 1
       116: 1
       120: 1
       199: 1

 200:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: 1
        34: 1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        72: 1
       106: 1
       113: 1
       114: 1
       117: 1
       125: 1
       200: 1

 201:    0: 1
         1: 1
         2: 1
         3: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
       107: 1
       114: 1
       115: 1
       201: 1

 202:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        85: 1
       108: 1
       115: 1
       116: 1
       120: 1
       202: 1

 203:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        72: 1
       109: 1
       115: 1
       117: 1
       125: 1
       203: 1

 204:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        41: 1
        47: 1
        48: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        68: 1
        69: 1
        98: 1
       110: 1
       116: 1
       117: 1
       118: 1
       130: 1
       204: 1

 205:    0: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         8: q+1
        10: q+1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: 1
        39: 1
        42: 1
        45: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        87: 1
        99: 1
       111: 1
       118: 1
       122: 1
       128: 1
       131: 1
       205: 1

 206:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: 1
        42: 1
        43: 1
        45: 1
        50: 1
        57: 1
        60: 1
        62: 1
        64: 1
        84: 1
        87: 1
        92: 1
       112: 1
       119: 1
       122: 1
       155: 1
       206: 1

 207:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        51: 1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        84: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
       113: 1
       119: 1
       123: 1
       129: 1
       156: 1
       173: 1
       207: 1

 208:    0: q+1
         1: q+1
         2: 1
         3: q+1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        92: 1
       114: 1
       119: 1
       120: 1
       121: 1
       157: 1
       208: 1

 209:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: q+1
        16: 1
        17: q+1
        18: 1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        53: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        85: 1
        86: 1
        89: 1
        91: 1
        92: 1
        93: 1
       115: 1
       120: 1
       121: 1
       158: 1
       167: 1
       169: 1
       209: 1

 210:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        41: 1
        42: 1
        43: 1
        45: 1
        54: 1
        59: 1
        60: 1
        63: 1
        64: 1
        86: 1
        87: 1
        92: 1
       116: 1
       121: 1
       122: 1
       159: 1
       210: 1

 211:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        55: 1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        68: 1
        69: 1
        86: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
       117: 1
       121: 1
       123: 1
       130: 1
       160: 1
       173: 1
       211: 1

 212:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        42: 1
        45: 1
        46: 1
        48: 1
        56: 1
        60: 1
        61: 1
        64: 1
        69: 1
        87: 1
        88: 1
        96: 1
       118: 1
       122: 1
       123: 1
       161: 1
       212: 1

 213:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        47: 1
        48: 1
        50: 1
        57: 1
        60: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        74: 1
        79: 1
        81: 1
        83: 1
        97: 1
       112: 1
       124: 1
       127: 1
       129: 1
       134: 1
       152: 1
       213: 1

 214:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        35: 1
        36: 1
        39: 1
        51: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        75: 1
        81: 1
       113: 1
       124: 1
       128: 1
       135: 1
       214: 1

 215:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        52: 1
        57: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        81: 1
       114: 1
       124: 1
       125: 1
       126: 1
       136: 1
       215: 1

 216:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        30: 1
        31: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        53: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        72: 1
        73: 1
        76: 1
        78: 1
        81: 1
        82: 1
       115: 1
       125: 1
       126: 1
       137: 1
       149: 1
       151: 1
       216: 1

 217:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        47: 1
        48: 1
        54: 1
        59: 1
        60: 1
        63: 1
        66: 1
        67: 1
        68: 1
        69: 1
        73: 1
        74: 1
        79: 1
        81: 1
        83: 1
        98: 1
       116: 1
       126: 1
       127: 1
       130: 1
       138: 1
       152: 1
       217: 1

 218:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        22: 1
        24: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: 1
        35: 1
        36: 1
        39: 1
        55: 1
        59: 1
        61: 1
        66: 1
        67: 1
        73: 1
        75: 1
        81: 1
       117: 1
       126: 1
       128: 1
       139: 1
       218: 1

 219:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        38: 1
        39: 1
        48: 1
        56: 1
        60: 1
        61: 1
        67: 1
        69: 1
        74: 1
        75: 1
        83: 1
       118: 1
       127: 1
       128: 1
       140: 1
       219: 1

 220:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        57: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        81: 1
        84: 1
        92: 1
        97: 1
        99: 1
       100: 1
       119: 1
       124: 1
       129: 1
       131: 1
       132: 1
       176: 1
       220: 1

 221:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        21: 1
        25: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        47: 1
        48: 1
        58: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        85: 1
        97: 1
        98: 1
       120: 1
       125: 1
       129: 1
       130: 1
       177: 1
       221: 1

 222:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        59: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        81: 1
        86: 1
        92: 1
        98: 1
        99: 1
       100: 1
       121: 1
       126: 1
       130: 1
       131: 1
       132: 1
       178: 1
       222: 1

 223:    0: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         8: 1
        10: 1
        11: q+1
        12: 1
        14: 1
        15: 1
        17: 1
        18: q+1
        19: 1
        23: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        45: q+1
        48: 1
        49: 1
        60: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        83: 1
        87: 1
        99: 1
       102: 1
       122: 1
       127: 1
       131: 1
       154: 1
       179: 1
       223: 1

 224:    0: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        12: q+1
        14: 1
        15: q+1
        17: 1
        18: 1
        19: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        39: q+1
        42: 1
        45: 1
        46: 1
        48: 1
        49: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        88: 1
        96: 1
        99: 1
       103: 1
       123: 1
       128: 1
       131: 1
       175: 1
       180: 1
       224: 1

 225:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        25: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        36: 1
        37: 1
        39: 1
        40: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        76: 1
        81: 1
        82: 1
        89: 1
        92: 1
        93: 1
        97: 1
       100: 1
       101: 1
       129: 1
       132: 1
       133: 1
       149: 1
       167: 1
       181: 1
       225: 1

 226:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         7: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        26: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        63: 1
        66: 1
        68: 1
        69: 1
        70: 1
        77: 1
        81: 1
        82: 1
        90: 1
        92: 1
        93: 1
        98: 1
       100: 1
       101: 1
       130: 1
       132: 1
       133: 1
       150: 1
       168: 1
       182: 1
       226: 1

 227:    0: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         8: q+1
        10: q+1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        45: 1
        48: 1
        49: 1
        64: 1
        67: 1
        69: 1
        70: 1
        78: 1
        82: 1
        91: 1
        93: 1
        99: 1
       101: 1
       131: 1
       133: 1
       151: 1
       169: 1
       183: 1
       227: 1

 228:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        47: 1
        48: 1
        50: 1
        51: 1
        56: 1
        68: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        97: 1
       104: 1
       134: 1
       135: 1
       140: 1
       152: 1
       228: 1

 229:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        28: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        52: 1
        54: 1
        71: 1
        72: 1
        73: 1
        74: 1
        79: 1
        85: 1
        97: 1
        98: 1
       105: 1
       134: 1
       136: 1
       138: 1
       177: 1
       229: 1

 230:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        24: 1
        30: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        51: 1
        52: 1
        55: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
       106: 1
       135: 1
       136: 1
       139: 1
       230: 1

 231:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        25: 1
        27: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        52: 1
        53: 1
        57: 1
        71: 1
        72: 1
        73: 1
        76: 1
        78: 1
       107: 1
       136: 1
       137: 1
       141: 1
       231: 1

 232:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        19: q+1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        47: 1
        48: q+1
        53: 1
        54: 1
        60: 1
        62: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        85: 1
        97: 1
        98: 1
       108: 1
       137: 1
       138: 1
       144: 1
       146: 1
       177: 1
       232: 1

 233:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: q+1
        15: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        53: 1
        55: 1
        61: 1
        65: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
       109: 1
       137: 1
       139: 1
       145: 1
       149: 1
       233: 1

 234:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        47: 1
        48: 1
        54: 1
        55: 1
        56: 1
        68: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        98: 1
       110: 1
       138: 1
       139: 1
       140: 1
       152: 1
       234: 1

 235:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        45: 1
        48: 1
        49: 1
        56: 1
        70: 1
        74: 1
        75: 1
        83: 1
        87: 1
        99: 1
       102: 1
       111: 1
       140: 1
       154: 1
       179: 1
       235: 1

 236:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        47: 1
        48: 1
        50: 1
        57: 1
        60: 1
        62: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        97: 1
       112: 1
       134: 1
       141: 1
       144: 1
       146: 1
       236: 1

 237:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        20: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        51: 1
        57: 1
        61: 1
        65: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
       113: 1
       135: 1
       141: 1
       145: 1
       149: 1
       237: 1

 238:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        13: q+1
        14: 1
        15: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        52: 1
        57: 1
        58: 1
        59: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
       114: 1
       136: 1
       141: 1
       142: 1
       143: 1
       238: 1

 239:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        53: 1
        58: 1
        59: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
       115: 1
       137: 1
       142: 1
       143: 1
       239: 1

 240:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        41: 1
        47: 1
        48: 1
        54: 1
        59: 1
        60: 1
        63: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        98: 1
       116: 1
       138: 1
       143: 1
       144: 1
       147: 1
       240: 1

 241:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        22: 1
        24: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        55: 1
        59: 1
        61: 1
        66: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
       117: 1
       139: 1
       143: 1
       145: 1
       150: 1
       241: 1

 242:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        48: q+1
        56: 1
        60: 1
        61: 1
        69: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
       118: 1
       140: 1
       144: 1
       145: 1
       153: 1
       242: 1

 243:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        35: 1
        36: q+1
        37: 1
        38: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        57: 1
        62: 1
        64: 1
        71: 1
        76: 1
        78: 1
        79: 1
        80: 1
        84: 1
        92: 1
        97: 1
        99: 1
       100: 1
       102: 1
       119: 1
       141: 1
       146: 1
       148: 1
       176: 1
       184: 1
       243: 1

 244:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        21: 1
        25: 1
        26: 1
        28: 1
        29: 1
        33: 1
        34: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        47: 1
        48: 1
        58: 1
        62: 1
        63: 1
        72: 1
        76: 1
        77: 1
        79: 1
        80: 1
        85: 1
        97: 1
        98: 1
       120: 1
       142: 1
       146: 1
       147: 1
       177: 1
       244: 1

 245:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        26: 1
        27: 1
        28: 1
        29: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        59: 1
        63: 1
        64: 1
        73: 1
        77: 1
        78: 1
        79: 1
        80: 1
        86: 1
        92: 1
        98: 1
        99: 1
       100: 1
       102: 1
       121: 1
       143: 1
       147: 1
       148: 1
       178: 1
       184: 1
       245: 1

 246:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        27: 1
        29: 1
        35: 1
        37: 1
        38: 1
        42: 1
        45: 1
        48: 1
        49: 1
        60: 1
        64: 1
        74: 1
        78: 1
        80: 1
        87: 1
        99: 1
       102: 1
       122: 1
       144: 1
       148: 1
       179: 1
       246: 1

 247:    0: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: 1
        19: q+1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: q+1
        42: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        61: 1
        64: 1
        69: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        88: 1
        96: 1
        99: 1
       102: 1
       103: 1
       123: 1
       145: 1
       148: 1
       153: 1
       180: 1
       188: 1
       247: 1

 248:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        57: 1
        65: 1
        67: 1
        71: 1
        76: 1
        78: 1
        81: 1
        82: 1
       124: 1
       141: 1
       149: 1
       151: 1
       248: 1

 249:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        21: 1
        25: 1
        26: 1
        30: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        58: 1
        65: 1
        66: 1
        72: 1
        76: 1
        77: 1
        81: 1
        82: 1
       125: 1
       142: 1
       149: 1
       150: 1
       249: 1

 250:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        22: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        59: 1
        66: 1
        67: 1
        73: 1
        77: 1
        78: 1
        81: 1
        82: 1
       126: 1
       143: 1
       150: 1
       151: 1
       250: 1

 251:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        19: 1
        23: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        48: 1
        60: 1
        67: 1
        69: 1
        74: 1
        78: 1
        80: 1
        82: 1
        83: 1
       127: 1
       144: 1
       151: 1
       153: 1
       251: 1

 252:    0: 1
         2: 1
         3: 1
         4: 1
         8: 1
        10: 1
        12: 1
        14: 1
        15: 1
        24: 1
        27: 1
        31: 1
        35: 1
        37: 1
        39: 1
        61: 1
        67: 1
        75: 1
        78: 1
        82: 1
       128: 1
       145: 1
       151: 1
       252: 1

 253:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        25: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        47: 1
        48: 1
        62: 1
        65: 1
        68: 1
        69: 1
        76: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        97: 1
       129: 1
       146: 1
       149: 1
       152: 1
       153: 1
       253: 1

 254:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        47: 1
        48: 1
        63: 1
        66: 1
        68: 1
        69: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        98: 1
       130: 1
       147: 1
       150: 1
       152: 1
       153: 1
       254: 1

 255:    0: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        12: q+1
        14: 1
        15: q+1
        17: 1
        18: 1
        19: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: q+1
        42: 1
        45: 1
        48: 1
        49: 1
        64: 1
        67: 1
        69: 1
        70: 1
        78: 1
        80: 1
        82: 1
        83: 1
        99: 1
       102: 1
       131: 1
       148: 1
       151: 1
       153: 1
       154: 1
       255: 1

 256:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        11: 1
        12: 1
        13: 1
        15: 1
        16: 1
        18: 1
        19: 1
        28: 1
        30: 1
        32: 1
        36: 1
        38: 1
        39: 1
        43: 1
        45: 1
        47: 1
        49: 1
        68: 1
        70: 1
        79: 1
        81: 1
        83: 1
        92: 1
       100: 1
       102: 1
       132: 1
       152: 1
       154: 1
       184: 1
       256: 1

 257:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        29: 1
        31: 1
        32: 1
        37: 1
        38: 1
        39: 1
        44: 1
        45: 1
        48: 1
        49: 1
        69: 1
        70: 1
        80: 1
        82: 1
        83: 1
        93: 1
       101: 1
       102: 1
       133: 1
       153: 1
       154: 1
       185: 1
       257: 1

 258:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        50: 1
        51: 1
        56: 1
        68: 1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
       104: 1
       155: 1
       156: 1
       161: 1
       173: 1
       258: 1

 259:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        23: 1
        28: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        50: 1
        52: 1
        54: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
       105: 1
       155: 1
       157: 1
       159: 1
       259: 1

 260:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        30: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        46: 1
        47: 1
        48: 1
        51: 1
        52: 1
        55: 1
        72: 1
        84: 1
        85: 1
        86: 1
        88: 1
        94: 1
        97: 1
        98: 1
       106: 1
       156: 1
       157: 1
       160: 1
       177: 1
       260: 1

 261:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        25: 1
        27: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        52: 1
        53: 1
        57: 1
        84: 1
        85: 1
        86: 1
        89: 1
        91: 1
       107: 1
       157: 1
       158: 1
       162: 1
       261: 1

 262:    0: q+1
         1: 1
         2: q+1
         3: 1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: q+1
        18: 1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        53: 1
        54: 1
        60: 1
        62: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
       108: 1
       158: 1
       159: 1
       165: 1
       167: 1
       262: 1

 263:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: q+1
        53: 1
        55: 1
        61: 1
        65: 1
        72: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
       109: 1
       158: 1
       160: 1
       166: 1
       170: 1
       177: 1
       263: 1

 264:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        34: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        54: 1
        55: 1
        56: 1
        68: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
       110: 1
       159: 1
       160: 1
       161: 1
       173: 1
       264: 1

 265:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        32: 1
        35: 1
        39: 1
        42: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        70: 1
        75: 1
        87: 1
        88: 1
        96: 1
        99: 1
       103: 1
       111: 1
       161: 1
       175: 1
       180: 1
       265: 1

 266:    0: q+1
         1: q+1
         2: q+1
         3: 1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        16: q+1
        17: q+1
        18: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        50: 1
        57: 1
        60: 1
        62: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
       112: 1
       155: 1
       162: 1
       165: 1
       167: 1
       266: 1

 267:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        40: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        51: 1
        57: 1
        61: 1
        65: 1
        84: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
       113: 1
       156: 1
       162: 1
       166: 1
       170: 1
       267: 1

 268:    0: q+1
         1: q+1
         2: 1
         3: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        16: q+1
        17: 1
        18: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        52: 1
        57: 1
        58: 1
        59: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
       114: 1
       157: 1
       162: 1
       163: 1
       164: 1
       268: 1

 269:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        16: 1
        17: 1
        18: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        53: 1
        58: 1
        59: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
       115: 1
       158: 1
       163: 1
       164: 1
       269: 1

 270:    0: q+1
         1: q+1
         2: q+1
         3: 1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        16: q+1
        17: q+1
        18: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        54: 1
        59: 1
        60: 1
        63: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
       116: 1
       159: 1
       164: 1
       165: 1
       168: 1
       270: 1

 271:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        55: 1
        59: 1
        61: 1
        66: 1
        86: 1
        88: 1
        90: 1
        91: 1
        94: 1
        95: 1
        98: 1
       117: 1
       160: 1
       164: 1
       166: 1
       171: 1
       271: 1

 272:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        56: 1
        60: 1
        61: 1
        69: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
       118: 1
       161: 1
       165: 1
       166: 1
       174: 1
       272: 1

 273:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        57: 1
        62: 1
        64: 1
        84: 1
        89: 1
        91: 1
        92: 1
        93: 1
       119: 1
       162: 1
       167: 1
       169: 1
       273: 1

 274:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        21: 1
        25: 1
        26: 1
        28: 1
        29: 1
        40: 1
        41: 1
        43: 1
        44: 1
        45: 1
        58: 1
        62: 1
        63: 1
        85: 1
        89: 1
        90: 1
        92: 1
        93: 1
       120: 1
       163: 1
       167: 1
       168: 1
       274: 1

 275:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        22: 1
        26: 1
        27: 1
        28: 1
        29: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        59: 1
        63: 1
        64: 1
        86: 1
        90: 1
        91: 1
        92: 1
        93: 1
       121: 1
       164: 1
       168: 1
       169: 1
       275: 1

 276:    0: 1
         2: 1
         3: 1
         5: 1
         8: 1
        10: 1
        11: 1
        17: 1
        18: 1
        23: 1
        27: 1
        29: 1
        42: 1
        44: 1
        45: 1
        60: 1
        64: 1
        87: 1
        91: 1
        93: 1
       122: 1
       165: 1
       169: 1
       276: 1

 277:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        17: 1
        18: 1
        19: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        61: 1
        64: 1
        69: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
       123: 1
       166: 1
       169: 1
       174: 1
       277: 1

 278:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         8: 1
         9: q+1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        20: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: q+1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        57: 1
        65: 1
        67: 1
        71: 1
        81: 1
        84: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        99: 1
       100: 1
       103: 1
       124: 1
       162: 1
       170: 1
       172: 1
       176: 1
       186: 1
       278: 1

 279:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        25: 1
        26: 1
        30: 1
        31: 1
        33: 1
        34: 1
        40: 1
        41: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        58: 1
        65: 1
        66: 1
        72: 1
        85: 1
        89: 1
        90: 1
        94: 1
        95: 1
        97: 1
        98: 1
       125: 1
       163: 1
       170: 1
       171: 1
       177: 1
       279: 1

 280:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        22: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        59: 1
        66: 1
        67: 1
        73: 1
        81: 1
        86: 1
        90: 1
        91: 1
        94: 1
        95: 1
        98: 1
        99: 1
       100: 1
       103: 1
       126: 1
       164: 1
       171: 1
       172: 1
       178: 1
       186: 1
       280: 1

 281:    0: q^2+2q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+2q+1
         8: 1
        10: 1
        11: q+1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: q+1
        46: 1
        48: q+1
        49: 1
        60: 1
        67: 1
        69: 1
        74: 1
        83: 1
        87: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       102: 1
       103: 1
       127: 1
       165: 1
       172: 1
       174: 1
       179: 1
       188: 1
       281: 1

 282:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        24: 1
        27: 1
        31: 1
        35: 1
        39: 1
        42: 1
        44: 1
        46: 1
        48: 1
        49: 1
        61: 1
        67: 1
        75: 1
        88: 1
        91: 1
        95: 1
        99: 1
       103: 1
       128: 1
       166: 1
       172: 1
       180: 1
       282: 1

 283:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        25: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        40: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        62: 1
        65: 1
        68: 1
        69: 1
        89: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
       129: 1
       167: 1
       170: 1
       173: 1
       174: 1
       283: 1

 284:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        63: 1
        66: 1
        68: 1
        69: 1
        90: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
       130: 1
       168: 1
       171: 1
       173: 1
       174: 1
       284: 1

 285:    0: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         8: 1
        10: 1
        11: q+1
        12: 1
        14: 1
        15: 1
        17: 1
        18: q+1
        19: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        39: 1
        42: 1
        44: 1
        45: q+1
        46: 1
        48: 1
        49: 1
        64: 1
        67: 1
        69: 1
        70: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       103: 1
       131: 1
       169: 1
       172: 1
       174: 1
       175: 1
       285: 1

 286:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        11: 1
        12: 1
        13: 1
        15: 1
        16: 1
        18: 1
        19: 1
        28: 1
        30: 1
        32: 1
        36: 1
        39: 1
        43: 1
        45: 1
        46: 1
        47: 1
        49: 1
        68: 1
        70: 1
        81: 1
        92: 1
        94: 1
        96: 1
       100: 1
       103: 1
       132: 1
       173: 1
       175: 1
       186: 1
       286: 1

 287:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        29: 1
        31: 1
        32: 1
        37: 1
        39: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        69: 1
        70: 1
        82: 1
        93: 1
        95: 1
        96: 1
       101: 1
       103: 1
       133: 1
       174: 1
       175: 1
       187: 1
       287: 1

 288:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        28: 1
        33: 1
        35: 1
        36: 1
        38: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        71: 1
        74: 1
        79: 1
        84: 1
        87: 1
        92: 1
        97: 1
        99: 1
       100: 1
       102: 1
       134: 1
       155: 1
       176: 1
       179: 1
       184: 1
       288: 1

 289:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        30: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        71: 1
        75: 1
        81: 1
        84: 1
        88: 1
        94: 1
        97: 1
        99: 1
       100: 1
       103: 1
       135: 1
       156: 1
       176: 1
       180: 1
       186: 1
       289: 1

 290:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        33: 1
        34: 1
        35: 1
        36: 1
        40: 1
        41: 1
        42: 1
        43: 1
        47: 1
        48: 1
        49: 1
        52: 1
        71: 1
        72: 1
        73: 1
        84: 1
        85: 1
        86: 1
        97: 1
        98: 1
        99: 1
       100: 1
       136: 1
       157: 1
       176: 1
       177: 1
       178: 1
       290: 1

 291:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        25: 1
        27: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        72: 1
        73: 1
        76: 1
        78: 1
        85: 1
        86: 1
        89: 1
        91: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       137: 1
       158: 1
       177: 1
       178: 1
       181: 1
       183: 1
       291: 1

 292:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        28: 1
        34: 1
        35: 1
        36: 1
        38: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        73: 1
        74: 1
        79: 1
        86: 1
        87: 1
        92: 1
        98: 1
        99: 1
       100: 1
       102: 1
       138: 1
       159: 1
       178: 1
       179: 1
       184: 1
       292: 1

 293:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        30: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: 1
        46: 1
        47: 1
        48: 1
        49: 1
        55: 1
        73: 1
        75: 1
        81: 1
        86: 1
        88: 1
        94: 1
        98: 1
        99: 1
       100: 1
       103: 1
       139: 1
       160: 1
       178: 1
       180: 1
       186: 1
       293: 1

 294:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: 1
        74: 1
        75: 1
        83: 1
        87: 1
        88: 1
        96: 1
        99: 1
       102: 1
       103: 1
       140: 1
       161: 1
       179: 1
       180: 1
       188: 1
       294: 1

 295:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        25: 1
        27: 1
        33: 1
        35: 1
        36: 1
        37: 1
        40: 1
        42: 1
        43: 1
        44: 1
        47: 1
        48: 1
        49: 1
        57: 1
        71: 1
        76: 1
        78: 1
        84: 1
        89: 1
        91: 1
        97: 1
        99: 1
       100: 1
       101: 1
       141: 1
       162: 1
       176: 1
       181: 1
       183: 1
       295: 1

 296:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        25: 1
        26: 1
        33: 1
        34: 1
        36: 1
        37: 1
        40: 1
        41: 1
        43: 1
        44: 1
        47: 1
        48: 1
        49: 1
        58: 1
        72: 1
        76: 1
        77: 1
        85: 1
        89: 1
        90: 1
        97: 1
        98: 1
       100: 1
       101: 1
       142: 1
       163: 1
       177: 1
       181: 1
       182: 1
       296: 1

 297:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        26: 1
        27: 1
        34: 1
        35: 1
        36: 1
        37: 1
        41: 1
        42: 1
        43: 1
        44: 1
        47: 1
        48: 1
        49: 1
        59: 1
        73: 1
        77: 1
        78: 1
        86: 1
        90: 1
        91: 1
        98: 1
        99: 1
       100: 1
       101: 1
       143: 1
       164: 1
       178: 1
       182: 1
       183: 1
       297: 1

 298:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        27: 1
        29: 1
        35: 1
        37: 1
        38: 1
        42: 1
        44: 1
        45: 1
        48: q+1
        49: 1
        60: 1
        74: 1
        78: 1
        80: 1
        87: 1
        91: 1
        93: 1
        99: 1
       101: 1
       102: 1
       144: 1
       165: 1
       179: 1
       183: 1
       185: 1
       298: 1

 299:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        24: 1
        27: 1
        31: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        46: 1
        48: q+1
        49: 1
        61: 1
        75: 1
        78: 1
        82: 1
        88: 1
        91: 1
        95: 1
        99: 1
       101: 1
       103: 1
       145: 1
       166: 1
       180: 1
       183: 1
       187: 1
       299: 1

 300:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        25: 1
        28: 1
        29: 1
        33: 1
        36: 1
        37: 1
        38: 1
        40: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        62: 1
        76: 1
        79: 1
        80: 1
        89: 1
        92: 1
        93: 1
        97: 1
       100: 1
       101: 1
       102: 1
       146: 1
       167: 1
       181: 1
       184: 1
       185: 1
       300: 1

 301:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        26: 1
        28: 1
        29: 1
        34: 1
        36: 1
        37: 1
        38: 1
        41: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        63: 1
        77: 1
        79: 1
        80: 1
        90: 1
        92: 1
        93: 1
        98: 1
       100: 1
       101: 1
       102: 1
       147: 1
       168: 1
       182: 1
       184: 1
       185: 1
       301: 1

 302:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        27: 1
        29: 1
        35: 1
        37: 1
        38: 1
        42: 1
        44: 1
        45: 1
        48: 1
        49: 1
        64: 1
        78: 1
        80: 1
        91: 1
        93: 1
        99: 1
       101: 1
       102: 1
       148: 1
       169: 1
       183: 1
       185: 1
       302: 1

 303:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        25: 1
        30: 1
        31: 1
        33: 1
        36: 1
        37: 1
        39: 1
        40: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        65: 1
        76: 1
        81: 1
        82: 1
        89: 1
        94: 1
        95: 1
        97: 1
       100: 1
       101: 1
       103: 1
       149: 1
       170: 1
       181: 1
       186: 1
       187: 1
       303: 1

 304:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        26: 1
        30: 1
        31: 1
        34: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        66: 1
        77: 1
        81: 1
        82: 1
        90: 1
        94: 1
        95: 1
        98: 1
       100: 1
       101: 1
       103: 1
       150: 1
       171: 1
       182: 1
       186: 1
       187: 1
       304: 1

 305:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        27: 1
        31: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        46: 1
        48: 1
        49: 1
        67: 1
        78: 1
        82: 1
        91: 1
        95: 1
        99: 1
       101: 1
       103: 1
       151: 1
       172: 1
       183: 1
       187: 1
       305: 1

 306:    0: q+1
         1: q+1
         3: 1
         4: q+1
         5: q+1
         9: 1
        11: 1
        12: 1
        13: q+1
        15: 1
        16: q+1
        18: 1
        19: q+1
        28: 1
        30: 1
        32: 1
        36: 1
        38: 1
        39: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        49: 1
        68: 1
        79: 1
        81: 1
        83: 1
        92: 1
        94: 1
        96: 1
       100: 1
       102: 1
       103: 1
       152: 1
       173: 1
       184: 1
       186: 1
       188: 1
       306: 1

 307:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        29: 1
        31: 1
        32: 1
        37: 1
        38: 1
        39: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        69: 1
        80: 1
        82: 1
        83: 1
        93: 1
        95: 1
        96: 1
       101: 1
       102: 1
       103: 1
       153: 1
       174: 1
       185: 1
       187: 1
       188: 1
       307: 1

 308:    0: 1
         3: 1
         4: 1
         5: 1
        11: 1
        12: 1
        15: 1
        18: 1
        19: 1
        32: 1
        38: 1
        39: 1
        45: 1
        46: 1
        49: 1
        70: 1
        83: 1
        96: 1
       102: 1
       103: 1
       154: 1
       175: 1
       188: 1
       308: 1

 309:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       129: 1
       132: 1
       133: 1
       135: 1
       141: 1
       145: 1
       149: 1
       155: 1
       162: 1
       165: 1
       167: 1
       176: 1
       181: 1
       183: 1
       189: 1
       197: 1
       198: 1
       225: 1
       237: 1
       266: 1
       295: 1
       309: 1

 310:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: q+1
        54: 1
        55: 1
        56: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       132: 1
       135: 1
       136: 1
       139: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       189: 1
       190: 1
       196: 1
       230: 1
       259: 1
       290: 1
       310: 1

 311:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        72: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       129: 1
       177: 1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       311: 1

 312:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
       105: 1
       107: 1
       108: 1
       112: 1
       119: 1
       122: 1
       155: 1
       157: 1
       159: 1
       191: 1
       193: 1
       206: 1
       259: 1
       312: 1

 313:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 1
        12: 2q+1
        13: q+1
        14: 2q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: 2q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 1
        34: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: 1
        46: q+1
        47: 1
        48: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       177: 1
       192: 1
       193: 1
       195: 1
       207: 1
       212: 1
       260: 1
       264: 1
       313: 1

 314:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 2q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: q+1
        17: 2q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 2q+1
        24: 1
        25: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        38: q+1
        39: 1
        40: 1
        41: q+1
        47: 1
        48: q+1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        97: 1
        98: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       177: 1
       191: 1
       194: 1
       195: 1
       213: 1
       219: 1
       229: 1
       234: 1
       314: 1

 315:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
       106: 1
       107: 1
       109: 1
       113: 1
       124: 1
       128: 1
       135: 1
       136: 1
       139: 1
       192: 1
       194: 1
       214: 1
       230: 1
       315: 1

 316:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: 1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       136: 1
       139: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       220: 1
       290: 1
       316: 1

 317:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: q+1
        54: 1
        55: 1
        56: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       129: 1
       132: 1
       133: 1
       137: 1
       139: 1
       145: 1
       149: 1
       158: 1
       159: 1
       165: 1
       167: 1
       177: 1
       178: 1
       181: 1
       183: 1
       195: 1
       196: 1
       197: 1
       225: 1
       233: 1
       262: 1
       291: 1
       317: 1

 318:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q+1
         5: q+1
         7: q^2+2q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: q+1
        23: 1
        24: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: q+1
        60: 1
        61: 1
        63: 1
        66: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       130: 1
       132: 1
       133: 1
       139: 1
       143: 1
       145: 1
       150: 1
       159: 1
       164: 1
       165: 1
       168: 1
       178: 1
       182: 1
       183: 1
       196: 1
       197: 1
       204: 1
       226: 1
       241: 1
       270: 1
       297: 1
       318: 1

 319:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        81: 1
        84: 1
        87: 1
        92: 1
        97: 1
        99: 1
       100: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       155: 1
       176: 1
       189: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       319: 1

 320:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        16: q+1
        17: 1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        40: 1
        41: 1
        47: q+1
        48: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        72: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       177: 1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       221: 1
       320: 1

 321:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        85: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       120: 1
       191: 1
       199: 1
       201: 1
       202: 1
       321: 1

 322:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        72: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       125: 1
       192: 1
       200: 1
       201: 1
       203: 1
       322: 1

 323:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         5: 1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: q+1
        23: 1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       157: 1
       159: 1
       193: 1
       201: 1
       202: 1
       208: 1
       210: 1
       323: 1

 324:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: q+1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       136: 1
       139: 1
       194: 1
       201: 1
       203: 1
       215: 1
       218: 1
       324: 1

 325:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        47: 1
        48: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        85: 1
        97: 1
        98: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       177: 1
       195: 1
       202: 1
       203: 1
       204: 1
       221: 1
       325: 1

 326:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: q+1
        23: 1
        24: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: q+1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        81: 1
        86: 1
        87: 1
        92: 1
        98: 1
        99: 1
       100: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       139: 1
       159: 1
       178: 1
       196: 1
       204: 1
       205: 1
       210: 1
       218: 1
       222: 1
       326: 1

 327:    0: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         8: q+1
        10: q+1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        45: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        78: 1
        82: 1
        87: 1
        91: 1
        93: 1
        99: 1
       101: 1
       111: 1
       118: 1
       122: 1
       128: 1
       131: 1
       133: 1
       145: 1
       151: 1
       165: 1
       169: 1
       183: 1
       197: 1
       205: 1
       227: 1
       252: 1
       276: 1
       327: 1

 328:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       155: 1
       156: 1
       161: 1
       173: 1
       198: 1
       206: 1
       207: 1
       212: 1
       258: 1
       328: 1

 329:    0: q+1
         1: q+1
         2: 1
         3: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        16: q+1
        17: 1
        18: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: q+1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       155: 1
       157: 1
       159: 1
       199: 1
       206: 1
       208: 1
       210: 1
       259: 1
       329: 1

 330:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       156: 1
       157: 1
       160: 1
       173: 1
       177: 1
       200: 1
       207: 1
       208: 1
       211: 1
       221: 1
       260: 1
       330: 1

 331:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         5: 1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        16: 1
        17: 1
        18: 1
        20: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        52: 1
        53: 1
        57: q+1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        89: 1
        91: 1
        92: 1
        93: 1
       107: 1
       114: 1
       115: 1
       119: 1
       120: 1
       121: 1
       157: 1
       158: 1
       162: 1
       167: 1
       169: 1
       201: 1
       208: 1
       209: 1
       261: 1
       273: 1
       331: 1

 332:    0: q+1
         1: 1
         2: q+1
         3: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        16: 1
        17: q+1
        18: 1
        21: 1
        22: 1
        23: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: q+1
        62: 1
        63: 1
        64: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
       108: 1
       115: 1
       116: 1
       120: 1
       121: 1
       122: 1
       158: 1
       159: 1
       165: 1
       167: 1
       169: 1
       202: 1
       209: 1
       210: 1
       262: 1
       276: 1
       332: 1

 333:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        53: 1
        55: 1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        68: 1
        69: q+1
        72: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       109: 1
       115: 1
       117: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       158: 1
       160: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       203: 1
       209: 1
       211: 1
       221: 1
       263: 1
       277: 1
       283: 1
       333: 1

 334:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        68: 1
        69: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       130: 1
       159: 1
       160: 1
       161: 1
       173: 1
       204: 1
       210: 1
       211: 1
       212: 1
       264: 1
       334: 1

 335:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        39: 1
        42: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        87: 1
        88: 1
        96: 1
        99: 1
       103: 1
       111: 1
       118: 1
       122: 1
       123: 1
       128: 1
       131: 1
       161: 1
       175: 1
       180: 1
       205: 1
       212: 1
       224: 1
       265: 1
       335: 1

 336:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        47: 1
        48: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        97: 1
       104: 1
       112: 1
       113: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       135: 1
       140: 1
       152: 1
       198: 1
       213: 1
       214: 1
       219: 1
       228: 1
       336: 1

 337:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        79: 1
        81: 1
        83: 1
        85: 1
        97: 1
        98: 1
       105: 1
       112: 1
       114: 1
       116: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       134: 1
       136: 1
       138: 1
       152: 1
       177: 1
       199: 1
       213: 1
       215: 1
       217: 1
       221: 1
       229: 1
       337: 1

 338:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        39: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: q+1
       106: 1
       113: 1
       114: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       139: 1
       200: 1
       214: 1
       215: 1
       218: 1
       230: 1
       338: 1

 339:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        20: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        52: 1
        53: 1
        57: q+1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        76: 1
        78: 1
        81: 1
        82: 1
       107: 1
       114: 1
       115: 1
       124: 1
       125: 1
       126: 1
       136: 1
       137: 1
       141: 1
       149: 1
       151: 1
       201: 1
       215: 1
       216: 1
       231: 1
       248: 1
       339: 1

 340:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: q+1
        17: 2q+1
        19: q+1
        21: 1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: 1
        47: 1
        48: q+1
        53: 1
        54: 1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       108: 1
       115: 1
       116: 1
       120: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       137: 1
       138: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       177: 1
       202: 1
       216: 1
       217: 1
       221: 1
       232: 1
       251: 1
       253: 1
       340: 1

 341:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        21: 1
        22: 1
        24: q+1
        25: 1
        26: 1
        27: q+1
        30: 1
        31: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: q+1
        65: 1
        66: 1
        67: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
       109: 1
       115: 1
       117: 1
       125: 1
       126: 1
       128: 1
       137: 1
       139: 1
       145: 1
       149: 1
       151: 1
       203: 1
       216: 1
       218: 1
       233: 1
       252: 1
       341: 1

 342:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        47: 1
        48: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        67: 1
        68: 1
        69: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        98: 1
       110: 1
       116: 1
       117: 1
       118: 1
       126: 1
       127: 1
       128: 1
       130: 1
       138: 1
       139: 1
       140: 1
       152: 1
       204: 1
       217: 1
       218: 1
       219: 1
       234: 1
       342: 1

 343:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        45: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        83: 1
        87: 1
        99: 1
       102: 1
       111: 1
       118: 1
       122: 1
       127: 1
       128: 1
       131: 1
       140: 1
       154: 1
       179: 1
       205: 1
       219: 1
       223: 1
       235: 1
       343: 1

 344:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: q+1
        45: q+1
        47: 1
        48: 1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        92: q+1
        97: 1
        99: 1
       100: 1
       102: 1
       112: 1
       119: 1
       122: 1
       124: 1
       127: 1
       129: 1
       131: 1
       132: 1
       134: 1
       152: 1
       154: 1
       155: 1
       176: 1
       179: 1
       184: 1
       206: 1
       213: 1
       220: 1
       223: 1
       256: 1
       288: 1
       344: 1

 345:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 1
        35: 1
        36: q+1
        39: q+1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        81: q+1
        84: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       103: 1
       113: 1
       119: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       156: 1
       173: 1
       175: 1
       176: 1
       180: 1
       186: 1
       207: 1
       214: 1
       220: 1
       224: 1
       286: 1
       289: 1
       345: 1

 346:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        81: 1
        84: 1
        85: 1
        86: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       114: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: 1
       157: 1
       176: 1
       177: 1
       178: 1
       208: 1
       215: 1
       220: 1
       221: 1
       222: 1
       290: 1
       346: 1

 347:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       115: 1
       120: 1
       121: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       149: 1
       151: 1
       158: 1
       167: 1
       169: 1
       177: 1
       178: 1
       181: 1
       183: 1
       209: 1
       216: 1
       221: 1
       222: 1
       225: 1
       227: 1
       291: 1
       347: 1

 348:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        47: 1
        48: 1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        92: q+1
        98: 1
        99: 1
       100: 1
       102: 1
       116: 1
       121: 1
       122: 1
       126: 1
       127: 1
       130: 1
       131: 1
       132: 1
       138: 1
       152: 1
       154: 1
       159: 1
       178: 1
       179: 1
       184: 1
       210: 1
       217: 1
       222: 1
       223: 1
       256: 1
       292: 1
       348: 1

 349:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: 1
        35: 1
        36: q+1
        39: q+1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        55: 1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        81: q+1
        86: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
        99: 1
       100: 1
       103: 1
       117: 1
       121: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       139: 1
       160: 1
       173: 1
       175: 1
       178: 1
       180: 1
       186: 1
       211: 1
       218: 1
       222: 1
       224: 1
       286: 1
       293: 1
       349: 1

 350:    0: 2q+1
         2: q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         8: 1
        10: q+1
        11: 2q+1
        12: 2q+1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: 2q+1
        23: 1
        24: 1
        27: 1
        29: q+1
        31: q+1
        32: 2q+1
        35: 1
        38: q+1
        39: q+1
        42: 1
        45: q+1
        46: q+1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: q+1
        70: 1
        74: 1
        75: 1
        83: q+1
        87: 1
        88: 1
        96: q+1
        99: 1
       102: 1
       103: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       140: 1
       154: 1
       161: 1
       175: 1
       179: 1
       180: 1
       188: 1
       212: 1
       219: 1
       223: 1
       224: 1
       294: 1
       308: 1
       350: 1

 351:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        57: q+1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        99: 1
       100: 1
       101: 1
       119: 1
       124: 1
       129: 1
       131: 1
       132: 1
       133: 1
       141: 1
       149: 1
       151: 1
       162: 1
       167: 1
       169: 1
       176: 1
       181: 1
       183: 1
       220: 1
       225: 1
       227: 1
       248: 1
       273: 1
       295: 1
       351: 1

 352:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: q+1
        25: q+1
        26: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        58: q+1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        72: 1
        76: 1
        77: 1
        81: 1
        82: 1
        85: 1
        89: 1
        90: 1
        92: 1
        93: 1
        97: 1
        98: 1
       100: 1
       101: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       142: 1
       149: 1
       150: 1
       163: 1
       167: 1
       168: 1
       177: 1
       181: 1
       182: 1
       221: 1
       225: 1
       226: 1
       249: 1
       274: 1
       296: 1
       352: 1

 353:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        59: q+1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: 1
        99: 1
       100: 1
       101: 1
       121: 1
       126: 1
       130: 1
       131: 1
       132: 1
       133: 1
       143: 1
       150: 1
       151: 1
       164: 1
       168: 1
       169: 1
       178: 1
       182: 1
       183: 1
       222: 1
       226: 1
       227: 1
       250: 1
       275: 1
       297: 1
       353: 1

 354:    0: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         8: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        14: q+1
        15: 1
        17: 2q+1
        18: q+1
        19: q+1
        23: q+1
        27: q+1
        29: 2q+1
        31: q+1
        32: q+1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: q+1
        45: q+1
        48: q+1
        49: 1
        60: q+1
        64: 1
        67: 1
        69: q+1
        70: 1
        74: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        91: 1
        93: q+1
        99: 1
       101: 1
       102: 1
       122: 1
       127: 1
       131: 1
       133: 1
       144: 1
       151: 1
       153: 1
       154: 1
       165: 1
       169: 1
       179: 1
       183: 1
       185: 1
       223: 1
       227: 1
       251: 1
       257: 1
       276: 1
       298: 1
       354: 1

 355:    0: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         8: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        14: 2q+1
        15: q+1
        17: q+1
        18: 1
        19: q+1
        24: q+1
        27: q+1
        29: q+1
        31: 2q+1
        32: q+1
        35: 1
        37: q+1
        39: q+1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        61: q+1
        64: 1
        67: 1
        69: q+1
        70: 1
        75: 1
        78: 1
        82: q+1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       103: 1
       123: 1
       128: 1
       131: 1
       133: 1
       145: 1
       151: 1
       166: 1
       169: 1
       174: 1
       175: 1
       180: 1
       183: 1
       187: 1
       224: 1
       227: 1
       252: 1
       277: 1
       287: 1
       299: 1
       355: 1

 356:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        68: 1
        70: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        92: 1
        97: 1
        99: 1
       100: 1
       102: 1
       104: 1
       111: 1
       132: 1
       134: 1
       135: 1
       140: 1
       152: 1
       154: 1
       155: 1
       176: 1
       179: 1
       184: 1
       189: 1
       228: 1
       235: 1
       256: 1
       288: 1
       356: 1

 357:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        68: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       110: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       177: 1
       190: 1
       228: 1
       229: 1
       230: 1
       234: 1
       357: 1

 358:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        85: 1
        97: 1
        98: 1
       105: 1
       107: 1
       108: 1
       112: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       177: 1
       191: 1
       229: 1
       231: 1
       232: 1
       236: 1
       358: 1

 359:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
       106: 1
       107: 1
       109: 1
       113: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       192: 1
       230: 1
       231: 1
       233: 1
       237: 1
       359: 1

 360:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 1
        25: 1
        27: q+1
        28: 1
        29: 1
        33: 1
        34: q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        64: 1
        71: 1
        72: 1
        73: q+1
        74: 1
        76: 1
        78: q+1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: 1
       107: 1
       108: 1
       119: 1
       122: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       193: 1
       231: 1
       232: 1
       243: 1
       246: 1
       290: 1
       292: 1
       360: 1

 361:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: q+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        39: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: q+1
        81: 1
        82: 1
       107: 1
       109: 1
       124: 1
       128: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       194: 1
       231: 1
       233: 1
       248: 1
       252: 1
       361: 1

 362:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        19: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: q+1
        53: 1
        54: 1
        55: 1
        56: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       108: 1
       109: 1
       110: 1
       118: 1
       129: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       177: 1
       195: 1
       232: 1
       233: 1
       234: 1
       242: 1
       253: 1
       362: 1

 363:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        68: 1
        70: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        92: 1
        98: 1
        99: 1
       100: 1
       102: 1
       110: 1
       111: 1
       132: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       159: 1
       178: 1
       179: 1
       184: 1
       196: 1
       234: 1
       235: 1
       256: 1
       292: 1
       363: 1

 364:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        69: 1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        91: 1
        93: 1
        99: 1
       101: 1
       102: 1
       111: 1
       118: 1
       133: 1
       140: 1
       144: 1
       145: 1
       153: 1
       154: 1
       165: 1
       179: 1
       183: 1
       185: 1
       197: 1
       235: 1
       242: 1
       257: 1
       298: 1
       364: 1

 365:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        47: q+1
        48: q+1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        97: q+1
       104: 1
       112: 1
       113: 1
       118: 1
       129: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       198: 1
       228: 1
       236: 1
       237: 1
       242: 1
       253: 1
       365: 1

 366:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        40: 1
        41: 1
        47: q+1
        48: 1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        85: 1
        97: 1
        98: 1
       105: 1
       112: 1
       114: 1
       116: 1
       120: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       177: 1
       199: 1
       229: 1
       236: 1
       238: 1
       240: 1
       244: 1
       366: 1

 367:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        39: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
       106: 1
       113: 1
       114: 1
       117: 1
       125: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       200: 1
       230: 1
       237: 1
       238: 1
       241: 1
       249: 1
       367: 1

 368:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
       107: 1
       114: 1
       115: 1
       136: 1
       137: 1
       141: 1
       142: 1
       143: 1
       201: 1
       231: 1
       238: 1
       239: 1
       368: 1

 369:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        47: 1
        48: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        85: 1
        97: 1
        98: 1
       108: 1
       115: 1
       116: 1
       120: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       177: 1
       202: 1
       232: 1
       239: 1
       240: 1
       244: 1
       369: 1

 370:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
       109: 1
       115: 1
       117: 1
       125: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       203: 1
       233: 1
       239: 1
       241: 1
       249: 1
       370: 1

 371:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        47: q+1
        48: q+1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        68: 1
        69: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        98: q+1
       110: 1
       116: 1
       117: 1
       118: 1
       130: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       152: 1
       153: 1
       204: 1
       234: 1
       240: 1
       241: 1
       242: 1
       254: 1
       371: 1

 372:    0: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         8: 2q+1
        10: q+1
        11: 1
        12: q+1
        14: 2q+1
        15: 2q+1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: q+1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: 2q+1
        37: q+1
        38: 1
        39: q+1
        42: q+1
        45: 1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: q+1
        78: q+1
        80: 1
        82: 1
        83: 1
        87: 1
        99: q+1
       102: 1
       111: 1
       118: 1
       122: 1
       128: 1
       131: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       179: 1
       205: 1
       235: 1
       242: 1
       246: 1
       252: 1
       255: 1
       372: 1

 373:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        64: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        84: 1
        87: 1
        92: 1
        97: 1
        99: 1
       100: 1
       102: 1
       112: 1
       119: 1
       122: 1
       134: 1
       141: 1
       144: 1
       146: 1
       148: 1
       155: 1
       176: 1
       179: 1
       184: 1
       206: 1
       236: 1
       243: 1
       246: 1
       288: 1
       373: 1

 374:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q+1
         6: q+1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        71: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       113: 1
       119: 1
       123: 1
       129: 1
       135: 1
       141: 1
       145: 1
       146: 1
       148: 1
       149: 1
       152: 1
       153: 1
       156: 1
       173: 1
       176: 1
       180: 1
       184: 1
       186: 1
       188: 1
       207: 1
       237: 1
       243: 1
       247: 1
       253: 1
       289: 1
       306: 1
       374: 1

 375:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       114: 1
       119: 1
       120: 1
       121: 1
       136: 1
       141: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       157: 1
       176: 1
       177: 1
       178: 1
       184: 1
       208: 1
       238: 1
       243: 1
       244: 1
       245: 1
       290: 1
       375: 1

 376:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: 2q+1
        38: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        72: 1
        73: 1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: q+1
        85: 1
        86: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       115: 1
       120: 1
       121: 1
       137: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       158: 1
       167: 1
       169: 1
       177: 1
       178: 1
       181: 1
       183: 1
       184: 1
       185: 1
       209: 1
       239: 1
       244: 1
       245: 1
       291: 1
       300: 1
       302: 1
       376: 1

 377:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        64: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        86: 1
        87: 1
        92: 1
        98: 1
        99: 1
       100: 1
       102: 1
       116: 1
       121: 1
       122: 1
       138: 1
       143: 1
       144: 1
       147: 1
       148: 1
       159: 1
       178: 1
       179: 1
       184: 1
       210: 1
       240: 1
       245: 1
       246: 1
       292: 1
       377: 1

 378:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: 1
        39: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        55: 1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        68: 1
        69: 1
        73: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        86: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       117: 1
       121: 1
       123: 1
       130: 1
       139: 1
       143: 1
       145: 1
       147: 1
       148: 1
       150: 1
       152: 1
       153: 1
       160: 1
       173: 1
       178: 1
       180: 1
       184: 1
       186: 1
       188: 1
       211: 1
       241: 1
       245: 1
       247: 1
       254: 1
       293: 1
       306: 1
       378: 1

 379:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        69: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        96: 1
        99: 1
       102: 1
       103: 1
       118: 1
       122: 1
       123: 1
       140: 1
       144: 1
       145: 1
       148: 1
       153: 1
       161: 1
       179: 1
       180: 1
       188: 1
       212: 1
       242: 1
       246: 1
       247: 1
       294: 1
       379: 1

 380:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        47: 1
        48: 1
        50: 1
        57: 1
        60: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        97: 1
       112: 1
       124: 1
       127: 1
       129: 1
       134: 1
       141: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       213: 1
       236: 1
       248: 1
       251: 1
       253: 1
       380: 1

 381:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        51: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
       113: 1
       124: 1
       128: 1
       135: 1
       141: 1
       145: 1
       149: 1
       151: 1
       214: 1
       237: 1
       248: 1
       252: 1
       381: 1

 382:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        39: q+1
        52: 1
        57: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
       114: 1
       124: 1
       125: 1
       126: 1
       136: 1
       141: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       215: 1
       238: 1
       248: 1
       249: 1
       250: 1
       382: 1

 383:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        53: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
       115: 1
       125: 1
       126: 1
       137: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       216: 1
       239: 1
       249: 1
       250: 1
       383: 1

 384:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        47: 1
        48: 1
        54: 1
        59: 1
        60: 1
        63: 1
        66: 1
        67: 1
        68: 1
        69: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        98: 1
       116: 1
       126: 1
       127: 1
       130: 1
       138: 1
       143: 1
       144: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       217: 1
       240: 1
       250: 1
       251: 1
       254: 1
       384: 1

 385:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        22: 1
        24: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        55: 1
        59: 1
        61: 1
        66: 1
        67: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
       117: 1
       126: 1
       128: 1
       139: 1
       143: 1
       145: 1
       150: 1
       151: 1
       218: 1
       241: 1
       250: 1
       252: 1
       385: 1

 386:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        48: 1
        56: 1
        60: 1
        61: 1
        67: 1
        69: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
       118: 1
       127: 1
       128: 1
       140: 1
       144: 1
       145: 1
       151: 1
       153: 1
       219: 1
       242: 1
       251: 1
       252: 1
       386: 1

 387:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 1
        35: 1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        57: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        92: 1
        97: 1
        99: 1
       100: 1
       102: 1
       119: 1
       124: 1
       129: 1
       131: 1
       132: 1
       141: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       176: 1
       184: 1
       220: 1
       243: 1
       248: 1
       253: 1
       255: 1
       256: 1
       387: 1

 388:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        21: 1
        25: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        58: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        76: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       120: 1
       125: 1
       129: 1
       130: 1
       142: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       177: 1
       221: 1
       244: 1
       249: 1
       253: 1
       254: 1
       388: 1

 389:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: 1
        39: q+1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        59: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        86: 1
        92: 1
        98: 1
        99: 1
       100: 1
       102: 1
       121: 1
       126: 1
       130: 1
       131: 1
       132: 1
       143: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       178: 1
       184: 1
       222: 1
       245: 1
       250: 1
       254: 1
       255: 1
       256: 1
       389: 1

 390:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        45: 1
        48: 1
        49: 1
        60: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        99: 1
       102: 1
       122: 1
       127: 1
       131: 1
       144: 1
       148: 1
       151: 1
       153: 1
       154: 1
       179: 1
       223: 1
       246: 1
       251: 1
       255: 1
       390: 1

 391:    0: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         8: 1
        10: 1
        11: 1
        12: q+1
        14: 1
        15: q+1
        17: 1
        18: 1
        19: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: q+1
        42: 1
        45: 1
        46: 1
        48: 1
        49: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        88: 1
        96: 1
        99: 1
       102: 1
       103: 1
       123: 1
       128: 1
       131: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       175: 1
       180: 1
       188: 1
       224: 1
       247: 1
       252: 1
       255: 1
       308: 1
       391: 1

 392:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        25: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        76: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        89: 1
        92: 1
        93: 1
        97: 1
       100: 1
       101: 1
       102: 1
       129: 1
       132: 1
       133: 1
       146: 1
       149: 1
       152: 1
       153: 1
       154: 1
       167: 1
       181: 1
       184: 1
       185: 1
       225: 1
       253: 1
       256: 1
       257: 1
       300: 1
       392: 1

 393:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        63: 1
        66: 1
        68: 1
        69: 1
        70: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        90: 1
        92: 1
        93: 1
        98: 1
       100: 1
       101: 1
       102: 1
       130: 1
       132: 1
       133: 1
       147: 1
       150: 1
       152: 1
       153: 1
       154: 1
       168: 1
       182: 1
       184: 1
       185: 1
       226: 1
       254: 1
       256: 1
       257: 1
       301: 1
       393: 1

 394:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        48: 1
        49: 1
        64: 1
        67: 1
        69: 1
        70: 1
        78: 1
        80: 1
        82: 1
        83: 1
        91: 1
        93: 1
        99: 1
       101: 1
       102: 1
       131: 1
       133: 1
       148: 1
       151: 1
       153: 1
       154: 1
       169: 1
       183: 1
       185: 1
       227: 1
       255: 1
       257: 1
       302: 1
       394: 1

 395:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        68: 1
        70: 1
        71: 1
        75: 1
        81: 1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       103: 1
       104: 1
       111: 1
       132: 1
       135: 1
       155: 1
       156: 1
       161: 1
       173: 1
       175: 1
       176: 1
       180: 1
       186: 1
       189: 1
       258: 1
       265: 1
       286: 1
       289: 1
       395: 1

 396:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        68: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       110: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       177: 1
       190: 1
       258: 1
       259: 1
       260: 1
       264: 1
       396: 1

 397:    0: q+1
         1: q+1
         2: q+1
         3: 1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        16: q+1
        17: q+1
        18: 1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
       105: 1
       107: 1
       108: 1
       112: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       191: 1
       259: 1
       261: 1
       262: 1
       266: 1
       397: 1

 398:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        72: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
       106: 1
       107: 1
       109: 1
       113: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       170: 1
       177: 1
       192: 1
       260: 1
       261: 1
       263: 1
       267: 1
       398: 1

 399:    0: q+1
         1: 1
         2: q+1
         3: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: 1
        16: 1
        17: q+1
        18: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        27: q+1
        28: 1
        29: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: q+1
        92: 1
        93: 1
       107: 1
       108: 1
       119: 1
       122: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       193: 1
       261: 1
       262: 1
       273: 1
       276: 1
       399: 1

 400:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        24: 1
        25: 1
        27: q+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        39: 1
        40: 1
        41: q+1
        42: 2q+1
        43: q+1
        44: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: q+1
        88: 1
        89: 1
        91: q+1
        94: 1
        95: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       103: 1
       107: 1
       109: 1
       124: 1
       128: 1
       136: 1
       139: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       170: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       194: 1
       261: 1
       263: 1
       278: 1
       282: 1
       290: 1
       293: 1
       400: 1

 401:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        53: 1
        54: 1
        55: 1
        56: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        72: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       108: 1
       109: 1
       110: 1
       118: 1
       129: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       177: 1
       195: 1
       262: 1
       263: 1
       264: 1
       272: 1
       283: 1
       401: 1

 402:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        68: 1
        70: 1
        73: 1
        75: 1
        81: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
        99: 1
       100: 1
       103: 1
       110: 1
       111: 1
       132: 1
       139: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       178: 1
       180: 1
       186: 1
       196: 1
       264: 1
       265: 1
       286: 1
       293: 1
       402: 1

 403:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        69: 1
        70: 1
        75: 1
        78: 1
        82: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       103: 1
       111: 1
       118: 1
       133: 1
       145: 1
       161: 1
       165: 1
       166: 1
       174: 1
       175: 1
       180: 1
       183: 1
       187: 1
       197: 1
       265: 1
       272: 1
       287: 1
       299: 1
       403: 1

 404:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
       104: 1
       112: 1
       113: 1
       118: 1
       129: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       198: 1
       258: 1
       266: 1
       267: 1
       272: 1
       283: 1
       404: 1

 405:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
       105: 1
       112: 1
       114: 1
       116: 1
       120: 1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       199: 1
       259: 1
       266: 1
       268: 1
       270: 1
       274: 1
       405: 1

 406:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: 1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        46: q+1
        47: q+1
        48: 1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        72: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: q+1
        95: 1
        97: 1
        98: 1
       106: 1
       113: 1
       114: 1
       117: 1
       125: 1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       177: 1
       200: 1
       260: 1
       267: 1
       268: 1
       271: 1
       279: 1
       406: 1

 407:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
       107: 1
       114: 1
       115: 1
       157: 1
       158: 1
       162: 1
       163: 1
       164: 1
       201: 1
       261: 1
       268: 1
       269: 1
       407: 1

 408:    0: q+1
         1: q+1
         2: q+1
         3: 1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        16: q+1
        17: q+1
        18: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
       108: 1
       115: 1
       116: 1
       120: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       202: 1
       262: 1
       269: 1
       270: 1
       274: 1
       408: 1

 409:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        72: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
       109: 1
       115: 1
       117: 1
       125: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       177: 1
       203: 1
       263: 1
       269: 1
       271: 1
       279: 1
       409: 1

 410:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        68: 1
        69: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
       110: 1
       116: 1
       117: 1
       118: 1
       130: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       171: 1
       173: 1
       174: 1
       204: 1
       264: 1
       270: 1
       271: 1
       272: 1
       284: 1
       410: 1

 411:    0: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         8: 2q+1
        10: q+1
        11: q+1
        12: 1
        14: q+1
        15: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        23: q+1
        24: 1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: q+1
        39: 1
        42: 2q+1
        44: q+1
        45: q+1
        46: 1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        87: q+1
        88: 1
        91: q+1
        93: 1
        95: 1
        96: 1
        99: q+1
       103: 1
       111: 1
       118: 1
       122: 1
       128: 1
       131: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       180: 1
       205: 1
       265: 1
       272: 1
       276: 1
       282: 1
       285: 1
       411: 1

 412:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        50: 1
        57: 1
        60: 1
        62: 1
        64: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
       112: 1
       119: 1
       122: 1
       155: 1
       162: 1
       165: 1
       167: 1
       169: 1
       206: 1
       266: 1
       273: 1
       276: 1
       412: 1

 413:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        51: 1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        84: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
       113: 1
       119: 1
       123: 1
       129: 1
       156: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       207: 1
       267: 1
       273: 1
       277: 1
       283: 1
       413: 1

 414:    0: q+1
         1: q+1
         2: 1
         3: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        16: q+1
        17: 1
        18: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
       114: 1
       119: 1
       120: 1
       121: 1
       157: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       208: 1
       268: 1
       273: 1
       274: 1
       275: 1
       414: 1

 415:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        53: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
       115: 1
       120: 1
       121: 1
       158: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       209: 1
       269: 1
       274: 1
       275: 1
       415: 1

 416:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        54: 1
        59: 1
        60: 1
        63: 1
        64: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
       116: 1
       121: 1
       122: 1
       159: 1
       164: 1
       165: 1
       168: 1
       169: 1
       210: 1
       270: 1
       275: 1
       276: 1
       416: 1

 417:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        55: 1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        68: 1
        69: 1
        86: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
       117: 1
       121: 1
       123: 1
       130: 1
       160: 1
       164: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       211: 1
       271: 1
       275: 1
       277: 1
       284: 1
       417: 1

 418:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        56: 1
        60: 1
        61: 1
        64: 1
        69: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
       118: 1
       122: 1
       123: 1
       161: 1
       165: 1
       166: 1
       169: 1
       174: 1
       212: 1
       272: 1
       276: 1
       277: 1
       418: 1

 419:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+2q+1
         6: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        23: 1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        74: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       112: 1
       124: 1
       127: 1
       129: 1
       134: 1
       152: 1
       155: 1
       162: 1
       165: 1
       167: 1
       170: 1
       172: 1
       173: 1
       174: 1
       176: 1
       179: 1
       184: 1
       186: 1
       188: 1
       213: 1
       266: 1
       278: 1
       281: 1
       283: 1
       288: 1
       306: 1
       419: 1

 420:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        75: 1
        81: 1
        84: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        99: 1
       100: 1
       103: 1
       113: 1
       124: 1
       128: 1
       135: 1
       156: 1
       162: 1
       166: 1
       170: 1
       172: 1
       176: 1
       180: 1
       186: 1
       214: 1
       267: 1
       278: 1
       282: 1
       289: 1
       420: 1

 421:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        57: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        81: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       114: 1
       124: 1
       125: 1
       126: 1
       136: 1
       157: 1
       162: 1
       163: 1
       164: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       186: 1
       215: 1
       268: 1
       278: 1
       279: 1
       280: 1
       290: 1
       421: 1

 422:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        30: 1
        31: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: 1
        42: q+1
        43: q+1
        44: 2q+1
        46: q+1
        47: 1
        48: q+1
        49: 1
        53: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        72: 1
        73: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        89: q+1
        90: 1
        91: q+1
        94: 1
        95: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       115: 1
       125: 1
       126: 1
       137: 1
       149: 1
       151: 1
       158: 1
       163: 1
       164: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       181: 1
       183: 1
       186: 1
       187: 1
       216: 1
       269: 1
       279: 1
       280: 1
       291: 1
       303: 1
       305: 1
       422: 1

 423:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+2q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q+1
        22: 1
        23: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        66: 1
        67: 1
        68: 1
        69: 1
        73: 1
        74: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       116: 1
       126: 1
       127: 1
       130: 1
       138: 1
       152: 1
       159: 1
       164: 1
       165: 1
       168: 1
       171: 1
       172: 1
       173: 1
       174: 1
       178: 1
       179: 1
       184: 1
       186: 1
       188: 1
       217: 1
       270: 1
       280: 1
       281: 1
       284: 1
       292: 1
       306: 1
       423: 1

 424:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        55: 1
        59: 1
        61: 1
        66: 1
        67: 1
        73: 1
        75: 1
        81: 1
        86: 1
        88: 1
        90: 1
        91: 1
        94: 1
        95: 1
        98: 1
        99: 1
       100: 1
       103: 1
       117: 1
       126: 1
       128: 1
       139: 1
       160: 1
       164: 1
       166: 1
       171: 1
       172: 1
       178: 1
       180: 1
       186: 1
       218: 1
       271: 1
       280: 1
       282: 1
       293: 1
       424: 1

 425:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        67: 1
        69: 1
        74: 1
        75: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       102: 1
       103: 1
       118: 1
       127: 1
       128: 1
       140: 1
       161: 1
       165: 1
       166: 1
       172: 1
       174: 1
       179: 1
       180: 1
       188: 1
       219: 1
       272: 1
       281: 1
       282: 1
       294: 1
       425: 1

 426:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        20: 1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        57: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        81: 1
        84: 1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       103: 1
       119: 1
       124: 1
       129: 1
       131: 1
       132: 1
       162: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       186: 1
       220: 1
       273: 1
       278: 1
       283: 1
       285: 1
       286: 1
       426: 1

 427:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        25: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        58: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        85: 1
        89: 1
        90: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       120: 1
       125: 1
       129: 1
       130: 1
       163: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: 1
       221: 1
       274: 1
       279: 1
       283: 1
       284: 1
       427: 1

 428:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        22: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        59: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        81: 1
        86: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       103: 1
       121: 1
       126: 1
       130: 1
       131: 1
       132: 1
       164: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       186: 1
       222: 1
       275: 1
       280: 1
       284: 1
       285: 1
       286: 1
       428: 1

 429:    0: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         8: 1
        10: 1
        11: q+1
        12: 1
        14: 1
        15: 1
        17: 1
        18: q+1
        19: 1
        23: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: q+1
        46: 1
        48: 1
        49: 1
        60: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        83: 1
        87: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       102: 1
       103: 1
       122: 1
       127: 1
       131: 1
       154: 1
       165: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: 1
       188: 1
       223: 1
       276: 1
       281: 1
       285: 1
       308: 1
       429: 1

 430:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       103: 1
       123: 1
       128: 1
       131: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       180: 1
       224: 1
       277: 1
       282: 1
       285: 1
       430: 1

 431:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        25: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        36: 1
        37: 1
        39: 1
        40: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        76: 1
        81: 1
        82: 1
        89: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
       100: 1
       101: 1
       103: 1
       129: 1
       132: 1
       133: 1
       149: 1
       167: 1
       170: 1
       173: 1
       174: 1
       175: 1
       181: 1
       186: 1
       187: 1
       225: 1
       283: 1
       286: 1
       287: 1
       303: 1
       431: 1

 432:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        36: 1
        37: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        63: 1
        66: 1
        68: 1
        69: 1
        70: 1
        77: 1
        81: 1
        82: 1
        90: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
       100: 1
       101: 1
       103: 1
       130: 1
       132: 1
       133: 1
       150: 1
       168: 1
       171: 1
       173: 1
       174: 1
       175: 1
       182: 1
       186: 1
       187: 1
       226: 1
       284: 1
       286: 1
       287: 1
       304: 1
       432: 1

 433:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        64: 1
        67: 1
        69: 1
        70: 1
        78: 1
        82: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       103: 1
       131: 1
       133: 1
       151: 1
       169: 1
       172: 1
       174: 1
       175: 1
       183: 1
       187: 1
       227: 1
       285: 1
       287: 1
       305: 1
       433: 1

 434:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        68: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       134: 1
       135: 1
       140: 1
       152: 1
       155: 1
       156: 1
       161: 1
       173: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       228: 1
       258: 1
       288: 1
       289: 1
       294: 1
       306: 1
       434: 1

 435:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        28: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        54: 1
        71: 1
        72: 1
        73: 1
        74: 1
        79: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       105: 1
       134: 1
       136: 1
       138: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       229: 1
       259: 1
       288: 1
       290: 1
       292: 1
       435: 1

 436:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        30: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        55: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        88: 1
        94: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       106: 1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       160: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       230: 1
       260: 1
       289: 1
       290: 1
       293: 1
       436: 1

 437:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        27: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: 1
        71: 1
        72: 1
        73: 1
        76: 1
        78: 1
        84: 1
        85: 1
        86: 1
        89: 1
        91: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       107: 1
       136: 1
       137: 1
       141: 1
       157: 1
       158: 1
       162: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: 1
       231: 1
       261: 1
       290: 1
       291: 1
       295: 1
       437: 1

 438:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        60: 1
        62: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       137: 1
       138: 1
       144: 1
       146: 1
       158: 1
       159: 1
       165: 1
       167: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       232: 1
       262: 1
       291: 1
       292: 1
       298: 1
       300: 1
       438: 1

 439:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        55: 1
        61: 1
        65: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       109: 1
       137: 1
       139: 1
       145: 1
       149: 1
       158: 1
       160: 1
       166: 1
       170: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       233: 1
       263: 1
       291: 1
       293: 1
       299: 1
       303: 1
       439: 1

 440:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        68: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       138: 1
       139: 1
       140: 1
       152: 1
       159: 1
       160: 1
       161: 1
       173: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       234: 1
       264: 1
       292: 1
       293: 1
       294: 1
       306: 1
       440: 1

 441:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        70: 1
        74: 1
        75: 1
        83: 1
        87: 1
        88: 1
        96: 1
        99: 1
       102: 1
       103: 1
       111: 1
       140: 1
       154: 1
       161: 1
       175: 1
       179: 1
       180: 1
       188: 1
       235: 1
       265: 1
       294: 1
       308: 1
       441: 1

 442:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       112: 1
       134: 1
       141: 1
       144: 1
       146: 1
       155: 1
       162: 1
       165: 1
       167: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       236: 1
       266: 1
       288: 1
       295: 1
       298: 1
       300: 1
       442: 1

 443:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        57: 1
        61: 1
        65: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       113: 1
       135: 1
       141: 1
       145: 1
       149: 1
       156: 1
       162: 1
       166: 1
       170: 1
       176: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       237: 1
       267: 1
       289: 1
       295: 1
       299: 1
       303: 1
       443: 1

 444:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        47: q+1
        48: 1
        49: q+1
        52: 1
        57: 1
        58: 1
        59: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       114: 1
       136: 1
       141: 1
       142: 1
       143: 1
       157: 1
       162: 1
       163: 1
       164: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       238: 1
       268: 1
       290: 1
       295: 1
       296: 1
       297: 1
       444: 1

 445:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        47: 1
        48: 1
        49: 1
        53: 1
        58: 1
        59: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       115: 1
       137: 1
       142: 1
       143: 1
       158: 1
       163: 1
       164: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       239: 1
       269: 1
       291: 1
       296: 1
       297: 1
       445: 1

 446:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       116: 1
       138: 1
       143: 1
       144: 1
       147: 1
       159: 1
       164: 1
       165: 1
       168: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       240: 1
       270: 1
       292: 1
       297: 1
       298: 1
       301: 1
       446: 1

 447:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        24: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        55: 1
        59: 1
        61: 1
        66: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        88: 1
        90: 1
        91: 1
        94: 1
        95: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       117: 1
       139: 1
       143: 1
       145: 1
       150: 1
       160: 1
       164: 1
       166: 1
       171: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       187: 1
       241: 1
       271: 1
       293: 1
       297: 1
       299: 1
       304: 1
       447: 1

 448:    0: 2q+1
         2: 2q+1
         3: 1
         4: 2q+1
         5: 2q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 2q+1
        15: 1
        17: 2q+1
        18: 1
        19: 2q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 2q+1
        49: 1
        56: 1
        60: 1
        61: 1
        69: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       118: 1
       140: 1
       144: 1
       145: 1
       153: 1
       161: 1
       165: 1
       166: 1
       174: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       242: 1
       272: 1
       294: 1
       298: 1
       299: 1
       307: 1
       448: 1

 449:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        57: 1
        62: 1
        64: 1
        71: 1
        76: 1
        78: 1
        79: 1
        80: 1
        84: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       119: 1
       141: 1
       146: 1
       148: 1
       162: 1
       167: 1
       169: 1
       176: 1
       181: 1
       183: 1
       184: 1
       185: 1
       243: 1
       273: 1
       295: 1
       300: 1
       302: 1
       449: 1

 450:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        25: 1
        26: 1
        28: 1
        29: 1
        33: 1
        34: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        58: 1
        62: 1
        63: 1
        72: 1
        76: 1
        77: 1
        79: 1
        80: 1
        85: 1
        89: 1
        90: 1
        92: 1
        93: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       120: 1
       142: 1
       146: 1
       147: 1
       163: 1
       167: 1
       168: 1
       177: 1
       181: 1
       182: 1
       184: 1
       185: 1
       244: 1
       274: 1
       296: 1
       300: 1
       301: 1
       450: 1

 451:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        26: 1
        27: 1
        28: 1
        29: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        59: 1
        63: 1
        64: 1
        73: 1
        77: 1
        78: 1
        79: 1
        80: 1
        86: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       121: 1
       143: 1
       147: 1
       148: 1
       164: 1
       168: 1
       169: 1
       178: 1
       182: 1
       183: 1
       184: 1
       185: 1
       245: 1
       275: 1
       297: 1
       301: 1
       302: 1
       451: 1

 452:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        27: 1
        29: 1
        35: 1
        37: 1
        38: 1
        42: 1
        44: 1
        45: 1
        48: 1
        49: 1
        60: 1
        64: 1
        74: 1
        78: 1
        80: 1
        87: 1
        91: 1
        93: 1
        99: 1
       101: 1
       102: 1
       122: 1
       144: 1
       148: 1
       165: 1
       169: 1
       179: 1
       183: 1
       185: 1
       246: 1
       276: 1
       298: 1
       302: 1
       452: 1

 453:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        61: 1
        64: 1
        69: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       123: 1
       145: 1
       148: 1
       153: 1
       166: 1
       169: 1
       174: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       247: 1
       277: 1
       299: 1
       302: 1
       307: 1
       453: 1

 454:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        57: 1
        65: 1
        67: 1
        71: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        99: 1
       100: 1
       101: 1
       103: 1
       124: 1
       141: 1
       149: 1
       151: 1
       162: 1
       170: 1
       172: 1
       176: 1
       181: 1
       183: 1
       186: 1
       187: 1
       248: 1
       278: 1
       295: 1
       303: 1
       305: 1
       454: 1

 455:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        25: 1
        26: 1
        30: 1
        31: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        58: 1
        65: 1
        66: 1
        72: 1
        76: 1
        77: 1
        81: 1
        82: 1
        85: 1
        89: 1
        90: 1
        94: 1
        95: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       125: 1
       142: 1
       149: 1
       150: 1
       163: 1
       170: 1
       171: 1
       177: 1
       181: 1
       182: 1
       186: 1
       187: 1
       249: 1
       279: 1
       296: 1
       303: 1
       304: 1
       455: 1

 456:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        59: 1
        66: 1
        67: 1
        73: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        90: 1
        91: 1
        94: 1
        95: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       126: 1
       143: 1
       150: 1
       151: 1
       164: 1
       171: 1
       172: 1
       178: 1
       182: 1
       183: 1
       186: 1
       187: 1
       250: 1
       280: 1
       297: 1
       304: 1
       305: 1
       456: 1

 457:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        60: 1
        67: 1
        69: 1
        74: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       127: 1
       144: 1
       151: 1
       153: 1
       165: 1
       172: 1
       174: 1
       179: 1
       183: 1
       185: 1
       187: 1
       188: 1
       251: 1
       281: 1
       298: 1
       305: 1
       307: 1
       457: 1

 458:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        24: 1
        27: 1
        31: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        46: 1
        48: 1
        49: 1
        61: 1
        67: 1
        75: 1
        78: 1
        82: 1
        88: 1
        91: 1
        95: 1
        99: 1
       101: 1
       103: 1
       128: 1
       145: 1
       151: 1
       166: 1
       172: 1
       180: 1
       183: 1
       187: 1
       252: 1
       282: 1
       299: 1
       305: 1
       458: 1

 459:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        25: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        62: 1
        65: 1
        68: 1
        69: 1
        76: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        89: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
       100: 1
       101: 1
       102: 1
       103: 1
       129: 1
       146: 1
       149: 1
       152: 1
       153: 1
       167: 1
       170: 1
       173: 1
       174: 1
       181: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       253: 1
       283: 1
       300: 1
       303: 1
       306: 1
       307: 1
       459: 1

 460:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        63: 1
        66: 1
        68: 1
        69: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        90: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
       100: 1
       101: 1
       102: 1
       103: 1
       130: 1
       147: 1
       150: 1
       152: 1
       153: 1
       168: 1
       171: 1
       173: 1
       174: 1
       182: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       254: 1
       284: 1
       301: 1
       304: 1
       306: 1
       307: 1
       460: 1

 461:    0: 2q+1
         2: q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         8: q+1
        10: 1
        11: q+1
        12: q+1
        14: q+1
        15: 2q+1
        17: q+1
        18: 2q+1
        19: 2q+1
        27: 1
        29: 1
        31: 1
        32: 1
        35: q+1
        37: 1
        38: q+1
        39: q+1
        42: q+1
        44: 1
        45: q+1
        46: q+1
        48: q+1
        49: 2q+1
        64: 1
        67: 1
        69: 1
        70: 1
        78: 1
        80: 1
        82: 1
        83: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: q+1
       101: 1
       102: q+1
       103: q+1
       131: 1
       148: 1
       151: 1
       153: 1
       154: 1
       169: 1
       172: 1
       174: 1
       175: 1
       183: 1
       185: 1
       187: 1
       188: 1
       255: 1
       285: 1
       302: 1
       305: 1
       307: 1
       308: 1
       461: 1

 462:    0: 1
         1: 1
         3: 1
         4: 1
         5: 1
         9: 1
        11: 1
        12: 1
        13: 1
        15: 1
        16: 1
        18: 1
        19: 1
        28: 1
        30: 1
        32: 1
        36: 1
        38: 1
        39: 1
        43: 1
        45: 1
        46: 1
        47: 1
        49: 1
        68: 1
        70: 1
        79: 1
        81: 1
        83: 1
        92: 1
        94: 1
        96: 1
       100: 1
       102: 1
       103: 1
       132: 1
       152: 1
       154: 1
       173: 1
       175: 1
       184: 1
       186: 1
       188: 1
       256: 1
       286: 1
       306: 1
       308: 1
       462: 1

 463:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        29: 1
        31: 1
        32: 1
        37: 1
        38: 1
        39: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        69: 1
        70: 1
        80: 1
        82: 1
        83: 1
        93: 1
        95: 1
        96: 1
       101: 1
       102: 1
       103: 1
       133: 1
       153: 1
       154: 1
       174: 1
       175: 1
       185: 1
       187: 1
       188: 1
       257: 1
       287: 1
       307: 1
       308: 1
       463: 1

 464:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       176: 1
       177: q+1
       178: 1
       181: 1
       182: 1
       183: 1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       221: 1
       225: 1
       226: 1
       230: 1
       237: 1
       238: 1
       241: 1
       249: 1
       259: 1
       266: 1
       268: 1
       270: 1
       274: 1
       290: 1
       295: 1
       296: 1
       297: 1
       309: 1
       310: 1
       318: 1
       320: 1
       352: 1
       367: 1
       405: 1
       444: 1
       464: 1

 465:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       129: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       176: 1
       177: q+1
       178: 1
       181: 1
       183: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       225: 1
       230: 1
       231: 1
       233: 1
       237: 1
       259: 1
       261: 1
       262: 1
       266: 1
       290: 1
       291: 1
       295: 1
       309: 1
       310: 1
       311: 1
       317: 1
       359: 1
       397: 1
       437: 1
       465: 1

 466:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       230: 1
       259: 1
       290: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       466: 1

 467:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       177: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       206: 1
       207: 1
       212: 1
       258: 1
       259: 1
       260: 1
       264: 1
       311: 1
       312: 1
       313: 1
       328: 1
       396: 1
       467: 1

 468:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       177: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       213: 1
       214: 1
       219: 1
       228: 1
       229: 1
       230: 1
       234: 1
       311: 1
       314: 1
       315: 1
       336: 1
       357: 1
       468: 1

 469:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 2q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 2q+1
        24: 1
        25: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        38: q+1
        39: 1
        40: 1
        41: q+1
        42: 2q+1
        43: q+1
        45: 2q+1
        47: 1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        64: q+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: q+1
        87: 2q+1
        92: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: q+1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       118: 1
       119: 1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       157: 1
       159: q+1
       176: 1
       177: 1
       178: 1
       179: q+1
       184: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       206: 1
       213: 1
       219: 1
       220: 1
       223: 1
       229: 1
       234: 1
       235: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       312: 1
       314: 1
       316: 1
       343: 1
       344: 1
       363: 1
       435: 1
       469: 1

 470:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: 2q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 1
        34: q+1
        35: 2q+1
        36: q+1
        39: 2q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: 1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: q+1
        75: 2q+1
        81: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: q+1
       129: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: q+1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: q+1
       186: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       230: 1
       260: 1
       264: 1
       265: 1
       286: 1
       289: 1
       290: 1
       293: 1
       313: 1
       315: 1
       316: 1
       335: 1
       345: 1
       402: 1
       436: 1
       470: 1

 471:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q^2+2q+1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        27: q^2+2q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        47: 1
        48: q+1
        49: q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: q+1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: q+1
        92: 1
        93: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       205: 1
       220: 1
       225: 1
       227: 1
       231: 1
       233: 1
       248: 1
       252: 1
       261: 1
       262: 1
       273: 1
       276: 1
       290: 1
       291: 1
       295: 1
       316: 1
       317: 1
       327: 1
       351: 1
       361: 1
       399: 1
       437: 1
       471: 1

 472:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q^2+2q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        53: q+1
        54: 1
        55: 1
        56: 1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       177: q+1
       178: 1
       181: 1
       182: 1
       183: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       221: 1
       225: 1
       226: 1
       233: 1
       239: 1
       241: 1
       249: 1
       262: 1
       269: 1
       270: 1
       274: 1
       291: 1
       296: 1
       297: 1
       317: 1
       318: 1
       325: 1
       352: 1
       370: 1
       408: 1
       445: 1
       472: 1

 473:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        99: 1
       100: 1
       101: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       181: 1
       183: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       225: 1
       227: 1
       237: 1
       248: 1
       252: 1
       266: 1
       273: 1
       276: 1
       295: 1
       309: 1
       319: 1
       327: 1
       351: 1
       381: 1
       412: 1
       473: 1

 474:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        81: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        92: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: 1
       136: 1
       139: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       230: 1
       259: 1
       290: 1
       310: 1
       319: 1
       320: 1
       326: 1
       329: 1
       338: 1
       346: 1
       474: 1

 475:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       177: 1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       221: 1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       475: 1

 476:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       155: 1
       157: 1
       159: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       210: 1
       259: 1
       312: 1
       321: 1
       323: 1
       329: 1
       476: 1

 477:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 1
        34: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       177: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       260: 1
       264: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       334: 1
       477: 1

 478:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: q+1
        47: 1
        48: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        97: 1
        98: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       177: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       229: 1
       234: 1
       314: 1
       321: 1
       324: 1
       325: 1
       337: 1
       342: 1
       478: 1

 479:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       139: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       218: 1
       230: 1
       315: 1
       322: 1
       324: 1
       338: 1
       479: 1

 480:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: 1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: 1
       139: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       290: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       346: 1
       480: 1

 481:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q^2+2q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q^2+2q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: q+1
        54: 1
        55: 1
        56: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       145: 1
       149: 1
       151: 1
       158: 1
       159: 1
       165: 1
       167: 1
       169: 1
       177: 1
       178: 1
       181: 1
       183: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       218: 1
       221: 1
       222: 1
       225: 1
       227: 1
       233: 1
       252: 1
       262: 1
       276: 1
       291: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       341: 1
       347: 1
       481: 1

 482:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: q+1
        23: 1
        24: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: q+1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: 1
        99: 1
       100: 1
       101: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       139: 1
       143: 1
       145: 1
       150: 1
       151: 1
       159: 1
       164: 1
       165: 1
       168: 1
       169: 1
       178: 1
       182: 1
       183: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: 1
       218: 1
       222: 1
       226: 1
       227: 1
       241: 1
       250: 1
       252: 1
       270: 1
       275: 1
       276: 1
       297: 1
       318: 1
       326: 1
       327: 1
       353: 1
       385: 1
       416: 1
       482: 1

 483:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        81: 1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       155: 1
       156: 1
       161: 1
       173: 1
       175: 1
       176: 1
       180: 1
       186: 1
       189: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       258: 1
       265: 1
       286: 1
       289: 1
       319: 1
       328: 1
       335: 1
       345: 1
       395: 1
       483: 1

 484:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: q+1
        94: q+1
        96: q+1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: q+1
       177: 1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       258: 1
       259: 1
       260: 1
       264: 1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       396: 1
       484: 1

 485:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        62: 2q+1
        63: q+1
        64: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: q+1
       169: 1
       191: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       321: 1
       329: 1
       331: 1
       332: 1
       397: 1
       412: 1
       485: 1

 486:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       192: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       221: 1
       260: 1
       261: 1
       263: 1
       267: 1
       273: 1
       277: 1
       283: 1
       322: 1
       330: 1
       331: 1
       333: 1
       398: 1
       413: 1
       486: 1

 487:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       193: 1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       261: 1
       262: 1
       273: 1
       276: 1
       323: 1
       331: 1
       332: 1
       399: 1
       487: 1

 488:    0: 2q^2+3q+1
         1: q^2+2q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: 2q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: q+1
        21: 1
        22: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q^2+3q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: 1
        35: 2q+1
        36: q+1
        39: 2q+1
        40: 1
        41: q+1
        42: 2q+1
        43: q+1
        44: q+1
        45: 2q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: 1
        59: q+1
        61: q+1
        62: 1
        63: q+1
        64: 2q+1
        65: q+1
        66: 1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        81: q+1
        84: 1
        85: 1
        86: q+1
        88: 1
        89: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: q+1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       136: 1
       139: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       194: 1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       261: 1
       263: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       290: 1
       293: 1
       324: 1
       331: 1
       333: 1
       346: 1
       349: 1
       400: 1
       426: 1
       430: 1
       488: 1

 489:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: q+1
        72: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       262: 1
       263: 1
       264: 1
       272: 1
       276: 1
       277: 1
       283: 1
       325: 1
       332: 1
       333: 1
       334: 1
       401: 1
       418: 1
       489: 1

 490:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        81: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
        99: 1
       100: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       139: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       178: 1
       180: 1
       186: 1
       196: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       218: 1
       222: 1
       224: 1
       264: 1
       265: 1
       286: 1
       293: 1
       326: 1
       334: 1
       335: 1
       349: 1
       402: 1
       490: 1

 491:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: q+1
        24: q+1
        27: q+1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: q+1
        60: q+1
        61: q+1
        64: 1
        67: 1
        69: q+1
        70: 1
        75: 1
        78: 1
        82: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       103: 1
       111: 1
       118: q+1
       122: 1
       123: 1
       128: 1
       131: 1
       133: 1
       145: 1
       151: 1
       161: 1
       165: 1
       166: 1
       169: 1
       174: 1
       175: 1
       180: 1
       183: 1
       187: 1
       197: 1
       205: 1
       212: 1
       224: 1
       227: 1
       252: 1
       265: 1
       272: 1
       276: 1
       277: 1
       287: 1
       299: 1
       327: 1
       335: 1
       355: 1
       403: 1
       418: 1
       491: 1

 492:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        92: 1
        97: 1
        99: 1
       100: 1
       102: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       140: 1
       152: 1
       154: 1
       155: 1
       176: 1
       179: 1
       184: 1
       189: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       228: 1
       235: 1
       256: 1
       288: 1
       319: 1
       336: 1
       343: 1
       344: 1
       356: 1
       492: 1

 493:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        38: q+1
        39: q+1
        40: 1
        41: 1
        47: q+1
        48: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: q+1
       177: 1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       320: 1
       336: 1
       337: 1
       338: 1
       342: 1
       357: 1
       493: 1

 494:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: 1
        47: 1
        48: 1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       177: 1
       191: 1
       199: 1
       201: 1
       202: 1
       213: 1
       215: 1
       216: 1
       217: 1
       221: 1
       229: 1
       231: 1
       232: 1
       236: 1
       248: 1
       251: 1
       253: 1
       321: 1
       337: 1
       339: 1
       340: 1
       358: 1
       380: 1
       494: 1

 495:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        20: q+1
        21: q+1
        22: 1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        30: 2q+1
        31: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: q+1
        59: 1
        61: q+1
        65: 2q+1
        66: q+1
        67: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        78: 1
        81: q+1
        82: q+1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: q+1
       151: 1
       192: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       216: 1
       218: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       322: 1
       338: 1
       339: 1
       341: 1
       359: 1
       381: 1
       495: 1

 496:    0: 2q^2+3q+1
         1: q^2+2q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: q+1
         8: q^2+3q+1
         9: q^2+2q+1
        10: q^2+3q+1
        11: 2q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: q+1
        21: 1
        22: q+1
        23: q+1
        25: q+1
        26: q+1
        27: q^2+3q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: 1
        34: q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: 1
        39: 2q+1
        40: q+1
        41: 1
        42: 2q+1
        43: q+1
        45: 2q+1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: 1
        59: q+1
        60: q+1
        62: q+1
        63: 1
        64: 2q+1
        65: 1
        66: q+1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: q+1
        74: 1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: 1
        86: 1
        87: q+1
        92: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: q+1
       127: 1
       129: 1
       130: 1
       131: q+1
       132: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       193: 1
       201: 1
       202: 1
       208: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       290: 1
       292: 1
       323: 1
       339: 1
       340: 1
       346: 1
       348: 1
       360: 1
       387: 1
       390: 1
       496: 1

 497:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       194: 1
       201: 1
       203: 1
       215: 1
       216: 1
       218: 1
       231: 1
       233: 1
       248: 1
       252: 1
       324: 1
       339: 1
       341: 1
       361: 1
       497: 1

 498:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        19: q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: q+1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       177: 1
       195: 1
       202: 1
       203: 1
       204: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       232: 1
       233: 1
       234: 1
       242: 1
       251: 1
       252: 1
       253: 1
       325: 1
       340: 1
       341: 1
       342: 1
       362: 1
       386: 1
       498: 1

 499:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        92: 1
        98: 1
        99: 1
       100: 1
       102: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       159: 1
       178: 1
       179: 1
       184: 1
       196: 1
       204: 1
       205: 1
       210: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       234: 1
       235: 1
       256: 1
       292: 1
       326: 1
       342: 1
       343: 1
       348: 1
       363: 1
       499: 1

 500:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: q+1
        24: q+1
        27: q+1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        48: q+1
        49: 1
        56: q+1
        60: q+1
        61: q+1
        64: 1
        67: 1
        69: q+1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        91: 1
        93: 1
        99: 1
       101: 1
       102: 1
       111: 1
       118: q+1
       122: 1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       151: 1
       153: 1
       154: 1
       165: 1
       169: 1
       179: 1
       183: 1
       185: 1
       197: 1
       205: 1
       219: 1
       223: 1
       227: 1
       235: 1
       242: 1
       251: 1
       252: 1
       257: 1
       276: 1
       298: 1
       327: 1
       343: 1
       354: 1
       364: 1
       386: 1
       500: 1

 501:    0: 2q+1
         1: 2q+1
         2: q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         8: 1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: q+1
        18: q+1
        19: 2q+1
        20: 1
        23: 1
        24: 1
        25: q+1
        27: 1
        28: 2q+1
        29: q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        33: q+1
        35: 1
        36: q+1
        38: q+1
        39: q+1
        40: q+1
        42: 1
        43: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: 2q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        84: 1
        87: 1
        88: 1
        92: q+1
        94: q+1
        96: q+1
        97: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       140: 1
       152: q+1
       154: 1
       155: 1
       156: 1
       161: 1
       173: q+1
       175: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       198: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: 1
       256: 1
       258: 1
       286: 1
       288: 1
       289: 1
       294: 1
       306: 1
       308: 1
       328: 1
       336: 1
       344: 1
       345: 1
       350: 1
       434: 1
       462: 1
       501: 1

 502:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       136: 1
       138: 1
       152: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       199: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       329: 1
       337: 1
       344: 1
       346: 1
       348: 1
       435: 1
       502: 1

 503:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: q+1
        84: 1
        85: 1
        86: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       160: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       200: 1
       207: 1
       208: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       260: 1
       286: 1
       289: 1
       290: 1
       293: 1
       330: 1
       338: 1
       345: 1
       346: 1
       349: 1
       436: 1
       503: 1

 504:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: q+1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       107: 1
       114: 1
       115: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       141: 1
       149: 1
       151: 1
       157: 1
       158: 1
       162: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: 1
       201: 1
       208: 1
       209: 1
       215: 1
       216: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       231: 1
       248: 1
       261: 1
       273: 1
       290: 1
       291: 1
       295: 1
       331: 1
       339: 1
       346: 1
       347: 1
       351: 1
       437: 1
       504: 1

 505:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: q+1
        17: 2q+1
        18: q+1
        19: q+1
        21: 1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: 1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       115: 1
       116: 1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       165: 1
       167: q+1
       169: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       202: 1
       209: 1
       210: 1
       216: 1
       217: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       232: 1
       251: 1
       253: 1
       256: 1
       257: 1
       262: 1
       276: 1
       291: 1
       292: 1
       298: 1
       300: 1
       332: 1
       340: 1
       347: 1
       348: 1
       354: 1
       392: 1
       438: 1
       505: 1

 506:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: 1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        75: 1
        76: q+1
        78: 1
        81: q+1
        82: q+1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       109: 1
       115: 1
       117: 1
       120: 1
       121: 1
       123: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       145: 1
       149: q+1
       151: 1
       158: 1
       160: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       203: 1
       209: 1
       211: 1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       233: 1
       252: 1
       263: 1
       277: 1
       283: 1
       286: 1
       287: 1
       291: 1
       293: 1
       299: 1
       303: 1
       333: 1
       341: 1
       347: 1
       349: 1
       355: 1
       431: 1
       439: 1
       506: 1

 507:    0: 2q+1
         1: 2q+1
         2: q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         7: q+1
         8: 1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: q+1
        18: q+1
        19: 2q+1
        22: 1
        23: 1
        24: 1
        26: q+1
        27: 1
        28: 2q+1
        29: q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        34: q+1
        35: 1
        36: q+1
        38: q+1
        39: q+1
        41: q+1
        42: 1
        43: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: 2q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        86: 1
        87: 1
        88: 1
        92: q+1
        94: q+1
        96: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       138: 1
       139: 1
       140: 1
       152: q+1
       154: 1
       159: 1
       160: 1
       161: 1
       173: q+1
       175: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       204: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       234: 1
       256: 1
       264: 1
       286: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       334: 1
       342: 1
       348: 1
       349: 1
       350: 1
       440: 1
       462: 1
       507: 1

 508:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        83: 1
        87: 1
        88: 1
        96: 1
        99: 1
       102: 1
       103: 1
       111: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       140: 1
       154: 1
       161: 1
       175: 1
       179: 1
       180: 1
       188: 1
       205: 1
       212: 1
       219: 1
       223: 1
       224: 1
       235: 1
       265: 1
       294: 1
       308: 1
       335: 1
       343: 1
       350: 1
       441: 1
       508: 1

 509:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: q+1
        20: q+1
        23: q+1
        25: 2q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        57: q+1
        60: q+1
        62: 2q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       112: q+1
       119: 1
       122: 1
       124: 1
       127: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       141: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       162: 1
       165: 1
       167: q+1
       169: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       206: 1
       213: 1
       220: 1
       223: 1
       225: 1
       227: 1
       236: 1
       248: 1
       251: 1
       253: 1
       256: 1
       257: 1
       266: 1
       273: 1
       276: 1
       288: 1
       295: 1
       298: 1
       300: 1
       344: 1
       351: 1
       354: 1
       380: 1
       392: 1
       412: 1
       442: 1
       509: 1

 510:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        24: q+1
        25: 2q+1
        27: q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: 2q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: q+1
        57: q+1
        61: q+1
        62: q+1
        64: 1
        65: 2q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        75: 1
        76: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       113: q+1
       119: 1
       123: 1
       124: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       141: 1
       145: 1
       149: q+1
       151: 1
       156: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       207: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       237: 1
       248: 1
       252: 1
       267: 1
       273: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       295: 1
       299: 1
       303: 1
       345: 1
       351: 1
       355: 1
       381: 1
       413: 1
       431: 1
       443: 1
       510: 1

 511:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        52: q+1
        57: q+1
        58: q+1
        59: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       114: q+1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       136: 1
       141: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       157: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       208: 1
       215: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       238: 1
       248: 1
       249: 1
       250: 1
       268: 1
       273: 1
       274: 1
       275: 1
       290: 1
       295: 1
       296: 1
       297: 1
       346: 1
       351: 1
       352: 1
       353: 1
       382: 1
       414: 1
       444: 1
       511: 1

 512:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: q+1
        22: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        53: q+1
        58: q+1
        59: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       115: q+1
       120: 1
       121: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       158: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       209: 1
       216: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       239: 1
       249: 1
       250: 1
       269: 1
       274: 1
       275: 1
       291: 1
       296: 1
       297: 1
       347: 1
       352: 1
       353: 1
       383: 1
       415: 1
       445: 1
       512: 1

 513:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         7: 2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: q+1
        22: q+1
        23: q+1
        26: 2q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: 1
        54: q+1
        59: q+1
        60: q+1
        63: 2q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       116: q+1
       121: 1
       122: 1
       126: 1
       127: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: 1
       143: 1
       144: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       164: 1
       165: 1
       168: q+1
       169: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       210: 1
       217: 1
       222: 1
       223: 1
       226: 1
       227: 1
       240: 1
       250: 1
       251: 1
       254: 1
       256: 1
       257: 1
       270: 1
       275: 1
       276: 1
       292: 1
       297: 1
       298: 1
       301: 1
       348: 1
       353: 1
       354: 1
       384: 1
       393: 1
       416: 1
       446: 1
       513: 1

 514:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         7: 2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: q+1
        24: q+1
        26: 2q+1
        27: q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        34: 2q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        55: q+1
        59: q+1
        61: q+1
        63: q+1
        64: 1
        66: 2q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        75: 1
        77: q+1
        78: 1
        81: q+1
        82: q+1
        86: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       117: q+1
       121: 1
       123: 1
       126: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       139: 1
       143: 1
       145: 1
       150: q+1
       151: 1
       160: 1
       164: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       187: 1
       211: 1
       218: 1
       222: 1
       224: 1
       226: 1
       227: 1
       241: 1
       250: 1
       252: 1
       271: 1
       275: 1
       277: 1
       284: 1
       286: 1
       287: 1
       293: 1
       297: 1
       299: 1
       304: 1
       349: 1
       353: 1
       355: 1
       385: 1
       417: 1
       432: 1
       447: 1
       514: 1

 515:    0: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         8: q+1
        10: 3q+1
        11: 3q+1
        12: 3q+1
        14: 3q+1
        15: q+1
        17: 3q+1
        18: q+1
        19: 3q+1
        23: q+1
        24: q+1
        27: q+1
        29: 3q+1
        31: 3q+1
        32: 3q+1
        35: 1
        37: q+1
        38: q+1
        39: q+1
        42: 1
        44: q+1
        45: q+1
        46: q+1
        48: 3q+1
        49: 1
        56: q+1
        60: q+1
        61: q+1
        64: 1
        67: 1
        69: 3q+1
        70: 1
        74: 1
        75: 1
        78: 1
        80: q+1
        82: q+1
        83: q+1
        87: 1
        88: 1
        91: 1
        93: q+1
        95: q+1
        96: q+1
        99: 1
       101: 1
       102: 1
       103: 1
       118: q+1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       151: 1
       153: q+1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       174: q+1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       212: 1
       219: 1
       223: 1
       224: 1
       227: 1
       242: 1
       251: 1
       252: 1
       257: 1
       272: 1
       276: 1
       277: 1
       287: 1
       294: 1
       298: 1
       299: 1
       307: 1
       308: 1
       350: 1
       354: 1
       355: 1
       386: 1
       418: 1
       448: 1
       463: 1
       515: 1

 516:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       129: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       154: 1
       155: 1
       162: 1
       165: 1
       167: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       189: 1
       197: 1
       198: 1
       225: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       253: 1
       256: 1
       257: 1
       266: 1
       288: 1
       295: 1
       298: 1
       300: 1
       309: 1
       356: 1
       364: 1
       365: 1
       392: 1
       442: 1
       516: 1

 517:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       189: 1
       190: 1
       196: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       310: 1
       356: 1
       357: 1
       363: 1
       435: 1
       517: 1

 518:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        47: q+1
        48: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        97: q+1
        98: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       129: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       177: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       253: 1
       311: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       518: 1

 519:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       119: 1
       122: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       191: 1
       193: 1
       206: 1
       229: 1
       231: 1
       232: 1
       236: 1
       243: 1
       246: 1
       259: 1
       288: 1
       290: 1
       292: 1
       312: 1
       358: 1
       360: 1
       373: 1
       435: 1
       519: 1

 520:    0: 2q^2+3q+1
         1: q^2+2q+1
         2: 2q^2+3q+1
         3: 2q+1
         4: 2q^2+3q+1
         5: q^2+2q+1
         6: q+1
         7: q^2+2q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 1
        12: 2q+1
        13: q^2+2q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 1
        24: 2q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q^2+2q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: 1
        39: 2q+1
        40: q+1
        41: q+1
        42: q+1
        43: 1
        45: 1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: q+1
        74: 1
        75: 2q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        92: 1
        94: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       152: 1
       153: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: q+1
       184: 1
       186: 1
       188: 1
       192: 1
       193: 1
       195: 1
       207: 1
       212: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       253: 1
       260: 1
       264: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       313: 1
       359: 1
       360: 1
       362: 1
       374: 1
       379: 1
       436: 1
       440: 1
       520: 1

 521:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: 1
        40: 1
        41: 1
        47: 1
        48: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: 1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: q+1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       177: 1
       191: 1
       194: 1
       195: 1
       213: 1
       219: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       314: 1
       358: 1
       361: 1
       362: 1
       380: 1
       386: 1
       521: 1

 522:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
       106: 1
       107: 1
       109: 1
       113: 1
       124: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       192: 1
       194: 1
       214: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       315: 1
       359: 1
       361: 1
       381: 1
       522: 1

 523:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: q+1
        74: 1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       220: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       290: 1
       292: 1
       316: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       387: 1
       523: 1

 524:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       129: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       165: 1
       167: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       195: 1
       196: 1
       197: 1
       225: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       253: 1
       256: 1
       257: 1
       262: 1
       291: 1
       292: 1
       298: 1
       300: 1
       317: 1
       362: 1
       363: 1
       364: 1
       392: 1
       438: 1
       524: 1

 525:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       130: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       152: 1
       153: 1
       154: 1
       159: 1
       164: 1
       165: 1
       168: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       196: 1
       197: 1
       204: 1
       226: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       254: 1
       256: 1
       257: 1
       270: 1
       292: 1
       297: 1
       298: 1
       301: 1
       318: 1
       363: 1
       364: 1
       371: 1
       393: 1
       446: 1
       525: 1

 526:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 2q+1
        23: 1
        24: q+1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        42: q+1
        43: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 2q+1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        87: 1
        92: 1
        97: q+1
        99: q+1
       100: q+1
       102: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       140: 1
       141: q+1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       176: q+1
       179: 1
       184: 1
       189: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       288: 1
       319: 1
       356: 1
       365: 1
       372: 1
       373: 1
       381: 1
       387: 1
       526: 1

 527:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        47: q^2+2q+1
        48: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        85: q+1
        97: q+1
        98: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: q+1
       153: 1
       177: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       320: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       388: 1
       527: 1

 528:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        85: 1
        97: 1
        98: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       120: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       177: 1
       191: 1
       199: 1
       201: 1
       202: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       244: 1
       321: 1
       358: 1
       366: 1
       368: 1
       369: 1
       528: 1

 529:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       125: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       192: 1
       200: 1
       201: 1
       203: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       249: 1
       322: 1
       359: 1
       367: 1
       368: 1
       370: 1
       529: 1

 530:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: 1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        33: 1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: q+1
        74: 1
        76: 1
        77: q+1
        78: q+1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       146: 1
       147: 1
       148: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       193: 1
       201: 1
       202: 1
       208: 1
       210: 1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       290: 1
       292: 1
       323: 1
       360: 1
       368: 1
       369: 1
       375: 1
       377: 1
       530: 1

 531:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        30: q+1
        31: 1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q+1
        52: q+1
        53: 1
        55: q+1
        57: 1
        58: 1
        59: q+1
        61: 1
        65: 1
        66: 1
        67: 1
        71: q+1
        72: q+1
        73: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        81: q+1
        82: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: q+1
       145: 1
       149: 1
       150: 1
       151: 1
       194: 1
       201: 1
       203: 1
       215: 1
       218: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       324: 1
       361: 1
       368: 1
       370: 1
       382: 1
       385: 1
       531: 1

 532:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        47: q+1
        48: q+1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        97: q+1
        98: q+1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       177: q+1
       195: 1
       202: 1
       203: 1
       204: 1
       221: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       325: 1
       362: 1
       369: 1
       370: 1
       371: 1
       388: 1
       532: 1

 533:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: 2q+1
        23: 1
        24: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 1
        39: q+1
        41: q+1
        42: q+1
        43: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        54: 1
        55: q+1
        56: 1
        59: q+1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 2q+1
        74: 1
        75: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        86: q+1
        87: 1
        92: 1
        98: q+1
        99: q+1
       100: q+1
       102: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: 1
       139: q+1
       140: 1
       143: q+1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       178: q+1
       179: 1
       184: 1
       196: 1
       204: 1
       205: 1
       210: 1
       218: 1
       222: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       250: 1
       252: 1
       254: 1
       255: 1
       256: 1
       292: 1
       326: 1
       363: 1
       371: 1
       372: 1
       377: 1
       385: 1
       389: 1
       533: 1

 534:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: 1
        12: 1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: 1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: q+1
        37: q+1
        38: 1
        39: 1
        42: q+1
        44: q+1
        45: 1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        78: q+1
        80: 1
        82: 1
        83: 1
        87: 1
        91: q+1
        93: 1
        99: q+1
       101: q+1
       102: 1
       111: 1
       118: 1
       122: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       165: 1
       169: 1
       179: 1
       183: q+1
       185: 1
       197: 1
       205: 1
       227: 1
       235: 1
       242: 1
       246: 1
       252: 1
       255: 1
       257: 1
       276: 1
       298: 1
       302: 1
       327: 1
       364: 1
       372: 1
       394: 1
       452: 1
       534: 1

 535:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       152: 1
       153: 1
       155: 1
       156: 1
       161: 1
       173: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       198: 1
       206: 1
       207: 1
       212: 1
       228: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       253: 1
       258: 1
       288: 1
       289: 1
       294: 1
       306: 1
       328: 1
       365: 1
       373: 1
       374: 1
       379: 1
       434: 1
       535: 1

 536:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       102: q+1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: q+1
       199: 1
       206: 1
       208: 1
       210: 1
       229: 1
       236: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       259: 1
       288: 1
       290: 1
       292: 1
       329: 1
       366: 1
       373: 1
       375: 1
       377: 1
       435: 1
       536: 1

 537:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: 1
       156: 1
       157: 1
       160: 1
       173: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       184: 1
       186: 1
       188: 1
       200: 1
       207: 1
       208: 1
       211: 1
       221: 1
       230: 1
       237: 1
       238: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       249: 1
       253: 1
       254: 1
       260: 1
       289: 1
       290: 1
       293: 1
       306: 1
       330: 1
       367: 1
       374: 1
       375: 1
       378: 1
       388: 1
       436: 1
       537: 1

 538:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: q+1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        71: q+1
        72: 1
        73: 1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       114: 1
       115: 1
       119: 1
       120: 1
       121: 1
       136: 1
       137: 1
       141: q+1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       157: 1
       158: 1
       162: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: 1
       184: 1
       185: 1
       201: 1
       208: 1
       209: 1
       231: 1
       238: 1
       239: 1
       243: 1
       244: 1
       245: 1
       261: 1
       273: 1
       290: 1
       291: 1
       295: 1
       300: 1
       302: 1
       331: 1
       368: 1
       375: 1
       376: 1
       437: 1
       449: 1
       538: 1

 539:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: q+1
        62: 1
        63: 1
        64: 1
        72: 1
        73: 1
        74: q+1
        76: 1
        77: 1
        78: q+1
        79: 1
        80: q+1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       115: 1
       116: 1
       120: 1
       121: 1
       122: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: q+1
       146: 1
       147: 1
       148: 1
       158: 1
       159: 1
       165: 1
       167: 1
       169: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       202: 1
       209: 1
       210: 1
       232: 1
       239: 1
       240: 1
       244: 1
       245: 1
       246: 1
       262: 1
       276: 1
       291: 1
       292: 1
       298: 1
       300: 1
       302: 1
       332: 1
       369: 1
       376: 1
       377: 1
       438: 1
       452: 1
       539: 1

 540:    0: 2q^2+3q+1
         1: q^2+2q+1
         2: 2q^2+3q+1
         3: 2q+1
         4: 2q^2+3q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: 1
        19: q^2+2q+1
        21: q+1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q^2+2q+1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        68: 1
        69: q+1
        72: q+1
        73: 1
        75: q+1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: q+1
        81: q+1
        82: 2q+1
        83: q+1
        85: q+1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       109: 1
       115: 1
       117: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       152: 1
       153: q+1
       158: 1
       160: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       203: 1
       209: 1
       211: 1
       221: 1
       233: 1
       239: 1
       241: 1
       244: 1
       245: 1
       247: 1
       249: 1
       253: 1
       254: 1
       263: 1
       277: 1
       283: 1
       291: 1
       293: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       333: 1
       370: 1
       376: 1
       378: 1
       388: 1
       439: 1
       453: 1
       459: 1
       540: 1

 541:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        68: 1
        69: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       130: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       152: 1
       153: 1
       159: 1
       160: 1
       161: 1
       173: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       204: 1
       210: 1
       211: 1
       212: 1
       234: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       254: 1
       264: 1
       292: 1
       293: 1
       294: 1
       306: 1
       334: 1
       371: 1
       377: 1
       378: 1
       379: 1
       440: 1
       541: 1

 542:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: 1
        11: 1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: q+1
        27: 1
        29: 1
        31: 1
        32: 1
        35: q+1
        37: 1
        38: 1
        39: q+1
        42: q+1
        45: 1
        46: q+1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: q+1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: q+1
        96: 1
        99: q+1
       102: 1
       103: q+1
       111: 1
       118: 1
       122: 1
       123: 1
       128: 1
       131: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       161: 1
       175: 1
       179: 1
       180: q+1
       188: 1
       205: 1
       212: 1
       224: 1
       235: 1
       242: 1
       246: 1
       247: 1
       252: 1
       255: 1
       265: 1
       294: 1
       308: 1
       335: 1
       372: 1
       379: 1
       391: 1
       441: 1
       542: 1

 543:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        47: 1
        48: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        97: 1
       104: 1
       112: 1
       113: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       198: 1
       213: 1
       214: 1
       219: 1
       228: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       336: 1
       365: 1
       380: 1
       381: 1
       386: 1
       543: 1

 544:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        47: q+1
        48: 1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        85: 1
        97: 1
        98: 1
       105: 1
       112: 1
       114: 1
       116: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       177: 1
       199: 1
       213: 1
       215: 1
       217: 1
       221: 1
       229: 1
       236: 1
       238: 1
       240: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       337: 1
       366: 1
       380: 1
       382: 1
       384: 1
       388: 1
       544: 1

 545:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        39: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
       106: 1
       113: 1
       114: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       200: 1
       214: 1
       215: 1
       218: 1
       230: 1
       237: 1
       238: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       338: 1
       367: 1
       381: 1
       382: 1
       385: 1
       545: 1

 546:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
       107: 1
       114: 1
       115: 1
       124: 1
       125: 1
       126: 1
       136: 1
       137: 1
       141: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       201: 1
       215: 1
       216: 1
       231: 1
       238: 1
       239: 1
       248: 1
       249: 1
       250: 1
       339: 1
       368: 1
       382: 1
       383: 1
       546: 1

 547:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       108: 1
       115: 1
       116: 1
       120: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       177: 1
       202: 1
       216: 1
       217: 1
       221: 1
       232: 1
       239: 1
       240: 1
       244: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       340: 1
       369: 1
       383: 1
       384: 1
       388: 1
       547: 1

 548:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
       109: 1
       115: 1
       117: 1
       125: 1
       126: 1
       128: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       203: 1
       216: 1
       218: 1
       233: 1
       239: 1
       241: 1
       249: 1
       250: 1
       252: 1
       341: 1
       370: 1
       383: 1
       385: 1
       548: 1

 549:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        47: 1
        48: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        67: 1
        68: 1
        69: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        98: 1
       110: 1
       116: 1
       117: 1
       118: 1
       126: 1
       127: 1
       128: 1
       130: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       204: 1
       217: 1
       218: 1
       219: 1
       234: 1
       240: 1
       241: 1
       242: 1
       250: 1
       251: 1
       252: 1
       254: 1
       342: 1
       371: 1
       384: 1
       385: 1
       386: 1
       549: 1

 550:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        45: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        99: 1
       102: 1
       111: 1
       118: 1
       122: 1
       127: 1
       128: 1
       131: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       179: 1
       205: 1
       219: 1
       223: 1
       235: 1
       242: 1
       246: 1
       251: 1
       252: 1
       255: 1
       343: 1
       372: 1
       386: 1
       390: 1
       550: 1

 551:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        92: 1
        97: 1
        99: 1
       100: 1
       102: 1
       112: 1
       119: 1
       122: 1
       124: 1
       127: 1
       129: 1
       131: 1
       132: 1
       134: 1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       176: 1
       179: 1
       184: 1
       206: 1
       213: 1
       220: 1
       223: 1
       236: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       288: 1
       344: 1
       373: 1
       380: 1
       387: 1
       390: 1
       551: 1

 552:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 1
        35: 1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       103: 1
       113: 1
       119: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       141: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       156: 1
       173: 1
       175: 1
       176: 1
       180: 1
       184: 1
       186: 1
       188: 1
       207: 1
       214: 1
       220: 1
       224: 1
       237: 1
       243: 1
       247: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       286: 1
       289: 1
       306: 1
       308: 1
       345: 1
       374: 1
       381: 1
       387: 1
       391: 1
       462: 1
       552: 1

 553:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       114: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: 1
       141: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       176: 1
       177: 1
       178: 1
       184: 1
       208: 1
       215: 1
       220: 1
       221: 1
       222: 1
       238: 1
       243: 1
       244: 1
       245: 1
       248: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       290: 1
       346: 1
       375: 1
       382: 1
       387: 1
       388: 1
       389: 1
       553: 1

 554:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: q+1
        81: q+1
        82: 2q+1
        83: q+1
        85: 1
        86: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       115: 1
       120: 1
       121: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: 1
       167: 1
       169: 1
       177: 1
       178: 1
       181: 1
       183: 1
       184: 1
       185: 1
       209: 1
       216: 1
       221: 1
       222: 1
       225: 1
       227: 1
       239: 1
       244: 1
       245: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       291: 1
       300: 1
       302: 1
       347: 1
       376: 1
       383: 1
       388: 1
       389: 1
       392: 1
       394: 1
       554: 1

 555:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        92: 1
        98: 1
        99: 1
       100: 1
       102: 1
       116: 1
       121: 1
       122: 1
       126: 1
       127: 1
       130: 1
       131: 1
       132: 1
       138: 1
       143: 1
       144: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       178: 1
       179: 1
       184: 1
       210: 1
       217: 1
       222: 1
       223: 1
       240: 1
       245: 1
       246: 1
       250: 1
       251: 1
       254: 1
       255: 1
       256: 1
       292: 1
       348: 1
       377: 1
       384: 1
       389: 1
       390: 1
       555: 1

 556:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: 1
        39: q+1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        55: 1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        86: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       117: 1
       121: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       139: 1
       143: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       160: 1
       173: 1
       175: 1
       178: 1
       180: 1
       184: 1
       186: 1
       188: 1
       211: 1
       218: 1
       222: 1
       224: 1
       241: 1
       245: 1
       247: 1
       250: 1
       252: 1
       254: 1
       255: 1
       256: 1
       286: 1
       293: 1
       306: 1
       308: 1
       349: 1
       378: 1
       385: 1
       389: 1
       391: 1
       462: 1
       556: 1

 557:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: 1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: q+1
        38: q+1
        39: q+1
        42: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: q+1
        70: 1
        74: 1
        75: 1
        78: 1
        80: q+1
        82: q+1
        83: q+1
        87: 1
        88: 1
        96: 1
        99: 1
       102: 1
       103: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: q+1
       154: 1
       161: 1
       175: 1
       179: 1
       180: 1
       188: 1
       212: 1
       219: 1
       223: 1
       224: 1
       242: 1
       246: 1
       247: 1
       251: 1
       252: 1
       255: 1
       294: 1
       308: 1
       350: 1
       379: 1
       386: 1
       390: 1
       391: 1
       557: 1

 558:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        57: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       119: 1
       124: 1
       129: 1
       131: 1
       132: 1
       133: 1
       141: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       162: 1
       167: 1
       169: 1
       176: 1
       181: 1
       183: 1
       184: 1
       185: 1
       220: 1
       225: 1
       227: 1
       243: 1
       248: 1
       253: 1
       255: 1
       256: 1
       257: 1
       273: 1
       295: 1
       300: 1
       302: 1
       351: 1
       387: 1
       392: 1
       394: 1
       449: 1
       558: 1

 559:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        25: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        58: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        72: 1
        76: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        89: 1
        90: 1
        92: 1
        93: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       142: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       154: 1
       163: 1
       167: 1
       168: 1
       177: 1
       181: 1
       182: 1
       184: 1
       185: 1
       221: 1
       225: 1
       226: 1
       244: 1
       249: 1
       253: 1
       254: 1
       256: 1
       257: 1
       274: 1
       296: 1
       300: 1
       301: 1
       352: 1
       388: 1
       392: 1
       393: 1
       450: 1
       559: 1

 560:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        59: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       121: 1
       126: 1
       130: 1
       131: 1
       132: 1
       133: 1
       143: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       164: 1
       168: 1
       169: 1
       178: 1
       182: 1
       183: 1
       184: 1
       185: 1
       222: 1
       226: 1
       227: 1
       245: 1
       250: 1
       254: 1
       255: 1
       256: 1
       257: 1
       275: 1
       297: 1
       301: 1
       302: 1
       353: 1
       389: 1
       393: 1
       394: 1
       451: 1
       560: 1

 561:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        48: 1
        49: 1
        60: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        91: 1
        93: 1
        99: 1
       101: 1
       102: 1
       122: 1
       127: 1
       131: 1
       133: 1
       144: 1
       148: 1
       151: 1
       153: 1
       154: 1
       165: 1
       169: 1
       179: 1
       183: 1
       185: 1
       223: 1
       227: 1
       246: 1
       251: 1
       255: 1
       257: 1
       276: 1
       298: 1
       302: 1
       354: 1
       390: 1
       394: 1
       452: 1
       561: 1

 562:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: 1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: 1
        19: q+1
        24: 1
        27: 1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: q+1
        38: q+1
        39: q+1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        61: 1
        64: 1
        67: 1
        69: q+1
        70: 1
        75: 1
        78: 1
        80: q+1
        82: q+1
        83: q+1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       123: 1
       128: 1
       131: 1
       133: 1
       145: 1
       148: 1
       151: 1
       153: q+1
       154: 1
       166: 1
       169: 1
       174: 1
       175: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       224: 1
       227: 1
       247: 1
       252: 1
       255: 1
       257: 1
       277: 1
       287: 1
       299: 1
       302: 1
       307: 1
       308: 1
       355: 1
       391: 1
       394: 1
       453: 1
       463: 1
       562: 1

 563:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       129: 1
       132: 1
       133: 1
       135: 1
       141: 1
       145: 1
       149: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       189: 1
       197: 1
       198: 1
       225: 1
       237: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       283: 1
       286: 1
       287: 1
       289: 1
       295: 1
       299: 1
       303: 1
       309: 1
       395: 1
       403: 1
       404: 1
       431: 1
       443: 1
       563: 1

 564:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       132: 1
       135: 1
       136: 1
       139: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       189: 1
       190: 1
       196: 1
       230: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       289: 1
       290: 1
       293: 1
       310: 1
       395: 1
       396: 1
       402: 1
       436: 1
       564: 1

 565:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        72: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       129: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       177: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       283: 1
       311: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       565: 1

 566:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
       105: 1
       107: 1
       108: 1
       112: 1
       119: 1
       122: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       191: 1
       193: 1
       206: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       312: 1
       397: 1
       399: 1
       412: 1
       566: 1

 567:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: 1
        12: q+1
        13: 1
        14: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: q+1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: q+1
        47: 1
        48: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       192: 1
       193: 1
       195: 1
       207: 1
       212: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       313: 1
       398: 1
       399: 1
       401: 1
       413: 1
       418: 1
       567: 1

 568:    0: 2q^2+3q+1
         1: q^2+2q+1
         2: 2q^2+3q+1
         3: 2q+1
         4: q^2+2q+1
         5: 2q^2+3q+1
         6: q+1
         7: q^2+2q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 2q+1
        12: 1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 2q+1
        24: 1
        25: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        39: 1
        40: q+1
        41: q^2+2q+1
        42: 2q+1
        43: q+1
        44: q+1
        45: 2q+1
        46: 1
        47: q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: q+1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: q+1
        86: q+1
        87: 2q+1
        88: 1
        89: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       155: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       170: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: 1
       184: 1
       186: 1
       188: 1
       191: 1
       194: 1
       195: 1
       213: 1
       219: 1
       229: 1
       234: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       272: 1
       278: 1
       281: 1
       282: 1
       283: 1
       288: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       314: 1
       397: 1
       400: 1
       401: 1
       419: 1
       425: 1
       435: 1
       440: 1
       568: 1

 569:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       124: 1
       128: 1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       170: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       192: 1
       194: 1
       214: 1
       230: 1
       260: 1
       261: 1
       263: 1
       267: 1
       278: 1
       282: 1
       289: 1
       290: 1
       293: 1
       315: 1
       398: 1
       400: 1
       420: 1
       436: 1
       569: 1

 570:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: q+1
        24: 1
        25: 1
        27: q+1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        39: 1
        40: 1
        41: q+1
        42: 2q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: q+1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       136: 1
       139: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       220: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       290: 1
       293: 1
       316: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       426: 1
       570: 1

 571:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       129: 1
       132: 1
       133: 1
       137: 1
       139: 1
       145: 1
       149: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       195: 1
       196: 1
       197: 1
       225: 1
       233: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       283: 1
       286: 1
       287: 1
       291: 1
       293: 1
       299: 1
       303: 1
       317: 1
       401: 1
       402: 1
       403: 1
       431: 1
       439: 1
       571: 1

 572:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       130: 1
       132: 1
       133: 1
       139: 1
       143: 1
       145: 1
       150: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       171: 1
       173: 1
       174: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       187: 1
       196: 1
       197: 1
       204: 1
       226: 1
       241: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       284: 1
       286: 1
       287: 1
       293: 1
       297: 1
       299: 1
       304: 1
       318: 1
       402: 1
       403: 1
       410: 1
       432: 1
       447: 1
       572: 1

 573:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 2q+1
        23: q+1
        24: 1
        25: q+1
        27: q+1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        39: 1
        40: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        75: 1
        81: 1
        84: 2q+1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       155: q+1
       156: 1
       161: 1
       162: q+1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       180: 1
       186: 1
       189: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: 1
       319: 1
       395: 1
       404: 1
       411: 1
       412: 1
       420: 1
       426: 1
       573: 1

 574:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        72: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       177: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       221: 1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       320: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       427: 1
       574: 1

 575:    0: q+1
         1: q+1
         2: q+1
         3: 1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        16: q+1
        17: q+1
        18: 1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       120: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       191: 1
       199: 1
       201: 1
       202: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       274: 1
       321: 1
       397: 1
       405: 1
       407: 1
       408: 1
       575: 1

 576:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        72: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       125: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       177: 1
       192: 1
       200: 1
       201: 1
       203: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       279: 1
       322: 1
       398: 1
       406: 1
       407: 1
       409: 1
       576: 1

 577:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        52: q+1
        53: 1
        54: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        62: 1
        63: 1
        64: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       193: 1
       201: 1
       202: 1
       208: 1
       210: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       323: 1
       399: 1
       407: 1
       408: 1
       414: 1
       416: 1
       577: 1

 578:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: q+1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: q+1
        88: 1
        89: 1
        90: q+1
        91: q+1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       136: 1
       139: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: q+1
       166: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       194: 1
       201: 1
       203: 1
       215: 1
       218: 1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       290: 1
       293: 1
       324: 1
       400: 1
       407: 1
       409: 1
       421: 1
       424: 1
       578: 1

 579:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: q+1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: q+1
       195: 1
       202: 1
       203: 1
       204: 1
       221: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       325: 1
       401: 1
       408: 1
       409: 1
       410: 1
       427: 1
       579: 1

 580:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        22: 2q+1
        23: q+1
        24: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        39: 1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        54: q+1
        55: 1
        56: 1
        59: q+1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        75: 1
        81: 1
        86: 2q+1
        87: q+1
        88: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       139: 1
       159: q+1
       160: 1
       161: 1
       164: q+1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       180: 1
       186: 1
       196: 1
       204: 1
       205: 1
       210: 1
       218: 1
       222: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       293: 1
       326: 1
       402: 1
       410: 1
       411: 1
       416: 1
       424: 1
       428: 1
       580: 1

 581:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: 1
        12: 1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: 1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: q+1
        37: q+1
        39: 1
        42: q+1
        44: q+1
        45: 1
        46: 1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        78: q+1
        82: 1
        87: 1
        88: 1
        91: q+1
        93: 1
        95: 1
        96: 1
        99: q+1
       101: q+1
       103: 1
       111: 1
       118: 1
       122: 1
       128: 1
       131: 1
       133: 1
       145: 1
       151: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       180: 1
       183: q+1
       187: 1
       197: 1
       205: 1
       227: 1
       252: 1
       265: 1
       272: 1
       276: 1
       282: 1
       285: 1
       287: 1
       299: 1
       305: 1
       327: 1
       403: 1
       411: 1
       433: 1
       458: 1
       581: 1

 582:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       198: 1
       206: 1
       207: 1
       212: 1
       258: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       328: 1
       404: 1
       412: 1
       413: 1
       418: 1
       582: 1

 583:    0: q+1
         1: q+1
         2: 1
         3: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        16: q+1
        17: 1
        18: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       199: 1
       206: 1
       208: 1
       210: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       329: 1
       405: 1
       412: 1
       414: 1
       416: 1
       583: 1

 584:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       177: 1
       200: 1
       207: 1
       208: 1
       211: 1
       221: 1
       260: 1
       267: 1
       268: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       330: 1
       406: 1
       413: 1
       414: 1
       417: 1
       427: 1
       584: 1

 585:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
       107: 1
       114: 1
       115: 1
       119: 1
       120: 1
       121: 1
       157: 1
       158: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       201: 1
       208: 1
       209: 1
       261: 1
       268: 1
       269: 1
       273: 1
       274: 1
       275: 1
       331: 1
       407: 1
       414: 1
       415: 1
       585: 1

 586:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
       108: 1
       115: 1
       116: 1
       120: 1
       121: 1
       122: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       202: 1
       209: 1
       210: 1
       262: 1
       269: 1
       270: 1
       274: 1
       275: 1
       276: 1
       332: 1
       408: 1
       415: 1
       416: 1
       586: 1

 587:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       109: 1
       115: 1
       117: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: 1
       203: 1
       209: 1
       211: 1
       221: 1
       263: 1
       269: 1
       271: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       333: 1
       409: 1
       415: 1
       417: 1
       427: 1
       587: 1

 588:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        68: 1
        69: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       130: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       204: 1
       210: 1
       211: 1
       212: 1
       264: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       284: 1
       334: 1
       410: 1
       416: 1
       417: 1
       418: 1
       588: 1

 589:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       103: 1
       111: 1
       118: 1
       122: 1
       123: 1
       128: 1
       131: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       180: 1
       205: 1
       212: 1
       224: 1
       265: 1
       272: 1
       276: 1
       277: 1
       282: 1
       285: 1
       335: 1
       411: 1
       418: 1
       430: 1
       589: 1

 590:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       135: 1
       140: 1
       152: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       172: 1
       173: 1
       174: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       198: 1
       213: 1
       214: 1
       219: 1
       228: 1
       258: 1
       266: 1
       267: 1
       272: 1
       278: 1
       281: 1
       282: 1
       283: 1
       288: 1
       289: 1
       294: 1
       306: 1
       336: 1
       404: 1
       419: 1
       420: 1
       425: 1
       434: 1
       590: 1

 591:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       105: 1
       112: 1
       114: 1
       116: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       134: 1
       136: 1
       138: 1
       152: 1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       184: 1
       186: 1
       188: 1
       199: 1
       213: 1
       215: 1
       217: 1
       221: 1
       229: 1
       259: 1
       266: 1
       268: 1
       270: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       288: 1
       290: 1
       292: 1
       306: 1
       337: 1
       405: 1
       419: 1
       421: 1
       423: 1
       427: 1
       435: 1
       591: 1

 592:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: q+1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: q+1
        95: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       103: q+1
       106: 1
       113: 1
       114: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: q+1
       200: 1
       214: 1
       215: 1
       218: 1
       230: 1
       260: 1
       267: 1
       268: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       289: 1
       290: 1
       293: 1
       338: 1
       406: 1
       420: 1
       421: 1
       424: 1
       436: 1
       592: 1

 593:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: 1
        42: q+1
        43: q+1
        44: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: q+1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: q+1
        85: 1
        86: 1
        89: q+1
        90: 1
        91: q+1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       114: 1
       115: 1
       124: 1
       125: 1
       126: 1
       136: 1
       137: 1
       141: 1
       149: 1
       151: 1
       157: 1
       158: 1
       162: q+1
       163: 1
       164: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: 1
       186: 1
       187: 1
       201: 1
       215: 1
       216: 1
       231: 1
       248: 1
       261: 1
       268: 1
       269: 1
       278: 1
       279: 1
       280: 1
       290: 1
       291: 1
       295: 1
       303: 1
       305: 1
       339: 1
       407: 1
       421: 1
       422: 1
       437: 1
       454: 1
       593: 1

 594:    0: 2q^2+3q+1
         1: q^2+2q+1
         2: 2q^2+3q+1
         3: 2q+1
         4: q^2+2q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: 1
        16: q^2+2q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+2q+1
        41: q+1
        42: q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: q+1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: 2q+1
        94: 1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       115: 1
       116: 1
       120: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       137: 1
       138: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: q+1
       167: q+1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: q+1
       177: q+1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       202: 1
       216: 1
       217: 1
       221: 1
       232: 1
       251: 1
       253: 1
       262: 1
       269: 1
       270: 1
       274: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       291: 1
       292: 1
       298: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       340: 1
       408: 1
       422: 1
       423: 1
       427: 1
       438: 1
       457: 1
       459: 1
       594: 1

 595:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        21: 1
        22: 1
        24: q+1
        25: 1
        26: 1
        27: q+1
        30: 1
        31: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        46: q+1
        47: 1
        48: q+1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: q+1
        65: 1
        66: 1
        67: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        88: q+1
        89: 1
        90: 1
        91: q+1
        94: 1
        95: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       109: 1
       115: 1
       117: 1
       125: 1
       126: 1
       128: 1
       137: 1
       139: 1
       145: 1
       149: 1
       151: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: q+1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       203: 1
       216: 1
       218: 1
       233: 1
       252: 1
       263: 1
       269: 1
       271: 1
       279: 1
       280: 1
       282: 1
       291: 1
       293: 1
       299: 1
       303: 1
       305: 1
       341: 1
       409: 1
       422: 1
       424: 1
       439: 1
       458: 1
       595: 1

 596:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        67: 1
        68: 1
        69: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       126: 1
       127: 1
       128: 1
       130: 1
       138: 1
       139: 1
       140: 1
       152: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       171: 1
       172: 1
       173: 1
       174: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       204: 1
       217: 1
       218: 1
       219: 1
       234: 1
       264: 1
       270: 1
       271: 1
       272: 1
       280: 1
       281: 1
       282: 1
       284: 1
       292: 1
       293: 1
       294: 1
       306: 1
       342: 1
       410: 1
       423: 1
       424: 1
       425: 1
       440: 1
       596: 1

 597:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: 1
        11: q+1
        12: 1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: q+1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: q+1
        38: q+1
        39: 1
        42: q+1
        44: 1
        45: q+1
        46: 1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: q+1
        75: 1
        83: 1
        87: q+1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: q+1
       102: q+1
       103: 1
       111: 1
       118: 1
       122: 1
       127: 1
       128: 1
       131: 1
       140: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: q+1
       180: 1
       188: 1
       205: 1
       219: 1
       223: 1
       235: 1
       265: 1
       272: 1
       276: 1
       281: 1
       282: 1
       285: 1
       294: 1
       308: 1
       343: 1
       411: 1
       425: 1
       429: 1
       441: 1
       597: 1

 598:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       103: 1
       112: 1
       119: 1
       122: 1
       124: 1
       127: 1
       129: 1
       131: 1
       132: 1
       134: 1
       152: 1
       154: 1
       155: 1
       162: 1
       165: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       184: 1
       186: 1
       188: 1
       206: 1
       213: 1
       220: 1
       223: 1
       256: 1
       266: 1
       273: 1
       276: 1
       278: 1
       281: 1
       283: 1
       285: 1
       286: 1
       288: 1
       306: 1
       308: 1
       344: 1
       412: 1
       419: 1
       426: 1
       429: 1
       462: 1
       598: 1

 599:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        81: 1
        84: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       103: 1
       113: 1
       119: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       156: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       180: 1
       186: 1
       207: 1
       214: 1
       220: 1
       224: 1
       267: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: 1
       345: 1
       413: 1
       420: 1
       426: 1
       430: 1
       599: 1

 600:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        81: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       114: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: 1
       157: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       186: 1
       208: 1
       215: 1
       220: 1
       221: 1
       222: 1
       268: 1
       273: 1
       274: 1
       275: 1
       278: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       290: 1
       346: 1
       414: 1
       421: 1
       426: 1
       427: 1
       428: 1
       600: 1

 601:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: 1
        42: q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: 1
        48: q+1
        49: 1
        53: 1
        58: 1
        59: 1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: 2q+1
        94: 1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       115: 1
       120: 1
       121: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       149: 1
       151: 1
       158: 1
       163: 1
       164: 1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: q+1
       175: 1
       177: 1
       178: 1
       181: 1
       183: 1
       186: 1
       187: 1
       209: 1
       216: 1
       221: 1
       222: 1
       225: 1
       227: 1
       269: 1
       274: 1
       275: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       303: 1
       305: 1
       347: 1
       415: 1
       422: 1
       427: 1
       428: 1
       431: 1
       433: 1
       601: 1

 602:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: 1
         5: q+1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: 1
        18: q+1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       116: 1
       121: 1
       122: 1
       126: 1
       127: 1
       130: 1
       131: 1
       132: 1
       138: 1
       152: 1
       154: 1
       159: 1
       164: 1
       165: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       184: 1
       186: 1
       188: 1
       210: 1
       217: 1
       222: 1
       223: 1
       256: 1
       270: 1
       275: 1
       276: 1
       280: 1
       281: 1
       284: 1
       285: 1
       286: 1
       292: 1
       306: 1
       308: 1
       348: 1
       416: 1
       423: 1
       428: 1
       429: 1
       462: 1
       602: 1

 603:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        55: 1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        81: 1
        86: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       103: 1
       117: 1
       121: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       139: 1
       160: 1
       164: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       180: 1
       186: 1
       211: 1
       218: 1
       222: 1
       224: 1
       271: 1
       275: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       293: 1
       349: 1
       417: 1
       424: 1
       428: 1
       430: 1
       603: 1

 604:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: 1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: 1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        38: 1
        39: 1
        42: 1
        44: q+1
        45: q+1
        46: q+1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: q+1
        70: 1
        74: 1
        75: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: q+1
        95: q+1
        96: q+1
        99: 1
       102: 1
       103: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       140: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: q+1
       175: 1
       179: 1
       180: 1
       188: 1
       212: 1
       219: 1
       223: 1
       224: 1
       272: 1
       276: 1
       277: 1
       281: 1
       282: 1
       285: 1
       294: 1
       308: 1
       350: 1
       418: 1
       425: 1
       429: 1
       430: 1
       604: 1

 605:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        57: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       101: 1
       103: 1
       119: 1
       124: 1
       129: 1
       131: 1
       132: 1
       133: 1
       141: 1
       149: 1
       151: 1
       162: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       181: 1
       183: 1
       186: 1
       187: 1
       220: 1
       225: 1
       227: 1
       248: 1
       273: 1
       278: 1
       283: 1
       285: 1
       286: 1
       287: 1
       295: 1
       303: 1
       305: 1
       351: 1
       426: 1
       431: 1
       433: 1
       454: 1
       605: 1

 606:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        25: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        58: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        72: 1
        76: 1
        77: 1
        81: 1
        82: 1
        85: 1
        89: 1
        90: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       100: 1
       101: 1
       103: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       142: 1
       149: 1
       150: 1
       163: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: 1
       181: 1
       182: 1
       186: 1
       187: 1
       221: 1
       225: 1
       226: 1
       249: 1
       274: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       296: 1
       303: 1
       304: 1
       352: 1
       427: 1
       431: 1
       432: 1
       455: 1
       606: 1

 607:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        59: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       121: 1
       126: 1
       130: 1
       131: 1
       132: 1
       133: 1
       143: 1
       150: 1
       151: 1
       164: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       182: 1
       183: 1
       186: 1
       187: 1
       222: 1
       226: 1
       227: 1
       250: 1
       275: 1
       280: 1
       284: 1
       285: 1
       286: 1
       287: 1
       297: 1
       304: 1
       305: 1
       353: 1
       428: 1
       432: 1
       433: 1
       456: 1
       607: 1

 608:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: 1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: 1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        27: 1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: q+1
        45: q+1
        46: q+1
        48: q+1
        49: 1
        60: 1
        64: 1
        67: 1
        69: q+1
        70: 1
        74: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        91: 1
        93: q+1
        95: q+1
        96: q+1
        99: 1
       101: 1
       102: 1
       103: 1
       122: 1
       127: 1
       131: 1
       133: 1
       144: 1
       151: 1
       153: 1
       154: 1
       165: 1
       169: 1
       172: 1
       174: q+1
       175: 1
       179: 1
       183: 1
       185: 1
       187: 1
       188: 1
       223: 1
       227: 1
       251: 1
       257: 1
       276: 1
       281: 1
       285: 1
       287: 1
       298: 1
       305: 1
       307: 1
       308: 1
       354: 1
       429: 1
       433: 1
       457: 1
       463: 1
       608: 1

 609:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        78: 1
        82: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       103: 1
       123: 1
       128: 1
       131: 1
       133: 1
       145: 1
       151: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       180: 1
       183: 1
       187: 1
       224: 1
       227: 1
       252: 1
       277: 1
       282: 1
       285: 1
       287: 1
       299: 1
       305: 1
       355: 1
       430: 1
       433: 1
       458: 1
       609: 1

 610:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        68: 1
        70: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       111: 1
       132: 1
       134: 1
       135: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       161: 1
       173: 1
       175: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       228: 1
       235: 1
       256: 1
       258: 1
       265: 1
       286: 1
       288: 1
       289: 1
       294: 1
       306: 1
       308: 1
       356: 1
       395: 1
       434: 1
       441: 1
       462: 1
       610: 1

 611:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        68: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       110: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       228: 1
       229: 1
       230: 1
       234: 1
       258: 1
       259: 1
       260: 1
       264: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       357: 1
       396: 1
       434: 1
       435: 1
       436: 1
       440: 1
       611: 1

 612:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       191: 1
       229: 1
       231: 1
       232: 1
       236: 1
       259: 1
       261: 1
       262: 1
       266: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       358: 1
       397: 1
       435: 1
       437: 1
       438: 1
       442: 1
       612: 1

 613:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       170: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       192: 1
       230: 1
       231: 1
       233: 1
       237: 1
       260: 1
       261: 1
       263: 1
       267: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       359: 1
       398: 1
       436: 1
       437: 1
       439: 1
       443: 1
       613: 1

 614:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        27: q+1
        28: 1
        29: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: q+1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: q+1
        92: 1
        93: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       107: 1
       108: 1
       119: 1
       122: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: q+1
       184: 1
       185: 1
       193: 1
       231: 1
       232: 1
       243: 1
       246: 1
       261: 1
       262: 1
       273: 1
       276: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       360: 1
       399: 1
       437: 1
       438: 1
       449: 1
       452: 1
       614: 1

 615:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: q+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: q+1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: q+1
        94: 1
        95: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       103: 1
       107: 1
       109: 1
       124: 1
       128: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       170: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: q+1
       186: 1
       187: 1
       194: 1
       231: 1
       233: 1
       248: 1
       252: 1
       261: 1
       263: 1
       278: 1
       282: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       361: 1
       400: 1
       437: 1
       439: 1
       454: 1
       458: 1
       615: 1

 616:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q^2+2q+1
        15: 1
        16: q+1
        17: q^2+2q+1
        18: 1
        19: q^2+2q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q^2+2q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       118: 1
       129: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       232: 1
       233: 1
       234: 1
       242: 1
       253: 1
       262: 1
       263: 1
       264: 1
       272: 1
       283: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       362: 1
       401: 1
       438: 1
       439: 1
       440: 1
       448: 1
       459: 1
       616: 1

 617:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        68: 1
        70: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       111: 1
       132: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       196: 1
       234: 1
       235: 1
       256: 1
       264: 1
       265: 1
       286: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       363: 1
       402: 1
       440: 1
       441: 1
       462: 1
       617: 1

 618:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        69: 1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       111: 1
       118: 1
       133: 1
       140: 1
       144: 1
       145: 1
       153: 1
       154: 1
       161: 1
       165: 1
       166: 1
       174: 1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       197: 1
       235: 1
       242: 1
       257: 1
       265: 1
       272: 1
       287: 1
       294: 1
       298: 1
       299: 1
       307: 1
       308: 1
       364: 1
       403: 1
       441: 1
       448: 1
       463: 1
       618: 1

 619:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 2q+1
        14: 2q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: 1
        19: 2q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 2q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 2q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 2q+1
        48: 2q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       129: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       198: 1
       228: 1
       236: 1
       237: 1
       242: 1
       253: 1
       258: 1
       266: 1
       267: 1
       272: 1
       283: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       365: 1
       404: 1
       434: 1
       442: 1
       443: 1
       448: 1
       459: 1
       619: 1

 620:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       105: 1
       112: 1
       114: 1
       116: 1
       120: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       199: 1
       229: 1
       236: 1
       238: 1
       240: 1
       244: 1
       259: 1
       266: 1
       268: 1
       270: 1
       274: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       366: 1
       405: 1
       435: 1
       442: 1
       444: 1
       446: 1
       450: 1
       620: 1

 621:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: q+1
        95: 1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       103: q+1
       106: 1
       113: 1
       114: 1
       117: 1
       125: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       200: 1
       230: 1
       237: 1
       238: 1
       241: 1
       249: 1
       260: 1
       267: 1
       268: 1
       271: 1
       279: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       367: 1
       406: 1
       436: 1
       443: 1
       444: 1
       447: 1
       455: 1
       621: 1

 622:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       107: 1
       114: 1
       115: 1
       136: 1
       137: 1
       141: 1
       142: 1
       143: 1
       157: 1
       158: 1
       162: 1
       163: 1
       164: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       201: 1
       231: 1
       238: 1
       239: 1
       261: 1
       268: 1
       269: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       368: 1
       407: 1
       437: 1
       444: 1
       445: 1
       622: 1

 623:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       115: 1
       116: 1
       120: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       202: 1
       232: 1
       239: 1
       240: 1
       244: 1
       262: 1
       269: 1
       270: 1
       274: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       369: 1
       408: 1
       438: 1
       445: 1
       446: 1
       450: 1
       623: 1

 624:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       109: 1
       115: 1
       117: 1
       125: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       203: 1
       233: 1
       239: 1
       241: 1
       249: 1
       263: 1
       269: 1
       271: 1
       279: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       370: 1
       409: 1
       439: 1
       445: 1
       447: 1
       455: 1
       624: 1

 625:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 1
         4: 2q+1
         5: 2q+1
         7: 2q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 2q+1
        14: 2q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: 1
        19: 2q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 2q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 2q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 2q+1
        48: 2q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        68: 1
        69: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 2q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       130: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       152: 1
       153: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       171: 1
       173: 1
       174: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       204: 1
       234: 1
       240: 1
       241: 1
       242: 1
       254: 1
       264: 1
       270: 1
       271: 1
       272: 1
       284: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       304: 1
       306: 1
       307: 1
       371: 1
       410: 1
       440: 1
       446: 1
       447: 1
       448: 1
       460: 1
       625: 1

 626:    0: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         8: 3q+1
        10: q+1
        11: q+1
        12: q+1
        14: 3q+1
        15: 3q+1
        17: 3q+1
        18: 3q+1
        19: 3q+1
        23: q+1
        24: q+1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: 3q+1
        37: q+1
        38: q+1
        39: q+1
        42: 3q+1
        44: q+1
        45: q+1
        46: q+1
        48: 3q+1
        49: 3q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: q+1
        75: q+1
        78: q+1
        80: 1
        82: 1
        83: 1
        87: q+1
        88: q+1
        91: q+1
        93: 1
        95: 1
        96: 1
        99: 3q+1
       101: q+1
       102: q+1
       103: q+1
       111: 1
       118: 1
       122: 1
       128: 1
       131: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: q+1
       180: q+1
       183: q+1
       185: 1
       187: 1
       188: 1
       205: 1
       235: 1
       242: 1
       246: 1
       252: 1
       255: 1
       265: 1
       272: 1
       276: 1
       282: 1
       285: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       372: 1
       411: 1
       441: 1
       448: 1
       452: 1
       458: 1
       461: 1
       626: 1

 627:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        64: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       112: 1
       119: 1
       122: 1
       134: 1
       141: 1
       144: 1
       146: 1
       148: 1
       155: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       206: 1
       236: 1
       243: 1
       246: 1
       266: 1
       273: 1
       276: 1
       288: 1
       295: 1
       298: 1
       300: 1
       302: 1
       373: 1
       412: 1
       442: 1
       449: 1
       452: 1
       627: 1

 628:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        71: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       113: 1
       119: 1
       123: 1
       129: 1
       135: 1
       141: 1
       145: 1
       146: 1
       148: 1
       149: 1
       152: 1
       153: 1
       156: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       176: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       207: 1
       237: 1
       243: 1
       247: 1
       253: 1
       267: 1
       273: 1
       277: 1
       283: 1
       289: 1
       295: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       374: 1
       413: 1
       443: 1
       449: 1
       453: 1
       459: 1
       628: 1

 629:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       114: 1
       119: 1
       120: 1
       121: 1
       136: 1
       141: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       157: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       208: 1
       238: 1
       243: 1
       244: 1
       245: 1
       268: 1
       273: 1
       274: 1
       275: 1
       290: 1
       295: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       375: 1
       414: 1
       444: 1
       449: 1
       450: 1
       451: 1
       629: 1

 630:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        53: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       115: 1
       120: 1
       121: 1
       137: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       158: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       209: 1
       239: 1
       244: 1
       245: 1
       269: 1
       274: 1
       275: 1
       291: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       376: 1
       415: 1
       445: 1
       450: 1
       451: 1
       630: 1

 631:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        64: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       116: 1
       121: 1
       122: 1
       138: 1
       143: 1
       144: 1
       147: 1
       148: 1
       159: 1
       164: 1
       165: 1
       168: 1
       169: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       210: 1
       240: 1
       245: 1
       246: 1
       270: 1
       275: 1
       276: 1
       292: 1
       297: 1
       298: 1
       301: 1
       302: 1
       377: 1
       416: 1
       446: 1
       451: 1
       452: 1
       631: 1

 632:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        55: 1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        68: 1
        69: 1
        73: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       117: 1
       121: 1
       123: 1
       130: 1
       139: 1
       143: 1
       145: 1
       147: 1
       148: 1
       150: 1
       152: 1
       153: 1
       160: 1
       164: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       178: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       211: 1
       241: 1
       245: 1
       247: 1
       254: 1
       271: 1
       275: 1
       277: 1
       284: 1
       293: 1
       297: 1
       299: 1
       301: 1
       302: 1
       304: 1
       306: 1
       307: 1
       378: 1
       417: 1
       447: 1
       451: 1
       453: 1
       460: 1
       632: 1

 633:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        69: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       118: 1
       122: 1
       123: 1
       140: 1
       144: 1
       145: 1
       148: 1
       153: 1
       161: 1
       165: 1
       166: 1
       169: 1
       174: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       212: 1
       242: 1
       246: 1
       247: 1
       272: 1
       276: 1
       277: 1
       294: 1
       298: 1
       299: 1
       302: 1
       307: 1
       379: 1
       418: 1
       448: 1
       452: 1
       453: 1
       633: 1

 634:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       112: 1
       124: 1
       127: 1
       129: 1
       134: 1
       141: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       155: 1
       162: 1
       165: 1
       167: 1
       170: 1
       172: 1
       173: 1
       174: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       213: 1
       236: 1
       248: 1
       251: 1
       253: 1
       266: 1
       278: 1
       281: 1
       283: 1
       288: 1
       295: 1
       298: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       380: 1
       419: 1
       442: 1
       454: 1
       457: 1
       459: 1
       634: 1

 635:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        99: 1
       100: 1
       101: 1
       103: 1
       113: 1
       124: 1
       128: 1
       135: 1
       141: 1
       145: 1
       149: 1
       151: 1
       156: 1
       162: 1
       166: 1
       170: 1
       172: 1
       176: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       214: 1
       237: 1
       248: 1
       252: 1
       267: 1
       278: 1
       282: 1
       289: 1
       295: 1
       299: 1
       303: 1
       305: 1
       381: 1
       420: 1
       443: 1
       454: 1
       458: 1
       635: 1

 636:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        52: 1
        57: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        94: q+1
        95: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       103: q+1
       114: 1
       124: 1
       125: 1
       126: 1
       136: 1
       141: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       157: 1
       162: 1
       163: 1
       164: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       215: 1
       238: 1
       248: 1
       249: 1
       250: 1
       268: 1
       278: 1
       279: 1
       280: 1
       290: 1
       295: 1
       296: 1
       297: 1
       303: 1
       304: 1
       305: 1
       382: 1
       421: 1
       444: 1
       454: 1
       455: 1
       456: 1
       636: 1

 637:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       115: 1
       125: 1
       126: 1
       137: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       158: 1
       163: 1
       164: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       216: 1
       239: 1
       249: 1
       250: 1
       269: 1
       279: 1
       280: 1
       291: 1
       296: 1
       297: 1
       303: 1
       304: 1
       305: 1
       383: 1
       422: 1
       445: 1
       455: 1
       456: 1
       637: 1

 638:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        66: 1
        67: 1
        68: 1
        69: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       116: 1
       126: 1
       127: 1
       130: 1
       138: 1
       143: 1
       144: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       159: 1
       164: 1
       165: 1
       168: 1
       171: 1
       172: 1
       173: 1
       174: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       217: 1
       240: 1
       250: 1
       251: 1
       254: 1
       270: 1
       280: 1
       281: 1
       284: 1
       292: 1
       297: 1
       298: 1
       301: 1
       304: 1
       305: 1
       306: 1
       307: 1
       384: 1
       423: 1
       446: 1
       456: 1
       457: 1
       460: 1
       638: 1

 639:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        30: 1
        31: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        55: 1
        59: 1
        61: 1
        66: 1
        67: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        88: 1
        90: 1
        91: 1
        94: 1
        95: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       117: 1
       126: 1
       128: 1
       139: 1
       143: 1
       145: 1
       150: 1
       151: 1
       160: 1
       164: 1
       166: 1
       171: 1
       172: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       187: 1
       218: 1
       241: 1
       250: 1
       252: 1
       271: 1
       280: 1
       282: 1
       293: 1
       297: 1
       299: 1
       304: 1
       305: 1
       385: 1
       424: 1
       447: 1
       456: 1
       458: 1
       639: 1

 640:    0: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         8: 1
        10: 1
        11: 1
        12: 1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        67: 1
        69: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       118: 1
       127: 1
       128: 1
       140: 1
       144: 1
       145: 1
       151: 1
       153: 1
       161: 1
       165: 1
       166: 1
       172: 1
       174: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       219: 1
       242: 1
       251: 1
       252: 1
       272: 1
       281: 1
       282: 1
       294: 1
       298: 1
       299: 1
       305: 1
       307: 1
       386: 1
       425: 1
       448: 1
       457: 1
       458: 1
       640: 1

 641:    0: 2q+1
         1: 2q+1
         2: q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         8: q+1
         9: 2q+1
        10: 1
        11: q+1
        12: q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 2q+1
        17: q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: 2q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        42: q+1
        43: 2q+1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        57: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: 2q+1
       101: 1
       102: q+1
       103: q+1
       119: 1
       124: 1
       129: 1
       131: 1
       132: 1
       141: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       162: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: 1
       220: 1
       243: 1
       248: 1
       253: 1
       255: 1
       256: 1
       273: 1
       278: 1
       283: 1
       285: 1
       286: 1
       295: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       387: 1
       426: 1
       449: 1
       454: 1
       459: 1
       461: 1
       462: 1
       641: 1

 642:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        25: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        58: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: q+1
        76: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        89: 1
        90: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
       100: 1
       101: 1
       102: 1
       103: 1
       120: 1
       125: 1
       129: 1
       130: 1
       142: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       163: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: q+1
       181: 1
       182: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       221: 1
       244: 1
       249: 1
       253: 1
       254: 1
       274: 1
       279: 1
       283: 1
       284: 1
       296: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       388: 1
       427: 1
       450: 1
       455: 1
       459: 1
       460: 1
       642: 1

 643:    0: 2q+1
         1: 2q+1
         2: q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 1
        11: q+1
        12: q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 2q+1
        17: q+1
        18: 2q+1
        19: 2q+1
        22: q+1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: 2q+1
        37: 1
        38: q+1
        39: q+1
        41: q+1
        42: q+1
        43: 2q+1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        59: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: 1
        86: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: 2q+1
       101: 1
       102: q+1
       103: q+1
       121: 1
       126: 1
       130: 1
       131: 1
       132: 1
       143: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       164: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: 1
       222: 1
       245: 1
       250: 1
       254: 1
       255: 1
       256: 1
       275: 1
       280: 1
       284: 1
       285: 1
       286: 1
       297: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       389: 1
       428: 1
       451: 1
       456: 1
       460: 1
       461: 1
       462: 1
       643: 1

 644:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: 1
        11: q+1
        12: 1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: q+1
        27: 1
        29: 1
        31: 1
        32: 1
        35: q+1
        37: 1
        38: q+1
        39: 1
        42: q+1
        44: 1
        45: q+1
        46: 1
        48: q+1
        49: q+1
        60: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: q+1
        78: 1
        80: 1
        82: 1
        83: 1
        87: q+1
        91: 1
        93: 1
        95: 1
        96: 1
        99: q+1
       101: 1
       102: q+1
       103: 1
       122: 1
       127: 1
       131: 1
       144: 1
       148: 1
       151: 1
       153: 1
       154: 1
       165: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: q+1
       183: 1
       185: 1
       187: 1
       188: 1
       223: 1
       246: 1
       251: 1
       255: 1
       276: 1
       281: 1
       285: 1
       298: 1
       302: 1
       305: 1
       307: 1
       308: 1
       390: 1
       429: 1
       452: 1
       457: 1
       461: 1
       644: 1

 645:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: 1
        11: 1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        24: q+1
        27: 1
        29: 1
        31: 1
        32: 1
        35: q+1
        37: 1
        38: 1
        39: q+1
        42: q+1
        44: 1
        45: 1
        46: q+1
        48: q+1
        49: q+1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: q+1
        78: 1
        80: 1
        82: 1
        83: 1
        88: q+1
        91: 1
        93: 1
        95: 1
        96: 1
        99: q+1
       101: 1
       102: 1
       103: q+1
       123: 1
       128: 1
       131: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       180: q+1
       183: 1
       185: 1
       187: 1
       188: 1
       224: 1
       247: 1
       252: 1
       255: 1
       277: 1
       282: 1
       285: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       391: 1
       430: 1
       453: 1
       458: 1
       461: 1
       645: 1

 646:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        25: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        76: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        89: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
       100: 1
       101: 1
       102: 1
       103: 1
       129: 1
       132: 1
       133: 1
       146: 1
       149: 1
       152: 1
       153: 1
       154: 1
       167: 1
       170: 1
       173: 1
       174: 1
       175: 1
       181: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       225: 1
       253: 1
       256: 1
       257: 1
       283: 1
       286: 1
       287: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       392: 1
       431: 1
       459: 1
       462: 1
       463: 1
       646: 1

 647:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        63: 1
        66: 1
        68: 1
        69: 1
        70: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        90: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
       100: 1
       101: 1
       102: 1
       103: 1
       130: 1
       132: 1
       133: 1
       147: 1
       150: 1
       152: 1
       153: 1
       154: 1
       168: 1
       171: 1
       173: 1
       174: 1
       175: 1
       182: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       226: 1
       254: 1
       256: 1
       257: 1
       284: 1
       286: 1
       287: 1
       301: 1
       304: 1
       306: 1
       307: 1
       308: 1
       393: 1
       432: 1
       460: 1
       462: 1
       463: 1
       647: 1

 648:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        64: 1
        67: 1
        69: 1
        70: 1
        78: 1
        80: 1
        82: 1
        83: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       131: 1
       133: 1
       148: 1
       151: 1
       153: 1
       154: 1
       169: 1
       172: 1
       174: 1
       175: 1
       183: 1
       185: 1
       187: 1
       188: 1
       227: 1
       255: 1
       257: 1
       285: 1
       287: 1
       302: 1
       305: 1
       307: 1
       308: 1
       394: 1
       433: 1
       461: 1
       463: 1
       648: 1

 649:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       176: 1
       177: q+1
       178: 1
       181: 1
       182: 1
       183: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       221: 1
       225: 1
       226: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       249: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       274: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       320: 1
       321: 1
       322: 1
       325: 1
       352: 1
       359: 1
       367: 1
       368: 1
       370: 1
       397: 1
       405: 1
       407: 1
       408: 1
       437: 1
       444: 1
       445: 1
       464: 1
       465: 1
       472: 1
       475: 1
       529: 1
       575: 1
       622: 1
       649: 1

 650:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       290: 1
       291: 1
       295: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       351: 1
       359: 1
       361: 1
       381: 1
       397: 1
       399: 1
       412: 1
       437: 1
       465: 1
       466: 1
       471: 1
       473: 1
       522: 1
       566: 1
       650: 1

 651:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       230: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       289: 1
       290: 1
       293: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       328: 1
       335: 1
       345: 1
       395: 1
       396: 1
       402: 1
       436: 1
       466: 1
       467: 1
       470: 1
       483: 1
       564: 1
       651: 1

 652:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       336: 1
       343: 1
       344: 1
       356: 1
       357: 1
       363: 1
       435: 1
       466: 1
       468: 1
       469: 1
       492: 1
       517: 1
       652: 1

 653:    0: q^2+3q+1
         1: 2q+1
         2: q^2+3q+1
         3: 3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q+1
         7: 2q+1
         8: 3q+1
         9: 2q+1
        10: 2q+1
        11: 3q+1
        12: 3q+1
        13: 2q+1
        14: q^2+3q+1
        15: 2q+1
        16: 2q+1
        17: q^2+3q+1
        18: 2q+1
        19: q^2+3q+1
        20: 1
        21: q+1
        22: 2q+1
        23: 3q+1
        24: 3q+1
        25: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 3q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q+1
        38: 2q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+3q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 3q+1
        57: 1
        60: 2q+1
        61: 2q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        79: q+1
        81: q+1
        83: 2q+1
        84: 1
        85: q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        92: q+1
        94: q+1
        96: 2q+1
        97: q+1
        98: 2q+1
        99: q+1
       100: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: 1
       112: 1
       113: 1
       118: 2q+1
       119: 1
       122: q+1
       123: q+1
       124: 1
       127: q+1
       128: q+1
       129: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: q+1
       139: q+1
       140: 2q+1
       152: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       159: q+1
       160: q+1
       161: 2q+1
       173: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: q+1
       184: 1
       186: 1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: q+1
       213: 1
       214: 1
       219: q+1
       220: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: q+1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: q+1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: q+1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       357: 1
       363: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       467: 1
       468: 1
       469: 1
       470: 1
       501: 1
       508: 1
       611: 1
       617: 1
       653: 1

 654:    0: 2q^2+3q+1
         1: 2q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: 2q^2+3q+1
         6: 2q+1
         7: 2q+1
         8: q^2+3q+1
         9: 2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: 2q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: 2q+1
        22: 2q+1
        23: q^2+3q+1
        24: q+1
        25: 2q+1
        27: q^2+3q+1
        28: 2q+1
        29: q^2+3q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: 1
        40: 2q+1
        41: 2q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: q+1
        60: q^2+3q+1
        61: q+1
        62: 2q+1
        64: q+1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: q+1
        75: 1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 2q+1
        86: q+1
        87: 2q+1
        89: q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       105: q+1
       107: q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       118: q+1
       119: 1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: q+1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: q+1
       159: q+1
       162: 1
       165: 2q+1
       167: q+1
       169: q+1
       176: 1
       177: q+1
       178: 1
       179: q+1
       181: 1
       183: q+1
       184: 1
       185: q+1
       191: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       205: 1
       206: 1
       213: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: q+1
       266: 1
       273: 1
       276: q+1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: q+1
       300: 1
       312: 1
       314: 1
       316: 1
       317: 1
       327: 1
       343: 1
       344: 1
       351: 1
       354: 1
       358: 1
       361: 1
       362: 1
       363: 1
       364: 1
       380: 1
       386: 1
       392: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       469: 1
       471: 1
       500: 1
       509: 1
       521: 1
       524: 1
       566: 1
       612: 1
       654: 1

 655:    0: 2q^2+3q+1
         1: 2q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: q^2+2q+1
         6: 2q+1
         7: 2q+1
         8: q^2+3q+1
         9: 2q+1
        10: q^2+3q+1
        11: q+1
        12: q^2+3q+1
        13: 2q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: q^2+3q+1
        25: 2q+1
        27: q^2+3q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: q^2+3q+1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: q+1
        60: q+1
        61: q^2+3q+1
        62: q+1
        64: 1
        65: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: 2q+1
        73: q+1
        75: 2q+1
        76: q+1
        78: 2q+1
        81: q+1
        82: 2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       113: q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: 1
       128: q+1
       129: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: q+1
       139: q+1
       141: 1
       145: 2q+1
       149: q+1
       151: q+1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: q+1
       181: 1
       183: q+1
       186: 1
       187: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       205: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: q+1
       237: 1
       248: 1
       252: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: q+1
       303: 1
       313: 1
       315: 1
       316: 1
       317: 1
       327: 1
       335: 1
       345: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       413: 1
       418: 1
       431: 1
       436: 1
       437: 1
       439: 1
       443: 1
       470: 1
       471: 1
       491: 1
       510: 1
       522: 1
       567: 1
       571: 1
       613: 1
       655: 1

 656:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: 2q+1
         5: 2q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: 2q^2+3q+1
        10: q^2+2q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: q+1
        24: q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q^2+2q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        81: q+1
        82: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       107: q+1
       108: 1
       109: 1
       110: q+1
       111: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: q+1
       145: 1
       149: 1
       150: 1
       151: 1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: 2q+1
       181: 1
       182: q+1
       183: q+1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: q+1
       291: 1
       295: 1
       296: 1
       297: q+1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       346: 1
       351: 1
       352: 1
       353: 1
       361: 1
       368: 1
       370: 1
       382: 1
       385: 1
       399: 1
       407: 1
       408: 1
       414: 1
       416: 1
       437: 1
       444: 1
       445: 1
       471: 1
       472: 1
       480: 1
       482: 1
       511: 1
       531: 1
       577: 1
       622: 1
       656: 1

 657:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       230: 1
       237: 1
       238: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: 1
       295: 1
       296: 1
       297: 1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       329: 1
       338: 1
       346: 1
       351: 1
       352: 1
       353: 1
       367: 1
       381: 1
       382: 1
       385: 1
       405: 1
       412: 1
       414: 1
       416: 1
       444: 1
       464: 1
       473: 1
       474: 1
       482: 1
       511: 1
       545: 1
       583: 1
       657: 1

 658:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: 2q+1
         5: 2q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q^2+3q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       104: q+1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: q+1
       151: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       181: q+1
       183: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       225: q+1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       290: 1
       291: 1
       295: 1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       359: 1
       381: 1
       397: 1
       412: 1
       437: 1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       485: 1
       495: 1
       504: 1
       658: 1

 659:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       230: 1
       259: 1
       290: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       338: 1
       346: 1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       659: 1

 660:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       177: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       258: 1
       259: 1
       260: 1
       264: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       334: 1
       396: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       660: 1

 661:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       177: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       336: 1
       337: 1
       338: 1
       342: 1
       357: 1
       468: 1
       475: 1
       478: 1
       479: 1
       493: 1
       661: 1

 662:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: q+1
        42: q+1
        43: q+1
        45: q+1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: q+1
        87: q+1
        92: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       157: 1
       159: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: q+1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: 1
       234: 1
       235: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       363: 1
       435: 1
       469: 1
       476: 1
       478: 1
       480: 1
       499: 1
       502: 1
       662: 1

 663:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: q+1
        75: q+1
        81: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: q+1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       260: 1
       264: 1
       265: 1
       286: 1
       289: 1
       290: 1
       293: 1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       402: 1
       436: 1
       470: 1
       477: 1
       479: 1
       480: 1
       490: 1
       503: 1
       663: 1

 664:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       231: 1
       233: 1
       248: 1
       252: 1
       261: 1
       262: 1
       273: 1
       276: 1
       290: 1
       291: 1
       295: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       361: 1
       399: 1
       437: 1
       471: 1
       480: 1
       481: 1
       487: 1
       497: 1
       504: 1
       664: 1

 665:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        53: q+1
        54: 1
        55: 1
        56: 1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: 1
       118: 1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       218: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       233: 1
       239: 1
       241: 1
       249: 1
       250: 1
       252: 1
       262: 1
       269: 1
       270: 1
       274: 1
       275: 1
       276: 1
       291: 1
       296: 1
       297: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: 1
       341: 1
       347: 1
       352: 1
       353: 1
       370: 1
       383: 1
       385: 1
       408: 1
       415: 1
       416: 1
       445: 1
       472: 1
       481: 1
       482: 1
       512: 1
       548: 1
       586: 1
       665: 1

 666:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       104: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       189: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       237: 1
       248: 1
       252: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       295: 1
       299: 1
       303: 1
       309: 1
       319: 1
       327: 1
       328: 1
       335: 1
       345: 1
       351: 1
       355: 1
       381: 1
       395: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       443: 1
       473: 1
       483: 1
       491: 1
       510: 1
       563: 1
       582: 1
       666: 1

 667:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        81: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: q+1
        94: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: 1
       136: 1
       139: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: q+1
       175: q+1
       176: 1
       177: 1
       178: 1
       180: 1
       186: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: q+1
       289: 1
       290: 1
       293: 1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       395: 1
       396: 1
       402: 1
       436: 1
       474: 1
       483: 1
       484: 1
       490: 1
       503: 1
       564: 1
       667: 1

 668:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        68: 2q+1
        69: 2q+1
        72: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       129: 2q+1
       130: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       177: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       565: 1
       582: 1
       668: 1

 669:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       312: 1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       397: 1
       399: 1
       412: 1
       476: 1
       485: 1
       487: 1
       566: 1
       669: 1

 670:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: 1
        12: q^2+1
        13: 1
        14: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: q^2+1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        30: 1
        31: q^2+1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       398: 1
       399: 1
       401: 1
       413: 1
       418: 1
       477: 1
       486: 1
       487: 1
       489: 1
       567: 1
       670: 1

 671:    0: 4q^2+4q+1
         1: 2q^2+3q+1
         2: 3q^2+4q+1
         3: 4q^2+4q+1
         4: q^2+3q+1
         5: 4q^2+4q+1
         6: 2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: 3q^2+4q+1
        11: 4q^2+4q+1
        12: q^2+3q+1
        13: 2q+1
        14: q^2+3q+1
        15: 2q+1
        16: 2q^2+3q+1
        17: 3q^2+4q+1
        18: 2q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: q+1
        23: q^2+3q+1
        24: q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: 3q^2+4q+1
        30: 2q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q^2+3q+1
        61: q+1
        62: 2q+1
        63: q^2+2q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: q^2+3q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: 2q+1
        75: q+1
        79: q+1
        81: q+1
        83: 2q+1
        84: 1
        85: q+1
        86: q+1
        87: 2q+1
        88: 1
        89: q+1
        91: q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: q+1
       100: 1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: 1
       134: q+1
       136: 1
       138: 1
       139: 1
       140: q+1
       152: q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: 1
       184: 1
       186: 1
       188: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       215: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: 1
       229: 1
       234: 1
       256: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       314: 1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       342: 1
       344: 1
       346: 1
       348: 1
       349: 1
       350: 1
       397: 1
       400: 1
       401: 1
       412: 1
       418: 1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       435: 1
       440: 1
       462: 1
       478: 1
       485: 1
       488: 1
       489: 1
       502: 1
       507: 1
       568: 1
       598: 1
       604: 1
       671: 1

 672:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        75: q+1
        81: q+1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       135: q+1
       136: 1
       139: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: q+1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       260: 1
       261: 1
       263: 1
       267: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: 1
       290: 1
       293: 1
       315: 1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       345: 1
       346: 1
       349: 1
       398: 1
       400: 1
       413: 1
       420: 1
       426: 1
       430: 1
       436: 1
       479: 1
       486: 1
       488: 1
       503: 1
       569: 1
       599: 1
       672: 1

 673:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: 2q+1
         6: 1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q^2+2q+1
        11: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q^2+2q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        39: q+1
        40: 1
        41: q+1
        42: 2q+1
        43: q+1
        44: q+1
        45: 2q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 2q+1
        61: q+1
        62: 1
        63: q+1
        64: 2q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: q+1
        81: 1
        84: 1
        85: 1
        86: q+1
        87: 2q+1
        88: 1
        89: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: q+1
       122: 2q+1
       123: 1
       124: 1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       136: 1
       139: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       290: 1
       293: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       346: 1
       349: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       418: 1
       426: 1
       430: 1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       570: 1
       589: 1
       673: 1

 674:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       145: 1
       149: 1
       151: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       233: 1
       252: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       291: 1
       293: 1
       299: 1
       303: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       341: 1
       347: 1
       349: 1
       355: 1
       401: 1
       402: 1
       403: 1
       418: 1
       431: 1
       439: 1
       481: 1
       489: 1
       490: 1
       491: 1
       506: 1
       571: 1
       674: 1

 675:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: q+1
        23: q+1
        24: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: q+1
        55: q+1
        56: q+1
        59: q+1
        60: q+1
        61: q+1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       110: q+1
       111: 1
       116: q+1
       117: q+1
       118: q+1
       121: 1
       122: 1
       123: 1
       126: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       139: 1
       143: 1
       145: 1
       150: 1
       151: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       187: 1
       196: 1
       197: 1
       204: q+1
       205: 1
       210: 1
       211: 1
       212: 1
       218: 1
       222: 1
       224: 1
       226: 1
       227: 1
       241: 1
       250: 1
       252: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       284: 1
       286: 1
       287: 1
       293: 1
       297: 1
       299: 1
       304: 1
       318: 1
       326: 1
       327: 1
       334: 1
       335: 1
       349: 1
       353: 1
       355: 1
       385: 1
       402: 1
       403: 1
       410: 1
       416: 1
       417: 1
       418: 1
       432: 1
       447: 1
       482: 1
       490: 1
       491: 1
       514: 1
       572: 1
       588: 1
       675: 1

 676:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       104: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       189: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       266: 1
       273: 1
       276: 1
       288: 1
       295: 1
       298: 1
       300: 1
       309: 1
       319: 1
       327: 1
       336: 1
       343: 1
       344: 1
       351: 1
       354: 1
       356: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       412: 1
       442: 1
       473: 1
       492: 1
       500: 1
       509: 1
       516: 1
       543: 1
       676: 1

 677:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        92: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       102: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: q+1
       154: q+1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: q+1
       259: 1
       288: 1
       290: 1
       292: 1
       310: 1
       319: 1
       320: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       363: 1
       435: 1
       474: 1
       492: 1
       493: 1
       499: 1
       502: 1
       517: 1
       677: 1

 678:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        47: 2q+1
        48: 2q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        85: q+1
        97: 2q+1
        98: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       177: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       380: 1
       381: 1
       386: 1
       475: 1
       493: 1
       494: 1
       495: 1
       498: 1
       518: 1
       543: 1
       678: 1

 679:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: 1
        42: q+1
        43: q+1
        45: q+1
        47: 1
        48: 1
        49: 1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: 1
        87: q+1
        92: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: q+1
       208: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: 1
       231: 1
       232: 1
       236: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       312: 1
       321: 1
       323: 1
       329: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       373: 1
       380: 1
       387: 1
       390: 1
       435: 1
       476: 1
       494: 1
       496: 1
       502: 1
       519: 1
       551: 1
       679: 1

 680:    0: 4q^2+4q+1
         1: 2q^2+3q+1
         2: 3q^2+4q+1
         3: 4q^2+4q+1
         4: 4q^2+4q+1
         5: q^2+3q+1
         6: 2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: 3q^2+4q+1
        11: q^2+3q+1
        12: 4q^2+4q+1
        13: 2q^2+3q+1
        14: 3q^2+4q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: q^2+3q+1
        18: 2q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q^2+3q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+3q+1
        28: 2q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: 3q^2+4q+1
        32: q^2+3q+1
        33: 2q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: 2q^2+3q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+3q+1
        49: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q^2+3q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q^2+2q+1
        67: 2q+1
        68: 2q+1
        69: q^2+3q+1
        70: q+1
        71: 1
        72: q+1
        73: q+1
        74: 1
        75: 2q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        88: 2q+1
        92: q+1
        94: q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: q+1
       100: 1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: 2q+1
       124: 1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       156: q+1
       157: 1
       159: 1
       160: 1
       161: q+1
       173: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: q+1
       184: 1
       186: 1
       188: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: q+1
       208: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: q+1
       253: q+1
       255: 1
       256: 1
       260: 1
       264: 1
       286: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       359: 1
       360: 1
       362: 1
       374: 1
       379: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       436: 1
       440: 1
       462: 1
       477: 1
       495: 1
       496: 1
       498: 1
       503: 1
       507: 1
       520: 1
       552: 1
       557: 1
       680: 1

 681:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: q^2+1
        19: 1
        20: 1
        21: 1
        22: 1
        23: q^2+1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: q^2+1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       177: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       314: 1
       321: 1
       324: 1
       325: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       358: 1
       361: 1
       362: 1
       380: 1
       386: 1
       478: 1
       494: 1
       497: 1
       498: 1
       521: 1
       681: 1

 682:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       216: 1
       218: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       315: 1
       322: 1
       324: 1
       338: 1
       339: 1
       341: 1
       359: 1
       361: 1
       381: 1
       479: 1
       495: 1
       497: 1
       522: 1
       682: 1

 683:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q+1
         6: 1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q^2+2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: q+1
        24: 2q+1
        25: 1
        26: q+1
        27: q^2+2q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: 1
        34: q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: 1
        39: 2q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: q+1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 2q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: q+1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: q+1
        74: 1
        75: 2q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q+1
        92: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: q+1
       127: 1
       128: 2q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       210: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       290: 1
       292: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       348: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       386: 1
       387: 1
       390: 1
       480: 1
       496: 1
       497: 1
       498: 1
       499: 1
       523: 1
       550: 1
       683: 1

 684:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       165: 1
       167: 1
       169: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       262: 1
       276: 1
       291: 1
       292: 1
       298: 1
       300: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       354: 1
       362: 1
       363: 1
       364: 1
       386: 1
       392: 1
       438: 1
       481: 1
       498: 1
       499: 1
       500: 1
       505: 1
       524: 1
       684: 1

 685:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: q+1
        23: q+1
        24: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        54: q+1
        55: q+1
        56: q+1
        59: q+1
        60: q+1
        61: q+1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       110: q+1
       111: 1
       116: q+1
       117: q+1
       118: q+1
       121: 1
       122: 1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       164: 1
       165: 1
       168: 1
       169: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       196: 1
       197: 1
       204: q+1
       205: 1
       210: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       250: 1
       251: 1
       252: 1
       254: 1
       256: 1
       257: 1
       270: 1
       275: 1
       276: 1
       292: 1
       297: 1
       298: 1
       301: 1
       318: 1
       326: 1
       327: 1
       342: 1
       343: 1
       348: 1
       353: 1
       354: 1
       363: 1
       364: 1
       371: 1
       384: 1
       385: 1
       386: 1
       393: 1
       416: 1
       446: 1
       482: 1
       499: 1
       500: 1
       513: 1
       525: 1
       549: 1
       685: 1

 686:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       161: 1
       173: 1
       175: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: 1
       235: 1
       256: 1
       258: 1
       265: 1
       286: 1
       288: 1
       289: 1
       294: 1
       306: 1
       308: 1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       356: 1
       395: 1
       434: 1
       441: 1
       462: 1
       483: 1
       492: 1
       501: 1
       508: 1
       610: 1
       686: 1

 687:    0: 2q+1
         1: 2q+1
         2: q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: q+1
         8: 1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: q+1
        18: q+1
        19: 2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: 2q+1
        29: q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: 2q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: q+1
        94: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       396: 1
       434: 1
       435: 1
       436: 1
       440: 1
       462: 1
       484: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       611: 1
       687: 1

 688:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       191: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       248: 1
       251: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       321: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 1
       380: 1
       392: 1
       397: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       485: 1
       494: 1
       502: 1
       504: 1
       505: 1
       509: 1
       612: 1
       688: 1

 689:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: q+1
        59: 1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: q+1
       121: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: q+1
       151: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       192: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: 1
       273: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       322: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       381: 1
       398: 1
       413: 1
       431: 1
       436: 1
       437: 1
       439: 1
       443: 1
       486: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       613: 1
       689: 1

 690:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: 2q+1
         6: q+1
         7: 1
         8: q^2+2q+1
         9: q+1
        10: q^2+2q+1
        11: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q^2+2q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: 2q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: q+1
        83: 1
        84: q+1
        85: 1
        86: 1
        87: q+1
        89: q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       162: q+1
       165: q+1
       167: q+1
       169: 2q+1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: q+1
       184: 1
       185: 1
       193: 1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: q+1
       231: 1
       232: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       273: q+1
       276: q+1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       323: 1
       331: 1
       332: 1
       339: 1
       340: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       360: 1
       387: 1
       390: 1
       392: 1
       394: 1
       399: 1
       437: 1
       438: 1
       449: 1
       452: 1
       487: 1
       496: 1
       504: 1
       505: 1
       558: 1
       561: 1
       614: 1
       690: 1

 691:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q+1
         6: q+1
         7: 1
         8: q^2+2q+1
         9: q+1
        10: q^2+2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: 1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q^2+2q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: 1
        35: 2q+1
        36: q+1
        37: 2q+1
        39: 2q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        76: q+1
        78: 2q+1
        81: q+1
        82: 2q+1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       145: q+1
       149: q+1
       151: 2q+1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: q+1
       186: 1
       187: 1
       194: 1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: q+1
       231: 1
       233: 1
       248: q+1
       252: q+1
       261: 1
       263: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       324: 1
       331: 1
       333: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       361: 1
       400: 1
       426: 1
       430: 1
       431: 1
       433: 1
       437: 1
       439: 1
       454: 1
       458: 1
       488: 1
       497: 1
       504: 1
       506: 1
       605: 1
       609: 1
       615: 1
       691: 1

 692:    0: q^2+3q+1
         1: 2q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: q^2+3q+1
        15: q+1
        16: 2q+1
        17: q^2+3q+1
        18: q+1
        19: q^2+3q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q^2+3q+1
        30: 2q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: q^2+3q+1
        70: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       175: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       232: 1
       233: 1
       234: 1
       242: 1
       251: 1
       252: 1
       253: q+1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       272: 1
       276: 1
       277: 1
       283: q+1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       325: 1
       332: 1
       333: 1
       334: 1
       340: 1
       341: 1
       342: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       362: 1
       386: 1
       392: 1
       401: 1
       418: 1
       431: 1
       438: 1
       439: 1
       440: 1
       448: 1
       459: 1
       462: 1
       463: 1
       489: 1
       498: 1
       505: 1
       506: 1
       507: 1
       515: 1
       616: 1
       646: 1
       692: 1

 693:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       196: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       234: 1
       235: 1
       256: 1
       264: 1
       265: 1
       286: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       326: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       363: 1
       402: 1
       440: 1
       441: 1
       462: 1
       490: 1
       499: 1
       507: 1
       508: 1
       617: 1
       693: 1

 694:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: 1
        17: q+1
        18: 1
        19: q+1
        23: q+1
        24: q+1
        27: q+1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: q+1
        60: q+1
        61: q+1
        64: 1
        67: 1
        69: q+1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       111: 1
       118: q+1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       151: 1
       153: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       174: 1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       197: 1
       205: 1
       212: 1
       219: 1
       223: 1
       224: 1
       227: 1
       235: 1
       242: 1
       251: 1
       252: 1
       257: 1
       265: 1
       272: 1
       276: 1
       277: 1
       287: 1
       294: 1
       298: 1
       299: 1
       307: 1
       308: 1
       327: 1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       364: 1
       386: 1
       403: 1
       418: 1
       441: 1
       448: 1
       463: 1
       491: 1
       500: 1
       508: 1
       515: 1
       618: 1
       694: 1

 695:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         6: 3q+1
         8: q+1
         9: 3q+1
        10: 3q+1
        11: 3q+1
        12: 3q+1
        13: 3q+1
        14: 3q+1
        15: q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 3q+1
        20: q+1
        23: q+1
        24: q+1
        25: 3q+1
        27: q+1
        28: 3q+1
        29: 3q+1
        30: 3q+1
        31: 3q+1
        32: 3q+1
        33: 3q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 3q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: 3q+1
        49: 1
        50: q+1
        51: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: 3q+1
        64: 1
        65: 3q+1
        67: 1
        68: 3q+1
        69: 3q+1
        70: 1
        71: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 3q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       112: q+1
       113: q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 3q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       198: q+1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       256: 1
       257: 1
       258: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: q+1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       328: 1
       336: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       442: 1
       443: 1
       448: 1
       459: 1
       462: 1
       463: 1
       501: 1
       509: 1
       510: 1
       515: 1
       543: 1
       582: 1
       619: 1
       646: 1
       695: 1

 696:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+2q+1
         5: 2q^2+3q+1
         6: 2q+1
         7: 2q+1
         8: q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: 2q^2+3q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: 2q^2+3q+1
        17: 2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: 2q+1
        22: q+1
        23: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 2q^2+3q+1
        29: 2q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 2q+1
        41: 2q+1
        42: 1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        54: q+1
        57: q+1
        58: 2q+1
        59: q+1
        60: q+1
        62: 2q+1
        63: 2q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 2q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q^2+2q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       105: q+1
       112: q+1
       114: q+1
       116: q+1
       119: 1
       120: 2q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       199: q+1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       236: 1
       238: 1
       240: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       329: 1
       337: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       366: 1
       380: 1
       382: 1
       384: 1
       388: 1
       392: 1
       393: 1
       405: 1
       412: 1
       414: 1
       416: 1
       435: 1
       442: 1
       444: 1
       446: 1
       450: 1
       502: 1
       509: 1
       511: 1
       513: 1
       544: 1
       559: 1
       583: 1
       620: 1
       696: 1

 697:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: q^2+2q+1
         6: 2q+1
         7: 2q+1
         8: q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: q^2+2q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: 2q+1
        22: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: 2q^2+3q+1
        31: 2q+1
        32: q^2+2q+1
        33: 2q+1
        34: 2q+1
        35: 1
        36: q^2+2q+1
        37: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        55: q+1
        57: q+1
        58: 2q+1
        59: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: 2q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        81: q^2+2q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       103: q+1
       106: q+1
       113: q+1
       114: q+1
       117: q+1
       119: 1
       120: q+1
       121: 1
       123: 1
       124: 1
       125: 2q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       149: q+1
       150: q+1
       151: 1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       200: q+1
       207: 1
       208: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       237: 1
       238: 1
       241: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       260: 1
       267: 1
       268: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       330: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       367: 1
       381: 1
       382: 1
       385: 1
       406: 1
       413: 1
       414: 1
       417: 1
       427: 1
       431: 1
       432: 1
       436: 1
       443: 1
       444: 1
       447: 1
       455: 1
       503: 1
       510: 1
       511: 1
       514: 1
       545: 1
       584: 1
       606: 1
       621: 1
       697: 1

 698:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: q+1
        22: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: q+1
        53: q+1
        57: q+1
        58: q+1
        59: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       107: q+1
       114: q+1
       115: q+1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       141: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       157: 1
       158: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       201: q+1
       208: 1
       209: 1
       215: 1
       216: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: 1
       238: 1
       239: 1
       248: 1
       249: 1
       250: 1
       261: 1
       268: 1
       269: 1
       273: 1
       274: 1
       275: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       331: 1
       339: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       368: 1
       382: 1
       383: 1
       407: 1
       414: 1
       415: 1
       437: 1
       444: 1
       445: 1
       504: 1
       511: 1
       512: 1
       546: 1
       585: 1
       622: 1
       698: 1

 699:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: q+1
        21: 2q+1
        22: q+1
        23: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 2q+1
        41: 2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: 1
        53: q+1
        54: q+1
        58: 2q+1
        59: q+1
        60: q+1
        62: 2q+1
        63: 2q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 2q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       108: q+1
       115: q+1
       116: q+1
       120: 2q+1
       121: 1
       122: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       202: q+1
       209: 1
       210: 1
       216: 1
       217: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       232: 1
       239: 1
       240: 1
       244: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       269: 1
       270: 1
       274: q+1
       275: 1
       276: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       332: 1
       340: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       369: 1
       383: 1
       384: 1
       388: 1
       392: 1
       393: 1
       408: 1
       415: 1
       416: 1
       438: 1
       445: 1
       446: 1
       450: 1
       505: 1
       512: 1
       513: 1
       547: 1
       559: 1
       586: 1
       623: 1
       699: 1

 700:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: 2q+1
        22: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: q+1
        55: q+1
        58: 2q+1
        59: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: 2q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        81: q+1
        82: q+1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       109: q+1
       115: q+1
       117: q+1
       120: q+1
       121: 1
       123: 1
       125: 2q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: q+1
       143: 1
       145: 1
       149: q+1
       150: q+1
       151: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       203: q+1
       209: 1
       211: 1
       216: 1
       218: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       233: 1
       239: 1
       241: 1
       249: q+1
       250: 1
       252: 1
       263: 1
       269: 1
       271: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       333: 1
       341: 1
       347: 1
       349: 1
       352: 1
       353: 1
       355: 1
       370: 1
       383: 1
       385: 1
       409: 1
       415: 1
       417: 1
       427: 1
       431: 1
       432: 1
       439: 1
       445: 1
       447: 1
       455: 1
       506: 1
       512: 1
       514: 1
       548: 1
       587: 1
       606: 1
       624: 1
       700: 1

 701:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         7: 3q+1
         8: q+1
         9: 3q+1
        10: 3q+1
        11: 3q+1
        12: 3q+1
        13: 3q+1
        14: 3q+1
        15: q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 3q+1
        22: q+1
        23: q+1
        24: q+1
        26: 3q+1
        27: q+1
        28: 3q+1
        29: 3q+1
        30: 3q+1
        31: 3q+1
        32: 3q+1
        34: 3q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        41: 3q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: 3q+1
        49: 1
        54: q+1
        55: q+1
        56: q+1
        59: q+1
        60: q+1
        61: q+1
        63: 3q+1
        64: 1
        66: 3q+1
        67: 1
        68: 3q+1
        69: 3q+1
        70: 1
        73: 1
        74: 1
        75: 1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        86: 1
        87: 1
        88: 1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        98: 3q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: q+1
       116: q+1
       117: q+1
       118: q+1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: 3q+1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: q+1
       169: 1
       171: q+1
       173: q+1
       174: q+1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       204: q+1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: 1
       240: 1
       241: 1
       242: 1
       250: 1
       251: 1
       252: 1
       254: q+1
       256: 1
       257: 1
       264: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       284: q+1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       304: 1
       306: 1
       307: 1
       308: 1
       334: 1
       342: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       371: 1
       384: 1
       385: 1
       386: 1
       393: 1
       410: 1
       416: 1
       417: 1
       418: 1
       432: 1
       440: 1
       446: 1
       447: 1
       448: 1
       460: 1
       462: 1
       463: 1
       507: 1
       513: 1
       514: 1
       515: 1
       549: 1
       588: 1
       625: 1
       647: 1
       701: 1

 702:    0: 3q^2+4q+1
         2: q^2+4q+1
         3: 3q^2+4q+1
         4: q^2+4q+1
         5: q^2+4q+1
         8: q^2+4q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^2+4q+1
        14: 4q+1
        15: q^2+4q+1
        17: 4q+1
        18: q^2+4q+1
        19: 4q+1
        23: 2q+1
        24: 2q+1
        27: q^2+4q+1
        29: 4q+1
        31: 4q+1
        32: 4q+1
        35: 4q+1
        37: 2q+1
        38: 2q+1
        39: q^2+4q+1
        42: 4q+1
        44: 2q+1
        45: q^2+4q+1
        46: 2q+1
        48: 4q+1
        49: 4q+1
        56: q+1
        60: 2q+1
        61: 2q+1
        64: 4q+1
        67: 4q+1
        69: 4q+1
        70: 4q+1
        74: q+1
        75: 2q+1
        78: 2q+1
        80: q+1
        82: 2q+1
        83: 2q+1
        87: 2q+1
        88: q+1
        91: 2q+1
        93: 2q+1
        95: q+1
        96: 2q+1
        99: 4q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       111: q+1
       118: q+1
       122: 2q+1
       123: q+1
       127: q+1
       128: 2q+1
       131: 4q+1
       133: q+1
       140: 1
       144: 1
       145: q+1
       148: q+1
       151: 2q+1
       153: q+1
       154: 2q+1
       161: 1
       165: q+1
       166: 1
       169: 2q+1
       172: q+1
       174: q+1
       175: 2q+1
       179: q+1
       180: q+1
       183: q+1
       185: 1
       187: 1
       188: q+1
       205: q+1
       212: 1
       219: 1
       223: q+1
       224: q+1
       227: q+1
       235: 1
       242: 1
       246: 1
       251: 1
       252: q+1
       255: q+1
       257: 1
       265: 1
       272: 1
       276: q+1
       277: 1
       282: 1
       285: q+1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: q+1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       372: 1
       386: 1
       390: 1
       394: 1
       411: 1
       418: 1
       430: 1
       433: 1
       441: 1
       448: 1
       452: 1
       458: 1
       461: 1
       463: 1
       508: 1
       515: 1
       550: 1
       561: 1
       589: 1
       609: 1
       626: 1
       648: 1
       702: 1

 703:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       221: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       259: 1
       266: 1
       268: 1
       270: 1
       274: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       309: 1
       310: 1
       318: 1
       320: 1
       352: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       388: 1
       392: 1
       393: 1
       405: 1
       435: 1
       442: 1
       444: 1
       446: 1
       450: 1
       464: 1
       516: 1
       517: 1
       525: 1
       527: 1
       559: 1
       620: 1
       703: 1

 704:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       129: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       225: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       309: 1
       310: 1
       311: 1
       317: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       392: 1
       397: 1
       435: 1
       437: 1
       438: 1
       442: 1
       465: 1
       516: 1
       517: 1
       518: 1
       524: 1
       612: 1
       704: 1

 705:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 1
        24: q+1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 2q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: 2q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 2q+1
        72: 2q+1
        73: 2q+1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        92: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: 1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       136: 2q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: q+1
       159: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       184: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: q+1
       292: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       381: 1
       387: 1
       435: 1
       466: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       705: 1

 706:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       206: 1
       207: 1
       212: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       253: 1
       258: 1
       259: 1
       260: 1
       264: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       311: 1
       312: 1
       313: 1
       328: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       373: 1
       374: 1
       379: 1
       396: 1
       434: 1
       435: 1
       436: 1
       440: 1
       467: 1
       518: 1
       519: 1
       520: 1
       535: 1
       611: 1
       706: 1

 707:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       177: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       213: 1
       214: 1
       219: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       311: 1
       314: 1
       315: 1
       336: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       380: 1
       381: 1
       386: 1
       468: 1
       518: 1
       521: 1
       522: 1
       543: 1
       707: 1

 708:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: q+1
        47: 1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        64: q+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: 1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q+1
        92: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: q+1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       118: 1
       119: 1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: q+1
       145: 1
       146: 1
       148: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: q+1
       184: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       206: 1
       213: 1
       219: 1
       220: 1
       223: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       243: 1
       246: q+1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       312: 1
       314: 1
       316: 1
       343: 1
       344: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       373: 1
       380: 1
       386: 1
       387: 1
       390: 1
       435: 1
       469: 1
       519: 1
       521: 1
       523: 1
       550: 1
       551: 1
       708: 1

 709:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: 2q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 1
        34: q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: 1
        39: 2q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: 1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: q+1
        74: 1
        75: 2q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: q+1
       129: 1
       131: 1
       132: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: q+1
       184: 1
       186: 1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       260: 1
       264: 1
       265: 1
       286: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       313: 1
       315: 1
       316: 1
       335: 1
       345: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       374: 1
       379: 1
       381: 1
       387: 1
       391: 1
       402: 1
       436: 1
       440: 1
       441: 1
       462: 1
       470: 1
       520: 1
       522: 1
       523: 1
       542: 1
       552: 1
       617: 1
       709: 1

 710:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: q+1
        92: 1
        93: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: q+1
       184: 1
       185: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       205: 1
       220: 1
       225: 1
       227: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       273: 1
       276: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       316: 1
       317: 1
       327: 1
       351: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       387: 1
       392: 1
       394: 1
       399: 1
       437: 1
       438: 1
       449: 1
       452: 1
       471: 1
       523: 1
       524: 1
       534: 1
       558: 1
       614: 1
       710: 1

 711:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       221: 1
       225: 1
       226: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       269: 1
       270: 1
       274: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       317: 1
       318: 1
       325: 1
       352: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       388: 1
       392: 1
       393: 1
       408: 1
       438: 1
       445: 1
       446: 1
       450: 1
       472: 1
       524: 1
       525: 1
       532: 1
       559: 1
       623: 1
       711: 1

 712:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        74: 1
        75: 1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        87: 1
        89: q+1
        91: q+1
        92: 1
        93: 1
        97: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: q+1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       162: q+1
       165: 1
       167: 1
       169: 1
       176: q+1
       179: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       266: 1
       273: 1
       276: 1
       288: 1
       295: q+1
       298: 1
       300: 1
       302: 1
       309: 1
       319: 1
       327: 1
       351: 1
       356: 1
       364: 1
       365: 1
       372: 1
       373: 1
       381: 1
       387: 1
       392: 1
       394: 1
       412: 1
       442: 1
       449: 1
       452: 1
       473: 1
       516: 1
       526: 1
       534: 1
       558: 1
       627: 1
       712: 1

 713:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: q^2+2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: q+1
        11: q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: 2q+1
        15: 2q^2+3q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: q+1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        45: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: 1
        51: q+1
        52: 2q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 2q+1
        72: 2q+1
        73: 2q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        92: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       102: q+1
       104: 1
       105: 1
       106: q+1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 1
       135: q+1
       136: 2q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: q+1
       159: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       184: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       228: 1
       229: 1
       230: q+1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       259: 1
       288: 1
       290: q+1
       292: 1
       310: 1
       319: 1
       320: 1
       326: 1
       329: 1
       338: 1
       346: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       435: 1
       474: 1
       517: 1
       526: 1
       527: 1
       533: 1
       536: 1
       545: 1
       553: 1
       713: 1

 714:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        47: q+1
        48: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        97: q+1
        98: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       177: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       221: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       388: 1
       475: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       714: 1

 715:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       210: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       259: 1
       288: 1
       290: 1
       292: 1
       312: 1
       321: 1
       323: 1
       329: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       377: 1
       435: 1
       476: 1
       519: 1
       528: 1
       530: 1
       536: 1
       715: 1

 716:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q+1
         6: q+1
         7: q^2+2q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       152: 1
       153: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       260: 1
       264: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       334: 1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       388: 1
       436: 1
       440: 1
       477: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       541: 1
       716: 1

 717:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: q+1
        40: q+1
        41: 2q+1
        47: 2q+1
        48: 2q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        85: q+1
        97: q+1
        98: 2q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       177: q+1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       314: 1
       321: 1
       324: 1
       325: 1
       337: 1
       342: 1
       358: 1
       361: 1
       362: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       478: 1
       521: 1
       528: 1
       531: 1
       532: 1
       544: 1
       549: 1
       717: 1

 718:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        20: q+1
        21: q+1
        22: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        39: q+1
        51: q+1
        52: q+1
        53: 1
        55: q+1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
       106: q+1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: q+1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       218: 1
       230: q+1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       315: 1
       322: 1
       324: 1
       338: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       385: 1
       479: 1
       522: 1
       529: 1
       531: 1
       545: 1
       718: 1

 719:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: 2q+1
        74: 1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        92: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: q+1
       159: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       184: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       290: q+1
       292: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       346: 1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       480: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       553: 1
       719: 1

 720:    0: 2q^2+3q+1
         1: 2q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: q^2+2q+1
         6: 2q+1
         7: 2q+1
         8: q^2+3q+1
         9: 2q+1
        10: q^2+3q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: q^2+3q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: q^2+3q+1
        36: 2q+1
        37: q^2+3q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        47: q+1
        48: q^2+2q+1
        49: q+1
        53: 2q+1
        54: 1
        55: q+1
        56: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: 2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: q^2+3q+1
        79: 1
        80: q+1
        81: q+1
        82: 2q+1
        83: q+1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        91: q+1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       108: 1
       109: q+1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 2q+1
       138: 1
       139: q+1
       140: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 2q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: q+1
       159: 1
       165: 1
       167: 1
       169: 1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       218: 1
       221: 1
       222: 1
       225: 1
       227: 1
       232: 1
       233: q+1
       234: 1
       235: 1
       239: q+1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: 1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       276: 1
       291: q+1
       292: 1
       298: 1
       300: 1
       302: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       341: 1
       347: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       383: 1
       385: 1
       388: 1
       389: 1
       392: 1
       394: 1
       438: 1
       452: 1
       481: 1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       548: 1
       554: 1
       720: 1

 721:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: 1
        24: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        54: 1
        55: 1
        56: 1
        59: q+1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        74: 1
        75: 1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: q+1
        87: 1
        90: q+1
        91: q+1
        92: 1
        93: 1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: q+1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       164: q+1
       165: 1
       168: 1
       169: 1
       178: q+1
       179: 1
       182: q+1
       183: q+1
       184: 1
       185: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: 1
       218: 1
       222: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       250: 1
       252: 1
       254: 1
       255: 1
       256: 1
       257: 1
       270: 1
       275: 1
       276: 1
       292: 1
       297: q+1
       298: 1
       301: 1
       302: 1
       318: 1
       326: 1
       327: 1
       353: 1
       363: 1
       364: 1
       371: 1
       372: 1
       377: 1
       385: 1
       389: 1
       393: 1
       394: 1
       416: 1
       446: 1
       451: 1
       452: 1
       482: 1
       525: 1
       533: 1
       534: 1
       560: 1
       631: 1
       721: 1

 722:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: 1
        24: q+1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        42: q+1
        43: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        74: 1
        75: q+1
        76: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        87: 1
        88: q+1
        92: 1
        94: q+1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       102: 1
       103: q+1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       161: 1
       173: 1
       175: 1
       176: q+1
       179: 1
       180: q+1
       184: 1
       186: q+1
       188: 1
       189: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       265: 1
       286: 1
       288: 1
       289: q+1
       294: 1
       306: 1
       308: 1
       319: 1
       328: 1
       335: 1
       345: 1
       356: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       381: 1
       387: 1
       391: 1
       395: 1
       434: 1
       441: 1
       462: 1
       483: 1
       526: 1
       535: 1
       542: 1
       552: 1
       610: 1
       722: 1

 723:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: q+1
        94: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: q+1
       153: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: q+1
       186: q+1
       188: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       258: 1
       259: 1
       260: 1
       264: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: q+1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       388: 1
       396: 1
       434: 1
       435: 1
       436: 1
       440: 1
       484: 1
       527: 1
       535: 1
       536: 1
       537: 1
       541: 1
       611: 1
       723: 1

 724:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        62: 2q+1
        63: q+1
        64: 1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        76: 2q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: 2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       134: q+1
       136: 1
       137: 1
       138: 1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       146: 2q+1
       147: q+1
       148: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       191: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       229: 1
       231: 1
       232: 1
       236: q+1
       238: 1
       239: 1
       240: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: q+1
       302: 1
       321: 1
       329: 1
       331: 1
       332: 1
       358: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       397: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       485: 1
       528: 1
       536: 1
       538: 1
       539: 1
       612: 1
       627: 1
       724: 1

 725:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q^2+2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        68: 1
        69: 1
        71: q+1
        72: q+1
        73: 1
        75: q+1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       135: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       152: 1
       153: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       221: 1
       230: 1
       231: 1
       233: 1
       237: q+1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       249: 1
       253: 1
       254: 1
       260: 1
       261: 1
       263: 1
       267: 1
       273: 1
       277: 1
       283: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       322: 1
       330: 1
       331: 1
       333: 1
       359: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       388: 1
       398: 1
       413: 1
       436: 1
       437: 1
       439: 1
       443: 1
       449: 1
       453: 1
       459: 1
       486: 1
       529: 1
       537: 1
       538: 1
       540: 1
       613: 1
       628: 1
       725: 1

 726:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: 1
        13: 1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        33: 1
        34: 1
        35: q^2+1
        36: 1
        37: q^2+1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: q^2+1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       193: 1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       261: 1
       262: 1
       273: 1
       276: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       323: 1
       331: 1
       332: 1
       360: 1
       368: 1
       369: 1
       375: 1
       376: 1
       377: 1
       399: 1
       437: 1
       438: 1
       449: 1
       452: 1
       487: 1
       530: 1
       538: 1
       539: 1
       614: 1
       726: 1

 727:    0: 4q^2+4q+1
         1: 2q^2+3q+1
         2: 3q^2+4q+1
         3: 4q^2+4q+1
         4: 4q^2+4q+1
         5: q^2+3q+1
         6: q^2+2q+1
         7: 2q+1
         8: 3q^2+4q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: 3q^2+4q+1
        15: 4q^2+4q+1
        16: 2q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q^2+3q+1
        28: q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: 2q+1
        35: 3q^2+4q+1
        36: 2q^2+3q+1
        37: q^2+3q+1
        38: 2q+1
        39: 2q^2+3q+1
        40: q+1
        41: 2q+1
        42: q^2+3q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        52: q+1
        53: 1
        55: q+1
        57: q+1
        58: 1
        59: q+1
        61: q+1
        62: 1
        63: q+1
        64: 2q+1
        65: q+1
        66: 1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q+1
        73: 2q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q^2+3q+1
        79: q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        88: q+1
        89: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: 2q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: q+1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       136: q+1
       137: 1
       139: q+1
       141: q+1
       142: 1
       143: q+1
       145: q+1
       146: 1
       147: q+1
       148: 2q+1
       149: q+1
       150: 1
       151: 2q+1
       152: 1
       153: q+1
       154: q+1
       157: q+1
       158: 1
       160: q+1
       162: 1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: 2q+1
       180: q+1
       181: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 1
       188: 1
       194: 1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: q+1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: q+1
       256: 1
       261: 1
       263: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       290: q+1
       291: 1
       293: q+1
       295: 1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       324: 1
       331: 1
       333: 1
       346: 1
       349: 1
       361: 1
       368: 1
       370: 1
       375: 1
       376: 1
       378: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       400: 1
       426: 1
       430: 1
       437: 1
       439: 1
       449: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       488: 1
       531: 1
       538: 1
       540: 1
       553: 1
       556: 1
       615: 1
       641: 1
       645: 1
       727: 1

 728:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q^2+2q+1
        18: 1
        19: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q^2+2q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: q+1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       142: 1
       143: 1
       144: q+1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: q+1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       262: 1
       263: 1
       264: 1
       272: 1
       276: 1
       277: 1
       283: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       325: 1
       332: 1
       333: 1
       334: 1
       362: 1
       369: 1
       370: 1
       371: 1
       376: 1
       377: 1
       378: 1
       379: 1
       388: 1
       401: 1
       418: 1
       438: 1
       439: 1
       440: 1
       448: 1
       452: 1
       453: 1
       459: 1
       489: 1
       532: 1
       539: 1
       540: 1
       541: 1
       616: 1
       633: 1
       728: 1

 729:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: 1
        24: q+1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        41: q+1
        42: q+1
        43: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        54: 1
        55: q+1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        74: 1
        75: q+1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        86: q+1
        87: 1
        88: q+1
        92: 1
        94: q+1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       102: 1
       103: q+1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: 1
       139: q+1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       160: q+1
       161: 1
       173: 1
       175: 1
       178: q+1
       179: 1
       180: q+1
       184: 1
       186: q+1
       188: 1
       196: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       218: 1
       222: 1
       224: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       252: 1
       254: 1
       255: 1
       256: 1
       264: 1
       265: 1
       286: 1
       292: 1
       293: q+1
       294: 1
       306: 1
       308: 1
       326: 1
       334: 1
       335: 1
       349: 1
       363: 1
       371: 1
       372: 1
       377: 1
       378: 1
       379: 1
       385: 1
       389: 1
       391: 1
       402: 1
       440: 1
       441: 1
       462: 1
       490: 1
       533: 1
       541: 1
       542: 1
       556: 1
       617: 1
       729: 1

 730:    0: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         8: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        14: q^2+2q+1
        15: 2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        23: q+1
        24: 2q+1
        27: 2q+1
        29: q+1
        31: 2q+1
        32: q+1
        35: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        42: q+1
        44: q+1
        45: 1
        46: q+1
        48: q^2+2q+1
        49: q+1
        56: q+1
        60: q+1
        61: 2q+1
        64: 1
        67: q+1
        69: q+1
        70: 1
        74: q+1
        75: 2q+1
        78: 2q+1
        80: q+1
        82: 2q+1
        83: q+1
        87: 1
        88: q+1
        91: q+1
        93: 1
        95: q+1
        96: 1
        99: q+1
       101: q+1
       102: 1
       103: q+1
       111: 1
       118: q+1
       122: 1
       123: 1
       128: q+1
       131: 1
       133: 1
       140: q+1
       144: q+1
       145: 2q+1
       148: 1
       151: q+1
       153: q+1
       154: 1
       161: 1
       165: 1
       166: q+1
       169: 1
       174: 1
       175: 1
       179: 1
       180: q+1
       183: q+1
       185: 1
       187: q+1
       188: 1
       197: 1
       205: 1
       212: 1
       224: 1
       227: 1
       235: 1
       242: q+1
       246: 1
       247: 1
       252: q+1
       255: 1
       257: 1
       265: 1
       272: 1
       276: 1
       277: 1
       287: 1
       294: 1
       298: 1
       299: q+1
       302: 1
       307: 1
       308: 1
       327: 1
       335: 1
       355: 1
       364: 1
       372: 1
       379: 1
       391: 1
       394: 1
       403: 1
       418: 1
       441: 1
       448: 1
       452: 1
       453: 1
       463: 1
       491: 1
       534: 1
       542: 1
       562: 1
       618: 1
       633: 1
       730: 1

 731:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        92: 1
        97: 1
        99: 1
       100: 1
       102: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       176: 1
       179: 1
       184: 1
       189: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       288: 1
       319: 1
       336: 1
       343: 1
       344: 1
       356: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       492: 1
       526: 1
       543: 1
       550: 1
       551: 1
       731: 1

 732:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        47: q+1
        48: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       177: 1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       320: 1
       336: 1
       337: 1
       338: 1
       342: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       493: 1
       527: 1
       543: 1
       544: 1
       545: 1
       549: 1
       732: 1

 733:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       177: 1
       191: 1
       199: 1
       201: 1
       202: 1
       213: 1
       215: 1
       216: 1
       217: 1
       221: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       321: 1
       337: 1
       339: 1
       340: 1
       358: 1
       366: 1
       368: 1
       369: 1
       380: 1
       382: 1
       383: 1
       384: 1
       388: 1
       494: 1
       528: 1
       544: 1
       546: 1
       547: 1
       733: 1

 734:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        30: q+1
        31: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: q+1
        59: 1
        61: 1
        65: q+1
        66: q+1
        67: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        81: q+1
        82: q+1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       149: q+1
       150: q+1
       151: 1
       192: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       216: 1
       218: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       322: 1
       338: 1
       339: 1
       341: 1
       359: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       495: 1
       529: 1
       545: 1
       546: 1
       548: 1
       734: 1

 735:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: 1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: q+1
        74: 1
        76: 1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: q+1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       193: 1
       201: 1
       202: 1
       208: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       290: 1
       292: 1
       323: 1
       339: 1
       340: 1
       346: 1
       348: 1
       360: 1
       368: 1
       369: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       496: 1
       530: 1
       546: 1
       547: 1
       553: 1
       555: 1
       735: 1

 736:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       194: 1
       201: 1
       203: 1
       215: 1
       216: 1
       218: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       324: 1
       339: 1
       341: 1
       361: 1
       368: 1
       370: 1
       382: 1
       383: 1
       385: 1
       497: 1
       531: 1
       546: 1
       548: 1
       736: 1

 737:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       177: 1
       195: 1
       202: 1
       203: 1
       204: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       325: 1
       340: 1
       341: 1
       342: 1
       362: 1
       369: 1
       370: 1
       371: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       498: 1
       532: 1
       547: 1
       548: 1
       549: 1
       737: 1

 738:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        92: 1
        98: 1
        99: 1
       100: 1
       102: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       178: 1
       179: 1
       184: 1
       196: 1
       204: 1
       205: 1
       210: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: 1
       292: 1
       326: 1
       342: 1
       343: 1
       348: 1
       363: 1
       371: 1
       372: 1
       377: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       499: 1
       533: 1
       549: 1
       550: 1
       555: 1
       738: 1

 739:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        91: 1
        93: 1
        99: 1
       101: 1
       102: 1
       111: 1
       118: 1
       122: 1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       165: 1
       169: 1
       179: 1
       183: 1
       185: 1
       197: 1
       205: 1
       219: 1
       223: 1
       227: 1
       235: 1
       242: 1
       246: 1
       251: 1
       252: 1
       255: 1
       257: 1
       276: 1
       298: 1
       302: 1
       327: 1
       343: 1
       354: 1
       364: 1
       372: 1
       386: 1
       390: 1
       394: 1
       452: 1
       500: 1
       534: 1
       550: 1
       561: 1
       739: 1

 740:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       148: 1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       161: 1
       173: 1
       175: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       198: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       255: 1
       256: 1
       258: 1
       286: 1
       288: 1
       289: 1
       294: 1
       306: 1
       308: 1
       328: 1
       336: 1
       344: 1
       345: 1
       350: 1
       365: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       434: 1
       462: 1
       501: 1
       535: 1
       543: 1
       551: 1
       552: 1
       557: 1
       740: 1

 741:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        92: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       102: q+1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: q+1
       199: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: 1
       236: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       259: 1
       288: 1
       290: 1
       292: 1
       329: 1
       337: 1
       344: 1
       346: 1
       348: 1
       366: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       435: 1
       502: 1
       536: 1
       544: 1
       551: 1
       553: 1
       555: 1
       741: 1

 742:    0: q^2+q+1
         1: q^2+q+1
         2: 1
         3: q^2+q+1
         4: q^2+q+1
         5: 1
         6: 1
         7: 1
         8: 1
         9: q^2+q+1
        10: 1
        11: 1
        12: q^2+q+1
        13: q^2+q+1
        14: 1
        15: q^2+q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q^2+q+1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: q^2+q+1
        37: 1
        38: 1
        39: q^2+q+1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q^2+q+1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       160: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       184: 1
       186: 1
       188: 1
       200: 1
       207: 1
       208: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       237: 1
       238: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       260: 1
       286: 1
       289: 1
       290: 1
       293: 1
       306: 1
       308: 1
       330: 1
       338: 1
       345: 1
       346: 1
       349: 1
       367: 1
       374: 1
       375: 1
       378: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       436: 1
       462: 1
       503: 1
       537: 1
       545: 1
       552: 1
       553: 1
       556: 1
       742: 1

 743:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: q+1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       114: 1
       115: 1
       119: 1
       120: 1
       121: 1
       124: q+1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       141: q+1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       162: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: 1
       184: 1
       185: 1
       201: 1
       208: 1
       209: 1
       215: 1
       216: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       231: 1
       238: 1
       239: 1
       243: 1
       244: 1
       245: 1
       248: q+1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       273: 1
       290: 1
       291: 1
       295: 1
       300: 1
       302: 1
       331: 1
       339: 1
       346: 1
       347: 1
       351: 1
       368: 1
       375: 1
       376: 1
       382: 1
       383: 1
       387: 1
       388: 1
       389: 1
       392: 1
       394: 1
       437: 1
       449: 1
       504: 1
       538: 1
       546: 1
       553: 1
       554: 1
       558: 1
       743: 1

 744:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        74: q+1
        76: 1
        77: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       115: 1
       116: 1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       127: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: 1
       159: 1
       165: 1
       167: 1
       169: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       202: 1
       209: 1
       210: 1
       216: 1
       217: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       232: 1
       239: 1
       240: 1
       244: 1
       245: 1
       246: 1
       249: 1
       250: 1
       251: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       276: 1
       291: 1
       292: 1
       298: 1
       300: 1
       302: 1
       332: 1
       340: 1
       347: 1
       348: 1
       354: 1
       369: 1
       376: 1
       377: 1
       383: 1
       384: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       438: 1
       452: 1
       505: 1
       539: 1
       547: 1
       554: 1
       555: 1
       561: 1
       744: 1

 745:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        75: q+1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: q+1
        81: q+1
        82: 2q+1
        83: q+1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       109: 1
       115: 1
       117: 1
       120: 1
       121: 1
       123: 1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: 1
       160: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       203: 1
       209: 1
       211: 1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       233: 1
       239: 1
       241: 1
       244: 1
       245: 1
       247: 1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       263: 1
       277: 1
       283: 1
       286: 1
       287: 1
       291: 1
       293: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       333: 1
       341: 1
       347: 1
       349: 1
       355: 1
       370: 1
       376: 1
       378: 1
       383: 1
       385: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       431: 1
       439: 1
       453: 1
       459: 1
       462: 1
       463: 1
       506: 1
       540: 1
       548: 1
       554: 1
       556: 1
       562: 1
       646: 1
       745: 1

 746:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        75: 1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: q+1
       148: 1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       204: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       234: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       251: 1
       252: 1
       254: q+1
       255: 1
       256: 1
       264: 1
       286: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       334: 1
       342: 1
       348: 1
       349: 1
       350: 1
       371: 1
       377: 1
       378: 1
       379: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       391: 1
       440: 1
       462: 1
       507: 1
       541: 1
       549: 1
       555: 1
       556: 1
       557: 1
       746: 1

 747:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        96: 1
        99: 1
       102: 1
       103: 1
       111: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       161: 1
       175: 1
       179: 1
       180: 1
       188: 1
       205: 1
       212: 1
       219: 1
       223: 1
       224: 1
       235: 1
       242: 1
       246: 1
       247: 1
       251: 1
       252: 1
       255: 1
       265: 1
       294: 1
       308: 1
       335: 1
       343: 1
       350: 1
       372: 1
       379: 1
       386: 1
       390: 1
       391: 1
       441: 1
       508: 1
       542: 1
       550: 1
       557: 1
       747: 1

 748:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       112: 1
       119: 1
       122: 1
       124: 1
       127: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       206: 1
       213: 1
       220: 1
       223: 1
       225: 1
       227: 1
       236: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       257: 1
       266: 1
       273: 1
       276: 1
       288: 1
       295: 1
       298: 1
       300: 1
       302: 1
       344: 1
       351: 1
       354: 1
       373: 1
       380: 1
       387: 1
       390: 1
       392: 1
       394: 1
       412: 1
       442: 1
       449: 1
       452: 1
       509: 1
       551: 1
       558: 1
       561: 1
       627: 1
       748: 1

 749:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        24: 1
        25: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        57: 1
        61: 1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       113: 1
       119: 1
       123: 1
       124: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       141: 1
       145: 1
       146: q+1
       148: 1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       156: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       207: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       237: 1
       243: 1
       247: 1
       248: 1
       252: 1
       253: q+1
       255: 1
       256: 1
       257: 1
       267: 1
       273: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       295: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       345: 1
       351: 1
       355: 1
       374: 1
       381: 1
       387: 1
       391: 1
       392: 1
       394: 1
       413: 1
       431: 1
       443: 1
       449: 1
       453: 1
       459: 1
       462: 1
       463: 1
       510: 1
       552: 1
       558: 1
       562: 1
       628: 1
       646: 1
       749: 1

 750:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       114: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       136: 1
       141: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       157: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       208: 1
       215: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       238: 1
       243: 1
       244: 1
       245: 1
       248: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       268: 1
       273: 1
       274: 1
       275: 1
       290: 1
       295: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       346: 1
       351: 1
       352: 1
       353: 1
       375: 1
       382: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       414: 1
       444: 1
       449: 1
       450: 1
       451: 1
       511: 1
       553: 1
       558: 1
       559: 1
       560: 1
       629: 1
       750: 1

 751:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        53: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       115: 1
       120: 1
       121: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       209: 1
       216: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       239: 1
       244: 1
       245: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       269: 1
       274: 1
       275: 1
       291: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       347: 1
       352: 1
       353: 1
       376: 1
       383: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       415: 1
       445: 1
       450: 1
       451: 1
       512: 1
       554: 1
       559: 1
       560: 1
       630: 1
       751: 1

 752:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       116: 1
       121: 1
       122: 1
       126: 1
       127: 1
       130: 1
       131: 1
       132: 1
       133: 1
       138: 1
       143: 1
       144: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       164: 1
       165: 1
       168: 1
       169: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       210: 1
       217: 1
       222: 1
       223: 1
       226: 1
       227: 1
       240: 1
       245: 1
       246: 1
       250: 1
       251: 1
       254: 1
       255: 1
       256: 1
       257: 1
       270: 1
       275: 1
       276: 1
       292: 1
       297: 1
       298: 1
       301: 1
       302: 1
       348: 1
       353: 1
       354: 1
       377: 1
       384: 1
       389: 1
       390: 1
       393: 1
       394: 1
       416: 1
       446: 1
       451: 1
       452: 1
       513: 1
       555: 1
       560: 1
       561: 1
       631: 1
       752: 1

 753:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        24: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        55: 1
        59: 1
        61: 1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        75: 1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        86: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       117: 1
       121: 1
       123: 1
       126: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       139: 1
       143: 1
       145: 1
       147: q+1
       148: 1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       160: 1
       164: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       211: 1
       218: 1
       222: 1
       224: 1
       226: 1
       227: 1
       241: 1
       245: 1
       247: 1
       250: 1
       252: 1
       254: q+1
       255: 1
       256: 1
       257: 1
       271: 1
       275: 1
       277: 1
       284: 1
       286: 1
       287: 1
       293: 1
       297: 1
       299: 1
       301: 1
       302: 1
       304: 1
       306: 1
       307: 1
       308: 1
       349: 1
       353: 1
       355: 1
       378: 1
       385: 1
       389: 1
       391: 1
       393: 1
       394: 1
       417: 1
       432: 1
       447: 1
       451: 1
       453: 1
       460: 1
       462: 1
       463: 1
       514: 1
       556: 1
       560: 1
       562: 1
       632: 1
       647: 1
       753: 1

 754:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: 1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: 1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: q+1
        38: q+1
        39: q+1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: q+1
        70: 1
        74: 1
        75: 1
        78: 1
        80: q+1
        82: q+1
        83: q+1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: q+1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       174: 1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       212: 1
       219: 1
       223: 1
       224: 1
       227: 1
       242: 1
       246: 1
       247: 1
       251: 1
       252: 1
       255: 1
       257: 1
       272: 1
       276: 1
       277: 1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       307: 1
       308: 1
       350: 1
       354: 1
       355: 1
       379: 1
       386: 1
       390: 1
       391: 1
       394: 1
       418: 1
       448: 1
       452: 1
       453: 1
       463: 1
       515: 1
       557: 1
       561: 1
       562: 1
       633: 1
       754: 1

 755:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       221: 1
       225: 1
       226: 1
       230: 1
       237: 1
       238: 1
       241: 1
       249: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       309: 1
       310: 1
       318: 1
       320: 1
       352: 1
       367: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       427: 1
       431: 1
       432: 1
       436: 1
       443: 1
       444: 1
       447: 1
       455: 1
       464: 1
       563: 1
       564: 1
       572: 1
       574: 1
       606: 1
       621: 1
       755: 1

 756:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       129: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       225: 1
       230: 1
       231: 1
       233: 1
       237: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       309: 1
       310: 1
       311: 1
       317: 1
       359: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       431: 1
       436: 1
       437: 1
       439: 1
       443: 1
       465: 1
       563: 1
       564: 1
       565: 1
       571: 1
       613: 1
       756: 1

 757:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: 1
        25: q+1
        27: q+1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        39: 1
        40: 2q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: 2q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        81: 1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       136: q+1
       139: 1
       155: q+1
       156: 1
       157: 2q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       186: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       230: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: 1
       290: q+1
       293: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       420: 1
       426: 1
       436: 1
       466: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       757: 1

 758:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       206: 1
       207: 1
       212: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       311: 1
       312: 1
       313: 1
       328: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       467: 1
       565: 1
       566: 1
       567: 1
       582: 1
       758: 1

 759:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       213: 1
       214: 1
       219: 1
       228: 1
       229: 1
       230: 1
       234: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       278: 1
       281: 1
       282: 1
       283: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       311: 1
       314: 1
       315: 1
       336: 1
       357: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       419: 1
       420: 1
       425: 1
       434: 1
       435: 1
       436: 1
       440: 1
       468: 1
       565: 1
       568: 1
       569: 1
       590: 1
       611: 1
       759: 1

 760:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: q+1
        11: 2q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 2q+1
        24: 1
        25: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        38: q+1
        39: 1
        40: 1
        41: q+1
        42: 2q+1
        43: q+1
        44: q+1
        45: 2q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        64: q+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: q+1
        87: 2q+1
        88: 1
        89: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       118: 1
       119: 1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: q+1
       180: 1
       184: 1
       186: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       206: 1
       213: 1
       219: 1
       220: 1
       223: 1
       229: 1
       234: 1
       235: 1
       256: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       272: 1
       273: 1
       276: q+1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       312: 1
       314: 1
       316: 1
       343: 1
       344: 1
       363: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       412: 1
       419: 1
       425: 1
       426: 1
       429: 1
       435: 1
       440: 1
       441: 1
       462: 1
       469: 1
       566: 1
       568: 1
       570: 1
       597: 1
       598: 1
       617: 1
       760: 1

 761:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: 1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: q+1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        39: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: q+1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: q+1
       129: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: q+1
       186: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       230: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: q+1
       283: 1
       285: 1
       286: 1
       289: 1
       290: 1
       293: 1
       313: 1
       315: 1
       316: 1
       335: 1
       345: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       436: 1
       470: 1
       567: 1
       569: 1
       570: 1
       589: 1
       599: 1
       761: 1

 762:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: q+1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: q+1
       186: 1
       187: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       205: 1
       220: 1
       225: 1
       227: 1
       231: 1
       233: 1
       248: 1
       252: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       316: 1
       317: 1
       327: 1
       351: 1
       361: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       426: 1
       431: 1
       433: 1
       437: 1
       439: 1
       454: 1
       458: 1
       471: 1
       570: 1
       571: 1
       581: 1
       605: 1
       615: 1
       762: 1

 763:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       221: 1
       225: 1
       226: 1
       233: 1
       239: 1
       241: 1
       249: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       317: 1
       318: 1
       325: 1
       352: 1
       370: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       427: 1
       431: 1
       432: 1
       439: 1
       445: 1
       447: 1
       455: 1
       472: 1
       571: 1
       572: 1
       579: 1
       606: 1
       624: 1
       763: 1

 764:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        39: 1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        75: 1
        76: q+1
        78: q+1
        81: 1
        82: 1
        84: q+1
        87: 1
        88: 1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       101: q+1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       141: q+1
       145: 1
       149: 1
       151: 1
       155: 1
       156: 1
       161: 1
       162: q+1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       180: 1
       181: q+1
       183: q+1
       186: 1
       187: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       225: 1
       227: 1
       237: 1
       248: 1
       252: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       295: q+1
       299: 1
       303: 1
       305: 1
       309: 1
       319: 1
       327: 1
       351: 1
       381: 1
       395: 1
       403: 1
       404: 1
       411: 1
       412: 1
       420: 1
       426: 1
       431: 1
       433: 1
       443: 1
       454: 1
       458: 1
       473: 1
       563: 1
       573: 1
       581: 1
       605: 1
       635: 1
       764: 1

 765:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: 2q^2+3q+1
         4: q^2+2q+1
         5: 2q^2+3q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: q+1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q+1
        18: 2q^2+3q+1
        19: q^2+2q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        39: q+1
        40: 2q+1
        41: 2q+1
        42: 2q+1
        43: 2q^2+3q+1
        44: q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: q+1
        51: 1
        52: 2q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        81: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: 1
       136: q+1
       139: 1
       155: q+1
       156: 1
       157: 2q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       186: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       230: 1
       258: 1
       259: q+1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       289: 1
       290: q+1
       293: 1
       310: 1
       319: 1
       320: 1
       326: 1
       329: 1
       338: 1
       346: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       436: 1
       474: 1
       564: 1
       573: 1
       574: 1
       580: 1
       583: 1
       592: 1
       600: 1
       765: 1

 766:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       221: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       427: 1
       475: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       766: 1

 767:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        16: q+1
        17: q+1
        18: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
       105: q+1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       210: 1
       259: q+1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       312: 1
       321: 1
       323: 1
       329: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       416: 1
       476: 1
       566: 1
       575: 1
       577: 1
       583: 1
       767: 1

 768:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: 2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        68: q+1
        69: 1
        72: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 2q+1
        95: q+1
        96: q+1
        97: q+1
        98: 2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       173: q+1
       174: 1
       177: q+1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       334: 1
       398: 1
       399: 1
       401: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       477: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: 1
       588: 1
       768: 1

 769:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q+1
         5: q^2+2q+1
         6: q+1
         7: q^2+2q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       155: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       229: 1
       234: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       314: 1
       321: 1
       324: 1
       325: 1
       337: 1
       342: 1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       427: 1
       435: 1
       440: 1
       478: 1
       568: 1
       575: 1
       578: 1
       579: 1
       591: 1
       596: 1
       769: 1

 770:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       218: 1
       230: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       289: 1
       290: 1
       293: 1
       315: 1
       322: 1
       324: 1
       338: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       420: 1
       421: 1
       424: 1
       436: 1
       479: 1
       569: 1
       576: 1
       578: 1
       592: 1
       770: 1

 771:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        39: 1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        81: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: 1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: q+1
       139: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       186: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       290: q+1
       293: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       346: 1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       416: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       480: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       600: 1
       771: 1

 772:    0: 2q^2+3q+1
         1: 2q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: q^2+2q+1
         5: 2q^2+3q+1
         6: 2q+1
         7: 2q+1
         8: q^2+3q+1
         9: 2q+1
        10: q^2+3q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: 2q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: q^2+2q+1
        21: 2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q^2+3q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: 1
        40: 2q+1
        41: 2q+1
        42: q^2+3q+1
        43: 2q+1
        44: q^2+3q+1
        45: 2q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        53: 2q+1
        54: q+1
        55: 1
        56: q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        78: q+1
        81: 1
        82: 1
        85: 2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: q^2+3q+1
        92: q+1
        93: 2q+1
        94: 1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: 1
       108: q+1
       109: 1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: q+1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       139: 1
       145: 1
       149: 1
       151: 1
       158: 2q+1
       159: q+1
       160: 1
       161: q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: q+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: q+1
       175: 1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       183: q+1
       186: 1
       187: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       218: 1
       221: 1
       222: 1
       225: 1
       227: 1
       233: 1
       252: 1
       262: q+1
       263: 1
       264: 1
       265: 1
       269: q+1
       270: 1
       271: 1
       272: q+1
       274: 1
       275: 1
       276: q+1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       293: 1
       299: 1
       303: 1
       305: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       341: 1
       347: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       422: 1
       424: 1
       427: 1
       428: 1
       431: 1
       433: 1
       439: 1
       458: 1
       481: 1
       571: 1
       579: 1
       580: 1
       581: 1
       586: 1
       595: 1
       601: 1
       772: 1

 773:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: 1
        24: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: 1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        54: 1
        55: 1
        56: 1
        59: q+1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        75: 1
        77: q+1
        78: q+1
        81: 1
        82: 1
        86: q+1
        87: 1
        88: 1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       139: 1
       143: q+1
       145: 1
       150: 1
       151: 1
       159: 1
       160: 1
       161: 1
       164: q+1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       180: 1
       182: q+1
       183: q+1
       186: 1
       187: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: 1
       218: 1
       222: 1
       226: 1
       227: 1
       241: 1
       250: 1
       252: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       293: 1
       297: q+1
       299: 1
       304: 1
       305: 1
       318: 1
       326: 1
       327: 1
       353: 1
       385: 1
       402: 1
       403: 1
       410: 1
       411: 1
       416: 1
       424: 1
       428: 1
       432: 1
       433: 1
       447: 1
       456: 1
       458: 1
       482: 1
       572: 1
       580: 1
       581: 1
       607: 1
       639: 1
       773: 1

 774:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        81: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       180: 1
       186: 1
       189: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: 1
       319: 1
       328: 1
       335: 1
       345: 1
       395: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       483: 1
       573: 1
       582: 1
       589: 1
       599: 1
       774: 1

 775:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       177: 1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       484: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       775: 1

 776:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        16: q+1
        17: q+1
        18: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        62: q+1
        63: q+1
        64: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       191: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       321: 1
       329: 1
       331: 1
       332: 1
       397: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       485: 1
       575: 1
       583: 1
       585: 1
       586: 1
       776: 1

 777:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: 1
       192: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       221: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       322: 1
       330: 1
       331: 1
       333: 1
       398: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       427: 1
       486: 1
       576: 1
       584: 1
       585: 1
       587: 1
       777: 1

 778:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       193: 1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       323: 1
       331: 1
       332: 1
       399: 1
       407: 1
       408: 1
       414: 1
       415: 1
       416: 1
       487: 1
       577: 1
       585: 1
       586: 1
       778: 1

 779:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: q+1
        88: 1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: 1
       139: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       194: 1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       290: 1
       293: 1
       324: 1
       331: 1
       333: 1
       346: 1
       349: 1
       400: 1
       407: 1
       409: 1
       414: 1
       415: 1
       417: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       488: 1
       578: 1
       585: 1
       587: 1
       600: 1
       603: 1
       779: 1

 780:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: 1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       325: 1
       332: 1
       333: 1
       334: 1
       401: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       489: 1
       579: 1
       586: 1
       587: 1
       588: 1
       780: 1

 781:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        81: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       139: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       180: 1
       186: 1
       196: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       218: 1
       222: 1
       224: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       293: 1
       326: 1
       334: 1
       335: 1
       349: 1
       402: 1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       424: 1
       428: 1
       430: 1
       490: 1
       580: 1
       588: 1
       589: 1
       603: 1
       781: 1

 782:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        78: 1
        82: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       103: 1
       111: 1
       118: 1
       122: 1
       123: 1
       128: 1
       131: 1
       133: 1
       145: 1
       151: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       180: 1
       183: 1
       187: 1
       197: 1
       205: 1
       212: 1
       224: 1
       227: 1
       252: 1
       265: 1
       272: 1
       276: 1
       277: 1
       282: 1
       285: 1
       287: 1
       299: 1
       305: 1
       327: 1
       335: 1
       355: 1
       403: 1
       411: 1
       418: 1
       430: 1
       433: 1
       458: 1
       491: 1
       581: 1
       589: 1
       609: 1
       782: 1

 783:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: q+1
        24: 1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        38: q+1
        39: 1
        40: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        74: q+1
        75: 1
        79: q+1
        81: 1
        83: 1
        84: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       102: q+1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: q+1
       135: 1
       140: 1
       152: 1
       154: 1
       155: q+1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       179: q+1
       180: 1
       184: q+1
       186: 1
       188: 1
       189: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       228: 1
       235: 1
       256: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: q+1
       289: 1
       294: 1
       306: 1
       308: 1
       319: 1
       336: 1
       343: 1
       344: 1
       356: 1
       395: 1
       404: 1
       411: 1
       412: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       434: 1
       441: 1
       462: 1
       492: 1
       573: 1
       590: 1
       597: 1
       598: 1
       610: 1
       783: 1

 784:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: q+1
       186: q+1
       188: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: q+1
       320: 1
       336: 1
       337: 1
       338: 1
       342: 1
       357: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       427: 1
       434: 1
       435: 1
       436: 1
       440: 1
       493: 1
       574: 1
       590: 1
       591: 1
       592: 1
       596: 1
       611: 1
       784: 1

 785:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+2q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       155: q+1
       157: 1
       158: 1
       159: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       167: q+1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       199: 1
       201: 1
       202: 1
       213: 1
       215: 1
       216: 1
       217: 1
       221: 1
       229: 1
       231: 1
       232: 1
       236: 1
       248: 1
       251: 1
       253: 1
       259: 1
       261: 1
       262: 1
       266: q+1
       268: 1
       269: 1
       270: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       321: 1
       337: 1
       339: 1
       340: 1
       358: 1
       380: 1
       397: 1
       405: 1
       407: 1
       408: 1
       419: 1
       421: 1
       422: 1
       423: 1
       427: 1
       435: 1
       437: 1
       438: 1
       442: 1
       454: 1
       457: 1
       459: 1
       494: 1
       575: 1
       591: 1
       593: 1
       594: 1
       612: 1
       634: 1
       785: 1

 786:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        30: 2q+1
        31: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: 2q+1
        44: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: q+1
        59: 1
        61: q+1
        65: 2q+1
        66: q+1
        67: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        78: 1
        81: q+1
        82: q+1
        84: q+1
        85: q+1
        86: 1
        88: q+1
        89: 2q+1
        90: q+1
        91: q+1
        94: 2q+1
        95: 2q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       103: q+1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: q+1
       151: 1
       156: q+1
       157: 1
       158: 1
       160: 1
       162: q+1
       163: q+1
       164: 1
       166: q+1
       170: 2q+1
       171: q+1
       172: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: q+1
       183: 1
       186: q+1
       187: q+1
       192: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       216: 1
       218: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: q+1
       268: 1
       269: 1
       271: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: q+1
       305: 1
       322: 1
       338: 1
       339: 1
       341: 1
       359: 1
       381: 1
       398: 1
       406: 1
       407: 1
       409: 1
       420: 1
       421: 1
       422: 1
       424: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       495: 1
       576: 1
       592: 1
       593: 1
       595: 1
       613: 1
       635: 1
       786: 1

 787:    0: 4q^2+4q+1
         1: 2q^2+3q+1
         2: 3q^2+4q+1
         3: 4q^2+4q+1
         4: q^2+3q+1
         5: 4q^2+4q+1
         6: q^2+2q+1
         7: 2q+1
         8: 3q^2+4q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: 2q+1
        13: 2q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 3q^2+4q+1
        18: 4q^2+4q+1
        19: q^2+3q+1
        20: q^2+2q+1
        21: q+1
        22: 2q+1
        23: q^2+2q+1
        25: q+1
        26: q+1
        27: q^2+3q+1
        28: q^2+2q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: q^2+3q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        41: 2q+1
        42: 3q^2+4q+1
        43: 2q^2+3q+1
        44: q^2+3q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        52: q+1
        53: 1
        54: q+1
        57: q+1
        58: 1
        59: q+1
        60: q+1
        62: q+1
        63: 1
        64: 2q+1
        65: 1
        66: q+1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        76: 1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q^2+2q+1
        85: q+1
        86: 2q+1
        87: q^2+2q+1
        89: q+1
        90: q+1
        91: q^2+3q+1
        92: q^2+2q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: q+1
        97: q+1
        98: 2q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: q+1
       127: 1
       129: 1
       130: 1
       131: q+1
       132: 1
       136: q+1
       137: 1
       138: q+1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: 1
       159: q+1
       162: q+1
       163: 1
       164: q+1
       165: q+1
       167: q+1
       168: 1
       169: 2q+1
       170: 1
       171: q+1
       172: 2q+1
       173: 1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       181: 1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: q+1
       188: 1
       193: 1
       201: 1
       202: 1
       208: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: q+1
       281: 1
       283: 1
       284: 1
       285: q+1
       286: 1
       290: q+1
       291: 1
       292: q+1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       323: 1
       339: 1
       340: 1
       346: 1
       348: 1
       360: 1
       387: 1
       390: 1
       399: 1
       407: 1
       408: 1
       414: 1
       416: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       437: 1
       438: 1
       449: 1
       452: 1
       454: 1
       457: 1
       459: 1
       461: 1
       462: 1
       496: 1
       577: 1
       593: 1
       594: 1
       600: 1
       602: 1
       614: 1
       641: 1
       644: 1
       787: 1

 788:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: q^2+1
        18: q^2+1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: q^2+1
        43: 1
        44: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       194: 1
       201: 1
       203: 1
       215: 1
       216: 1
       218: 1
       231: 1
       233: 1
       248: 1
       252: 1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       324: 1
       339: 1
       341: 1
       361: 1
       400: 1
       407: 1
       409: 1
       421: 1
       422: 1
       424: 1
       437: 1
       439: 1
       454: 1
       458: 1
       497: 1
       578: 1
       593: 1
       595: 1
       615: 1
       788: 1

 789:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: 1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       163: 1
       164: 1
       165: q+1
       166: q+1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: q+1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       232: 1
       233: 1
       234: 1
       242: 1
       251: 1
       252: 1
       253: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       325: 1
       340: 1
       341: 1
       342: 1
       362: 1
       386: 1
       401: 1
       408: 1
       409: 1
       410: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       438: 1
       439: 1
       440: 1
       448: 1
       457: 1
       458: 1
       459: 1
       498: 1
       579: 1
       594: 1
       595: 1
       596: 1
       616: 1
       640: 1
       789: 1

 790:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: q+1
        24: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        39: 1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        54: q+1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        74: q+1
        75: 1
        79: q+1
        81: 1
        83: 1
        86: q+1
        87: q+1
        88: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: q+1
       139: 1
       140: 1
       152: 1
       154: 1
       159: q+1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       179: q+1
       180: 1
       184: q+1
       186: 1
       188: 1
       196: 1
       204: 1
       205: 1
       210: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       234: 1
       235: 1
       256: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       280: 1
       281: 1
       282: 1
       284: 1
       285: 1
       286: 1
       292: q+1
       293: 1
       294: 1
       306: 1
       308: 1
       326: 1
       342: 1
       343: 1
       348: 1
       363: 1
       402: 1
       410: 1
       411: 1
       416: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       440: 1
       441: 1
       462: 1
       499: 1
       580: 1
       596: 1
       597: 1
       602: 1
       617: 1
       790: 1

 791:    0: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        14: q^2+2q+1
        15: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        23: 2q+1
        24: q+1
        27: 2q+1
        29: 2q+1
        31: q+1
        32: q+1
        35: q+1
        37: q+1
        38: q+1
        39: 1
        42: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        48: q^2+2q+1
        49: q+1
        56: q+1
        60: 2q+1
        61: q+1
        64: q+1
        67: 1
        69: q+1
        70: 1
        74: q+1
        75: 1
        78: q+1
        80: q+1
        82: 1
        83: 1
        87: 2q+1
        88: q+1
        91: 2q+1
        93: 2q+1
        95: q+1
        96: q+1
        99: q+1
       101: q+1
       102: q+1
       103: 1
       111: 1
       118: q+1
       122: q+1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: q+1
       145: 1
       151: 1
       153: 1
       154: 1
       161: q+1
       165: 2q+1
       166: q+1
       169: q+1
       172: 1
       174: q+1
       175: 1
       179: q+1
       180: 1
       183: q+1
       185: q+1
       187: 1
       188: 1
       197: 1
       205: 1
       219: 1
       223: 1
       227: 1
       235: 1
       242: 1
       251: 1
       252: 1
       257: 1
       265: 1
       272: q+1
       276: q+1
       281: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: q+1
       299: 1
       305: 1
       307: 1
       308: 1
       327: 1
       343: 1
       354: 1
       364: 1
       386: 1
       403: 1
       411: 1
       425: 1
       429: 1
       433: 1
       441: 1
       448: 1
       457: 1
       458: 1
       463: 1
       500: 1
       581: 1
       597: 1
       608: 1
       618: 1
       640: 1
       791: 1

 792:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       198: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: 1
       256: 1
       258: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       288: 1
       289: 1
       294: 1
       306: 1
       308: 1
       328: 1
       336: 1
       344: 1
       345: 1
       350: 1
       404: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: 1
       462: 1
       501: 1
       582: 1
       590: 1
       598: 1
       599: 1
       604: 1
       792: 1

 793:    0: q^2+q+1
         1: q^2+q+1
         2: 1
         3: q^2+q+1
         4: 1
         5: q^2+q+1
         6: 1
         7: 1
         8: 1
         9: q^2+q+1
        10: 1
        11: q^2+q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+q+1
        17: 1
        18: q^2+q+1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q^2+q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: q^2+q+1
        44: 1
        45: q^2+q+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q^2+q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       136: 1
       138: 1
       152: 1
       154: 1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       186: 1
       188: 1
       199: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: 1
       256: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: 1
       290: 1
       292: 1
       306: 1
       308: 1
       329: 1
       337: 1
       344: 1
       346: 1
       348: 1
       405: 1
       412: 1
       414: 1
       416: 1
       419: 1
       421: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       435: 1
       462: 1
       502: 1
       583: 1
       591: 1
       598: 1
       600: 1
       602: 1
       793: 1

 794:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        81: q+1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       103: q+1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       180: 1
       186: q+1
       200: 1
       207: 1
       208: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       260: 1
       267: 1
       268: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       289: 1
       290: 1
       293: 1
       330: 1
       338: 1
       345: 1
       346: 1
       349: 1
       406: 1
       413: 1
       414: 1
       417: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       436: 1
       503: 1
       584: 1
       592: 1
       599: 1
       600: 1
       603: 1
       794: 1

 795:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: q+1
        21: 1
        22: 1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: 1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: q+1
        58: 1
        59: 1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: q+1
        85: 1
        86: 1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       114: 1
       115: 1
       119: q+1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       141: 1
       149: 1
       151: 1
       157: 1
       158: 1
       162: q+1
       163: 1
       164: 1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: 1
       186: 1
       187: 1
       201: 1
       208: 1
       209: 1
       215: 1
       216: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       231: 1
       248: 1
       261: 1
       268: 1
       269: 1
       273: q+1
       274: 1
       275: 1
       278: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       295: 1
       303: 1
       305: 1
       331: 1
       339: 1
       346: 1
       347: 1
       351: 1
       407: 1
       414: 1
       415: 1
       421: 1
       422: 1
       426: 1
       427: 1
       428: 1
       431: 1
       433: 1
       437: 1
       454: 1
       504: 1
       585: 1
       593: 1
       600: 1
       601: 1
       605: 1
       795: 1

 796:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        21: 1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: 1
        42: q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: q+1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: 2q+1
        94: 1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       115: 1
       116: 1
       120: 1
       121: 1
       122: q+1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: q+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: q+1
       175: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       202: 1
       209: 1
       210: 1
       216: 1
       217: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       232: 1
       251: 1
       253: 1
       256: 1
       257: 1
       262: 1
       269: 1
       270: 1
       274: 1
       275: 1
       276: q+1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       298: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       332: 1
       340: 1
       347: 1
       348: 1
       354: 1
       392: 1
       408: 1
       415: 1
       416: 1
       422: 1
       423: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       438: 1
       457: 1
       459: 1
       462: 1
       463: 1
       505: 1
       586: 1
       594: 1
       601: 1
       602: 1
       608: 1
       646: 1
       796: 1

 797:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        21: 1
        22: 1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: q+1
        47: 1
        48: q+1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        88: q+1
        89: 1
        90: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       109: 1
       115: 1
       117: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       145: 1
       149: 1
       151: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: q+1
       167: 1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: q+1
       175: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       203: 1
       209: 1
       211: 1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       233: 1
       252: 1
       263: 1
       269: 1
       271: 1
       274: 1
       275: 1
       277: q+1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       293: 1
       299: 1
       303: 1
       305: 1
       333: 1
       341: 1
       347: 1
       349: 1
       355: 1
       409: 1
       415: 1
       417: 1
       422: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       439: 1
       458: 1
       506: 1
       587: 1
       595: 1
       601: 1
       603: 1
       609: 1
       797: 1

 798:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: q+1
       169: 1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       204: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       234: 1
       256: 1
       264: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       281: 1
       282: 1
       284: q+1
       285: 1
       286: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       334: 1
       342: 1
       348: 1
       349: 1
       350: 1
       410: 1
       416: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       440: 1
       462: 1
       507: 1
       588: 1
       596: 1
       602: 1
       603: 1
       604: 1
       798: 1

 799:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       102: 1
       103: 1
       111: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       140: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: 1
       180: 1
       188: 1
       205: 1
       212: 1
       219: 1
       223: 1
       224: 1
       235: 1
       265: 1
       272: 1
       276: 1
       277: 1
       281: 1
       282: 1
       285: 1
       294: 1
       308: 1
       335: 1
       343: 1
       350: 1
       411: 1
       418: 1
       425: 1
       429: 1
       430: 1
       441: 1
       508: 1
       589: 1
       597: 1
       604: 1
       799: 1

 800:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        23: 1
        25: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        57: 1
        60: 1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       112: 1
       119: 1
       122: 1
       124: 1
       127: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       141: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       162: 1
       165: 1
       167: q+1
       169: 1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       206: 1
       213: 1
       220: 1
       223: 1
       225: 1
       227: 1
       236: 1
       248: 1
       251: 1
       253: 1
       256: 1
       257: 1
       266: 1
       273: 1
       276: 1
       278: 1
       281: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       295: 1
       298: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       344: 1
       351: 1
       354: 1
       380: 1
       392: 1
       412: 1
       419: 1
       426: 1
       429: 1
       431: 1
       433: 1
       442: 1
       454: 1
       457: 1
       459: 1
       462: 1
       463: 1
       509: 1
       598: 1
       605: 1
       608: 1
       634: 1
       646: 1
       800: 1

 801:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       101: 1
       103: 1
       113: 1
       119: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       141: 1
       145: 1
       149: 1
       151: 1
       156: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       207: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       237: 1
       248: 1
       252: 1
       267: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       295: 1
       299: 1
       303: 1
       305: 1
       345: 1
       351: 1
       355: 1
       381: 1
       413: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       443: 1
       454: 1
       458: 1
       510: 1
       599: 1
       605: 1
       609: 1
       635: 1
       801: 1

 802:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       103: q+1
       114: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       136: 1
       141: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       157: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       208: 1
       215: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       238: 1
       248: 1
       249: 1
       250: 1
       268: 1
       273: 1
       274: 1
       275: 1
       278: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: 1
       295: 1
       296: 1
       297: 1
       303: 1
       304: 1
       305: 1
       346: 1
       351: 1
       352: 1
       353: 1
       382: 1
       414: 1
       421: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       444: 1
       454: 1
       455: 1
       456: 1
       511: 1
       600: 1
       605: 1
       606: 1
       607: 1
       636: 1
       802: 1

 803:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       115: 1
       120: 1
       121: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       158: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       209: 1
       216: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       239: 1
       249: 1
       250: 1
       269: 1
       274: 1
       275: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       296: 1
       297: 1
       303: 1
       304: 1
       305: 1
       347: 1
       352: 1
       353: 1
       383: 1
       415: 1
       422: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       445: 1
       455: 1
       456: 1
       512: 1
       601: 1
       606: 1
       607: 1
       637: 1
       803: 1

 804:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: 1
        23: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        54: 1
        59: 1
        60: 1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       116: 1
       121: 1
       122: 1
       126: 1
       127: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: 1
       143: 1
       144: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       164: 1
       165: 1
       168: q+1
       169: 1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       210: 1
       217: 1
       222: 1
       223: 1
       226: 1
       227: 1
       240: 1
       250: 1
       251: 1
       254: 1
       256: 1
       257: 1
       270: 1
       275: 1
       276: 1
       280: 1
       281: 1
       284: q+1
       285: 1
       286: 1
       287: 1
       292: 1
       297: 1
       298: 1
       301: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       348: 1
       353: 1
       354: 1
       384: 1
       393: 1
       416: 1
       423: 1
       428: 1
       429: 1
       432: 1
       433: 1
       446: 1
       456: 1
       457: 1
       460: 1
       462: 1
       463: 1
       513: 1
       602: 1
       607: 1
       608: 1
       638: 1
       647: 1
       804: 1

 805:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        55: 1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       117: 1
       121: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       139: 1
       143: 1
       145: 1
       150: 1
       151: 1
       160: 1
       164: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       187: 1
       211: 1
       218: 1
       222: 1
       224: 1
       226: 1
       227: 1
       241: 1
       250: 1
       252: 1
       271: 1
       275: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       293: 1
       297: 1
       299: 1
       304: 1
       305: 1
       349: 1
       353: 1
       355: 1
       385: 1
       417: 1
       424: 1
       428: 1
       430: 1
       432: 1
       433: 1
       447: 1
       456: 1
       458: 1
       514: 1
       603: 1
       607: 1
       609: 1
       639: 1
       805: 1

 806:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: 1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: 1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: q+1
        45: q+1
        46: q+1
        48: q+1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: q+1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: q+1
        95: q+1
        96: q+1
        99: 1
       101: 1
       102: 1
       103: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       151: 1
       153: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: q+1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       212: 1
       219: 1
       223: 1
       224: 1
       227: 1
       242: 1
       251: 1
       252: 1
       257: 1
       272: 1
       276: 1
       277: 1
       281: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: 1
       299: 1
       305: 1
       307: 1
       308: 1
       350: 1
       354: 1
       355: 1
       386: 1
       418: 1
       425: 1
       429: 1
       430: 1
       433: 1
       448: 1
       457: 1
       458: 1
       463: 1
       515: 1
       604: 1
       608: 1
       609: 1
       640: 1
       806: 1

 807:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       129: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: 1
       225: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       253: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       309: 1
       356: 1
       364: 1
       365: 1
       392: 1
       395: 1
       403: 1
       404: 1
       431: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       459: 1
       462: 1
       463: 1
       516: 1
       563: 1
       610: 1
       618: 1
       619: 1
       646: 1
       807: 1

 808:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        28: 1
        30: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        68: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       190: 1
       196: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       517: 1
       564: 1
       610: 1
       611: 1
       617: 1
       808: 1

 809:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 2q+1
        14: 2q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: 1
        19: 2q+1
        20: 1
        21: 2q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 2q+1
        34: 2q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 2q+1
        41: 2q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 2q+1
        48: 2q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        71: 1
        72: 2q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 2q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       129: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       176: 1
       177: 2q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       253: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       283: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       311: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       459: 1
       518: 1
       565: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       809: 1

 810:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        60: 1
        62: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       119: 1
       122: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       191: 1
       193: 1
       206: 1
       229: 1
       231: 1
       232: 1
       236: 1
       243: 1
       246: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       312: 1
       358: 1
       360: 1
       373: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       519: 1
       566: 1
       612: 1
       614: 1
       627: 1
       810: 1

 811:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: 1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: q+1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       152: 1
       153: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: q+1
       188: 1
       192: 1
       193: 1
       195: 1
       207: 1
       212: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       253: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       313: 1
       359: 1
       360: 1
       362: 1
       374: 1
       379: 1
       398: 1
       399: 1
       401: 1
       413: 1
       418: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       520: 1
       567: 1
       613: 1
       614: 1
       616: 1
       628: 1
       633: 1
       811: 1

 812:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: q+1
        24: 1
        25: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: q+1
        75: 1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: q+1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       170: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: 1
       194: 1
       195: 1
       213: 1
       219: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       272: 1
       278: 1
       281: 1
       282: 1
       283: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       314: 1
       358: 1
       361: 1
       362: 1
       380: 1
       386: 1
       397: 1
       400: 1
       401: 1
       419: 1
       425: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       521: 1
       568: 1
       612: 1
       615: 1
       616: 1
       634: 1
       640: 1
       812: 1

 813:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        61: 1
        65: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       124: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       170: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       192: 1
       194: 1
       214: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: 1
       278: 1
       282: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       315: 1
       359: 1
       361: 1
       381: 1
       398: 1
       400: 1
       420: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       522: 1
       569: 1
       613: 1
       615: 1
       635: 1
       813: 1

 814:    0: q^2+3q+1
         1: 2q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q+1
         7: 2q+1
         8: q^2+3q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: 2q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: q+1
        25: 1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: 2q+1
        35: q^2+3q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: q^2+3q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: q+1
        76: 1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: 1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: 2q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: 1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       220: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       387: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       426: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       523: 1
       570: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       641: 1
       814: 1

 815:    0: q+1
         1: 1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       129: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       225: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       253: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       283: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       317: 1
       362: 1
       363: 1
       364: 1
       392: 1
       401: 1
       402: 1
       403: 1
       431: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       459: 1
       462: 1
       463: 1
       524: 1
       571: 1
       616: 1
       617: 1
       618: 1
       646: 1
       815: 1

 816:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       130: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       152: 1
       153: 1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       171: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: 1
       226: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       254: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       284: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       304: 1
       306: 1
       307: 1
       308: 1
       318: 1
       363: 1
       364: 1
       371: 1
       393: 1
       402: 1
       403: 1
       410: 1
       432: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       460: 1
       462: 1
       463: 1
       525: 1
       572: 1
       617: 1
       618: 1
       625: 1
       647: 1
       816: 1

 817:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         6: 3q+1
         8: 3q+1
         9: 3q+1
        10: q+1
        11: q+1
        12: q+1
        13: 3q+1
        14: 3q+1
        15: 3q+1
        16: 3q+1
        17: 3q+1
        18: 3q+1
        19: 3q+1
        20: 3q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 3q+1
        35: 3q+1
        36: 3q+1
        37: q+1
        38: q+1
        39: q+1
        40: 3q+1
        42: 3q+1
        43: 3q+1
        44: q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: 3q+1
        49: 3q+1
        50: q+1
        51: q+1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 3q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 3q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: 3q+1
        99: 3q+1
       100: 3q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: q+1
       135: q+1
       140: 1
       141: q+1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       161: 1
       162: q+1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 3q+1
       179: q+1
       180: q+1
       181: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: 1
       189: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: q+1
       289: q+1
       294: 1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       319: 1
       356: 1
       365: 1
       372: 1
       373: 1
       381: 1
       387: 1
       395: 1
       404: 1
       411: 1
       412: 1
       420: 1
       426: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       526: 1
       573: 1
       610: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       817: 1

 818:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q+1
         3: q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q+1
         7: 2q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: 2q^2+3q+1
        14: 2q+1
        15: q+1
        16: 2q^2+3q+1
        17: 2q+1
        18: q+1
        19: 2q^2+3q+1
        20: 1
        21: 2q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 2q+1
        41: 2q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: 2q^2+3q+1
        48: 2q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        71: 1
        72: 2q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 2q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 2q+1
        98: 2q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: q+1
       153: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       176: 1
       177: 2q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       320: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       388: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       427: 1
       434: 1
       435: 1
       436: 1
       440: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       527: 1
       574: 1
       611: 1
       619: 1
       620: 1
       621: 1
       625: 1
       642: 1
       818: 1

 819:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       120: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       191: 1
       199: 1
       201: 1
       202: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       244: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       274: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       321: 1
       358: 1
       366: 1
       368: 1
       369: 1
       397: 1
       405: 1
       407: 1
       408: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       450: 1
       528: 1
       575: 1
       612: 1
       620: 1
       622: 1
       623: 1
       819: 1

 820:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       125: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       192: 1
       200: 1
       201: 1
       203: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       249: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       279: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       322: 1
       359: 1
       367: 1
       368: 1
       370: 1
       398: 1
       406: 1
       407: 1
       409: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       455: 1
       529: 1
       576: 1
       613: 1
       621: 1
       622: 1
       624: 1
       820: 1

 821:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        62: 1
        63: 1
        64: 1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       136: q+1
       137: 1
       138: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       146: 1
       147: 1
       148: 1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       193: 1
       201: 1
       202: 1
       208: 1
       210: 1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       323: 1
       360: 1
       368: 1
       369: 1
       375: 1
       377: 1
       399: 1
       407: 1
       408: 1
       414: 1
       416: 1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       530: 1
       577: 1
       614: 1
       622: 1
       623: 1
       629: 1
       631: 1
       821: 1

 822:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        30: q+1
        31: 1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        55: q+1
        57: 1
        58: 1
        59: q+1
        61: 1
        65: 1
        66: 1
        67: 1
        71: q+1
        72: q+1
        73: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        81: q+1
        82: 1
        84: q+1
        85: q+1
        86: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        94: q+1
        95: 1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       103: q+1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: q+1
       145: 1
       149: 1
       150: 1
       151: 1
       157: q+1
       158: 1
       160: q+1
       162: 1
       163: 1
       164: q+1
       166: 1
       170: 1
       171: 1
       172: 1
       176: q+1
       177: q+1
       178: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       186: q+1
       187: 1
       194: 1
       201: 1
       203: 1
       215: 1
       218: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: q+1
       299: 1
       303: 1
       304: 1
       305: 1
       324: 1
       361: 1
       368: 1
       370: 1
       382: 1
       385: 1
       400: 1
       407: 1
       409: 1
       421: 1
       424: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       531: 1
       578: 1
       615: 1
       622: 1
       624: 1
       636: 1
       639: 1
       822: 1

 823:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 2q+1
        14: 2q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: 1
        19: 2q+1
        21: 2q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 2q+1
        34: 2q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 2q+1
        41: 2q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 2q+1
        48: 2q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 2q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 2q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 2q+1
        98: 2q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: 2q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       221: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       325: 1
       362: 1
       369: 1
       370: 1
       371: 1
       388: 1
       401: 1
       408: 1
       409: 1
       410: 1
       427: 1
       438: 1
       439: 1
       440: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       532: 1
       579: 1
       616: 1
       623: 1
       624: 1
       625: 1
       642: 1
       823: 1

 824:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         7: 3q+1
         8: 3q+1
         9: 3q+1
        10: q+1
        11: q+1
        12: q+1
        13: 3q+1
        14: 3q+1
        15: 3q+1
        16: 3q+1
        17: 3q+1
        18: 3q+1
        19: 3q+1
        22: 3q+1
        23: q+1
        24: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: 3q+1
        35: 3q+1
        36: 3q+1
        37: q+1
        38: q+1
        39: q+1
        41: 3q+1
        42: 3q+1
        43: 3q+1
        44: q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: 3q+1
        49: 3q+1
        54: q+1
        55: q+1
        56: 1
        59: q+1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 3q+1
        74: q+1
        75: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: 1
        86: 3q+1
        87: q+1
        88: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: 1
        98: 3q+1
        99: 3q+1
       100: 3q+1
       101: q+1
       102: q+1
       103: q+1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: q+1
       139: q+1
       140: 1
       143: q+1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: q+1
       160: q+1
       161: 1
       164: q+1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 3q+1
       179: q+1
       180: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: 1
       196: 1
       204: 1
       205: 1
       210: 1
       218: 1
       222: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       250: 1
       252: 1
       254: 1
       255: 1
       256: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       292: q+1
       293: q+1
       294: 1
       297: q+1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       326: 1
       363: 1
       371: 1
       372: 1
       377: 1
       385: 1
       389: 1
       402: 1
       410: 1
       411: 1
       416: 1
       424: 1
       428: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       456: 1
       458: 1
       460: 1
       461: 1
       462: 1
       533: 1
       580: 1
       617: 1
       625: 1
       626: 1
       631: 1
       639: 1
       643: 1
       824: 1

 825:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: 1
        12: 1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: 1
        27: q+1
        29: 1
        31: 1
        32: 1
        35: q+1
        37: q+1
        38: 1
        39: 1
        42: q+1
        44: q+1
        45: 1
        46: 1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        78: q+1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        91: q+1
        93: 1
        95: 1
        96: 1
        99: q+1
       101: q+1
       102: 1
       103: 1
       111: 1
       118: 1
       122: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: 1
       180: 1
       183: q+1
       185: 1
       187: 1
       188: 1
       197: 1
       205: 1
       227: 1
       235: 1
       242: 1
       246: 1
       252: 1
       255: 1
       257: 1
       265: 1
       272: 1
       276: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       327: 1
       364: 1
       372: 1
       394: 1
       403: 1
       411: 1
       433: 1
       441: 1
       448: 1
       452: 1
       458: 1
       461: 1
       463: 1
       534: 1
       581: 1
       618: 1
       626: 1
       648: 1
       825: 1

 826:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       152: 1
       153: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       198: 1
       206: 1
       207: 1
       212: 1
       228: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       253: 1
       258: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       328: 1
       365: 1
       373: 1
       374: 1
       379: 1
       404: 1
       412: 1
       413: 1
       418: 1
       434: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       535: 1
       582: 1
       619: 1
       627: 1
       628: 1
       633: 1
       826: 1

 827:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       199: 1
       206: 1
       208: 1
       210: 1
       229: 1
       236: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       329: 1
       366: 1
       373: 1
       375: 1
       377: 1
       405: 1
       412: 1
       414: 1
       416: 1
       435: 1
       442: 1
       444: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       536: 1
       583: 1
       620: 1
       627: 1
       629: 1
       631: 1
       827: 1

 828:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: q+1
       153: 1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       200: 1
       207: 1
       208: 1
       211: 1
       221: 1
       230: 1
       237: 1
       238: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       249: 1
       253: 1
       254: 1
       260: 1
       267: 1
       268: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       330: 1
       367: 1
       374: 1
       375: 1
       378: 1
       388: 1
       406: 1
       413: 1
       414: 1
       417: 1
       427: 1
       436: 1
       443: 1
       444: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       455: 1
       459: 1
       460: 1
       537: 1
       584: 1
       621: 1
       628: 1
       629: 1
       632: 1
       642: 1
       828: 1

 829:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       114: 1
       115: 1
       119: 1
       120: 1
       121: 1
       136: 1
       137: 1
       141: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       157: 1
       158: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       201: 1
       208: 1
       209: 1
       231: 1
       238: 1
       239: 1
       243: 1
       244: 1
       245: 1
       261: 1
       268: 1
       269: 1
       273: 1
       274: 1
       275: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       331: 1
       368: 1
       375: 1
       376: 1
       407: 1
       414: 1
       415: 1
       437: 1
       444: 1
       445: 1
       449: 1
       450: 1
       451: 1
       538: 1
       585: 1
       622: 1
       629: 1
       630: 1
       829: 1

 830:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       115: 1
       116: 1
       120: 1
       121: 1
       122: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       202: 1
       209: 1
       210: 1
       232: 1
       239: 1
       240: 1
       244: 1
       245: 1
       246: 1
       262: 1
       269: 1
       270: 1
       274: 1
       275: 1
       276: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       332: 1
       369: 1
       376: 1
       377: 1
       408: 1
       415: 1
       416: 1
       438: 1
       445: 1
       446: 1
       450: 1
       451: 1
       452: 1
       539: 1
       586: 1
       623: 1
       630: 1
       631: 1
       830: 1

 831:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       109: 1
       115: 1
       117: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       203: 1
       209: 1
       211: 1
       221: 1
       233: 1
       239: 1
       241: 1
       244: 1
       245: 1
       247: 1
       249: 1
       253: 1
       254: 1
       263: 1
       269: 1
       271: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       333: 1
       370: 1
       376: 1
       378: 1
       388: 1
       409: 1
       415: 1
       417: 1
       427: 1
       439: 1
       445: 1
       447: 1
       450: 1
       451: 1
       453: 1
       455: 1
       459: 1
       460: 1
       540: 1
       587: 1
       624: 1
       630: 1
       632: 1
       642: 1
       831: 1

 832:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        68: 1
        69: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       130: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       152: 1
       153: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       204: 1
       210: 1
       211: 1
       212: 1
       234: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       254: 1
       264: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       284: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       306: 1
       307: 1
       334: 1
       371: 1
       377: 1
       378: 1
       379: 1
       410: 1
       416: 1
       417: 1
       418: 1
       440: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       460: 1
       541: 1
       588: 1
       625: 1
       631: 1
       632: 1
       633: 1
       832: 1

 833:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: 1
        11: 1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: q+1
        27: 1
        29: 1
        31: 1
        32: 1
        35: q+1
        37: 1
        38: 1
        39: q+1
        42: q+1
        44: 1
        45: 1
        46: q+1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: q+1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: q+1
        91: 1
        93: 1
        95: 1
        96: 1
        99: q+1
       101: 1
       102: 1
       103: q+1
       111: 1
       118: 1
       122: 1
       123: 1
       128: 1
       131: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: 1
       180: q+1
       183: 1
       185: 1
       187: 1
       188: 1
       205: 1
       212: 1
       224: 1
       235: 1
       242: 1
       246: 1
       247: 1
       252: 1
       255: 1
       265: 1
       272: 1
       276: 1
       277: 1
       282: 1
       285: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       335: 1
       372: 1
       379: 1
       391: 1
       411: 1
       418: 1
       430: 1
       441: 1
       448: 1
       452: 1
       453: 1
       458: 1
       461: 1
       542: 1
       589: 1
       626: 1
       633: 1
       645: 1
       833: 1

 834:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       172: 1
       173: 1
       174: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       198: 1
       213: 1
       214: 1
       219: 1
       228: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       258: 1
       266: 1
       267: 1
       272: 1
       278: 1
       281: 1
       282: 1
       283: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       336: 1
       365: 1
       380: 1
       381: 1
       386: 1
       404: 1
       419: 1
       420: 1
       425: 1
       434: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       543: 1
       590: 1
       619: 1
       634: 1
       635: 1
       640: 1
       834: 1

 835:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       105: 1
       112: 1
       114: 1
       116: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       199: 1
       213: 1
       215: 1
       217: 1
       221: 1
       229: 1
       236: 1
       238: 1
       240: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       259: 1
       266: 1
       268: 1
       270: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       337: 1
       366: 1
       380: 1
       382: 1
       384: 1
       388: 1
       405: 1
       419: 1
       421: 1
       423: 1
       427: 1
       435: 1
       442: 1
       444: 1
       446: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       544: 1
       591: 1
       620: 1
       634: 1
       636: 1
       638: 1
       642: 1
       835: 1

 836:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: q+1
        95: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       103: q+1
       106: 1
       113: 1
       114: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       200: 1
       214: 1
       215: 1
       218: 1
       230: 1
       237: 1
       238: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       260: 1
       267: 1
       268: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       338: 1
       367: 1
       381: 1
       382: 1
       385: 1
       406: 1
       420: 1
       421: 1
       424: 1
       436: 1
       443: 1
       444: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       545: 1
       592: 1
       621: 1
       635: 1
       636: 1
       639: 1
       836: 1

 837:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       114: 1
       115: 1
       124: 1
       125: 1
       126: 1
       136: 1
       137: 1
       141: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       157: 1
       158: 1
       162: 1
       163: 1
       164: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       201: 1
       215: 1
       216: 1
       231: 1
       238: 1
       239: 1
       248: 1
       249: 1
       250: 1
       261: 1
       268: 1
       269: 1
       278: 1
       279: 1
       280: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       303: 1
       304: 1
       305: 1
       339: 1
       368: 1
       382: 1
       383: 1
       407: 1
       421: 1
       422: 1
       437: 1
       444: 1
       445: 1
       454: 1
       455: 1
       456: 1
       546: 1
       593: 1
       622: 1
       636: 1
       637: 1
       837: 1

 838:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       115: 1
       116: 1
       120: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       202: 1
       216: 1
       217: 1
       221: 1
       232: 1
       239: 1
       240: 1
       244: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       262: 1
       269: 1
       270: 1
       274: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       340: 1
       369: 1
       383: 1
       384: 1
       388: 1
       408: 1
       422: 1
       423: 1
       427: 1
       438: 1
       445: 1
       446: 1
       450: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       547: 1
       594: 1
       623: 1
       637: 1
       638: 1
       642: 1
       838: 1

 839:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       109: 1
       115: 1
       117: 1
       125: 1
       126: 1
       128: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       172: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       203: 1
       216: 1
       218: 1
       233: 1
       239: 1
       241: 1
       249: 1
       250: 1
       252: 1
       263: 1
       269: 1
       271: 1
       279: 1
       280: 1
       282: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       341: 1
       370: 1
       383: 1
       385: 1
       409: 1
       422: 1
       424: 1
       439: 1
       445: 1
       447: 1
       455: 1
       456: 1
       458: 1
       548: 1
       595: 1
       624: 1
       637: 1
       639: 1
       839: 1

 840:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        66: 1
        67: 1
        68: 1
        69: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       126: 1
       127: 1
       128: 1
       130: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       171: 1
       172: 1
       173: 1
       174: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       204: 1
       217: 1
       218: 1
       219: 1
       234: 1
       240: 1
       241: 1
       242: 1
       250: 1
       251: 1
       252: 1
       254: 1
       264: 1
       270: 1
       271: 1
       272: 1
       280: 1
       281: 1
       282: 1
       284: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       304: 1
       305: 1
       306: 1
       307: 1
       342: 1
       371: 1
       384: 1
       385: 1
       386: 1
       410: 1
       423: 1
       424: 1
       425: 1
       440: 1
       446: 1
       447: 1
       448: 1
       456: 1
       457: 1
       458: 1
       460: 1
       549: 1
       596: 1
       625: 1
       638: 1
       639: 1
       640: 1
       840: 1

 841:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: 1
        11: q+1
        12: 1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: q+1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: q+1
        37: 1
        38: q+1
        39: 1
        42: q+1
        44: 1
        45: q+1
        46: 1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: q+1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: q+1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: q+1
       101: 1
       102: q+1
       103: 1
       111: 1
       118: 1
       122: 1
       127: 1
       128: 1
       131: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: q+1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       205: 1
       219: 1
       223: 1
       235: 1
       242: 1
       246: 1
       251: 1
       252: 1
       255: 1
       265: 1
       272: 1
       276: 1
       281: 1
       282: 1
       285: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       343: 1
       372: 1
       386: 1
       390: 1
       411: 1
       425: 1
       429: 1
       441: 1
       448: 1
       452: 1
       457: 1
       458: 1
       461: 1
       550: 1
       597: 1
       626: 1
       640: 1
       644: 1
       841: 1

 842:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: q+1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        40: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        57: 1
        60: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        74: q+1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        87: q+1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       112: 1
       119: 1
       122: 1
       124: 1
       127: 1
       129: 1
       131: 1
       132: 1
       134: q+1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       162: 1
       165: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       179: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       206: 1
       213: 1
       220: 1
       223: 1
       236: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       266: 1
       273: 1
       276: 1
       278: 1
       281: 1
       283: 1
       285: 1
       286: 1
       288: q+1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       344: 1
       373: 1
       380: 1
       387: 1
       390: 1
       412: 1
       419: 1
       426: 1
       429: 1
       442: 1
       449: 1
       452: 1
       454: 1
       457: 1
       459: 1
       461: 1
       462: 1
       551: 1
       598: 1
       627: 1
       634: 1
       641: 1
       644: 1
       842: 1

 843:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        24: q+1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        75: q+1
        76: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        88: q+1
        89: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       113: 1
       119: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: q+1
       141: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       156: q+1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       180: q+1
       181: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       207: 1
       214: 1
       220: 1
       224: 1
       237: 1
       243: 1
       247: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       267: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: q+1
       295: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       345: 1
       374: 1
       381: 1
       387: 1
       391: 1
       413: 1
       420: 1
       426: 1
       430: 1
       443: 1
       449: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       552: 1
       599: 1
       628: 1
       635: 1
       641: 1
       645: 1
       843: 1

 844:    0: 2q+1
         1: 2q+1
         2: q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 1
        11: q+1
        12: q+1
        13: 2q+1
        14: q+1
        15: 2q+1
        16: 2q+1
        17: q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: 2q+1
        44: 1
        45: q+1
        46: q+1
        47: 2q+1
        48: q+1
        49: 2q+1
        52: q+1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 2q+1
       101: 1
       102: q+1
       103: q+1
       114: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: q+1
       141: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: q+1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: 1
       208: 1
       215: 1
       220: 1
       221: 1
       222: 1
       238: 1
       243: 1
       244: 1
       245: 1
       248: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       268: 1
       273: 1
       274: 1
       275: 1
       278: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       290: q+1
       295: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       346: 1
       375: 1
       382: 1
       387: 1
       388: 1
       389: 1
       414: 1
       421: 1
       426: 1
       427: 1
       428: 1
       444: 1
       449: 1
       450: 1
       451: 1
       454: 1
       455: 1
       456: 1
       459: 1
       460: 1
       461: 1
       462: 1
       553: 1
       600: 1
       629: 1
       636: 1
       641: 1
       642: 1
       643: 1
       844: 1

 845:    0: q^2+3q+1
         1: 2q+1
         2: q^2+3q+1
         3: 3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: 2q+1
        10: 3q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: q^2+3q+1
        15: 3q+1
        16: 2q+1
        17: q^2+3q+1
        18: 3q+1
        19: q^2+3q+1
        21: q+1
        22: q+1
        25: 2q+1
        26: 1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 3q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: 3q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+3q+1
        49: 3q+1
        53: q+1
        58: 1
        59: 1
        62: q+1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: q+1
        73: q+1
        76: 2q+1
        77: 1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: 2q+1
        83: q+1
        85: q+1
        86: q+1
        89: 2q+1
        90: 1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 3q+1
       102: 2q+1
       103: 2q+1
       115: 1
       120: 1
       121: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       142: 1
       143: 1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: q+1
       163: 1
       164: 1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: 1
       177: q+1
       178: q+1
       181: 2q+1
       182: 1
       183: 2q+1
       184: q+1
       185: 2q+1
       186: q+1
       187: 2q+1
       188: q+1
       209: 1
       216: 1
       221: 1
       222: 1
       225: 1
       227: 1
       239: 1
       244: 1
       245: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       269: 1
       274: 1
       275: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       296: 1
       297: 1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: q+1
       308: 1
       347: 1
       376: 1
       383: 1
       388: 1
       389: 1
       392: 1
       394: 1
       415: 1
       422: 1
       427: 1
       428: 1
       431: 1
       433: 1
       445: 1
       450: 1
       451: 1
       455: 1
       456: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       554: 1
       601: 1
       630: 1
       637: 1
       642: 1
       643: 1
       646: 1
       648: 1
       845: 1

 846:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: q+1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        54: q+1
        59: 1
        60: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        74: q+1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        86: q+1
        87: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       116: 1
       121: 1
       122: 1
       126: 1
       127: 1
       130: 1
       131: 1
       132: 1
       138: q+1
       143: 1
       144: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: q+1
       164: 1
       165: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       179: q+1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       210: 1
       217: 1
       222: 1
       223: 1
       240: 1
       245: 1
       246: 1
       250: 1
       251: 1
       254: 1
       255: 1
       256: 1
       270: 1
       275: 1
       276: 1
       280: 1
       281: 1
       284: 1
       285: 1
       286: 1
       292: q+1
       297: 1
       298: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       348: 1
       377: 1
       384: 1
       389: 1
       390: 1
       416: 1
       423: 1
       428: 1
       429: 1
       446: 1
       451: 1
       452: 1
       456: 1
       457: 1
       460: 1
       461: 1
       462: 1
       555: 1
       602: 1
       631: 1
       638: 1
       643: 1
       644: 1
       846: 1

 847:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        24: q+1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        55: q+1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        75: q+1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        86: q+1
        88: q+1
        90: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       117: 1
       121: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       139: q+1
       143: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       160: q+1
       164: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       180: q+1
       182: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       211: 1
       218: 1
       222: 1
       224: 1
       241: 1
       245: 1
       247: 1
       250: 1
       252: 1
       254: 1
       255: 1
       256: 1
       271: 1
       275: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       293: q+1
       297: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       349: 1
       378: 1
       385: 1
       389: 1
       391: 1
       417: 1
       424: 1
       428: 1
       430: 1
       447: 1
       451: 1
       453: 1
       456: 1
       458: 1
       460: 1
       461: 1
       462: 1
       556: 1
       603: 1
       632: 1
       639: 1
       643: 1
       645: 1
       847: 1

 848:    0: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         8: q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        14: q^2+2q+1
        15: 2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        23: q+1
        24: q+1
        27: 1
        29: q+1
        31: q+1
        32: 2q+1
        35: q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        42: q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        48: q^2+2q+1
        49: 2q+1
        56: q+1
        60: 1
        61: 1
        64: 1
        67: 1
        69: q+1
        70: q+1
        74: q+1
        75: q+1
        78: 1
        80: q+1
        82: q+1
        83: 2q+1
        87: q+1
        88: q+1
        91: 1
        93: q+1
        95: q+1
        96: 2q+1
        99: q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       140: q+1
       144: 1
       145: 1
       148: 1
       151: 1
       153: q+1
       154: q+1
       161: q+1
       165: 1
       166: 1
       169: 1
       172: 1
       174: q+1
       175: q+1
       179: q+1
       180: q+1
       183: 1
       185: q+1
       187: q+1
       188: 2q+1
       212: 1
       219: 1
       223: 1
       224: 1
       242: 1
       246: 1
       247: 1
       251: 1
       252: 1
       255: 1
       272: 1
       276: 1
       277: 1
       281: 1
       282: 1
       285: 1
       294: q+1
       298: 1
       299: 1
       302: 1
       305: 1
       307: q+1
       308: q+1
       350: 1
       379: 1
       386: 1
       390: 1
       391: 1
       418: 1
       425: 1
       429: 1
       430: 1
       448: 1
       452: 1
       453: 1
       457: 1
       458: 1
       461: 1
       557: 1
       604: 1
       633: 1
       640: 1
       644: 1
       645: 1
       848: 1

 849:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        57: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       119: 1
       124: 1
       129: 1
       131: 1
       132: 1
       133: 1
       141: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       162: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       220: 1
       225: 1
       227: 1
       243: 1
       248: 1
       253: 1
       255: 1
       256: 1
       257: 1
       273: 1
       278: 1
       283: 1
       285: 1
       286: 1
       287: 1
       295: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       351: 1
       387: 1
       392: 1
       394: 1
       426: 1
       431: 1
       433: 1
       449: 1
       454: 1
       459: 1
       461: 1
       462: 1
       463: 1
       558: 1
       605: 1
       641: 1
       646: 1
       648: 1
       849: 1

 850:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        25: 1
        26: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        58: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        72: 1
        76: 1
        77: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        89: 1
        90: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       100: 1
       101: 1
       102: 1
       103: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       142: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       154: 1
       163: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: 1
       181: 1
       182: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       221: 1
       225: 1
       226: 1
       244: 1
       249: 1
       253: 1
       254: 1
       256: 1
       257: 1
       274: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       296: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       352: 1
       388: 1
       392: 1
       393: 1
       427: 1
       431: 1
       432: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       559: 1
       606: 1
       642: 1
       646: 1
       647: 1
       850: 1

 851:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        59: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       121: 1
       126: 1
       130: 1
       131: 1
       132: 1
       133: 1
       143: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       164: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       222: 1
       226: 1
       227: 1
       245: 1
       250: 1
       254: 1
       255: 1
       256: 1
       257: 1
       275: 1
       280: 1
       284: 1
       285: 1
       286: 1
       287: 1
       297: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       353: 1
       389: 1
       393: 1
       394: 1
       428: 1
       432: 1
       433: 1
       451: 1
       456: 1
       460: 1
       461: 1
       462: 1
       463: 1
       560: 1
       607: 1
       643: 1
       647: 1
       648: 1
       851: 1

 852:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        60: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       122: 1
       127: 1
       131: 1
       133: 1
       144: 1
       148: 1
       151: 1
       153: 1
       154: 1
       165: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: 1
       183: 1
       185: 1
       187: 1
       188: 1
       223: 1
       227: 1
       246: 1
       251: 1
       255: 1
       257: 1
       276: 1
       281: 1
       285: 1
       287: 1
       298: 1
       302: 1
       305: 1
       307: 1
       308: 1
       354: 1
       390: 1
       394: 1
       429: 1
       433: 1
       452: 1
       457: 1
       461: 1
       463: 1
       561: 1
       608: 1
       644: 1
       648: 1
       852: 1

 853:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       123: 1
       128: 1
       131: 1
       133: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       224: 1
       227: 1
       247: 1
       252: 1
       255: 1
       257: 1
       277: 1
       282: 1
       285: 1
       287: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       355: 1
       391: 1
       394: 1
       430: 1
       433: 1
       453: 1
       458: 1
       461: 1
       463: 1
       562: 1
       609: 1
       645: 1
       648: 1
       853: 1

 854:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q^2+2q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       181: 1
       182: 1
       183: 1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       259: q+1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: q+1
       291: 1
       295: 1
       296: 1
       297: 1
       309: 1
       310: q+1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       338: 1
       346: 1
       351: 1
       352: 1
       353: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       385: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       416: 1
       437: 1
       444: 1
       445: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       482: 1
       511: 1
       522: 1
       529: 1
       531: 1
       545: 1
       566: 1
       575: 1
       577: 1
       583: 1
       622: 1
       649: 1
       650: 1
       656: 1
       657: 1
       659: 1
       718: 1
       767: 1
       854: 1

 855:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 1
       345: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       436: 1
       437: 1
       439: 1
       443: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       510: 1
       522: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       613: 1
       650: 1
       651: 1
       655: 1
       666: 1
       756: 1
       758: 1
       855: 1

 856:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       336: 1
       343: 1
       344: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       492: 1
       500: 1
       509: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       566: 1
       612: 1
       650: 1
       652: 1
       654: 1
       676: 1
       704: 1
       707: 1
       856: 1

 857:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       483: 1
       492: 1
       501: 1
       508: 1
       517: 1
       564: 1
       610: 1
       611: 1
       617: 1
       651: 1
       652: 1
       653: 1
       686: 1
       808: 1
       857: 1

 858:    0: 3q^2+4q+1
         1: 3q+1
         2: 3q^2+4q+1
         3: q^2+4q+1
         4: 3q^2+4q+1
         5: 3q^2+4q+1
         6: 3q+1
         7: 3q+1
         8: q^2+4q+1
         9: 3q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^2+4q+1
        13: 3q+1
        14: 3q^2+4q+1
        15: 2q+1
        16: 3q+1
        17: 3q^2+4q+1
        18: 2q+1
        19: 3q^2+4q+1
        20: q+1
        21: 3q+1
        22: 3q+1
        23: q^2+4q+1
        24: q^2+4q+1
        25: 3q+1
        27: q^2+4q+1
        28: 3q+1
        29: q^2+4q+1
        30: 3q+1
        31: q^2+4q+1
        32: q^2+4q+1
        33: 3q+1
        34: 3q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 3q+1
        41: 3q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 3q+1
        48: 3q^2+4q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+4q+1
        57: q+1
        60: q^2+4q+1
        61: q^2+4q+1
        62: 3q+1
        64: q+1
        65: 3q+1
        67: q+1
        68: 3q+1
        69: q^2+4q+1
        70: 1
        71: 1
        72: 3q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: 3q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: 2q+1
        97: 3q+1
        98: 3q+1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 3q+1
       109: 3q+1
       110: 3q+1
       111: 1
       112: q+1
       113: q+1
       118: q^2+4q+1
       119: 1
       122: q+1
       123: q+1
       124: 1
       127: q+1
       128: q+1
       129: 3q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: 2q+1
       141: 1
       144: 2q+1
       145: 2q+1
       146: q+1
       149: q+1
       151: q+1
       152: q+1
       153: 2q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: 2q+1
       162: 1
       165: 2q+1
       166: 2q+1
       167: q+1
       169: q+1
       170: q+1
       173: q+1
       174: 2q+1
       175: 1
       176: 1
       177: 3q+1
       178: 1
       179: q+1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: q+1
       188: q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 3q+1
       196: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       207: 1
       212: q+1
       213: 1
       214: 1
       219: q+1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       242: 2q+1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       272: 2q+1
       273: 1
       276: q+1
       277: q+1
       283: q+1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: q+1
       295: 1
       298: q+1
       299: q+1
       300: 1
       303: 1
       306: 1
       307: q+1
       308: 1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: q+1
       392: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: q+1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: q+1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: q+1
       459: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       491: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       646: 1
       653: 1
       654: 1
       655: 1
       694: 1
       695: 1
       707: 1
       758: 1
       809: 1
       815: 1
       858: 1

 859:    0: 4q^2+4q+1
         1: 4q^2+4q+1
         2: 4q^2+4q+1
         3: 3q^2+4q+1
         4: 2q^2+3q+1
         5: 4q^2+4q+1
         6: 2q^2+3q+1
         7: 4q^2+4q+1
         8: 3q^2+4q+1
         9: 3q^2+4q+1
        10: q^2+3q+1
        11: 3q^2+4q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 4q^2+4q+1
        17: 4q^2+4q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: 3q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 3q^2+4q+1
        29: q^2+3q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: q+1
        40: 2q^2+3q+1
        41: 4q^2+4q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: 3q^2+4q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q+1
        58: 2q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q+1
        62: 2q+1
        63: q^2+3q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: 2q^2+3q+1
        86: q^2+3q+1
        87: q^2+3q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       105: q^2+2q+1
       107: q+1
       108: 2q+1
       109: q+1
       110: q^2+2q+1
       111: q+1
       112: q+1
       114: q+1
       115: 2q+1
       116: q^2+3q+1
       117: q+1
       118: q+1
       119: 1
       120: 2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q^2+3q+1
       162: 1
       163: q+1
       164: 2q+1
       165: 2q+1
       167: q+1
       168: 2q+1
       169: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       191: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 1
       199: q+1
       201: q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       210: q+1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: q+1
       266: 1
       268: 1
       269: q+1
       270: 2q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       300: 1
       301: q+1
       312: 1
       314: 1
       316: 1
       317: 1
       318: 1
       321: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: q+1
       412: 1
       414: 1
       416: q+1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: q+1
       450: 1
       469: 1
       471: 1
       472: 1
       476: 1
       478: 1
       480: 1
       482: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       521: 1
       524: 1
       525: 1
       528: 1
       531: 1
       532: 1
       544: 1
       549: 1
       559: 1
       566: 1
       575: 1
       577: 1
       583: 1
       612: 1
       620: 1
       622: 1
       623: 1
       654: 1
       656: 1
       662: 1
       685: 1
       696: 1
       711: 1
       717: 1
       767: 1
       819: 1
       859: 1

 860:    0: 4q^2+4q+1
         1: 4q^2+4q+1
         2: 4q^2+4q+1
         3: 3q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: 4q^2+4q+1
         8: 3q^2+4q+1
         9: 3q^2+4q+1
        10: q^2+3q+1
        11: q^2+2q+1
        12: 3q^2+4q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: 2q^2+3q+1
        22: 3q^2+4q+1
        23: q^2+2q+1
        24: 3q^2+4q+1
        25: 2q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: q^2+2q+1
        29: q+1
        30: 3q^2+4q+1
        31: q^2+3q+1
        32: q^2+2q+1
        33: 2q^2+3q+1
        34: 4q^2+4q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: 2q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q^2+2q+1
        55: 3q^2+4q+1
        56: q^2+2q+1
        57: q+1
        58: 2q+1
        59: q^2+3q+1
        60: q+1
        61: q^2+3q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q^2+3q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: 2q^2+3q+1
        73: q^2+3q+1
        75: q^2+3q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        81: q^2+3q+1
        82: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 2q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       103: 2q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: q^2+2q+1
       111: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: q+1
       117: q^2+3q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: q+1
       139: q^2+3q+1
       141: 1
       142: q+1
       143: 2q+1
       145: 2q+1
       149: q+1
       150: 2q+1
       151: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       186: 2q+1
       187: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       233: q+1
       237: 1
       238: 1
       239: q+1
       241: 2q+1
       248: 1
       249: q+1
       250: q+1
       252: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       293: 2q+1
       295: 1
       296: 1
       297: q+1
       299: q+1
       303: 1
       304: q+1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: q+1
       381: 1
       382: 1
       385: q+1
       398: 1
       399: 1
       401: 1
       402: q+1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: q+1
       455: 1
       470: 1
       471: 1
       472: 1
       477: 1
       479: 1
       480: 1
       482: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       567: 1
       571: 1
       572: 1
       576: 1
       577: 1
       579: 1
       584: 1
       588: 1
       606: 1
       613: 1
       621: 1
       622: 1
       624: 1
       655: 1
       656: 1
       663: 1
       675: 1
       697: 1
       718: 1
       763: 1
       768: 1
       820: 1
       860: 1

 861:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       149: q+1
       150: q+1
       151: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       181: q+1
       182: q+1
       183: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       225: q+1
       226: q+1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       290: 1
       291: 1
       295: 1
       296: q+1
       297: 1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: q+1
       353: 1
       359: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       397: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       437: 1
       444: 1
       445: 1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       485: 1
       495: 1
       504: 1
       511: 1
       512: 1
       529: 1
       545: 1
       546: 1
       548: 1
       575: 1
       583: 1
       585: 1
       586: 1
       622: 1
       649: 1
       657: 1
       658: 1
       665: 1
       698: 1
       734: 1
       776: 1
       861: 1

 862:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       183: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       290: 1
       291: 1
       295: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       359: 1
       361: 1
       381: 1
       397: 1
       399: 1
       412: 1
       437: 1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       495: 1
       497: 1
       504: 1
       522: 1
       566: 1
       650: 1
       658: 1
       659: 1
       664: 1
       669: 1
       682: 1
       862: 1

 863:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       289: 1
       290: 1
       293: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       395: 1
       396: 1
       402: 1
       436: 1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       503: 1
       564: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       863: 1

 864:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       363: 1
       435: 1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       492: 1
       493: 1
       499: 1
       502: 1
       517: 1
       652: 1
       659: 1
       661: 1
       662: 1
       677: 1
       864: 1

 865:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: 1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: q+1
        36: q+1
        38: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: q+1
        43: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        79: q+1
        81: q+1
        83: q+1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        92: q+1
        94: q+1
        96: q+1
        97: q+1
        98: 2q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: q+1
       139: q+1
       140: q+1
       152: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       159: q+1
       160: q+1
       161: q+1
       173: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: q+1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: q+1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       363: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       490: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       611: 1
       617: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       687: 1
       693: 1
       865: 1

 866:    0: q^2+2q+1
         1: 2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: 2q+1
         7: 2q+1
         8: q^2+2q+1
         9: 2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: 2q+1
        17: q^2+2q+1
        18: q+1
        19: q+1
        20: q+1
        21: 2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 2q+1
        41: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 2q+1
        86: q+1
        87: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       105: q+1
       107: q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 1
       120: 2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: q+1
       159: q+1
       162: 1
       165: q+1
       167: q+1
       169: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       191: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       199: q+1
       201: q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: q+1
       266: 1
       273: 1
       276: q+1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       312: 1
       314: 1
       316: 1
       317: 1
       321: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 1
       361: 1
       362: 1
       363: 1
       364: 1
       380: 1
       386: 1
       392: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       521: 1
       524: 1
       566: 1
       612: 1
       654: 1
       662: 1
       664: 1
       669: 1
       681: 1
       684: 1
       688: 1
       866: 1

 867:    0: q^2+2q+1
         1: 2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: q^2+2q+1
         9: 2q+1
        10: q^2+2q+1
        11: q+1
        12: q^2+2q+1
        13: 2q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: q^2+2q+1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: q+1
        52: q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: q^2+2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: 2q+1
        73: q+1
        75: q+1
        76: q+1
        78: q+1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       106: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       113: q+1
       114: q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: q+1
       139: q+1
       141: 1
       145: q+1
       149: q+1
       151: q+1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: q+1
       237: 1
       248: 1
       252: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       313: 1
       315: 1
       316: 1
       317: 1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       413: 1
       418: 1
       431: 1
       436: 1
       437: 1
       439: 1
       443: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       567: 1
       571: 1
       613: 1
       655: 1
       663: 1
       664: 1
       670: 1
       674: 1
       682: 1
       689: 1
       867: 1

 868:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       361: 1
       368: 1
       370: 1
       382: 1
       383: 1
       385: 1
       399: 1
       407: 1
       408: 1
       414: 1
       415: 1
       416: 1
       437: 1
       444: 1
       445: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: 1
       497: 1
       504: 1
       511: 1
       512: 1
       531: 1
       546: 1
       548: 1
       577: 1
       585: 1
       586: 1
       622: 1
       656: 1
       664: 1
       665: 1
       698: 1
       736: 1
       778: 1
       868: 1

 869:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       189: 1
       190: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       237: 1
       238: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       309: 1
       310: 1
       318: 1
       319: 1
       320: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       367: 1
       381: 1
       382: 1
       385: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       436: 1
       443: 1
       444: 1
       447: 1
       455: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       545: 1
       563: 1
       564: 1
       572: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       621: 1
       657: 1
       666: 1
       667: 1
       675: 1
       697: 1
       755: 1
       775: 1
       869: 1

 870:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: q+1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: q+1
       183: 1
       186: q+1
       187: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: q+1
       286: q+1
       287: q+1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       381: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: q+1
       436: 1
       437: 1
       439: 1
       443: 1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       563: 1
       564: 1
       565: 1
       571: 1
       582: 1
       613: 1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       689: 1
       756: 1
       870: 1

 871:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: 2q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: q^2+3q+1
        19: 2q+1
        20: q^2+3q+1
        21: 2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+3q+1
        26: 2q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: 3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        39: 2q+1
        40: 3q+1
        41: 2q+1
        42: 3q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        57: q^2+3q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 3q+1
        63: 2q+1
        64: 3q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        75: q+1
        81: 2q+1
        84: 3q+1
        85: 2q+1
        86: 2q+1
        87: 2q+1
        88: 1
        89: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       103: q+1
       104: q+1
       105: q+1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 2q+1
       113: q+1
       114: 2q+1
       115: q+1
       116: q+1
       117: 1
       118: q+1
       119: 3q+1
       120: 2q+1
       121: 2q+1
       122: 2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       135: q+1
       136: q+1
       139: 1
       155: 2q+1
       156: 1
       157: 2q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q+1
       177: q+1
       178: q+1
       180: 1
       186: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: q+1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: 1
       208: 2q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       214: q+1
       215: q+1
       218: 1
       220: 2q+1
       221: q+1
       222: q+1
       224: 1
       230: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: 2q+1
       276: q+1
       277: 1
       278: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       289: 1
       290: q+1
       293: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: q+1
       349: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: q+1
       430: 1
       436: 1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       599: 1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       757: 1
       774: 1
       871: 1

 872:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       177: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       565: 1
       566: 1
       567: 1
       582: 1
       660: 1
       668: 1
       669: 1
       670: 1
       758: 1
       872: 1

 873:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: 1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        79: q+1
        81: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: 1
       134: q+1
       135: q+1
       136: 1
       138: 1
       139: 1
       140: q+1
       152: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: 1
       230: 1
       234: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: q+1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       462: 1
       468: 1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       565: 1
       568: 1
       569: 1
       582: 1
       590: 1
       598: 1
       599: 1
       604: 1
       611: 1
       661: 1
       668: 1
       671: 1
       672: 1
       687: 1
       759: 1
       792: 1
       873: 1

 874:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        38: q+1
        39: q+1
        40: 1
        41: q+1
        42: 2q+1
        43: q+1
        44: q+1
        45: 2q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 2q+1
        61: q+1
        62: 1
        63: q+1
        64: 2q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: q+1
        79: 1
        81: 1
        83: q+1
        84: 1
        85: 1
        86: q+1
        87: 2q+1
        88: 1
        89: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: q+1
       122: 2q+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: q+1
       152: 1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: q+1
       180: 1
       184: 1
       186: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       229: 1
       234: 1
       235: q+1
       256: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       342: 1
       343: q+1
       344: 1
       346: 1
       348: 1
       349: 1
       350: 1
       363: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       412: 1
       418: 1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       435: 1
       440: 1
       441: 1
       462: 1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       499: 1
       502: 1
       507: 1
       508: 1
       566: 1
       568: 1
       570: 1
       589: 1
       597: 1
       598: 1
       604: 1
       617: 1
       662: 1
       669: 1
       671: 1
       673: 1
       693: 1
       760: 1
       799: 1
       874: 1

 875:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: 1
        12: q^2+1
        13: 1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: q^2+1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        30: 1
        31: q^2+1
        32: 1
        33: 1
        34: 1
        35: q^2+1
        36: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: q^2+1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: 1
       290: 1
       293: 1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       436: 1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       567: 1
       569: 1
       570: 1
       589: 1
       599: 1
       663: 1
       670: 1
       672: 1
       673: 1
       761: 1
       875: 1

 876:    0: q^2+q+1
         1: 1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q^2+q+1
         9: 1
        10: q^2+q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q^2+q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: q+1
        76: 1
        78: q+1
        81: 1
        82: q+1
        84: 1
        85: 1
        86: 1
        87: q+1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: 1
       137: 1
       139: 1
       141: 1
       145: q+1
       149: 1
       151: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: q+1
       186: 1
       187: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: q+1
       231: 1
       233: 1
       248: 1
       252: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       361: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       418: 1
       426: 1
       430: 1
       431: 1
       433: 1
       437: 1
       439: 1
       454: 1
       458: 1
       471: 1
       480: 1
       481: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       497: 1
       504: 1
       506: 1
       570: 1
       571: 1
       581: 1
       589: 1
       605: 1
       609: 1
       615: 1
       664: 1
       673: 1
       674: 1
       691: 1
       762: 1
       782: 1
       876: 1

 877:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       195: q+1
       196: 1
       197: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       218: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       233: 1
       239: 1
       241: 1
       249: 1
       250: 1
       252: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       317: 1
       318: 1
       325: q+1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       341: 1
       347: 1
       349: 1
       352: 1
       353: 1
       355: 1
       370: 1
       383: 1
       385: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       439: 1
       445: 1
       447: 1
       455: 1
       472: 1
       481: 1
       482: 1
       489: 1
       490: 1
       491: 1
       506: 1
       512: 1
       514: 1
       548: 1
       571: 1
       572: 1
       579: 1
       586: 1
       587: 1
       588: 1
       606: 1
       624: 1
       665: 1
       674: 1
       675: 1
       700: 1
       763: 1
       780: 1
       877: 1

 878:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       104: q+1
       105: q+1
       106: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       189: 1
       190: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       309: 1
       310: 1
       318: 1
       319: 1
       320: q+1
       326: 1
       327: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       405: 1
       412: 1
       414: 1
       416: 1
       435: 1
       442: 1
       444: 1
       446: 1
       450: 1
       464: 1
       473: 1
       474: 1
       482: 1
       492: 1
       493: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       516: 1
       517: 1
       525: 1
       527: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       583: 1
       620: 1
       657: 1
       676: 1
       677: 1
       685: 1
       696: 1
       703: 1
       732: 1
       878: 1

 879:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       256: q+1
       257: q+1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: q+1
       397: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       485: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       524: 1
       543: 1
       612: 1
       658: 1
       676: 1
       677: 1
       678: 1
       684: 1
       688: 1
       704: 1
       879: 1

 880:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+3q+1
         5: 2q+1
         6: q^2+3q+1
         7: 2q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q+1
        12: q^2+3q+1
        13: q^2+3q+1
        14: 3q+1
        15: q^2+3q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q^2+3q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: q^2+3q+1
        26: 2q+1
        27: q^2+3q+1
        28: 2q+1
        29: 2q+1
        30: q^2+3q+1
        31: 3q+1
        32: 2q+1
        33: 3q+1
        34: 2q+1
        35: 3q+1
        36: q^2+3q+1
        37: 2q+1
        38: q+1
        39: q^2+3q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        45: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        57: q^2+3q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 3q+1
        66: 2q+1
        67: 3q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 3q+1
        72: 2q+1
        73: 2q+1
        74: 1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        92: 2q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       102: q+1
       104: q+1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       124: 3q+1
       125: 2q+1
       126: 2q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       134: 1
       135: 2q+1
       136: 2q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: 2q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       157: q+1
       159: 1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       184: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       208: q+1
       210: 1
       213: 1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       248: 2q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q+1
       259: 1
       288: 1
       290: q+1
       292: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       348: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       435: 1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       543: 1
       550: 1
       551: 1
       659: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       705: 1
       731: 1
       880: 1

 881:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        92: q+1
        94: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       148: 1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: q+1
       156: q+1
       157: 1
       159: 1
       160: 1
       161: q+1
       173: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: q+1
       207: q+1
       208: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       255: 1
       256: 1
       258: q+1
       259: 1
       260: 1
       264: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: q+1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       396: 1
       434: 1
       435: 1
       436: 1
       440: 1
       462: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       507: 1
       518: 1
       519: 1
       520: 1
       535: 1
       543: 1
       551: 1
       552: 1
       557: 1
       611: 1
       660: 1
       678: 1
       679: 1
       680: 1
       687: 1
       706: 1
       740: 1
       881: 1

 882:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       177: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       380: 1
       381: 1
       386: 1
       468: 1
       475: 1
       478: 1
       479: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       518: 1
       521: 1
       522: 1
       543: 1
       661: 1
       678: 1
       681: 1
       682: 1
       707: 1
       882: 1

 883:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: q^2+1
        18: q^2+1
        19: 1
        20: 1
        21: 1
        22: 1
        23: q^2+1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: q^2+1
        43: 1
        45: q^2+1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: q^2+1
        61: 1
        62: 1
        63: 1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q^2+1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: q^2+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       373: 1
       380: 1
       386: 1
       387: 1
       390: 1
       435: 1
       469: 1
       476: 1
       478: 1
       480: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       519: 1
       521: 1
       523: 1
       550: 1
       551: 1
       662: 1
       679: 1
       681: 1
       683: 1
       708: 1
       883: 1

 884:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: q+1
        23: q+1
        24: 2q+1
        25: 1
        26: q+1
        27: 2q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: 1
        34: q+1
        35: 2q+1
        36: q+1
        37: q+1
        38: 1
        39: 2q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        45: q+1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 2q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: q+1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: q+1
        74: 1
        75: 2q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q+1
        88: q+1
        92: 1
        94: 1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: 1
       126: q+1
       127: 1
       128: 2q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: q+1
       173: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: q+1
       184: 1
       186: 1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       207: 1
       208: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       260: 1
       264: 1
       265: q+1
       286: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       334: 1
       335: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       374: 1
       379: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       402: 1
       436: 1
       440: 1
       441: 1
       462: 1
       470: 1
       477: 1
       479: 1
       480: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: 1
       507: 1
       508: 1
       520: 1
       522: 1
       523: 1
       542: 1
       550: 1
       552: 1
       557: 1
       617: 1
       663: 1
       680: 1
       682: 1
       683: 1
       693: 1
       709: 1
       747: 1
       884: 1

 885:    0: q^2+q+1
         1: 1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q^2+q+1
         9: 1
        10: q^2+q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q^2+q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q+1
        89: 1
        91: q+1
        92: 1
        93: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: q+1
       167: 1
       169: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: q+1
       184: 1
       185: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       273: 1
       276: q+1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       331: 1
       332: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       399: 1
       437: 1
       438: 1
       449: 1
       452: 1
       471: 1
       480: 1
       481: 1
       487: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       523: 1
       524: 1
       534: 1
       550: 1
       558: 1
       561: 1
       614: 1
       664: 1
       683: 1
       684: 1
       690: 1
       710: 1
       739: 1
       885: 1

 886:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: q+1
       121: 1
       122: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       195: q+1
       196: 1
       197: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       209: 1
       210: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       269: 1
       270: 1
       274: 1
       275: 1
       276: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       317: 1
       318: 1
       325: q+1
       326: 1
       327: 1
       332: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       408: 1
       415: 1
       416: 1
       438: 1
       445: 1
       446: 1
       450: 1
       472: 1
       481: 1
       482: 1
       498: 1
       499: 1
       500: 1
       505: 1
       512: 1
       513: 1
       524: 1
       525: 1
       532: 1
       547: 1
       548: 1
       549: 1
       559: 1
       586: 1
       623: 1
       665: 1
       684: 1
       685: 1
       699: 1
       711: 1
       737: 1
       886: 1

 887:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       459: 1
       462: 1
       463: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       543: 1
       563: 1
       582: 1
       610: 1
       618: 1
       619: 1
       646: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       807: 1
       887: 1

 888:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: q+1
        94: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: q+1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: q+1
       186: q+1
       188: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: q+1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: q+1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: q+1
       308: q+1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: q+1
       474: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: 1
       564: 1
       610: 1
       611: 1
       617: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       808: 1
       888: 1

 889:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         6: 3q+1
         7: 2q+1
         8: q+1
         9: 3q+1
        10: 3q+1
        11: 3q+1
        12: 3q+1
        13: 3q+1
        14: 3q+1
        15: q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 3q+1
        20: q+1
        21: 2q+1
        22: 1
        23: q+1
        24: q+1
        25: 3q+1
        26: 2q+1
        27: q+1
        28: 3q+1
        29: 3q+1
        30: 3q+1
        31: 3q+1
        32: 3q+1
        33: 3q+1
        34: 2q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 3q+1
        41: 2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: 3q+1
        49: 1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: 2q+1
        59: 1
        60: q+1
        61: q+1
        62: 3q+1
        63: 2q+1
        64: 1
        65: 3q+1
        66: 2q+1
        67: 1
        68: 3q+1
        69: 3q+1
        70: 1
        71: 1
        72: 2q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: 2q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 3q+1
        98: 2q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 2q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+1
       126: 1
       127: 1
       128: 1
       129: 3q+1
       130: 2q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: 2q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: q+1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       459: 1
       462: 1
       463: 1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       493: 1
       494: 1
       495: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: 1
       543: 1
       565: 1
       582: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       646: 1
       668: 1
       678: 1
       687: 1
       688: 1
       689: 1
       692: 1
       695: 1
       809: 1
       889: 1

 890:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: 1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        47: 1
        48: 1
        49: 1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: 1
        87: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: 1
       158: 1
       159: 1
       162: q+1
       165: q+1
       167: q+1
       169: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: q+1
       273: q+1
       276: q+1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       312: 1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 1
       360: 1
       373: 1
       380: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: q+1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       476: 1
       485: 1
       487: 1
       494: 1
       496: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: 1
       551: 1
       558: 1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       669: 1
       679: 1
       688: 1
       690: 1
       748: 1
       810: 1
       890: 1

 891:    0: 2q^2+3q+1
         1: 2q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: q^2+3q+1
         6: 2q+1
         7: q+1
         8: q^2+2q+1
         9: 2q+1
        10: 2q^2+3q+1
        11: q^2+3q+1
        12: 2q^2+3q+1
        13: 2q+1
        14: 2q^2+3q+1
        15: q^2+2q+1
        16: 2q+1
        17: q^2+3q+1
        18: 2q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q^2+2q+1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q^2+3q+1
        32: q^2+3q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+3q+1
        49: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q^2+2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: q^2+3q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        88: 2q+1
        89: q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: 2q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: 1
       133: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: q+1
       165: q+1
       166: 2q+1
       167: q+1
       169: 2q+1
       170: q+1
       173: q+1
       174: 2q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: q+1
       188: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: 1
       227: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       277: 2q+1
       283: q+1
       286: 1
       287: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: q+1
       359: 1
       360: 1
       362: 1
       374: 1
       379: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       401: 1
       413: q+1
       418: q+1
       431: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       477: 1
       486: 1
       487: 1
       489: 1
       495: 1
       496: 1
       498: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       510: 1
       515: 1
       520: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       613: 1
       614: 1
       616: 1
       628: 1
       633: 1
       646: 1
       670: 1
       680: 1
       689: 1
       690: 1
       692: 1
       749: 1
       754: 1
       811: 1
       891: 1

 892:    0: 2q^2+3q+1
         1: 2q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+3q+1
         5: 2q^2+3q+1
         6: 2q+1
         7: q+1
         8: q^2+2q+1
         9: 2q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: q^2+3q+1
        15: 2q+1
        16: 2q+1
        17: 2q^2+3q+1
        18: q^2+2q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q^2+3q+1
        30: 2q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q^2+2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: q^2+3q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: 2q+1
        75: q+1
        76: q+1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: 1
       133: q+1
       134: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: q+1
       144: 2q+1
       145: q+1
       146: q+1
       149: q+1
       151: 2q+1
       152: q+1
       153: 2q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: 1
       227: q+1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: q+1
       242: q+1
       248: q+1
       251: 2q+1
       252: q+1
       253: q+1
       256: 1
       257: q+1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       314: 1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: q+1
       355: 1
       358: 1
       361: 1
       362: 1
       380: q+1
       386: q+1
       392: 1
       397: 1
       400: 1
       401: 1
       412: 1
       418: 1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       478: 1
       485: 1
       488: 1
       489: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       515: 1
       521: 1
       568: 1
       598: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       634: 1
       640: 1
       646: 1
       671: 1
       681: 1
       688: 1
       691: 1
       692: 1
       800: 1
       806: 1
       812: 1
       892: 1

 893:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        75: q+1
        76: q+1
        78: q+1
        81: q+1
        82: q+1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       145: q+1
       149: q+1
       151: q+1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: q+1
       248: q+1
       252: q+1
       260: 1
       261: 1
       263: 1
       267: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       315: 1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: q+1
       398: 1
       400: 1
       413: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       479: 1
       486: 1
       488: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       569: 1
       599: 1
       605: 1
       609: 1
       613: 1
       615: 1
       635: 1
       672: 1
       682: 1
       689: 1
       691: 1
       801: 1
       813: 1
       893: 1

 894:    0: q^3+4q^2+4q+1
         1: 2q^2+3q+1
         2: 2q^2+4q+1
         3: q^3+4q^2+4q+1
         4: 2q^2+4q+1
         5: 2q^2+4q+1
         6: 2q+1
         7: 2q+1
         8: 2q^2+4q+1
         9: 2q^2+3q+1
        10: 2q^2+4q+1
        11: 2q^2+4q+1
        12: 2q^2+4q+1
        13: q^2+3q+1
        14: q^2+4q+1
        15: 2q^2+4q+1
        16: q^2+3q+1
        17: q^2+4q+1
        18: 2q^2+4q+1
        19: q^2+4q+1
        20: 2q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q^2+4q+1
        28: q^2+3q+1
        29: q^2+4q+1
        30: q^2+3q+1
        31: q^2+4q+1
        32: q^2+4q+1
        33: 2q+1
        34: 2q+1
        35: q^2+4q+1
        36: q^2+3q+1
        37: 2q+1
        38: 2q+1
        39: 2q^2+4q+1
        40: 2q+1
        41: 2q+1
        42: q^2+4q+1
        43: q^2+3q+1
        44: 2q+1
        45: 2q^2+4q+1
        46: 2q+1
        47: 3q+1
        48: q^2+4q+1
        49: q^2+4q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q^2+4q+1
        65: 2q+1
        66: 2q+1
        67: q^2+4q+1
        68: 3q+1
        69: q^2+4q+1
        70: q^2+4q+1
        71: 2q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: q+1
        78: 2q+1
        79: 2q+1
        80: q+1
        81: q^2+3q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: 2q+1
        98: 2q+1
        99: q^2+4q+1
       100: 3q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: 2q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: q^2+4q+1
       132: 3q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: q+1
       151: 2q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: 2q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: 1
       183: q+1
       184: 2q+1
       185: 1
       186: 2q+1
       187: 1
       188: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: 1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: q+1
       246: 1
       248: q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: 2q+1
       257: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: q+1
       276: q+1
       277: 1
       278: q+1
       282: 1
       283: q+1
       285: q+1
       286: 2q+1
       287: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: 1
       351: 1
       354: 1
       355: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       386: 1
       387: q+1
       390: 1
       392: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       418: 1
       426: q+1
       430: 1
       431: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       496: 1
       497: 1
       498: 1
       499: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       523: 1
       550: 1
       558: 1
       561: 1
       570: 1
       589: 1
       605: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       641: 1
       646: 1
       648: 1
       673: 1
       683: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       814: 1
       849: 1
       894: 1

 895:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       362: 1
       363: 1
       364: 1
       386: 1
       392: 1
       401: 1
       402: 1
       403: 1
       418: 1
       431: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       459: 1
       462: 1
       463: 1
       481: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       524: 1
       571: 1
       616: 1
       617: 1
       618: 1
       646: 1
       674: 1
       684: 1
       692: 1
       693: 1
       694: 1
       815: 1
       895: 1

 896:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: q+1
        23: q+1
        24: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: q+1
        55: q+1
        56: q+1
        59: q+1
        60: q+1
        61: q+1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: q+1
       111: 1
       116: q+1
       117: q+1
       118: q+1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: q+1
       205: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       250: 1
       251: 1
       252: 1
       254: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       284: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       304: 1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       363: 1
       364: 1
       371: 1
       384: 1
       385: 1
       386: 1
       393: 1
       402: 1
       403: 1
       410: 1
       416: 1
       417: 1
       418: 1
       432: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       460: 1
       462: 1
       463: 1
       482: 1
       490: 1
       491: 1
       499: 1
       500: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       525: 1
       549: 1
       572: 1
       588: 1
       617: 1
       618: 1
       625: 1
       647: 1
       675: 1
       685: 1
       693: 1
       694: 1
       701: 1
       816: 1
       896: 1

 897:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^2+4q+1
         3: 3q^2+4q+1
         4: q^2+4q+1
         5: q^2+4q+1
         6: q^2+4q+1
         8: q^2+4q+1
         9: 3q^2+4q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^2+4q+1
        13: q^2+4q+1
        14: 4q+1
        15: q^2+4q+1
        16: q^2+4q+1
        17: 4q+1
        18: q^2+4q+1
        19: 4q+1
        20: q^2+4q+1
        23: 2q+1
        24: 2q+1
        25: q^2+4q+1
        27: q^2+4q+1
        28: q^2+4q+1
        29: 4q+1
        30: q^2+4q+1
        31: 4q+1
        32: 4q+1
        33: 4q+1
        35: 4q+1
        36: q^2+4q+1
        37: 2q+1
        38: 2q+1
        39: q^2+4q+1
        40: 4q+1
        42: 4q+1
        43: q^2+4q+1
        44: 2q+1
        45: q^2+4q+1
        46: 2q+1
        47: 4q+1
        48: 4q+1
        49: 4q+1
        50: 2q+1
        51: 2q+1
        56: q+1
        57: q^2+4q+1
        60: 2q+1
        61: 2q+1
        62: 4q+1
        64: 4q+1
        65: 4q+1
        67: 4q+1
        68: 4q+1
        69: 4q+1
        70: 4q+1
        71: 4q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: 2q+1
        80: q+1
        81: q^2+4q+1
        82: 2q+1
        83: 2q+1
        84: 4q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        91: 2q+1
        92: q^2+4q+1
        93: 2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: 4q+1
        99: 4q+1
       100: 4q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       118: q+1
       119: 4q+1
       122: 2q+1
       123: q+1
       124: 4q+1
       127: q+1
       128: 2q+1
       129: 4q+1
       131: 4q+1
       132: 4q+1
       133: q+1
       134: q+1
       135: 2q+1
       140: 1
       141: 2q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       155: 2q+1
       156: q+1
       161: 1
       162: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: 4q+1
       179: q+1
       180: q+1
       181: q+1
       183: q+1
       184: 2q+1
       185: 1
       186: 2q+1
       187: 1
       188: q+1
       189: q+1
       198: q+1
       205: q+1
       206: 2q+1
       207: q+1
       212: 1
       213: q+1
       214: 2q+1
       219: 1
       220: 4q+1
       223: q+1
       224: q+1
       225: q+1
       227: q+1
       228: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       248: 2q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: 2q+1
       257: 1
       258: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: 2q+1
       276: q+1
       277: 1
       278: q+1
       282: 1
       283: q+1
       285: q+1
       286: 2q+1
       287: 1
       288: q+1
       289: q+1
       294: 1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       319: q+1
       328: 1
       335: 1
       336: 1
       343: 1
       344: q+1
       345: q+1
       350: 1
       351: q+1
       354: 1
       355: 1
       356: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       392: 1
       394: 1
       395: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: q+1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       483: 1
       492: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       526: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       573: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       646: 1
       648: 1
       686: 1
       695: 1
       702: 1
       731: 1
       748: 1
       774: 1
       801: 1
       817: 1
       849: 1
       897: 1

 898:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q+1
         3: 3q^2+4q+1
         4: 3q^2+4q+1
         5: 3q^2+4q+1
         6: 3q+1
         7: 3q+1
         8: q+1
         9: 3q^2+4q+1
        10: 3q+1
        11: 3q^2+4q+1
        12: 3q^2+4q+1
        13: 3q^2+4q+1
        14: 3q+1
        15: q^2+2q+1
        16: 3q^2+4q+1
        17: 3q+1
        18: q^2+2q+1
        19: 3q^2+4q+1
        20: q+1
        21: 3q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: 3q+1
        27: q+1
        28: 3q^2+4q+1
        29: 3q+1
        30: 3q^2+4q+1
        31: 3q+1
        32: 3q^2+4q+1
        33: 3q+1
        34: 3q+1
        35: 1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 3q+1
        41: 3q+1
        42: 1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 3q^2+4q+1
        48: 3q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 3q+1
        59: q+1
        60: q+1
        61: q+1
        62: 3q+1
        63: 3q+1
        64: 1
        65: 3q+1
        66: 3q+1
        67: 1
        68: 3q^2+4q+1
        69: 3q+1
        70: q+1
        71: 1
        72: 3q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: 3q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: 3q+1
        98: 3q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       110: q+1
       112: q+1
       113: q+1
       114: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: 3q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 3q+1
       126: 1
       127: 1
       128: 1
       129: 3q+1
       130: 3q+1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: 1
       177: 3q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: q+1
       198: q+1
       199: q+1
       200: q+1
       204: q+1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 3q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       320: q+1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       392: 1
       393: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       440: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       484: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       527: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       611: 1
       619: 1
       620: 1
       621: 1
       625: 1
       642: 1
       646: 1
       647: 1
       687: 1
       695: 1
       696: 1
       697: 1
       701: 1
       732: 1
       775: 1
       818: 1
       850: 1
       898: 1

 899:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: q+1
        20: q+1
        21: 2q+1
        22: q+1
        23: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 2q+1
        41: 2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        57: q+1
        58: 2q+1
        59: q+1
        60: q+1
        62: 2q+1
        63: 2q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 2q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       105: q+1
       107: q+1
       108: q+1
       112: q+1
       114: q+1
       115: q+1
       116: q+1
       119: 1
       120: 2q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       191: q+1
       199: q+1
       201: q+1
       202: q+1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       321: q+1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       366: 1
       368: 1
       369: 1
       380: 1
       382: 1
       383: 1
       384: 1
       388: 1
       392: 1
       393: 1
       397: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       450: 1
       485: 1
       494: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       528: 1
       544: 1
       546: 1
       547: 1
       559: 1
       575: 1
       583: 1
       585: 1
       586: 1
       612: 1
       620: 1
       622: 1
       623: 1
       688: 1
       696: 1
       698: 1
       699: 1
       733: 1
       776: 1
       819: 1
       899: 1

 900:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 2q+1
        22: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: q+1
        52: q+1
        53: q+1
        55: q+1
        57: q+1
        58: 2q+1
        59: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: 2q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       106: q+1
       107: q+1
       109: q+1
       113: q+1
       114: q+1
       115: q+1
       117: q+1
       119: 1
       120: q+1
       121: 1
       123: 1
       124: 1
       125: 2q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       149: q+1
       150: q+1
       151: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       192: q+1
       200: q+1
       201: q+1
       203: q+1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       322: q+1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       398: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       427: 1
       431: 1
       432: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       455: 1
       486: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       529: 1
       545: 1
       546: 1
       548: 1
       576: 1
       584: 1
       585: 1
       587: 1
       606: 1
       613: 1
       621: 1
       622: 1
       624: 1
       689: 1
       697: 1
       698: 1
       700: 1
       734: 1
       777: 1
       820: 1
       900: 1

 901:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q+1
         5: q^2+3q+1
         6: 2q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+3q+1
        17: 3q+1
        18: q^2+3q+1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: q^2+3q+1
        23: 2q+1
        25: 2q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: 3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: 2q+1
        41: 3q+1
        42: 3q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: 2q+1
        53: q+1
        54: 2q+1
        57: 2q+1
        58: 2q+1
        59: q^2+3q+1
        60: 2q+1
        62: 2q+1
        63: 3q+1
        64: 3q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: 2q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       107: q+1
       108: q+1
       114: 2q+1
       115: q+1
       116: 2q+1
       119: 2q+1
       120: 2q+1
       121: 3q+1
       122: 2q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       157: 2q+1
       158: 1
       159: 2q+1
       162: q+1
       163: q+1
       164: 2q+1
       165: q+1
       167: q+1
       168: 2q+1
       169: 2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       193: q+1
       201: q+1
       202: q+1
       208: 2q+1
       209: 1
       210: 2q+1
       215: q+1
       216: 1
       217: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       261: 1
       262: 1
       268: q+1
       269: 1
       270: q+1
       273: q+1
       274: q+1
       275: 2q+1
       276: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       323: q+1
       331: 1
       332: 1
       339: 1
       340: 1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       360: 1
       368: 1
       369: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 1
       407: 1
       408: 1
       414: q+1
       415: 1
       416: q+1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       487: 1
       496: 1
       504: 1
       505: 1
       511: 1
       512: 1
       513: 1
       530: 1
       546: 1
       547: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       577: 1
       585: 1
       586: 1
       614: 1
       622: 1
       623: 1
       629: 1
       631: 1
       690: 1
       698: 1
       699: 1
       735: 1
       750: 1
       752: 1
       778: 1
       821: 1
       901: 1

 902:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+3q+1
         5: 2q+1
         6: 2q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q+1
        12: q^2+3q+1
        13: q^2+3q+1
        14: 3q+1
        15: q^2+3q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: q^2+3q+1
        24: 2q+1
        25: 2q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 2q+1
        29: 2q+1
        30: q^2+3q+1
        31: 3q+1
        32: 2q+1
        33: 2q+1
        34: 3q+1
        35: 3q+1
        36: q^2+3q+1
        37: 2q+1
        39: q^2+3q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: 2q+1
        53: q+1
        55: 2q+1
        57: 2q+1
        58: 2q+1
        59: q^2+3q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: 2q+1
        66: 3q+1
        67: 3q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: 2q+1
        73: 3q+1
        75: 2q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        81: q^2+3q+1
        82: 2q+1
        84: q+1
        85: q+1
        86: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       103: q+1
       107: q+1
       109: q+1
       114: 2q+1
       115: q+1
       117: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       123: q+1
       124: 2q+1
       125: 2q+1
       126: 3q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: 2q+1
       137: 1
       139: 2q+1
       141: q+1
       142: q+1
       143: 2q+1
       145: q+1
       149: q+1
       150: 2q+1
       151: 2q+1
       157: q+1
       158: 1
       160: q+1
       162: 1
       163: 1
       164: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       186: q+1
       187: 1
       194: q+1
       201: q+1
       203: q+1
       208: q+1
       209: 1
       211: q+1
       215: 2q+1
       216: 1
       218: 2q+1
       220: q+1
       221: q+1
       222: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       233: 1
       238: q+1
       239: 1
       241: q+1
       248: q+1
       249: q+1
       250: 2q+1
       252: q+1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: q+1
       299: 1
       303: 1
       304: 1
       305: 1
       324: q+1
       331: 1
       333: 1
       339: 1
       341: 1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: q+1
       355: 1
       361: 1
       368: 1
       370: 1
       382: q+1
       383: 1
       385: q+1
       400: 1
       407: 1
       409: 1
       414: 1
       415: 1
       417: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       488: 1
       497: 1
       504: 1
       506: 1
       511: 1
       512: 1
       514: 1
       531: 1
       546: 1
       548: 1
       578: 1
       585: 1
       587: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       615: 1
       622: 1
       624: 1
       636: 1
       639: 1
       691: 1
       698: 1
       700: 1
       736: 1
       779: 1
       802: 1
       805: 1
       822: 1
       902: 1

 903:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         6: 3q+1
         7: 3q+1
         8: q+1
         9: 3q+1
        10: 3q+1
        11: 3q+1
        12: 3q+1
        13: 3q+1
        14: 3q+1
        15: q+1
        16: 3q+1
        17: 3q+1
        18: q+1
        19: 3q+1
        21: 3q+1
        22: q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: 3q+1
        27: q+1
        28: 3q+1
        29: 3q+1
        30: 3q+1
        31: 3q+1
        32: 3q+1
        33: 3q+1
        34: 3q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 3q+1
        41: 3q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: 3q+1
        49: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        58: 3q+1
        59: q+1
        60: q+1
        61: q+1
        62: 3q+1
        63: 3q+1
        64: 1
        65: 3q+1
        66: 3q+1
        67: 1
        68: 3q+1
        69: 3q+1
        70: 1
        72: 3q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        85: 3q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 3q+1
        98: 3q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: q+1
       109: q+1
       110: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: 3q+1
       121: 1
       122: 1
       123: 1
       125: 3q+1
       126: 1
       127: 1
       128: 1
       129: 3q+1
       130: 3q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       175: 1
       177: 3q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: q+1
       202: q+1
       203: q+1
       204: q+1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 3q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       325: q+1
       332: 1
       333: 1
       334: 1
       340: 1
       341: 1
       342: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       362: 1
       369: 1
       370: 1
       371: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       392: 1
       393: 1
       401: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       431: 1
       432: 1
       438: 1
       439: 1
       440: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       489: 1
       498: 1
       505: 1
       506: 1
       507: 1
       512: 1
       513: 1
       514: 1
       515: 1
       532: 1
       547: 1
       548: 1
       549: 1
       559: 1
       579: 1
       586: 1
       587: 1
       588: 1
       606: 1
       616: 1
       623: 1
       624: 1
       625: 1
       642: 1
       646: 1
       647: 1
       692: 1
       699: 1
       700: 1
       701: 1
       737: 1
       780: 1
       823: 1
       850: 1
       903: 1

 904:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^2+4q+1
         3: 3q^2+4q+1
         4: q^2+4q+1
         5: q^2+4q+1
         7: q^2+4q+1
         8: q^2+4q+1
         9: 3q^2+4q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^2+4q+1
        13: q^2+4q+1
        14: 4q+1
        15: q^2+4q+1
        16: q^2+4q+1
        17: 4q+1
        18: q^2+4q+1
        19: 4q+1
        22: q^2+4q+1
        23: 2q+1
        24: 2q+1
        26: q^2+4q+1
        27: q^2+4q+1
        28: q^2+4q+1
        29: 4q+1
        30: q^2+4q+1
        31: 4q+1
        32: 4q+1
        34: 4q+1
        35: 4q+1
        36: q^2+4q+1
        37: 2q+1
        38: 2q+1
        39: q^2+4q+1
        41: 4q+1
        42: 4q+1
        43: q^2+4q+1
        44: 2q+1
        45: q^2+4q+1
        46: 2q+1
        47: 4q+1
        48: 4q+1
        49: 4q+1
        54: 2q+1
        55: 2q+1
        56: q+1
        59: q^2+4q+1
        60: 2q+1
        61: 2q+1
        63: 4q+1
        64: 4q+1
        66: 4q+1
        67: 4q+1
        68: 4q+1
        69: 4q+1
        70: 4q+1
        73: 4q+1
        74: q+1
        75: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: q+1
        81: q^2+4q+1
        82: 2q+1
        83: 2q+1
        86: 4q+1
        87: 2q+1
        88: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+4q+1
        93: 2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        98: 4q+1
        99: 4q+1
       100: 4q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       110: q+1
       111: q+1
       116: 2q+1
       117: 2q+1
       118: q+1
       121: 4q+1
       122: 2q+1
       123: q+1
       126: 4q+1
       127: q+1
       128: 2q+1
       130: 4q+1
       131: 4q+1
       132: 4q+1
       133: q+1
       138: q+1
       139: 2q+1
       140: 1
       143: 2q+1
       144: 1
       145: q+1
       147: q+1
       148: q+1
       150: 2q+1
       151: 2q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       159: 2q+1
       160: q+1
       161: 1
       164: 2q+1
       165: q+1
       166: 1
       168: 2q+1
       169: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       178: 4q+1
       179: q+1
       180: q+1
       182: q+1
       183: q+1
       184: 2q+1
       185: 1
       186: 2q+1
       187: 1
       188: q+1
       196: q+1
       204: q+1
       205: q+1
       210: 2q+1
       211: q+1
       212: 1
       217: q+1
       218: 2q+1
       219: 1
       222: 4q+1
       223: q+1
       224: q+1
       226: q+1
       227: q+1
       234: 1
       235: 1
       240: 1
       241: q+1
       242: 1
       245: q+1
       246: 1
       250: 2q+1
       251: 1
       252: q+1
       254: q+1
       255: q+1
       256: 2q+1
       257: 1
       264: 1
       265: 1
       270: q+1
       271: 1
       272: 1
       275: 2q+1
       276: q+1
       277: 1
       280: q+1
       282: 1
       284: q+1
       285: q+1
       286: 2q+1
       287: 1
       292: q+1
       293: q+1
       294: 1
       297: q+1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       326: q+1
       334: 1
       335: 1
       342: 1
       343: 1
       348: q+1
       349: q+1
       350: 1
       353: q+1
       354: 1
       355: 1
       363: 1
       371: 1
       372: 1
       377: 1
       384: 1
       385: q+1
       386: 1
       389: q+1
       390: 1
       393: 1
       394: 1
       402: 1
       410: 1
       411: 1
       416: q+1
       417: 1
       418: 1
       424: 1
       428: q+1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       456: 1
       458: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       490: 1
       499: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       533: 1
       549: 1
       550: 1
       555: 1
       560: 1
       561: 1
       580: 1
       588: 1
       589: 1
       603: 1
       607: 1
       609: 1
       617: 1
       625: 1
       626: 1
       631: 1
       639: 1
       643: 1
       647: 1
       648: 1
       693: 1
       701: 1
       702: 1
       738: 1
       752: 1
       781: 1
       805: 1
       824: 1
       851: 1
       904: 1

 905:    0: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         8: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: q+1
        24: q+1
        27: q^2+q+1
        29: q+1
        31: q+1
        32: q+1
        35: q+1
        37: q+1
        38: 1
        39: q+1
        42: q+1
        44: q+1
        45: q+1
        46: 1
        48: q+1
        49: q+1
        56: q+1
        60: q+1
        61: q+1
        64: q+1
        67: q+1
        69: q+1
        70: q+1
        74: 1
        75: q+1
        78: q+1
        80: 1
        82: q+1
        83: 1
        87: q+1
        88: 1
        91: q+1
        93: q+1
        95: 1
        96: 1
        99: q+1
       101: q+1
       102: 1
       103: 1
       111: q+1
       118: q+1
       122: q+1
       123: 1
       127: 1
       128: q+1
       131: q+1
       133: q+1
       140: 1
       144: 1
       145: q+1
       148: 1
       151: q+1
       153: 1
       154: 1
       161: 1
       165: q+1
       166: 1
       169: q+1
       172: 1
       174: 1
       175: 1
       179: 1
       180: 1
       183: q+1
       185: 1
       187: 1
       188: 1
       197: q+1
       205: q+1
       212: 1
       219: 1
       223: 1
       224: 1
       227: q+1
       235: 1
       242: 1
       246: 1
       251: 1
       252: q+1
       255: 1
       257: 1
       265: 1
       272: 1
       276: q+1
       277: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       327: q+1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       364: 1
       372: 1
       386: 1
       390: 1
       394: 1
       403: 1
       411: 1
       418: 1
       430: 1
       433: 1
       441: 1
       448: 1
       452: 1
       458: 1
       461: 1
       463: 1
       491: 1
       500: 1
       508: 1
       515: 1
       534: 1
       550: 1
       561: 1
       581: 1
       589: 1
       609: 1
       618: 1
       626: 1
       648: 1
       694: 1
       702: 1
       739: 1
       782: 1
       825: 1
       905: 1

 906:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: 1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: 1
        16: q^2+q+1
        17: q^2+q+1
        18: 1
        19: q^2+q+1
        20: 1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q^2+q+1
        34: q^2+q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+q+1
        41: q^2+q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q^2+q+1
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: q^2+q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q^2+q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: q^2+q+1
        98: q^2+q+1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       176: 1
       177: q^2+q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       221: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       274: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       320: 1
       321: 1
       322: 1
       325: 1
       352: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       388: 1
       392: 1
       393: 1
       397: 1
       405: 1
       407: 1
       408: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       450: 1
       464: 1
       465: 1
       472: 1
       475: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       532: 1
       559: 1
       575: 1
       612: 1
       620: 1
       622: 1
       623: 1
       649: 1
       703: 1
       704: 1
       711: 1
       714: 1
       819: 1
       906: 1

 907:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        91: q+1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: q+1
       158: q+1
       159: 1
       162: q+1
       165: 1
       167: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: q+1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: q+1
       291: q+1
       292: 1
       295: q+1
       298: 1
       300: 1
       302: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       351: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       381: 1
       387: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: q+1
       438: 1
       442: 1
       449: 1
       452: 1
       465: 1
       466: 1
       471: 1
       473: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       558: 1
       566: 1
       612: 1
       614: 1
       627: 1
       650: 1
       704: 1
       705: 1
       710: 1
       712: 1
       810: 1
       907: 1

 908:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        92: 1
        94: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: 1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       157: q+1
       159: 1
       160: q+1
       161: 1
       173: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       184: 1
       186: q+1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       259: 1
       260: q+1
       264: 1
       265: 1
       286: 1
       288: 1
       289: q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       328: 1
       335: 1
       345: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       381: 1
       387: 1
       391: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: q+1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       470: 1
       483: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       552: 1
       564: 1
       610: 1
       611: 1
       617: 1
       651: 1
       705: 1
       706: 1
       709: 1
       722: 1
       808: 1
       908: 1

 909:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       336: 1
       343: 1
       344: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       435: 1
       466: 1
       468: 1
       469: 1
       492: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       543: 1
       550: 1
       551: 1
       652: 1
       705: 1
       707: 1
       708: 1
       731: 1
       909: 1

 910:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: q+1
        43: 1
        45: q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: 1
        60: 2q+1
        61: 2q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: q+1
        69: 2q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        92: 1
        94: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       118: 2q+1
       119: 1
       122: q+1
       123: q+1
       124: 1
       127: q+1
       128: q+1
       129: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: 2q+1
       141: 1
       144: 2q+1
       145: 2q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q+1
       153: 2q+1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: q+1
       173: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: q+1
       184: 1
       186: 1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: q+1
       213: 1
       214: 1
       219: q+1
       220: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       242: 2q+1
       243: 1
       246: q+1
       247: q+1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: q+1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: q+1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       467: 1
       468: 1
       469: 1
       470: 1
       501: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       611: 1
       617: 1
       653: 1
       706: 1
       707: 1
       708: 1
       709: 1
       740: 1
       747: 1
       910: 1

 911:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        47: 1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        64: q+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: 1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q+1
        89: 1
        91: q+1
        92: 1
        93: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       118: 1
       119: 1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: q+1
       145: 1
       146: 1
       148: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: q+1
       167: 1
       169: q+1
       176: 1
       177: 1
       178: 1
       179: q+1
       181: 1
       183: q+1
       184: 1
       185: q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       205: 1
       206: 1
       213: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       243: 1
       246: q+1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: q+1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: q+1
       300: 1
       302: q+1
       312: 1
       314: 1
       316: 1
       317: 1
       327: 1
       343: 1
       344: 1
       351: 1
       354: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       373: 1
       380: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: q+1
       469: 1
       471: 1
       500: 1
       509: 1
       519: 1
       521: 1
       523: 1
       524: 1
       534: 1
       550: 1
       551: 1
       558: 1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       654: 1
       708: 1
       710: 1
       739: 1
       748: 1
       810: 1
       911: 1

 912:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        60: q+1
        61: 2q+1
        62: q+1
        64: 1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: 2q+1
        76: q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: q+1
        82: 2q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       113: 1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: 1
       128: q+1
       129: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: q+1
       145: 2q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: q+1
       188: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       205: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       237: 1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       252: q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       317: 1
       327: 1
       335: 1
       345: 1
       351: 1
       355: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       372: 1
       374: 1
       379: 1
       381: 1
       387: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       413: 1
       418: 1
       431: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       470: 1
       471: 1
       491: 1
       510: 1
       520: 1
       522: 1
       523: 1
       524: 1
       534: 1
       542: 1
       552: 1
       558: 1
       562: 1
       567: 1
       571: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       628: 1
       633: 1
       646: 1
       655: 1
       709: 1
       710: 1
       730: 1
       749: 1
       811: 1
       815: 1
       912: 1

 913:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       346: 1
       351: 1
       352: 1
       353: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       399: 1
       407: 1
       408: 1
       414: 1
       416: 1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       471: 1
       472: 1
       480: 1
       482: 1
       511: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       553: 1
       558: 1
       559: 1
       560: 1
       577: 1
       614: 1
       622: 1
       623: 1
       629: 1
       631: 1
       656: 1
       710: 1
       711: 1
       719: 1
       721: 1
       750: 1
       821: 1
       913: 1

 914:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: 1
        51: 1
        52: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: q+1
       159: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: 1
       266: 1
       268: q+1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: q+1
       292: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       329: 1
       338: 1
       346: 1
       351: 1
       352: 1
       353: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       405: 1
       412: 1
       414: 1
       416: 1
       435: 1
       442: 1
       444: q+1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       464: 1
       473: 1
       474: 1
       482: 1
       511: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: 1
       533: 1
       534: 1
       536: 1
       545: 1
       553: 1
       558: 1
       559: 1
       560: 1
       583: 1
       620: 1
       627: 1
       629: 1
       631: 1
       657: 1
       703: 1
       712: 1
       713: 1
       721: 1
       750: 1
       827: 1
       914: 1

 915:    0: 4q^2+4q+1
         1: 4q^2+4q+1
         2: 4q^2+4q+1
         3: 3q^2+4q+1
         4: 4q^2+4q+1
         5: 2q^2+3q+1
         6: 4q^2+4q+1
         7: 2q^2+3q+1
         8: q^2+3q+1
         9: 3q^2+4q+1
        10: 3q^2+4q+1
        11: 2q+1
        12: q^2+3q+1
        13: 4q^2+4q+1
        14: 4q^2+4q+1
        15: 3q^2+4q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: 2q^2+3q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 3q^2+4q+1
        26: q^2+2q+1
        27: q^2+3q+1
        28: 2q+1
        29: 2q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: 2q+1
        33: 4q^2+4q+1
        34: 2q^2+3q+1
        35: q^2+3q+1
        36: 3q^2+4q+1
        37: 3q^2+4q+1
        38: 2q+1
        39: q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+2q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 1
        55: q+1
        56: q+1
        57: q^2+3q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 1
        65: q^2+3q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: 2q^2+3q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 3q^2+4q+1
        77: q^2+2q+1
        78: q^2+3q+1
        79: 2q+1
        80: 2q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        89: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       104: q+1
       105: 1
       106: q+1
       107: 2q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: q+1
       125: q+1
       126: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 1
       139: q+1
       140: q+1
       141: q^2+3q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 1
       149: q^2+3q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 1
       157: q+1
       158: q+1
       159: 1
       162: q+1
       165: 1
       167: q+1
       169: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       181: q^2+2q+1
       183: q+1
       184: q+1
       185: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       225: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: 1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: 1
       261: q+1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: q+1
       291: q+1
       292: 1
       295: q+1
       298: 1
       300: q+1
       302: 1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       392: q+1
       394: 1
       397: 1
       412: 1
       435: 1
       437: q+1
       438: 1
       442: 1
       449: 1
       452: 1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       485: 1
       495: 1
       504: 1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       545: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       612: 1
       627: 1
       658: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       724: 1
       734: 1
       743: 1
       915: 1

 916:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 2q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: 2q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 2q+1
        72: 2q+1
        73: 2q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        92: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: 1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       136: 2q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: q+1
       159: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       184: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: q+1
       292: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       338: 1
       346: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       435: 1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       545: 1
       553: 1
       659: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       916: 1

 917:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       258: 1
       259: 1
       260: 1
       264: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       334: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       388: 1
       396: 1
       434: 1
       435: 1
       436: 1
       440: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       541: 1
       611: 1
       660: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       917: 1

 918:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        47: q+1
        48: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        85: q+1
        97: q+1
        98: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       177: q+1
       190: q+1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       336: 1
       337: 1
       338: 1
       342: 1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       468: 1
       475: 1
       478: 1
       479: 1
       493: 1
       518: 1
       521: 1
       522: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       549: 1
       661: 1
       707: 1
       714: 1
       717: 1
       718: 1
       732: 1
       918: 1

 919:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        45: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        92: 2q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       102: 2q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       159: 2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       184: 2q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: q+1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: 1
       244: 1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       259: q+1
       288: q+1
       290: q+1
       292: 2q+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: q+1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       435: q+1
       469: 1
       476: 1
       478: 1
       480: 1
       499: 1
       502: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       544: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       662: 1
       708: 1
       715: 1
       717: 1
       719: 1
       738: 1
       741: 1
       919: 1

 920:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: 1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: 1
        24: q^2+2q+1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q^2+2q+1
        31: q+1
        32: 1
        33: q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: 1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q^2+2q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q^2+2q+1
        74: 1
        75: q^2+2q+1
        76: 1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q^2+2q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        92: 1
        94: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: 1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q^2+2q+1
       140: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       159: 1
       160: q+1
       161: 1
       173: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       184: 1
       186: q+1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       260: q+1
       264: 1
       265: 1
       286: 1
       289: q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       306: 1
       308: 1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: q+1
       387: 1
       388: 1
       389: 1
       391: 1
       402: 1
       436: q+1
       440: 1
       441: 1
       462: 1
       470: 1
       477: 1
       479: 1
       480: 1
       490: 1
       503: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       617: 1
       663: 1
       709: 1
       716: 1
       718: 1
       719: 1
       729: 1
       742: 1
       920: 1

 921:    0: q^2+2q+1
         1: 2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: q^2+2q+1
         9: 2q+1
        10: q^2+2q+1
        11: 1
        12: q+1
        13: 2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 1
        24: q+1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 2q+1
        34: 2q+1
        35: q^2+2q+1
        36: 2q+1
        37: q^2+2q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        52: 2q+1
        53: 2q+1
        54: 1
        55: q+1
        56: 1
        57: 2q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 2q+1
        72: 2q+1
        73: 2q+1
        74: 1
        75: q+1
        76: 2q+1
        77: q+1
        78: q^2+2q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        91: q+1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       107: 2q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 2q+1
       137: 2q+1
       138: 1
       139: q+1
       140: 1
       141: 2q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: 1
       162: q+1
       165: 1
       167: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       231: 2q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: 1
       273: 1
       276: 1
       290: q+1
       291: q+1
       292: 1
       295: q+1
       298: 1
       300: 1
       302: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       394: 1
       399: 1
       437: q+1
       438: 1
       449: 1
       452: 1
       471: 1
       480: 1
       481: 1
       487: 1
       497: 1
       504: 1
       523: 1
       524: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       614: 1
       664: 1
       710: 1
       719: 1
       720: 1
       726: 1
       736: 1
       743: 1
       921: 1

 922:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: 1
       118: 1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: 1
       139: 1
       140: 1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: q+1
       159: 1
       163: q+1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       218: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: q+1
       240: 1
       241: 1
       242: 1
       244: 1
       245: 1
       246: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       269: q+1
       270: 1
       274: 1
       275: 1
       276: 1
       291: q+1
       292: 1
       296: q+1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: 1
       341: 1
       347: 1
       352: 1
       353: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       383: 1
       385: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       408: 1
       415: 1
       416: 1
       438: 1
       445: q+1
       446: 1
       450: 1
       451: 1
       452: 1
       472: 1
       481: 1
       482: 1
       512: 1
       524: 1
       525: 1
       532: 1
       533: 1
       534: 1
       539: 1
       548: 1
       554: 1
       559: 1
       560: 1
       586: 1
       623: 1
       630: 1
       631: 1
       665: 1
       711: 1
       720: 1
       721: 1
       751: 1
       830: 1
       922: 1

 923:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: 2q+1
        56: q+1
        57: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        64: 1
        65: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 2q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       104: q+1
       111: 1
       112: q+1
       113: 2q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: q+1
       128: q+1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 2q+1
       140: q+1
       141: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       148: 1
       149: 2q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       189: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       207: 1
       212: 1
       214: q+1
       220: 1
       224: 1
       225: 1
       227: 1
       228: q+1
       235: 1
       236: q+1
       237: 2q+1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: q+1
       252: q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       267: q+1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       328: 1
       335: 1
       345: 1
       351: 1
       355: 1
       356: 1
       364: 1
       365: q+1
       372: 1
       373: 1
       374: 1
       379: 1
       381: q+1
       387: 1
       391: 1
       392: 1
       394: 1
       395: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       473: 1
       483: 1
       491: 1
       510: 1
       516: 1
       526: 1
       534: 1
       535: 1
       542: 1
       552: 1
       558: 1
       562: 1
       563: 1
       582: 1
       610: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       666: 1
       712: 1
       722: 1
       730: 1
       749: 1
       807: 1
       826: 1
       923: 1

 924:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: 1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: 1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: 1
        51: q+1
        52: q+1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        92: q+1
        94: q^2+2q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       102: q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: q+1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 1
       135: q+1
       136: q+1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       159: 1
       160: q+1
       161: 1
       173: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       184: q+1
       186: q^2+2q+1
       188: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       228: 1
       229: 1
       230: q+1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: 1
       259: 1
       260: q+1
       264: 1
       265: 1
       286: q+1
       288: 1
       289: q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       306: q+1
       308: q+1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: q+1
       440: 1
       441: 1
       462: q+1
       474: 1
       483: 1
       484: 1
       490: 1
       503: 1
       517: 1
       526: 1
       527: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       564: 1
       610: 1
       611: 1
       617: 1
       667: 1
       713: 1
       722: 1
       723: 1
       729: 1
       742: 1
       808: 1
       924: 1

 925:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        68: 2q+1
        69: 2q+1
        71: q+1
        72: q^2+2q+1
        73: 1
        74: q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       129: 2q+1
       130: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       152: 2q+1
       153: 2q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       249: q+1
       253: 2q+1
       254: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       302: 1
       303: q+1
       306: q+1
       307: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       388: q+1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: q+1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       565: 1
       582: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       668: 1
       714: 1
       723: 1
       724: 1
       725: 1
       728: 1
       809: 1
       826: 1
       925: 1

 926:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       312: 1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       476: 1
       485: 1
       487: 1
       519: 1
       528: 1
       530: 1
       536: 1
       538: 1
       539: 1
       566: 1
       612: 1
       614: 1
       627: 1
       669: 1
       715: 1
       724: 1
       726: 1
       810: 1
       926: 1

 927:    0: q^3+q^2+q+1
         1: q+1
         2: q^3+q^2+q+1
         3: q^2+1
         4: q^3+q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q^2+1
         9: 1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q+1
        14: q^3+q^2+q+1
        15: q^2+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: q^2+1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        30: 1
        31: q^2+1
        32: 1
        33: q+1
        34: q+1
        35: q^2+1
        36: 1
        37: q^2+1
        38: 1
        39: q^2+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: q^2+1
        76: 1
        77: 1
        78: q^2+1
        79: 1
        80: 1
        81: 1
        82: q^2+1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       388: 1
       398: 1
       399: 1
       401: 1
       413: 1
       418: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       477: 1
       486: 1
       487: 1
       489: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       567: 1
       613: 1
       614: 1
       616: 1
       628: 1
       633: 1
       670: 1
       716: 1
       725: 1
       726: 1
       728: 1
       811: 1
       927: 1

 928:    0: q^3+7q^2+5q+1
         1: 4q^2+4q+1
         2: q^3+6q^2+5q+1
         3: 6q^2+5q+1
         4: q^3+7q^2+5q+1
         5: q^3+7q^2+5q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 3q^2+4q+1
         9: 3q^2+4q+1
        10: 3q^2+4q+1
        11: 6q^2+5q+1
        12: 3q^2+4q+1
        13: 4q^2+4q+1
        14: q^3+6q^2+5q+1
        15: 6q^2+5q+1
        16: 4q^2+4q+1
        17: q^3+6q^2+5q+1
        18: 3q^2+4q+1
        19: q^3+7q^2+5q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 3q^2+4q+1
        24: q^2+2q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+3q+1
        28: 3q^2+4q+1
        29: 3q^2+4q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: 3q^2+4q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 3q^2+4q+1
        36: 3q^2+4q+1
        37: 3q^2+4q+1
        38: 6q^2+5q+1
        39: 3q^2+4q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q^2+2q+1
        45: 3q^2+4q+1
        46: 2q+1
        47: 4q^2+4q+1
        48: q^3+6q^2+5q+1
        49: 3q^2+4q+1
        50: q^2+2q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q^2+3q+1
        61: q+1
        62: 2q+1
        63: q^2+2q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: q^2+3q+1
        69: q^2+3q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 3q^2+4q+1
        75: q^2+2q+1
        76: 2q+1
        77: q^2+2q+1
        78: q^2+3q+1
        79: 3q^2+4q+1
        80: 3q^2+4q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: 3q^2+4q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+3q+1
        88: q+1
        89: q+1
        91: q+1
        92: q^2+3q+1
        93: q^2+2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: q^2+2q+1
       102: 3q^2+4q+1
       103: 2q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: q+1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: q+1
       134: q^2+2q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q^2+2q+1
       141: q+1
       142: q+1
       143: q+1
       144: q^2+3q+1
       145: q+1
       146: 2q+1
       147: q^2+2q+1
       148: 2q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: q^2+3q+1
       153: q^2+3q+1
       154: q^2+2q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q^2+3q+1
       180: q+1
       181: q+1
       183: q+1
       184: q^2+3q+1
       185: q^2+2q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       215: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: q+1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: q+1
       246: 2q+1
       247: 1
       248: q+1
       249: q+1
       250: 1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: q+1
       256: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: q+1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       298: q+1
       299: 1
       300: q+1
       302: q+1
       303: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       314: 1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       342: 1
       344: 1
       346: 1
       348: 1
       349: 1
       350: 1
       358: 1
       361: 1
       362: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       375: 1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: q+1
       382: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: q+1
       391: 1
       397: 1
       400: 1
       401: 1
       412: 1
       418: 1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       448: 1
       449: 1
       452: q+1
       453: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       478: 1
       485: 1
       488: 1
       489: 1
       502: 1
       507: 1
       521: 1
       528: 1
       531: 1
       532: 1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       544: 1
       549: 1
       551: 1
       553: 1
       555: 1
       556: 1
       557: 1
       568: 1
       598: 1
       604: 1
       612: 1
       615: 1
       616: 1
       627: 1
       633: 1
       634: 1
       640: 1
       641: 1
       644: 1
       645: 1
       671: 1
       717: 1
       724: 1
       727: 1
       728: 1
       741: 1
       746: 1
       812: 1
       842: 1
       848: 1
       928: 1

 929:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: 1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        24: q^2+2q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q^2+2q+1
        31: q+1
        32: 1
        33: q^2+2q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: 1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q^2+2q+1
        52: q+1
        53: 1
        55: q+1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q^2+2q+1
        72: q+1
        73: q+1
        75: q^2+2q+1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: 1
        81: q^2+2q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        88: q+1
        89: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       106: q+1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       135: q^2+2q+1
       136: q+1
       137: 1
       139: q+1
       141: q+1
       142: 1
       143: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       158: 1
       160: q+1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: q+1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: q+1
       231: 1
       233: 1
       237: q+1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       260: q+1
       261: 1
       263: 1
       267: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: q+1
       290: q+1
       291: 1
       293: q+1
       295: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       315: 1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       345: 1
       346: 1
       349: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       381: q+1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       398: 1
       400: 1
       413: 1
       420: 1
       426: 1
       430: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       449: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       479: 1
       486: 1
       488: 1
       503: 1
       522: 1
       529: 1
       531: 1
       537: 1
       538: 1
       540: 1
       545: 1
       552: 1
       553: 1
       556: 1
       569: 1
       599: 1
       613: 1
       615: 1
       628: 1
       635: 1
       641: 1
       645: 1
       672: 1
       718: 1
       725: 1
       727: 1
       742: 1
       813: 1
       843: 1
       929: 1

 930:    0: 2q^2+3q+1
         1: 2q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: q^2+3q+1
         6: q+1
         7: 2q+1
         8: 2q^2+3q+1
         9: 2q+1
        10: q^2+2q+1
        11: 2q+1
        12: q^2+2q+1
        13: 2q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 2q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q^2+2q+1
        25: 1
        26: q+1
        27: q^2+2q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q^2+3q+1
        36: 2q+1
        37: q^2+2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q+1
        41: 2q+1
        42: q^2+3q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 2q+1
        61: q+1
        62: 1
        63: q+1
        64: 2q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: q^2+2q+1
        76: 1
        77: q+1
        78: q^2+2q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: 2q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: q+1
       122: 2q+1
       123: 1
       124: 1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 2q+1
       145: q+1
       146: 1
       147: q+1
       148: 2q+1
       149: 1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: q+1
       243: 1
       244: 1
       245: q+1
       246: 2q+1
       247: 1
       248: 1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: q+1
       256: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       346: 1
       349: 1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       375: 1
       376: 1
       377: q+1
       378: 1
       379: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       418: 1
       426: 1
       430: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: q+1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       553: 1
       556: 1
       570: 1
       589: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       633: 1
       641: 1
       645: 1
       673: 1
       719: 1
       726: 1
       727: 1
       728: 1
       729: 1
       814: 1
       833: 1
       930: 1

 931:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: q+1
        26: 1
        27: 2q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: 2q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: q+1
        73: q+1
        74: q+1
        75: 2q+1
        76: q+1
        77: 1
        78: 2q+1
        79: 1
        80: q+1
        81: q+1
        82: 2q+1
        83: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: 1
       139: q+1
       140: q+1
       142: 1
       143: 1
       144: q+1
       145: 2q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: q+1
       159: 1
       160: q+1
       161: 1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: q+1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       232: 1
       233: q+1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       263: q+1
       264: 1
       265: 1
       272: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       291: q+1
       292: 1
       293: q+1
       294: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: q+1
       306: 1
       307: 1
       308: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       341: 1
       347: 1
       349: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: 1
       385: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       401: 1
       402: 1
       403: 1
       418: 1
       431: 1
       438: 1
       439: q+1
       440: 1
       441: 1
       448: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       481: 1
       489: 1
       490: 1
       491: 1
       506: 1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       548: 1
       554: 1
       556: 1
       562: 1
       571: 1
       616: 1
       617: 1
       618: 1
       633: 1
       646: 1
       674: 1
       720: 1
       728: 1
       729: 1
       730: 1
       745: 1
       815: 1
       931: 1

 932:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        54: q+1
        55: 2q+1
        56: q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        63: q+1
        64: 1
        66: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        73: 2q+1
        74: q+1
        75: 2q+1
        77: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        86: q+1
        87: 1
        88: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       110: q+1
       111: 1
       116: q+1
       117: 2q+1
       118: q+1
       121: 1
       122: 1
       123: 1
       126: q+1
       128: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: q+1
       139: 2q+1
       140: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       147: q+1
       148: 1
       150: 2q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       159: 1
       160: q+1
       161: 1
       164: q+1
       165: 1
       166: q+1
       168: 1
       169: 1
       171: q+1
       173: 1
       174: 1
       175: 1
       178: q+1
       179: 1
       180: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       196: 1
       197: 1
       204: q+1
       205: 1
       210: 1
       211: 1
       212: 1
       218: q+1
       222: 1
       224: 1
       226: 1
       227: 1
       234: q+1
       235: 1
       240: q+1
       241: 2q+1
       242: q+1
       245: 1
       246: 1
       247: 1
       250: q+1
       252: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: 1
       271: q+1
       272: 1
       275: 1
       276: 1
       277: 1
       284: 1
       286: 1
       287: 1
       292: 1
       293: q+1
       294: 1
       297: q+1
       298: 1
       299: q+1
       301: 1
       302: 1
       304: q+1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       334: 1
       335: 1
       349: 1
       353: 1
       355: 1
       363: 1
       364: 1
       371: q+1
       372: 1
       377: 1
       378: 1
       379: 1
       385: q+1
       389: 1
       391: 1
       393: 1
       394: 1
       402: 1
       403: 1
       410: 1
       416: 1
       417: 1
       418: 1
       432: 1
       440: 1
       441: 1
       446: 1
       447: q+1
       448: 1
       451: 1
       452: 1
       453: 1
       460: 1
       462: 1
       463: 1
       482: 1
       490: 1
       491: 1
       514: 1
       525: 1
       533: 1
       534: 1
       541: 1
       542: 1
       556: 1
       560: 1
       562: 1
       572: 1
       588: 1
       617: 1
       618: 1
       625: 1
       631: 1
       632: 1
       633: 1
       647: 1
       675: 1
       721: 1
       729: 1
       730: 1
       753: 1
       816: 1
       832: 1
       932: 1

 933:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       266: 1
       273: 1
       276: 1
       288: 1
       295: 1
       298: 1
       300: 1
       302: 1
       309: 1
       319: 1
       327: 1
       336: 1
       343: 1
       344: 1
       351: 1
       354: 1
       356: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       412: 1
       442: 1
       449: 1
       452: 1
       473: 1
       492: 1
       500: 1
       509: 1
       516: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       627: 1
       676: 1
       712: 1
       731: 1
       739: 1
       748: 1
       933: 1

 934:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        92: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       102: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       259: 1
       288: 1
       290: 1
       292: 1
       310: 1
       319: 1
       320: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       435: 1
       474: 1
       492: 1
       493: 1
       499: 1
       502: 1
       517: 1
       526: 1
       527: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       677: 1
       713: 1
       731: 1
       732: 1
       738: 1
       741: 1
       934: 1

 935:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        47: q+1
        48: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        85: q+1
        97: q+1
        98: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       177: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       475: 1
       493: 1
       494: 1
       495: 1
       498: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       678: 1
       714: 1
       732: 1
       733: 1
       734: 1
       737: 1
       935: 1

 936:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       312: 1
       321: 1
       323: 1
       329: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       435: 1
       476: 1
       494: 1
       496: 1
       502: 1
       519: 1
       528: 1
       530: 1
       536: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       555: 1
       679: 1
       715: 1
       733: 1
       735: 1
       741: 1
       936: 1

 937:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q+1
         6: q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q+1
        33: q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q^2+2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q^2+2q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q^2+2q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       260: 1
       264: 1
       286: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       436: 1
       440: 1
       462: 1
       477: 1
       495: 1
       496: 1
       498: 1
       503: 1
       507: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       541: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       680: 1
       716: 1
       734: 1
       735: 1
       737: 1
       742: 1
       746: 1
       937: 1

 938:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       177: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       314: 1
       321: 1
       324: 1
       325: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       358: 1
       361: 1
       362: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       478: 1
       494: 1
       497: 1
       498: 1
       521: 1
       528: 1
       531: 1
       532: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       681: 1
       717: 1
       733: 1
       736: 1
       737: 1
       938: 1

 939:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       216: 1
       218: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       315: 1
       322: 1
       324: 1
       338: 1
       339: 1
       341: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       479: 1
       495: 1
       497: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       682: 1
       718: 1
       734: 1
       736: 1
       939: 1

 940:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: q+1
        74: 1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: q+1
       127: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       290: 1
       292: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       348: 1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       480: 1
       496: 1
       497: 1
       498: 1
       499: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       555: 1
       683: 1
       719: 1
       735: 1
       736: 1
       737: 1
       738: 1
       940: 1

 941:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       142: 1
       143: 1
       144: q+1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: 1
       159: 1
       165: 1
       167: 1
       169: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: 1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       276: 1
       291: 1
       292: 1
       298: 1
       300: 1
       302: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       354: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       438: 1
       452: 1
       481: 1
       498: 1
       499: 1
       500: 1
       505: 1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       561: 1
       684: 1
       720: 1
       737: 1
       738: 1
       739: 1
       744: 1
       941: 1

 942:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       164: 1
       165: 1
       168: 1
       169: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: 1
       257: 1
       270: 1
       275: 1
       276: 1
       292: 1
       297: 1
       298: 1
       301: 1
       302: 1
       318: 1
       326: 1
       327: 1
       342: 1
       343: 1
       348: 1
       353: 1
       354: 1
       363: 1
       364: 1
       371: 1
       372: 1
       377: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       416: 1
       446: 1
       451: 1
       452: 1
       482: 1
       499: 1
       500: 1
       513: 1
       525: 1
       533: 1
       534: 1
       549: 1
       550: 1
       555: 1
       560: 1
       561: 1
       631: 1
       685: 1
       721: 1
       738: 1
       739: 1
       752: 1
       942: 1

 943:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       161: 1
       173: 1
       175: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       265: 1
       286: 1
       288: 1
       289: 1
       294: 1
       306: 1
       308: 1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       356: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       395: 1
       434: 1
       441: 1
       462: 1
       483: 1
       492: 1
       501: 1
       508: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       610: 1
       686: 1
       722: 1
       731: 1
       740: 1
       747: 1
       943: 1

 944:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: q+1
        94: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: q+1
       186: q+1
       188: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       258: 1
       259: 1
       260: 1
       264: 1
       286: q+1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: q+1
       308: q+1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: 1
       434: 1
       435: 1
       436: 1
       440: 1
       462: q+1
       484: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       527: 1
       535: 1
       536: 1
       537: 1
       541: 1
       543: 1
       544: 1
       545: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       611: 1
       687: 1
       723: 1
       732: 1
       740: 1
       741: 1
       742: 1
       746: 1
       944: 1

 945:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        76: 2q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       136: 1
       137: 1
       138: 1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       191: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: q+1
       215: 1
       216: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       229: 1
       231: 1
       232: 1
       236: q+1
       238: 1
       239: 1
       240: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: q+1
       302: 1
       321: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: q+1
       382: 1
       383: 1
       384: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       394: 1
       397: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       485: 1
       494: 1
       502: 1
       504: 1
       505: 1
       509: 1
       528: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       612: 1
       627: 1
       688: 1
       724: 1
       733: 1
       741: 1
       743: 1
       744: 1
       748: 1
       945: 1

 946:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        24: q+1
        25: q^2+2q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: q+1
        59: 1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q^2+2q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q+1
        73: 1
        75: q+1
        76: q^2+2q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: q+1
       121: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: q+1
       143: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q^2+2q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: q+1
       238: 1
       239: 1
       241: 1
       243: 1
       244: q+1
       245: 1
       247: 1
       248: q+1
       249: q+1
       250: 1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       263: 1
       267: 1
       273: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       322: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       394: 1
       398: 1
       413: 1
       431: 1
       436: 1
       437: 1
       439: 1
       443: 1
       449: 1
       453: 1
       459: 1
       462: 1
       463: 1
       486: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       529: 1
       537: 1
       538: 1
       540: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       613: 1
       628: 1
       646: 1
       689: 1
       725: 1
       734: 1
       742: 1
       743: 1
       745: 1
       749: 1
       946: 1

 947:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: 1
        12: q^2+1
        13: 1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        30: 1
        31: q^2+1
        32: 1
        33: 1
        34: 1
        35: q^2+1
        36: 1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: q^2+1
        79: 1
        80: 1
        81: 1
        82: q^2+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       193: 1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       273: 1
       276: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       323: 1
       331: 1
       332: 1
       339: 1
       340: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       360: 1
       368: 1
       369: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       399: 1
       437: 1
       438: 1
       449: 1
       452: 1
       487: 1
       496: 1
       504: 1
       505: 1
       530: 1
       538: 1
       539: 1
       546: 1
       547: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       614: 1
       690: 1
       726: 1
       735: 1
       743: 1
       744: 1
       947: 1

 948:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: q+1
         7: 1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: 2q+1
        15: 2q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: 1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: 2q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: 1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: q+1
        72: 1
        73: 1
        75: q+1
        76: q+1
        77: 1
        78: 2q+1
        79: 1
        80: q+1
        81: q+1
        82: 2q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: 1
       145: q+1
       146: 1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: 2q+1
       152: 1
       153: q+1
       154: q+1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: 1
       188: 1
       194: 1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: q+1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: q+1
       256: 1
       257: q+1
       261: 1
       263: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       324: 1
       331: 1
       333: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       361: 1
       368: 1
       370: 1
       375: 1
       376: 1
       378: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: q+1
       400: 1
       426: 1
       430: 1
       431: 1
       433: 1
       437: 1
       439: 1
       449: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       488: 1
       497: 1
       504: 1
       506: 1
       531: 1
       538: 1
       540: 1
       546: 1
       548: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       605: 1
       609: 1
       615: 1
       641: 1
       645: 1
       646: 1
       648: 1
       691: 1
       727: 1
       736: 1
       743: 1
       745: 1
       849: 1
       853: 1
       948: 1

 949:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q^2+2q+1
        18: 1
        19: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q^2+2q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q^2+2q+1
        70: 1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q^2+2q+1
        81: q+1
        82: q^2+2q+1
        83: q^2+2q+1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       142: q+1
       143: 1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q^2+2q+1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       244: q+1
       245: 1
       246: 1
       247: 1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       272: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       325: 1
       332: 1
       333: 1
       334: 1
       340: 1
       341: 1
       342: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       362: 1
       369: 1
       370: 1
       371: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       401: 1
       418: 1
       431: 1
       438: 1
       439: 1
       440: 1
       448: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       489: 1
       498: 1
       505: 1
       506: 1
       507: 1
       515: 1
       532: 1
       539: 1
       540: 1
       541: 1
       547: 1
       548: 1
       549: 1
       554: 1
       555: 1
       556: 1
       557: 1
       561: 1
       562: 1
       616: 1
       633: 1
       646: 1
       692: 1
       728: 1
       737: 1
       744: 1
       745: 1
       746: 1
       754: 1
       949: 1

 950:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       196: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: 1
       264: 1
       265: 1
       286: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       326: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       363: 1
       371: 1
       372: 1
       377: 1
       378: 1
       379: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       391: 1
       402: 1
       440: 1
       441: 1
       462: 1
       490: 1
       499: 1
       507: 1
       508: 1
       533: 1
       541: 1
       542: 1
       549: 1
       550: 1
       555: 1
       556: 1
       557: 1
       617: 1
       693: 1
       729: 1
       738: 1
       746: 1
       747: 1
       950: 1

 951:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: 1
        19: q+1
        23: q+1
        24: q+1
        27: q+1
        29: q+1
        31: q+1
        32: q+1
        35: q+1
        37: q+1
        38: q+1
        39: q+1
        42: 1
        44: 1
        45: 1
        46: 1
        48: q+1
        49: 1
        56: q+1
        60: q+1
        61: q+1
        64: 1
        67: q+1
        69: q+1
        70: 1
        74: q+1
        75: q+1
        78: q+1
        80: q+1
        82: q+1
        83: q+1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       111: 1
       118: q+1
       122: 1
       123: 1
       127: q+1
       128: q+1
       131: 1
       133: 1
       140: q+1
       144: q+1
       145: q+1
       148: 1
       151: q+1
       153: q+1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       174: 1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       197: 1
       205: 1
       212: 1
       219: q+1
       223: 1
       224: 1
       227: 1
       235: 1
       242: q+1
       246: 1
       247: 1
       251: q+1
       252: q+1
       255: 1
       257: 1
       265: 1
       272: 1
       276: 1
       277: 1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       307: 1
       308: 1
       327: 1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       364: 1
       372: 1
       379: 1
       386: q+1
       390: 1
       391: 1
       394: 1
       403: 1
       418: 1
       441: 1
       448: 1
       452: 1
       453: 1
       463: 1
       491: 1
       500: 1
       508: 1
       515: 1
       534: 1
       542: 1
       550: 1
       557: 1
       561: 1
       562: 1
       618: 1
       633: 1
       694: 1
       730: 1
       739: 1
       747: 1
       754: 1
       951: 1

 952:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       148: 1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       198: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       328: 1
       336: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       365: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       501: 1
       509: 1
       510: 1
       515: 1
       535: 1
       543: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       582: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       695: 1
       740: 1
       748: 1
       749: 1
       754: 1
       826: 1
       952: 1

 953:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       199: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       236: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       329: 1
       337: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       366: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       405: 1
       412: 1
       414: 1
       416: 1
       435: 1
       442: 1
       444: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       502: 1
       509: 1
       511: 1
       513: 1
       536: 1
       544: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       583: 1
       620: 1
       627: 1
       629: 1
       631: 1
       696: 1
       741: 1
       748: 1
       750: 1
       752: 1
       827: 1
       953: 1

 954:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: q+1
        59: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: q+1
       121: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q^2+2q+1
       153: q+1
       154: q+1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       200: 1
       207: 1
       208: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       237: 1
       238: 1
       241: 1
       243: 1
       244: q+1
       245: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       260: 1
       267: 1
       268: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       330: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       367: 1
       374: 1
       375: 1
       378: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       406: 1
       413: 1
       414: 1
       417: 1
       427: 1
       431: 1
       432: 1
       436: 1
       443: 1
       444: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       503: 1
       510: 1
       511: 1
       514: 1
       537: 1
       545: 1
       552: 1
       553: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       584: 1
       606: 1
       621: 1
       628: 1
       629: 1
       632: 1
       642: 1
       646: 1
       647: 1
       697: 1
       742: 1
       749: 1
       750: 1
       753: 1
       828: 1
       850: 1
       954: 1

 955:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       114: 1
       115: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       141: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       201: 1
       208: 1
       209: 1
       215: 1
       216: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: 1
       238: 1
       239: 1
       243: 1
       244: 1
       245: 1
       248: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       268: 1
       269: 1
       273: 1
       274: 1
       275: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       331: 1
       339: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       368: 1
       375: 1
       376: 1
       382: 1
       383: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       407: 1
       414: 1
       415: 1
       437: 1
       444: 1
       445: 1
       449: 1
       450: 1
       451: 1
       504: 1
       511: 1
       512: 1
       538: 1
       546: 1
       553: 1
       554: 1
       558: 1
       559: 1
       560: 1
       585: 1
       622: 1
       629: 1
       630: 1
       698: 1
       743: 1
       750: 1
       751: 1
       829: 1
       955: 1

 956:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       115: 1
       116: 1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       202: 1
       209: 1
       210: 1
       216: 1
       217: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       232: 1
       239: 1
       240: 1
       244: 1
       245: 1
       246: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       269: 1
       270: 1
       274: 1
       275: 1
       276: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       332: 1
       340: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       369: 1
       376: 1
       377: 1
       383: 1
       384: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       408: 1
       415: 1
       416: 1
       438: 1
       445: 1
       446: 1
       450: 1
       451: 1
       452: 1
       505: 1
       512: 1
       513: 1
       539: 1
       547: 1
       554: 1
       555: 1
       559: 1
       560: 1
       561: 1
       586: 1
       623: 1
       630: 1
       631: 1
       699: 1
       744: 1
       751: 1
       752: 1
       830: 1
       956: 1

 957:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        55: 1
        58: q+1
        59: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       109: 1
       115: 1
       117: 1
       120: q+1
       121: 1
       123: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: q+1
       143: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       203: 1
       209: 1
       211: 1
       216: 1
       218: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       233: 1
       239: 1
       241: 1
       244: q+1
       245: 1
       247: 1
       249: q+1
       250: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       263: 1
       269: 1
       271: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       333: 1
       341: 1
       347: 1
       349: 1
       352: 1
       353: 1
       355: 1
       370: 1
       376: 1
       378: 1
       383: 1
       385: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       409: 1
       415: 1
       417: 1
       427: 1
       431: 1
       432: 1
       439: 1
       445: 1
       447: 1
       450: 1
       451: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       506: 1
       512: 1
       514: 1
       540: 1
       548: 1
       554: 1
       556: 1
       559: 1
       560: 1
       562: 1
       587: 1
       606: 1
       624: 1
       630: 1
       632: 1
       642: 1
       646: 1
       647: 1
       700: 1
       745: 1
       751: 1
       753: 1
       831: 1
       850: 1
       957: 1

 958:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        75: 1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: q+1
       148: 1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       204: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       251: 1
       252: 1
       254: q+1
       255: 1
       256: 1
       257: 1
       264: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       284: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       306: 1
       307: 1
       308: 1
       334: 1
       342: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       371: 1
       377: 1
       378: 1
       379: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       391: 1
       393: 1
       394: 1
       410: 1
       416: 1
       417: 1
       418: 1
       432: 1
       440: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       460: 1
       462: 1
       463: 1
       507: 1
       513: 1
       514: 1
       515: 1
       541: 1
       549: 1
       555: 1
       556: 1
       557: 1
       560: 1
       561: 1
       562: 1
       588: 1
       625: 1
       631: 1
       632: 1
       633: 1
       647: 1
       701: 1
       746: 1
       752: 1
       753: 1
       754: 1
       832: 1
       958: 1

 959:    0: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q^2+q+1
        14: q+1
        15: q^2+q+1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: q+1
        27: q+1
        29: q+1
        31: q+1
        32: q+1
        35: q+1
        37: q+1
        38: q+1
        39: q^2+q+1
        42: q+1
        44: 1
        45: q+1
        46: q+1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: q+1
        64: q+1
        67: q+1
        69: q+1
        70: q+1
        74: 1
        75: q+1
        78: q+1
        80: q+1
        82: q+1
        83: q+1
        87: 1
        88: q+1
        91: 1
        93: 1
        95: 1
        96: q+1
        99: q+1
       101: 1
       102: q+1
       103: q+1
       111: 1
       118: 1
       122: 1
       123: q+1
       127: 1
       128: q+1
       131: q+1
       133: 1
       140: 1
       144: 1
       145: q+1
       148: q+1
       151: q+1
       153: q+1
       154: q+1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: q+1
       179: 1
       180: q+1
       183: 1
       185: 1
       187: 1
       188: q+1
       205: 1
       212: 1
       219: 1
       223: 1
       224: q+1
       227: 1
       235: 1
       242: 1
       246: 1
       247: q+1
       251: 1
       252: q+1
       255: q+1
       257: 1
       265: 1
       272: 1
       276: 1
       277: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: q+1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       372: 1
       379: 1
       386: 1
       390: 1
       391: q+1
       394: 1
       411: 1
       418: 1
       430: 1
       433: 1
       441: 1
       448: 1
       452: 1
       453: 1
       458: 1
       461: 1
       463: 1
       508: 1
       515: 1
       542: 1
       550: 1
       557: 1
       561: 1
       562: 1
       589: 1
       609: 1
       626: 1
       633: 1
       645: 1
       648: 1
       702: 1
       747: 1
       754: 1
       833: 1
       853: 1
       959: 1

 960:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: 1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: 1
        16: q^2+q+1
        17: q^2+q+1
        18: 1
        19: q^2+q+1
        20: 1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q^2+q+1
        34: q^2+q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q^2+q+1
        41: q^2+q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q^2+q+1
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: q^2+q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: q^2+q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: 1
       100: 1
       101: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q^2+q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       221: 1
       225: 1
       226: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       249: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       320: 1
       321: 1
       322: 1
       325: 1
       352: 1
       359: 1
       367: 1
       368: 1
       370: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       427: 1
       431: 1
       432: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       455: 1
       464: 1
       465: 1
       472: 1
       475: 1
       529: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       579: 1
       606: 1
       613: 1
       621: 1
       622: 1
       624: 1
       649: 1
       755: 1
       756: 1
       763: 1
       766: 1
       820: 1
       960: 1

 961:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        78: q+1
        81: 1
        82: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: q+1
       137: q+1
       139: 1
       141: q+1
       145: 1
       149: 1
       151: 1
       155: 1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       183: q+1
       186: 1
       187: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       225: 1
       227: 1
       230: 1
       231: q+1
       233: 1
       237: 1
       248: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: q+1
       291: q+1
       293: 1
       295: q+1
       299: 1
       303: 1
       305: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       351: 1
       359: 1
       361: 1
       381: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       420: 1
       426: 1
       431: 1
       433: 1
       436: 1
       437: q+1
       439: 1
       443: 1
       454: 1
       458: 1
       465: 1
       466: 1
       471: 1
       473: 1
       522: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       605: 1
       613: 1
       615: 1
       635: 1
       650: 1
       756: 1
       757: 1
       762: 1
       764: 1
       813: 1
       961: 1

 962:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       230: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: 1
       290: 1
       293: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       328: 1
       335: 1
       345: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       436: 1
       466: 1
       467: 1
       470: 1
       483: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       599: 1
       651: 1
       757: 1
       758: 1
       761: 1
       774: 1
       962: 1

 963:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        79: q+1
        81: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       139: 1
       140: 1
       152: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       184: q+1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       228: 1
       229: q+1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: q+1
       289: 1
       290: q+1
       292: q+1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       336: 1
       343: 1
       344: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       434: 1
       435: q+1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       468: 1
       469: 1
       492: 1
       517: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       590: 1
       597: 1
       598: 1
       610: 1
       611: 1
       617: 1
       652: 1
       757: 1
       759: 1
       760: 1
       783: 1
       808: 1
       963: 1

 964:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: 1
        60: 2q+1
        61: 2q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: q+1
        69: 2q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        79: 1
        81: 1
        83: q+1
        84: 1
        85: q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       118: 2q+1
       119: 1
       122: q+1
       123: q+1
       124: 1
       127: q+1
       128: q+1
       129: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: q+1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: 2q+1
       162: 1
       165: 2q+1
       166: 2q+1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q+1
       174: 2q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: q+1
       184: 1
       186: 1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: q+1
       213: 1
       214: 1
       219: q+1
       220: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       272: 2q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: q+1
       282: q+1
       283: q+1
       285: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: q+1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       357: 1
       363: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: q+1
       426: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       467: 1
       468: 1
       469: 1
       470: 1
       501: 1
       508: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       611: 1
       617: 1
       653: 1
       758: 1
       759: 1
       760: 1
       761: 1
       792: 1
       799: 1
       964: 1

 965:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: q+1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        60: 2q+1
        61: q+1
        62: q+1
        64: q+1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: q+1
        75: 1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: q+1
        87: 2q+1
        88: q+1
        89: q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       118: q+1
       119: 1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: q+1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: 2q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       205: 1
       206: 1
       213: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       272: q+1
       273: 1
       276: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       327: 1
       343: 1
       344: 1
       351: 1
       354: 1
       358: 1
       361: 1
       362: 1
       363: 1
       364: 1
       380: 1
       386: 1
       392: 1
       397: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       403: 1
       411: 1
       412: 1
       419: 1
       425: 1
       426: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       469: 1
       471: 1
       500: 1
       509: 1
       521: 1
       524: 1
       566: 1
       568: 1
       570: 1
       571: 1
       581: 1
       597: 1
       598: 1
       605: 1
       608: 1
       612: 1
       615: 1
       616: 1
       617: 1
       618: 1
       634: 1
       640: 1
       646: 1
       654: 1
       760: 1
       762: 1
       791: 1
       800: 1
       812: 1
       815: 1
       965: 1

 966:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: 1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: q+1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        39: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: q+1
        76: 1
        78: q+1
        81: 1
        82: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: q+1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: q+1
       149: 1
       151: q+1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: q+1
       181: 1
       183: q+1
       186: 1
       187: q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       205: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: q+1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: q+1
       303: 1
       305: q+1
       313: 1
       315: 1
       316: 1
       317: 1
       327: 1
       335: 1
       345: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: q+1
       470: 1
       471: 1
       491: 1
       510: 1
       522: 1
       567: 1
       569: 1
       570: 1
       571: 1
       581: 1
       589: 1
       599: 1
       605: 1
       609: 1
       613: 1
       615: 1
       635: 1
       655: 1
       761: 1
       762: 1
       782: 1
       801: 1
       813: 1
       966: 1

 967:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        81: q+1
        82: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: q+1
       145: 1
       149: 1
       150: 1
       151: 1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       186: q+1
       187: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: q+1
       299: 1
       303: 1
       304: 1
       305: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       346: 1
       351: 1
       352: 1
       353: 1
       361: 1
       368: 1
       370: 1
       382: 1
       385: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       416: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       471: 1
       472: 1
       480: 1
       482: 1
       511: 1
       531: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       600: 1
       605: 1
       606: 1
       607: 1
       615: 1
       622: 1
       624: 1
       636: 1
       639: 1
       656: 1
       762: 1
       763: 1
       771: 1
       773: 1
       802: 1
       822: 1
       967: 1

 968:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: 1
        51: 1
        52: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        81: q+1
        82: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: 1
       136: q+1
       139: 1
       141: q+1
       142: q+1
       143: q+1
       145: 1
       149: 1
       150: 1
       151: 1
       155: 1
       156: 1
       157: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       186: q+1
       187: 1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       230: 1
       237: 1
       238: q+1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: 1
       290: q+1
       293: 1
       295: q+1
       296: q+1
       297: q+1
       299: 1
       303: 1
       304: 1
       305: 1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       329: 1
       338: 1
       346: 1
       351: 1
       352: 1
       353: 1
       367: 1
       381: 1
       382: 1
       385: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       436: 1
       443: 1
       444: q+1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       464: 1
       473: 1
       474: 1
       482: 1
       511: 1
       545: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: 1
       580: 1
       581: 1
       583: 1
       592: 1
       600: 1
       605: 1
       606: 1
       607: 1
       621: 1
       635: 1
       636: 1
       639: 1
       657: 1
       755: 1
       764: 1
       765: 1
       773: 1
       802: 1
       836: 1
       968: 1

 969:    0: 4q^2+4q+1
         1: 4q^2+4q+1
         2: 4q^2+4q+1
         3: 3q^2+4q+1
         4: 2q^2+3q+1
         5: 4q^2+4q+1
         6: 4q^2+4q+1
         7: 2q^2+3q+1
         8: q^2+3q+1
         9: 3q^2+4q+1
        10: 3q^2+4q+1
        11: q^2+3q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+2q+1
        16: 4q^2+4q+1
        17: 4q^2+4q+1
        18: 3q^2+4q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: 2q^2+3q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 3q^2+4q+1
        26: q^2+2q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q+1
        40: 4q^2+4q+1
        41: 2q^2+3q+1
        42: q^2+3q+1
        43: 3q^2+4q+1
        44: 3q^2+4q+1
        45: q^2+3q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 1
        56: q+1
        57: q^2+3q+1
        58: q^2+2q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: q^2+3q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        75: 1
        76: q^2+2q+1
        78: q+1
        81: q+1
        82: q+1
        84: q^2+3q+1
        85: 2q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 3q^2+4q+1
        90: q^2+2q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       103: q+1
       104: q+1
       105: q+1
       106: 1
       107: 2q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: q+1
       137: q+1
       139: 1
       141: q+1
       145: 1
       149: q+1
       151: 1
       155: 2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: q+1
       160: 1
       161: q+1
       162: q^2+3q+1
       163: q^2+2q+1
       164: q+1
       165: 2q+1
       166: q+1
       167: q^2+3q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       180: 1
       181: q^2+2q+1
       183: q+1
       186: q+1
       187: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       225: q+1
       227: 1
       230: 1
       231: q+1
       233: 1
       237: 1
       248: 1
       252: 1
       258: q+1
       259: q+1
       260: 1
       261: 2q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: 2q+1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 1
       290: q+1
       291: q+1
       293: 1
       295: q+1
       299: 1
       303: q+1
       305: 1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       359: 1
       381: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       431: q+1
       433: 1
       436: 1
       437: q+1
       439: 1
       443: 1
       454: 1
       458: 1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       485: 1
       495: 1
       504: 1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       592: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       613: 1
       635: 1
       658: 1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       776: 1
       786: 1
       795: 1
       969: 1

 970:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        39: 1
        40: 2q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: 2q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        81: 1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: q+1
       139: 1
       155: q+1
       156: 1
       157: 2q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       186: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       230: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       289: 1
       290: q+1
       293: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       338: 1
       346: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       436: 1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       592: 1
       600: 1
       659: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       970: 1

 971:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        72: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       177: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       334: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       565: 1
       566: 1
       567: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       588: 1
       660: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: 1
       971: 1

 972:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       336: 1
       337: 1
       338: 1
       342: 1
       357: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       427: 1
       434: 1
       435: 1
       436: 1
       440: 1
       468: 1
       475: 1
       478: 1
       479: 1
       493: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       590: 1
       591: 1
       592: 1
       596: 1
       611: 1
       661: 1
       759: 1
       766: 1
       769: 1
       770: 1
       784: 1
       972: 1

 973:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        39: 1
        40: q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: 1
        54: q^2+2q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        79: q+1
        81: 1
        83: 1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 1
        89: 1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       103: 1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+1
       136: q+1
       138: q+1
       139: 1
       140: 1
       152: 1
       154: 1
       155: q+1
       157: q+1
       158: 1
       159: q^2+2q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       184: q+1
       186: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: q+1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: q+1
       234: 1
       235: 1
       256: 1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+1
       290: q+1
       292: q+1
       293: 1
       294: 1
       306: 1
       308: 1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       363: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: q+1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       435: q+1
       440: 1
       441: 1
       462: 1
       469: 1
       476: 1
       478: 1
       480: 1
       499: 1
       502: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       617: 1
       662: 1
       760: 1
       767: 1
       769: 1
       771: 1
       790: 1
       793: 1
       973: 1

 974:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: 2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        75: 2q+1
        81: 2q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 2q+1
        95: q+1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       103: 2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: q+1
       136: q+1
       139: 2q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       180: 2q+1
       186: 2q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       230: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       289: q+1
       290: q+1
       293: 2q+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       436: q+1
       470: 1
       477: 1
       479: 1
       480: 1
       490: 1
       503: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       663: 1
       761: 1
       768: 1
       770: 1
       771: 1
       781: 1
       794: 1
       974: 1

 975:    0: q^2+2q+1
         1: 2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: 2q+1
         7: 2q+1
         8: q^2+2q+1
         9: 2q+1
        10: q^2+2q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: 1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: 1
        40: 2q+1
        41: 2q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^2+2q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 1
        56: 1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        78: q+1
        81: 1
        82: 1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 1
        89: 2q+1
        90: q+1
        91: q^2+2q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: 1
       107: 2q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       139: 1
       141: q+1
       145: 1
       149: 1
       151: 1
       157: 2q+1
       158: 2q+1
       159: q+1
       160: 1
       161: 1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       183: q+1
       186: 1
       187: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       231: q+1
       233: 1
       248: 1
       252: 1
       261: 2q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       293: 1
       295: q+1
       299: 1
       303: 1
       305: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       361: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       433: 1
       437: q+1
       439: 1
       454: 1
       458: 1
       471: 1
       480: 1
       481: 1
       487: 1
       497: 1
       504: 1
       570: 1
       571: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       615: 1
       664: 1
       762: 1
       771: 1
       772: 1
       778: 1
       788: 1
       795: 1
       975: 1

 976:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        81: 1
        82: 1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: 1
       118: 1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       139: 1
       142: q+1
       143: q+1
       145: 1
       149: 1
       150: 1
       151: 1
       158: q+1
       159: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       186: 1
       187: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       218: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       233: 1
       239: q+1
       241: 1
       249: 1
       250: 1
       252: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: q+1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       293: 1
       296: q+1
       297: q+1
       299: 1
       303: 1
       304: 1
       305: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: 1
       341: 1
       347: 1
       352: 1
       353: 1
       370: 1
       383: 1
       385: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       422: 1
       424: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       439: 1
       445: q+1
       447: 1
       455: 1
       456: 1
       458: 1
       472: 1
       481: 1
       482: 1
       512: 1
       548: 1
       571: 1
       572: 1
       579: 1
       580: 1
       581: 1
       586: 1
       595: 1
       601: 1
       606: 1
       607: 1
       624: 1
       637: 1
       639: 1
       665: 1
       763: 1
       772: 1
       773: 1
       803: 1
       839: 1
       976: 1

 977:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       101: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       237: 1
       248: 1
       252: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       295: 1
       299: 1
       303: 1
       305: 1
       309: 1
       319: 1
       327: 1
       328: 1
       335: 1
       345: 1
       351: 1
       355: 1
       381: 1
       395: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       443: 1
       454: 1
       458: 1
       473: 1
       483: 1
       491: 1
       510: 1
       563: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       635: 1
       666: 1
       764: 1
       774: 1
       782: 1
       801: 1
       977: 1

 978:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        81: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: 1
       136: 1
       139: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       180: 1
       186: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       289: 1
       290: 1
       293: 1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       436: 1
       474: 1
       483: 1
       484: 1
       490: 1
       503: 1
       564: 1
       573: 1
       574: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       667: 1
       765: 1
       774: 1
       775: 1
       781: 1
       794: 1
       978: 1

 979:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        68: q+1
        69: q+1
        72: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       129: q+1
       130: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       177: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       668: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       979: 1

 980:    0: 1
         1: 1
         2: 1
         3: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        16: 1
        17: 1
        18: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       312: 1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       476: 1
       485: 1
       487: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       669: 1
       767: 1
       776: 1
       778: 1
       980: 1

 981:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       398: 1
       399: 1
       401: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       477: 1
       486: 1
       487: 1
       489: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       670: 1
       768: 1
       777: 1
       778: 1
       780: 1
       981: 1

 982:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q^2+2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q^2+2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       229: 1
       234: 1
       256: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       314: 1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       342: 1
       344: 1
       346: 1
       348: 1
       349: 1
       350: 1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       435: 1
       440: 1
       462: 1
       478: 1
       485: 1
       488: 1
       489: 1
       502: 1
       507: 1
       568: 1
       575: 1
       578: 1
       579: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       591: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       671: 1
       769: 1
       776: 1
       779: 1
       780: 1
       793: 1
       798: 1
       982: 1

 983:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       289: 1
       290: 1
       293: 1
       315: 1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       345: 1
       346: 1
       349: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       436: 1
       479: 1
       486: 1
       488: 1
       503: 1
       569: 1
       576: 1
       578: 1
       584: 1
       585: 1
       587: 1
       592: 1
       599: 1
       600: 1
       603: 1
       672: 1
       770: 1
       777: 1
       779: 1
       794: 1
       983: 1

 984:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: 1
       139: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       290: 1
       293: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       346: 1
       349: 1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       600: 1
       603: 1
       673: 1
       771: 1
       778: 1
       779: 1
       780: 1
       781: 1
       984: 1

 985:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: q+1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: q+1
       123: q+1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       145: 1
       149: 1
       151: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       163: 1
       164: 1
       165: q+1
       166: q+1
       167: 1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: q+1
       175: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       233: 1
       252: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       293: 1
       299: 1
       303: 1
       305: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       341: 1
       347: 1
       349: 1
       355: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       422: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       439: 1
       458: 1
       481: 1
       489: 1
       490: 1
       491: 1
       506: 1
       571: 1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       595: 1
       601: 1
       603: 1
       609: 1
       674: 1
       772: 1
       780: 1
       781: 1
       782: 1
       797: 1
       985: 1

 986:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        77: 1
        78: 1
        81: 1
        82: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       139: 1
       143: 1
       145: 1
       150: 1
       151: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: 1
       186: 1
       187: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       218: 1
       222: 1
       224: 1
       226: 1
       227: 1
       241: 1
       250: 1
       252: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       293: 1
       297: 1
       299: 1
       304: 1
       305: 1
       318: 1
       326: 1
       327: 1
       334: 1
       335: 1
       349: 1
       353: 1
       355: 1
       385: 1
       402: 1
       403: 1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       424: 1
       428: 1
       430: 1
       432: 1
       433: 1
       447: 1
       456: 1
       458: 1
       482: 1
       490: 1
       491: 1
       514: 1
       572: 1
       580: 1
       581: 1
       588: 1
       589: 1
       603: 1
       607: 1
       609: 1
       639: 1
       675: 1
       773: 1
       781: 1
       782: 1
       805: 1
       986: 1

 987:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        51: q+1
        56: q+1
        57: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        64: q+1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 2q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: q+1
       111: 1
       112: 2q+1
       113: q+1
       118: q+1
       119: q+1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 2q+1
       156: q+1
       161: q+1
       162: 2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: q+1
       205: 1
       206: q+1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: q+1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: q+1
       265: 1
       266: 2q+1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       336: 1
       343: 1
       344: 1
       351: 1
       354: 1
       356: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       403: 1
       404: q+1
       411: 1
       412: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       473: 1
       492: 1
       500: 1
       509: 1
       516: 1
       543: 1
       563: 1
       573: 1
       581: 1
       590: 1
       597: 1
       598: 1
       605: 1
       608: 1
       610: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       676: 1
       764: 1
       783: 1
       791: 1
       800: 1
       807: 1
       834: 1
       987: 1

 988:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: 1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q^2+2q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        38: q^2+2q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: 1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: q+1
        51: 1
        52: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        79: q^2+2q+1
        81: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q^2+2q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       102: q^2+2q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       139: 1
       140: 1
       152: q+1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       184: q^2+2q+1
       186: q+1
       188: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: q+1
       230: 1
       234: 1
       235: 1
       256: q+1
       258: 1
       259: q+1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       289: 1
       290: q+1
       292: q+1
       293: 1
       294: 1
       306: q+1
       308: q+1
       310: 1
       319: 1
       320: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       434: 1
       435: q+1
       436: 1
       440: 1
       441: 1
       462: q+1
       474: 1
       492: 1
       493: 1
       499: 1
       502: 1
       517: 1
       564: 1
       573: 1
       574: 1
       580: 1
       583: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       610: 1
       611: 1
       617: 1
       677: 1
       765: 1
       783: 1
       784: 1
       790: 1
       793: 1
       808: 1
       988: 1

 989:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        71: 1
        72: q^2+2q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 1
        87: q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       155: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: q+1
       167: 2q+1
       168: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       258: q+1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: 2q+1
       284: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       380: 1
       381: 1
       386: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       475: 1
       493: 1
       494: 1
       495: 1
       498: 1
       518: 1
       543: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       634: 1
       635: 1
       640: 1
       678: 1
       766: 1
       784: 1
       785: 1
       786: 1
       789: 1
       809: 1
       834: 1
       989: 1

 990:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        25: q+1
        26: 1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        40: q^2+2q+1
        41: q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+2q+1
        52: q+1
        53: 1
        54: q+1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+2q+1
        85: q+1
        86: q+1
        87: q^2+2q+1
        89: q+1
        90: 1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       105: q+1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q^2+2q+1
       157: q+1
       158: 1
       159: q+1
       162: q+1
       163: 1
       164: 1
       165: q+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: q+1
       208: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: q+1
       231: 1
       232: 1
       236: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       259: q+1
       261: 1
       262: 1
       266: q+1
       268: 1
       269: 1
       270: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       321: 1
       323: 1
       329: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       373: 1
       380: 1
       387: 1
       390: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: q+1
       414: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       435: q+1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       454: 1
       457: 1
       459: 1
       461: 1
       462: 1
       476: 1
       494: 1
       496: 1
       502: 1
       519: 1
       551: 1
       566: 1
       575: 1
       577: 1
       583: 1
       591: 1
       593: 1
       594: 1
       598: 1
       600: 1
       602: 1
       612: 1
       614: 1
       627: 1
       634: 1
       641: 1
       644: 1
       679: 1
       767: 1
       785: 1
       787: 1
       793: 1
       810: 1
       842: 1
       990: 1

 991:    0: q^3+7q^2+5q+1
         1: 4q^2+4q+1
         2: q^3+6q^2+5q+1
         3: 6q^2+5q+1
         4: q^3+7q^2+5q+1
         5: q^3+7q^2+5q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 3q^2+4q+1
         9: 3q^2+4q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: 6q^2+5q+1
        13: 4q^2+4q+1
        14: q^3+6q^2+5q+1
        15: 3q^2+4q+1
        16: 4q^2+4q+1
        17: q^3+6q^2+5q+1
        18: 6q^2+5q+1
        19: q^3+7q^2+5q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 3q^2+4q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 3q^2+4q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q^2+2q+1
        38: 2q+1
        39: 3q^2+4q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 3q^2+4q+1
        43: 3q^2+4q+1
        44: 3q^2+4q+1
        45: 3q^2+4q+1
        46: 6q^2+5q+1
        47: 4q^2+4q+1
        48: q^3+6q^2+5q+1
        49: 3q^2+4q+1
        51: q^2+2q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q^2+3q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q^2+2q+1
        67: 2q+1
        68: q^2+3q+1
        69: q^2+3q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: q^2+3q+1
        76: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q^2+3q+1
        82: q^2+2q+1
        83: 2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: 3q^2+4q+1
        89: 2q+1
        90: q^2+2q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 3q^2+4q+1
        95: 3q^2+4q+1
        96: 3q^2+4q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: q^2+2q+1
       102: 2q+1
       103: 3q^2+4q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: 2q+1
       124: 1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       144: 1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: 2q+1
       153: q+1
       154: q+1
       156: q^2+2q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+3q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q^2+2q+1
       172: 2q+1
       173: q^2+3q+1
       174: q^2+3q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q+1
       180: q^2+3q+1
       181: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q^2+3q+1
       187: q^2+2q+1
       188: 2q+1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: q+1
       208: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: q+1
       253: q+1
       255: 1
       256: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: 2q+1
       278: 1
       279: q+1
       280: q+1
       281: 1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: q+1
       286: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       298: 1
       299: q+1
       300: q+1
       302: 1
       303: q+1
       305: q+1
       306: 2q+1
       307: q+1
       308: q+1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       359: 1
       360: 1
       362: 1
       374: 1
       379: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       398: 1
       399: 1
       401: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: q+1
       414: 1
       416: 1
       417: 1
       418: q+1
       420: 1
       421: 1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: q+1
       459: q+1
       461: 1
       462: q+1
       477: 1
       495: 1
       496: 1
       498: 1
       503: 1
       507: 1
       520: 1
       552: 1
       557: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: 1
       588: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       613: 1
       614: 1
       616: 1
       628: 1
       633: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       680: 1
       768: 1
       786: 1
       787: 1
       789: 1
       794: 1
       798: 1
       811: 1
       843: 1
       848: 1
       991: 1

 992:    0: q^3+q^2+q+1
         1: q+1
         2: q^3+q^2+q+1
         3: q^2+1
         4: q+1
         5: q^3+q^2+q+1
         6: q+1
         7: q+1
         8: q^2+1
         9: 1
        10: q^2+1
        11: q^2+1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q^3+q^2+q+1
        18: q^2+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: q^2+1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q^2+1
        43: 1
        44: q^2+1
        45: q^2+1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: q^2+1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: 1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: q^2+1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       314: 1
       321: 1
       324: 1
       325: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       358: 1
       361: 1
       362: 1
       380: 1
       386: 1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       478: 1
       494: 1
       497: 1
       498: 1
       521: 1
       568: 1
       575: 1
       578: 1
       579: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       612: 1
       615: 1
       616: 1
       634: 1
       640: 1
       681: 1
       769: 1
       785: 1
       788: 1
       789: 1
       812: 1
       992: 1

 993:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       216: 1
       218: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       315: 1
       322: 1
       324: 1
       338: 1
       339: 1
       341: 1
       359: 1
       361: 1
       381: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       420: 1
       421: 1
       422: 1
       424: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       479: 1
       495: 1
       497: 1
       522: 1
       569: 1
       576: 1
       578: 1
       592: 1
       593: 1
       595: 1
       613: 1
       615: 1
       635: 1
       682: 1
       770: 1
       786: 1
       788: 1
       813: 1
       993: 1

 994:    0: 2q^2+3q+1
         1: 2q+1
         2: 2q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+3q+1
         5: 2q^2+3q+1
         6: q+1
         7: 2q+1
         8: 2q^2+3q+1
         9: 2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q+1
        13: 2q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: 2q+1
        17: 2q^2+3q+1
        18: 2q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q+1
        25: 1
        26: q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: q^2+3q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q^2+3q+1
        43: 2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 2q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: q+1
        67: 2q+1
        68: 1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q^2+2q+1
        92: q+1
        93: q+1
        94: q+1
        95: 2q+1
        96: q+1
        97: q+1
        98: 2q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: q+1
       127: 1
       128: 2q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 2q+1
       167: 1
       168: 1
       169: q+1
       170: 1
       171: q+1
       172: 2q+1
       173: 1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: q+1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       210: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: q+1
       273: 1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: q+1
       281: 1
       282: 2q+1
       283: 1
       284: 1
       285: q+1
       286: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       348: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       386: 1
       387: 1
       390: 1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       414: 1
       416: 1
       421: 1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: q+1
       459: 1
       461: 1
       462: 1
       480: 1
       496: 1
       497: 1
       498: 1
       499: 1
       523: 1
       550: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: 1
       602: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       640: 1
       641: 1
       644: 1
       683: 1
       771: 1
       787: 1
       788: 1
       789: 1
       790: 1
       814: 1
       841: 1
       994: 1

 995:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: q+1
        26: 1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: 2q+1
        61: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: 1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: 1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       108: q+1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: q+1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: q+1
       139: 1
       140: 1
       144: q+1
       145: 1
       146: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: q+1
       159: q+1
       160: 1
       161: q+1
       163: 1
       164: 1
       165: 2q+1
       166: q+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: q+1
       175: 1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       232: q+1
       233: 1
       234: 1
       235: 1
       242: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       262: q+1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: 1
       275: 1
       276: q+1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       292: q+1
       293: 1
       294: 1
       298: q+1
       299: 1
       300: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       354: 1
       362: 1
       363: 1
       364: 1
       386: 1
       392: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       438: q+1
       439: 1
       440: 1
       441: 1
       448: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       481: 1
       498: 1
       499: 1
       500: 1
       505: 1
       524: 1
       571: 1
       579: 1
       580: 1
       581: 1
       586: 1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       608: 1
       616: 1
       617: 1
       618: 1
       640: 1
       646: 1
       684: 1
       772: 1
       789: 1
       790: 1
       791: 1
       796: 1
       815: 1
       995: 1

 996:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        54: 2q+1
        55: q+1
        56: q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        63: 2q+1
        64: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: q+1
        74: q+1
        75: 1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        86: 2q+1
        87: 2q+1
        88: q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       110: q+1
       111: 1
       116: 2q+1
       117: q+1
       118: q+1
       121: q+1
       122: q+1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: q+1
       139: 1
       140: 1
       143: q+1
       144: q+1
       145: 1
       147: q+1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 2q+1
       160: q+1
       161: q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       168: 2q+1
       169: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       178: q+1
       179: q+1
       180: 1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: q+1
       205: 1
       210: q+1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: q+1
       241: 1
       242: 1
       250: 1
       251: 1
       252: 1
       254: 1
       256: 1
       257: 1
       264: q+1
       265: 1
       270: 2q+1
       271: q+1
       272: q+1
       275: q+1
       276: q+1
       280: 1
       281: 1
       282: 1
       284: q+1
       285: 1
       286: 1
       287: 1
       292: q+1
       293: 1
       294: 1
       297: q+1
       298: q+1
       299: 1
       301: q+1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       342: 1
       343: 1
       348: 1
       353: 1
       354: 1
       363: 1
       364: 1
       371: 1
       384: 1
       385: 1
       386: 1
       393: 1
       402: 1
       403: 1
       410: q+1
       411: 1
       416: q+1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: q+1
       447: 1
       448: 1
       456: 1
       457: 1
       458: 1
       460: 1
       462: 1
       463: 1
       482: 1
       499: 1
       500: 1
       513: 1
       525: 1
       549: 1
       572: 1
       580: 1
       581: 1
       596: 1
       597: 1
       602: 1
       607: 1
       608: 1
       617: 1
       618: 1
       625: 1
       638: 1
       639: 1
       640: 1
       647: 1
       685: 1
       773: 1
       790: 1
       791: 1
       804: 1
       816: 1
       840: 1
       996: 1

 997:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: 1
       235: 1
       256: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: 1
       289: 1
       294: 1
       306: 1
       308: 1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       356: 1
       395: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: 1
       441: 1
       462: 1
       483: 1
       492: 1
       501: 1
       508: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       610: 1
       686: 1
       774: 1
       783: 1
       792: 1
       799: 1
       997: 1

 998:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: q+1
       186: q+1
       188: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       256: q+1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: q+1
       308: q+1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       462: q+1
       484: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       590: 1
       591: 1
       592: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: 1
       687: 1
       775: 1
       784: 1
       792: 1
       793: 1
       794: 1
       798: 1
       998: 1

 999:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        25: q^2+2q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+2q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        62: q^2+2q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        89: q^2+2q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: 1
       158: 1
       159: 1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       167: q^2+2q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       199: 1
       201: 1
       202: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       248: 1
       251: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: q+1
       268: 1
       269: 1
       270: 1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       321: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 1
       380: 1
       392: 1
       397: 1
       405: 1
       407: 1
       408: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       442: 1
       454: 1
       457: 1
       459: 1
       462: 1
       463: 1
       485: 1
       494: 1
       502: 1
       504: 1
       505: 1
       509: 1
       575: 1
       583: 1
       585: 1
       586: 1
       591: 1
       593: 1
       594: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       612: 1
       634: 1
       646: 1
       688: 1
       776: 1
       785: 1
       793: 1
       795: 1
       796: 1
       800: 1
       999: 1

1000:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: q+1
        59: 1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        78: 1
        81: q+1
        82: q+1
        84: q+1
        85: q+1
        86: 1
        88: q+1
        89: 2q+1
        90: q+1
        91: q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       103: q+1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: q+1
       120: q+1
       121: 1
       123: q+1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: q+1
       151: 1
       156: q+1
       157: 1
       158: 1
       160: 1
       162: q+1
       163: q+1
       164: 1
       166: q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: q+1
       183: 1
       186: q+1
       187: q+1
       192: 1
       200: 1
       201: 1
       203: 1
       207: q+1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: q+1
       268: 1
       269: 1
       271: 1
       273: q+1
       274: q+1
       275: 1
       277: q+1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: q+1
       305: 1
       322: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       381: 1
       398: 1
       406: 1
       407: 1
       409: 1
       413: q+1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       486: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       576: 1
       584: 1
       585: 1
       587: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: 1
       635: 1
       689: 1
       777: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: 1
      1000: 1

1001:    0: 2q+1
         1: q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: q+1
         7: 1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: q+1
        21: 1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: 1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: 2q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: q+1
        83: 1
        84: q+1
        85: 1
        86: 1
        87: q+1
        89: q+1
        90: 1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: 1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       167: q+1
       168: 1
       169: 2q+1
       170: 1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: q+1
       188: 1
       193: 1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: q+1
       231: 1
       232: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: q+1
       286: 1
       287: q+1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       323: 1
       331: 1
       332: 1
       339: 1
       340: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       360: 1
       387: 1
       390: 1
       392: 1
       394: 1
       399: 1
       407: 1
       408: 1
       414: 1
       415: 1
       416: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: q+1
       437: 1
       438: 1
       449: 1
       452: 1
       454: 1
       457: 1
       459: 1
       461: 1
       462: 1
       463: 1
       487: 1
       496: 1
       504: 1
       505: 1
       558: 1
       561: 1
       577: 1
       585: 1
       586: 1
       593: 1
       594: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       614: 1
       641: 1
       644: 1
       646: 1
       648: 1
       690: 1
       778: 1
       787: 1
       795: 1
       796: 1
       849: 1
       852: 1
      1001: 1

1002:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: q^2+1
        18: q^2+1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: q^2+1
        43: 1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: 1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       194: 1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       231: 1
       233: 1
       248: 1
       252: 1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       324: 1
       331: 1
       333: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       361: 1
       400: 1
       407: 1
       409: 1
       414: 1
       415: 1
       417: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       437: 1
       439: 1
       454: 1
       458: 1
       488: 1
       497: 1
       504: 1
       506: 1
       578: 1
       585: 1
       587: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       615: 1
       691: 1
       779: 1
       788: 1
       795: 1
       797: 1
      1002: 1

1003:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q^2+2q+1
        15: 1
        16: q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q+1
        48: q^2+2q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q^2+2q+1
        70: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q^2+2q+1
        94: q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       163: q+1
       164: 1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q^2+2q+1
       175: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       232: 1
       233: 1
       234: 1
       242: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       325: 1
       332: 1
       333: 1
       334: 1
       340: 1
       341: 1
       342: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       362: 1
       386: 1
       392: 1
       401: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       422: 1
       423: 1
       424: 1
       425: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       433: 1
       438: 1
       439: 1
       440: 1
       448: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       489: 1
       498: 1
       505: 1
       506: 1
       507: 1
       515: 1
       579: 1
       586: 1
       587: 1
       588: 1
       594: 1
       595: 1
       596: 1
       601: 1
       602: 1
       603: 1
       604: 1
       608: 1
       609: 1
       616: 1
       640: 1
       646: 1
       692: 1
       780: 1
       789: 1
       796: 1
       797: 1
       798: 1
       806: 1
      1003: 1

1004:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       196: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       234: 1
       235: 1
       256: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       281: 1
       282: 1
       284: 1
       285: 1
       286: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       326: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       363: 1
       402: 1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       440: 1
       441: 1
       462: 1
       490: 1
       499: 1
       507: 1
       508: 1
       580: 1
       588: 1
       589: 1
       596: 1
       597: 1
       602: 1
       603: 1
       604: 1
       617: 1
       693: 1
       781: 1
       790: 1
       798: 1
       799: 1
      1004: 1

1005:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: 1
        17: q+1
        18: q+1
        19: q+1
        23: q+1
        24: q+1
        27: q+1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: 1
        38: 1
        39: 1
        42: q+1
        44: q+1
        45: q+1
        46: q+1
        48: q+1
        49: 1
        56: q+1
        60: q+1
        61: q+1
        64: q+1
        67: 1
        69: q+1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: q+1
        88: q+1
        91: q+1
        93: q+1
        95: q+1
        96: q+1
        99: 1
       101: 1
       102: 1
       103: 1
       111: 1
       118: q+1
       122: q+1
       123: q+1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       151: 1
       153: 1
       154: 1
       161: q+1
       165: q+1
       166: q+1
       169: q+1
       172: 1
       174: q+1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       197: 1
       205: 1
       212: q+1
       219: 1
       223: 1
       224: 1
       227: 1
       235: 1
       242: 1
       251: 1
       252: 1
       257: 1
       265: 1
       272: q+1
       276: q+1
       277: q+1
       281: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: 1
       299: 1
       305: 1
       307: 1
       308: 1
       327: 1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       364: 1
       386: 1
       403: 1
       411: 1
       418: q+1
       425: 1
       429: 1
       430: 1
       433: 1
       441: 1
       448: 1
       457: 1
       458: 1
       463: 1
       491: 1
       500: 1
       508: 1
       515: 1
       581: 1
       589: 1
       597: 1
       604: 1
       608: 1
       609: 1
       618: 1
       640: 1
       694: 1
       782: 1
       791: 1
       799: 1
       806: 1
      1005: 1

1006:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       198: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       328: 1
       336: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       404: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       501: 1
       509: 1
       510: 1
       515: 1
       543: 1
       582: 1
       590: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       695: 1
       792: 1
       800: 1
       801: 1
       806: 1
       834: 1
      1006: 1

1007:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        27: 1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       199: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       236: 1
       238: 1
       240: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       329: 1
       337: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       366: 1
       380: 1
       382: 1
       384: 1
       388: 1
       392: 1
       393: 1
       405: 1
       412: 1
       414: 1
       416: 1
       419: 1
       421: 1
       423: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       435: 1
       442: 1
       444: 1
       446: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       502: 1
       509: 1
       511: 1
       513: 1
       544: 1
       559: 1
       583: 1
       591: 1
       598: 1
       600: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       620: 1
       634: 1
       636: 1
       638: 1
       642: 1
       646: 1
       647: 1
       696: 1
       793: 1
       800: 1
       802: 1
       804: 1
       835: 1
       850: 1
      1007: 1

1008:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       103: q+1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       200: 1
       207: 1
       208: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       237: 1
       238: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       260: 1
       267: 1
       268: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       330: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       367: 1
       381: 1
       382: 1
       385: 1
       406: 1
       413: 1
       414: 1
       417: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: 1
       443: 1
       444: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       503: 1
       510: 1
       511: 1
       514: 1
       545: 1
       584: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       621: 1
       635: 1
       636: 1
       639: 1
       697: 1
       794: 1
       801: 1
       802: 1
       805: 1
       836: 1
      1008: 1

1009:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       114: 1
       115: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       141: 1
       142: 1
       143: 1
       149: 1
       150: 1
       151: 1
       157: 1
       158: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       201: 1
       208: 1
       209: 1
       215: 1
       216: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: 1
       238: 1
       239: 1
       248: 1
       249: 1
       250: 1
       261: 1
       268: 1
       269: 1
       273: 1
       274: 1
       275: 1
       278: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       303: 1
       304: 1
       305: 1
       331: 1
       339: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       368: 1
       382: 1
       383: 1
       407: 1
       414: 1
       415: 1
       421: 1
       422: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       437: 1
       444: 1
       445: 1
       454: 1
       455: 1
       456: 1
       504: 1
       511: 1
       512: 1
       546: 1
       585: 1
       593: 1
       600: 1
       601: 1
       605: 1
       606: 1
       607: 1
       622: 1
       636: 1
       637: 1
       698: 1
       795: 1
       802: 1
       803: 1
       837: 1
      1009: 1

1010:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        58: q+1
        59: 1
        60: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       115: 1
       116: 1
       120: q+1
       121: 1
       122: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       202: 1
       209: 1
       210: 1
       216: 1
       217: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       232: 1
       239: 1
       240: 1
       244: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       269: 1
       270: 1
       274: q+1
       275: 1
       276: 1
       279: q+1
       280: 1
       281: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       332: 1
       340: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       369: 1
       383: 1
       384: 1
       388: 1
       392: 1
       393: 1
       408: 1
       415: 1
       416: 1
       422: 1
       423: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       438: 1
       445: 1
       446: 1
       450: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       462: 1
       463: 1
       505: 1
       512: 1
       513: 1
       547: 1
       559: 1
       586: 1
       594: 1
       601: 1
       602: 1
       606: 1
       607: 1
       608: 1
       623: 1
       637: 1
       638: 1
       642: 1
       646: 1
       647: 1
       699: 1
       796: 1
       803: 1
       804: 1
       838: 1
       850: 1
      1010: 1

1011:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       109: 1
       115: 1
       117: 1
       120: 1
       121: 1
       123: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       203: 1
       209: 1
       211: 1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       233: 1
       239: 1
       241: 1
       249: 1
       250: 1
       252: 1
       263: 1
       269: 1
       271: 1
       274: 1
       275: 1
       277: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       333: 1
       341: 1
       347: 1
       349: 1
       352: 1
       353: 1
       355: 1
       370: 1
       383: 1
       385: 1
       409: 1
       415: 1
       417: 1
       422: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       439: 1
       445: 1
       447: 1
       455: 1
       456: 1
       458: 1
       506: 1
       512: 1
       514: 1
       548: 1
       587: 1
       595: 1
       601: 1
       603: 1
       606: 1
       607: 1
       609: 1
       624: 1
       637: 1
       639: 1
       700: 1
       797: 1
       803: 1
       805: 1
       839: 1
      1011: 1

1012:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: q+1
       169: 1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       204: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: 1
       240: 1
       241: 1
       242: 1
       250: 1
       251: 1
       252: 1
       254: 1
       256: 1
       257: 1
       264: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       281: 1
       282: 1
       284: q+1
       285: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       334: 1
       342: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       371: 1
       384: 1
       385: 1
       386: 1
       393: 1
       410: 1
       416: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       432: 1
       433: 1
       440: 1
       446: 1
       447: 1
       448: 1
       456: 1
       457: 1
       458: 1
       460: 1
       462: 1
       463: 1
       507: 1
       513: 1
       514: 1
       515: 1
       549: 1
       588: 1
       596: 1
       602: 1
       603: 1
       604: 1
       607: 1
       608: 1
       609: 1
       625: 1
       638: 1
       639: 1
       640: 1
       647: 1
       701: 1
       798: 1
       804: 1
       805: 1
       806: 1
       840: 1
      1012: 1

1013:    0: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         8: q+1
        10: q+1
        11: q^2+q+1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: q^2+q+1
        19: q+1
        23: q+1
        24: 1
        27: q+1
        29: q+1
        31: q+1
        32: q+1
        35: q+1
        37: 1
        38: q+1
        39: q+1
        42: q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        48: q+1
        49: q+1
        56: 1
        60: q+1
        61: 1
        64: q+1
        67: q+1
        69: q+1
        70: q+1
        74: q+1
        75: 1
        78: 1
        80: 1
        82: 1
        83: q+1
        87: q+1
        88: 1
        91: q+1
        93: q+1
        95: q+1
        96: q+1
        99: q+1
       101: 1
       102: q+1
       103: q+1
       111: 1
       118: 1
       122: q+1
       123: 1
       127: q+1
       128: 1
       131: q+1
       133: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: q+1
       161: 1
       165: q+1
       166: 1
       169: q+1
       172: q+1
       174: q+1
       175: q+1
       179: q+1
       180: 1
       183: 1
       185: 1
       187: 1
       188: q+1
       205: 1
       212: 1
       219: 1
       223: q+1
       224: 1
       227: 1
       235: 1
       242: 1
       246: 1
       251: 1
       252: 1
       255: 1
       257: 1
       265: 1
       272: 1
       276: q+1
       277: 1
       281: q+1
       282: 1
       285: q+1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: q+1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       372: 1
       386: 1
       390: 1
       394: 1
       411: 1
       418: 1
       425: 1
       429: q+1
       430: 1
       433: 1
       441: 1
       448: 1
       452: 1
       457: 1
       458: 1
       461: 1
       463: 1
       508: 1
       515: 1
       550: 1
       561: 1
       589: 1
       597: 1
       604: 1
       608: 1
       609: 1
       626: 1
       640: 1
       644: 1
       648: 1
       702: 1
       799: 1
       806: 1
       841: 1
       852: 1
      1013: 1

1014:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       221: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       320: 1
       352: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       388: 1
       392: 1
       393: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       516: 1
       517: 1
       525: 1
       527: 1
       559: 1
       563: 1
       564: 1
       572: 1
       574: 1
       606: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       625: 1
       642: 1
       646: 1
       647: 1
       703: 1
       755: 1
       807: 1
       808: 1
       816: 1
       818: 1
       850: 1
      1014: 1

1015:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       129: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       225: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       253: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       317: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       392: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       459: 1
       462: 1
       463: 1
       465: 1
       516: 1
       517: 1
       518: 1
       524: 1
       563: 1
       564: 1
       565: 1
       571: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       646: 1
       704: 1
       756: 1
       807: 1
       808: 1
       809: 1
       815: 1
      1015: 1

1016:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         6: 3q+1
         7: 3q+1
         8: 3q+1
         9: 3q+1
        10: q+1
        11: q+1
        12: q+1
        13: 3q+1
        14: 3q+1
        15: 3q+1
        16: 3q+1
        17: 3q+1
        18: 3q+1
        19: 3q+1
        20: 3q+1
        21: 3q+1
        22: 3q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 3q+1
        34: 3q+1
        35: 3q+1
        36: 3q+1
        37: q+1
        38: q+1
        39: q+1
        40: 3q+1
        41: 3q+1
        42: 3q+1
        43: 3q+1
        44: q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: 3q+1
        49: 3q+1
        50: q+1
        51: q+1
        52: 3q+1
        53: q+1
        54: q+1
        55: q+1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 3q+1
        72: 3q+1
        73: 3q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 3q+1
        85: 3q+1
        86: 3q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: 3q+1
        98: 3q+1
        99: 3q+1
       100: 3q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: q+1
       135: q+1
       136: 3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: 3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 3q+1
       177: 3q+1
       178: 3q+1
       179: q+1
       180: q+1
       181: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: q+1
       289: q+1
       290: 3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       381: 1
       387: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       420: 1
       426: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       466: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       705: 1
       757: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
      1016: 1

1017:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       129: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       206: 1
       207: 1
       212: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       253: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       311: 1
       312: 1
       313: 1
       328: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       373: 1
       374: 1
       379: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       467: 1
       518: 1
       519: 1
       520: 1
       535: 1
       565: 1
       566: 1
       567: 1
       582: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       706: 1
       758: 1
       809: 1
       810: 1
       811: 1
       826: 1
      1017: 1

1018:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        65: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       118: 1
       124: 1
       127: 1
       128: 1
       129: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       170: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       213: 1
       214: 1
       219: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       278: 1
       281: 1
       282: 1
       283: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       311: 1
       314: 1
       315: 1
       336: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       380: 1
       381: 1
       386: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       419: 1
       420: 1
       425: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       468: 1
       518: 1
       521: 1
       522: 1
       543: 1
       565: 1
       568: 1
       569: 1
       590: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       634: 1
       635: 1
       640: 1
       707: 1
       759: 1
       809: 1
       812: 1
       813: 1
       834: 1
      1018: 1

1019:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: q^2+2q+1
        12: 1
        13: q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: 1
        25: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q+1
        37: q+1
        38: q^2+2q+1
        39: 1
        40: q+1
        41: q+1
        42: q^2+2q+1
        43: q+1
        44: q+1
        45: q^2+2q+1
        46: 1
        47: q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        64: q+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q^2+2q+1
        75: 1
        76: 1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q^2+2q+1
        88: 1
        89: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q^2+2q+1
       103: 1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       118: 1
       119: 1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       144: q+1
       145: 1
       146: 1
       148: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q^2+2q+1
       180: 1
       181: 1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       206: 1
       213: 1
       219: 1
       220: 1
       223: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       243: 1
       246: q+1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       272: 1
       273: 1
       276: q+1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       343: 1
       344: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       373: 1
       380: 1
       386: 1
       387: 1
       390: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       412: 1
       419: 1
       425: 1
       426: 1
       429: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       449: 1
       452: q+1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       469: 1
       519: 1
       521: 1
       523: 1
       550: 1
       551: 1
       566: 1
       568: 1
       570: 1
       597: 1
       598: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       627: 1
       634: 1
       640: 1
       641: 1
       644: 1
       708: 1
       760: 1
       810: 1
       812: 1
       814: 1
       841: 1
       842: 1
      1019: 1

1020:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q^2+2q+1
         9: q+1
        10: q+1
        11: 1
        12: q^2+2q+1
        13: q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q^2+2q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q+1
        37: q+1
        38: 1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q^2+2q+1
        43: q+1
        44: q+1
        45: 1
        46: q^2+2q+1
        47: q+1
        48: q^2+2q+1
        49: q^2+2q+1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q^2+2q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q^2+2q+1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: 1
       103: q^2+2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: q+1
       129: 1
       131: 1
       132: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q^2+2q+1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       205: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: q+1
       283: 1
       285: 1
       286: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       335: 1
       345: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       374: 1
       379: 1
       381: 1
       387: 1
       391: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: q+1
       459: 1
       461: 1
       462: 1
       470: 1
       520: 1
       522: 1
       523: 1
       542: 1
       552: 1
       567: 1
       569: 1
       570: 1
       589: 1
       599: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       709: 1
       761: 1
       811: 1
       813: 1
       814: 1
       833: 1
       843: 1
      1020: 1

1021:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       205: 1
       220: 1
       225: 1
       227: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       327: 1
       351: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       387: 1
       392: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       426: 1
       431: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       471: 1
       523: 1
       524: 1
       534: 1
       558: 1
       570: 1
       571: 1
       581: 1
       605: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       641: 1
       646: 1
       648: 1
       710: 1
       762: 1
       814: 1
       815: 1
       825: 1
       849: 1
      1021: 1

1022:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       221: 1
       225: 1
       226: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: 1
       352: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       388: 1
       392: 1
       393: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       427: 1
       431: 1
       432: 1
       438: 1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       472: 1
       524: 1
       525: 1
       532: 1
       559: 1
       571: 1
       572: 1
       579: 1
       606: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       642: 1
       646: 1
       647: 1
       711: 1
       763: 1
       815: 1
       816: 1
       823: 1
       850: 1
      1022: 1

1023:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        74: 1
        75: 1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        87: 1
        88: 1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: q+1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       161: 1
       162: q+1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       179: 1
       180: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       351: 1
       356: 1
       364: 1
       365: 1
       372: 1
       373: 1
       381: 1
       387: 1
       392: 1
       394: 1
       395: 1
       403: 1
       404: 1
       411: 1
       412: 1
       420: 1
       426: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       473: 1
       516: 1
       526: 1
       534: 1
       558: 1
       563: 1
       573: 1
       581: 1
       605: 1
       610: 1
       618: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       646: 1
       648: 1
       712: 1
       764: 1
       807: 1
       817: 1
       825: 1
       849: 1
      1023: 1

1024:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: 3q+1
         3: 3q^2+4q+1
         4: 3q^2+4q+1
         5: 3q^2+4q+1
         6: 3q+1
         7: 3q+1
         8: 3q+1
         9: 3q^2+4q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: 3q^2+4q+1
        14: 3q+1
        15: 3q^2+4q+1
        16: 3q^2+4q+1
        17: 3q+1
        18: 3q^2+4q+1
        19: 3q^2+4q+1
        20: 3q+1
        21: 3q+1
        22: 3q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: 1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: 3q+1
        34: 3q+1
        35: 3q+1
        36: 3q^2+4q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 3q+1
        41: 3q+1
        42: 3q+1
        43: 3q^2+4q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 3q^2+4q+1
        48: 3q+1
        49: 3q^2+4q+1
        50: q+1
        51: q+1
        52: 3q+1
        54: q+1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 3q+1
        72: 3q+1
        73: 3q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: 1
        81: q^2+2q+1
        82: 1
        83: q+1
        84: 3q+1
        85: 3q+1
        86: 3q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: 1
        94: q^2+2q+1
        95: 1
        96: q+1
        97: 3q+1
        98: 3q+1
        99: 3q+1
       100: 3q^2+4q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: 1
       105: q+1
       106: q+1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: 3q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: 3q+1
       159: q+1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 3q+1
       177: 3q+1
       178: 3q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       228: 1
       229: q+1
       230: q+1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: 1
       259: q+1
       260: q+1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: 3q+1
       292: q+1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       319: 1
       320: 1
       326: 1
       329: 1
       338: 1
       346: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       434: 1
       435: q+1
       436: q+1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       474: 1
       517: 1
       526: 1
       527: 1
       533: 1
       536: 1
       545: 1
       553: 1
       564: 1
       573: 1
       574: 1
       580: 1
       583: 1
       592: 1
       600: 1
       610: 1
       611: 1
       617: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       713: 1
       765: 1
       808: 1
       817: 1
       818: 1
       824: 1
       827: 1
       836: 1
       844: 1
      1024: 1

1025:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 1
        19: q^2+2q+1
        20: 1
        21: q^2+2q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        71: 1
        72: q^2+2q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       221: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       388: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       427: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       475: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       642: 1
       714: 1
       766: 1
       809: 1
       818: 1
       819: 1
       820: 1
       823: 1
      1025: 1

1026:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       105: q+1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       210: 1
       229: q+1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       259: q+1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       312: 1
       321: 1
       323: 1
       329: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       377: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       416: 1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       476: 1
       519: 1
       528: 1
       530: 1
       536: 1
       566: 1
       575: 1
       577: 1
       583: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       631: 1
       715: 1
       767: 1
       810: 1
       819: 1
       821: 1
       827: 1
      1026: 1

1027:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: 2q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        68: q+1
        69: 1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 2q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       152: q+1
       153: 1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       173: q+1
       174: 1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       306: q+1
       307: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       334: 1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       388: 1
       398: 1
       399: 1
       401: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       477: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       541: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: 1
       588: 1
       613: 1
       614: 1
       616: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       716: 1
       768: 1
       811: 1
       820: 1
       821: 1
       823: 1
       828: 1
       832: 1
      1027: 1

1028:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 2q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       314: 1
       321: 1
       324: 1
       325: 1
       337: 1
       342: 1
       358: 1
       361: 1
       362: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       427: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       478: 1
       521: 1
       528: 1
       531: 1
       532: 1
       544: 1
       549: 1
       568: 1
       575: 1
       578: 1
       579: 1
       591: 1
       596: 1
       612: 1
       615: 1
       616: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       717: 1
       769: 1
       812: 1
       819: 1
       822: 1
       823: 1
       835: 1
       840: 1
      1028: 1

1029:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        30: q+1
        31: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: 1
        55: q+1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: q+1
        85: q+1
        86: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        94: q+1
        95: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       103: q+1
       106: q+1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: q+1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       156: q+1
       157: q+1
       158: 1
       160: q+1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       172: 1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       218: 1
       230: q+1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       260: q+1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       289: q+1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       315: 1
       322: 1
       324: 1
       338: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       385: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       420: 1
       421: 1
       424: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       479: 1
       522: 1
       529: 1
       531: 1
       545: 1
       569: 1
       576: 1
       578: 1
       592: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       639: 1
       718: 1
       770: 1
       813: 1
       820: 1
       822: 1
       836: 1
      1029: 1

1030:    0: 3q+1
         1: 3q+1
         2: 3q+1
         3: 3q+1
         4: 3q+1
         5: 3q+1
         6: 2q+1
         7: 3q+1
         8: 3q+1
         9: 3q+1
        10: q+1
        11: q+1
        12: q+1
        13: 3q+1
        14: 3q+1
        15: 3q+1
        16: 3q+1
        17: 3q+1
        18: 3q+1
        19: 3q+1
        20: 2q+1
        21: 2q+1
        22: 3q+1
        23: q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: 2q+1
        34: 3q+1
        35: 3q+1
        36: 3q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: 3q+1
        42: 3q+1
        43: 3q+1
        44: q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: 3q+1
        49: 3q+1
        52: 2q+1
        53: 1
        54: q+1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 2q+1
        72: 2q+1
        73: 3q+1
        74: q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: 2q+1
        85: 2q+1
        86: 3q+1
        87: q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: 2q+1
        98: 3q+1
        99: 3q+1
       100: 3q+1
       101: q+1
       102: q+1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: 2q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 2q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 2q+1
       177: 2q+1
       178: 3q+1
       179: q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       290: 2q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       346: 1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       416: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       480: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       553: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       600: 1
       614: 1
       615: 1
       616: 1
       617: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       631: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       719: 1
       771: 1
       814: 1
       821: 1
       822: 1
       823: 1
       824: 1
       844: 1
      1030: 1

1031:    0: 3q^2+4q+1
         1: 3q+1
         2: 3q^2+4q+1
         3: q^2+4q+1
         4: 3q^2+4q+1
         5: 3q^2+4q+1
         6: 3q+1
         7: 3q+1
         8: q^2+4q+1
         9: 3q+1
        10: q^2+4q+1
        11: 2q+1
        12: 2q+1
        13: 3q+1
        14: 3q^2+4q+1
        15: q^2+4q+1
        16: 3q+1
        17: 3q^2+4q+1
        18: q^2+4q+1
        19: 3q^2+4q+1
        21: 3q+1
        22: 3q+1
        23: 2q+1
        24: 2q+1
        25: 3q+1
        26: q+1
        27: q^2+4q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: 3q+1
        34: 3q+1
        35: q^2+4q+1
        36: 3q+1
        37: q^2+4q+1
        38: 2q+1
        39: 2q+1
        40: 3q+1
        41: 3q+1
        42: q^2+4q+1
        43: 3q+1
        44: q^2+4q+1
        45: 2q+1
        46: 2q+1
        47: 3q+1
        48: 3q^2+4q+1
        49: q^2+4q+1
        53: 3q+1
        54: q+1
        55: q+1
        56: q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: 3q+1
        73: 3q+1
        74: 2q+1
        75: 2q+1
        76: 3q+1
        77: q+1
        78: q^2+4q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: 2q+1
        83: q+1
        85: 3q+1
        86: 3q+1
        87: 2q+1
        88: 2q+1
        89: 3q+1
        90: q+1
        91: q^2+4q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: q+1
        97: 3q+1
        98: 3q+1
        99: q^2+4q+1
       100: 3q+1
       101: q^2+4q+1
       102: 2q+1
       103: 2q+1
       108: q+1
       109: q+1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 3q+1
       138: q+1
       139: q+1
       140: q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: 3q+1
       159: q+1
       160: q+1
       161: q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: 1
       177: 3q+1
       178: 3q+1
       179: 2q+1
       180: 2q+1
       181: 3q+1
       182: q+1
       183: q^2+4q+1
       184: q+1
       185: 2q+1
       186: q+1
       187: 2q+1
       188: q+1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       218: 1
       221: 1
       222: 1
       225: 1
       227: 1
       232: q+1
       233: q+1
       234: 1
       235: 1
       239: q+1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: q+1
       263: q+1
       264: 1
       265: 1
       269: q+1
       270: 1
       271: 1
       272: q+1
       274: 1
       275: 1
       276: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 3q+1
       292: q+1
       293: q+1
       294: q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: q+1
       308: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       341: 1
       347: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       383: 1
       385: 1
       388: 1
       389: 1
       392: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       422: 1
       424: 1
       427: 1
       428: 1
       431: 1
       433: 1
       438: q+1
       439: q+1
       440: 1
       441: 1
       445: q+1
       446: 1
       447: 1
       448: q+1
       450: 1
       451: 1
       452: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       481: 1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       548: 1
       554: 1
       571: 1
       579: 1
       580: 1
       581: 1
       586: 1
       595: 1
       601: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       637: 1
       639: 1
       642: 1
       643: 1
       646: 1
       648: 1
       720: 1
       772: 1
       815: 1
       823: 1
       824: 1
       825: 1
       830: 1
       839: 1
       845: 1
      1031: 1

1032:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: 1
        24: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        54: 1
        55: 1
        56: 1
        59: q+1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        74: 1
        75: 1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: q+1
        87: 1
        88: 1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: q+1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       160: 1
       161: 1
       164: q+1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       179: 1
       180: 1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: 1
       218: 1
       222: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       250: 1
       252: 1
       254: 1
       255: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: q+1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       353: 1
       363: 1
       364: 1
       371: 1
       372: 1
       377: 1
       385: 1
       389: 1
       393: 1
       394: 1
       402: 1
       403: 1
       410: 1
       411: 1
       416: 1
       424: 1
       428: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       456: 1
       458: 1
       460: 1
       461: 1
       462: 1
       463: 1
       482: 1
       525: 1
       533: 1
       534: 1
       560: 1
       572: 1
       580: 1
       581: 1
       607: 1
       617: 1
       618: 1
       625: 1
       626: 1
       631: 1
       639: 1
       643: 1
       647: 1
       648: 1
       721: 1
       773: 1
       816: 1
       824: 1
       825: 1
       851: 1
      1032: 1

1033:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: 1
        24: q+1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        74: 1
        75: q+1
        76: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        87: 1
        88: q+1
        89: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       179: 1
       180: q+1
       181: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       189: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: 1
       289: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       319: 1
       328: 1
       335: 1
       345: 1
       356: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       381: 1
       387: 1
       391: 1
       395: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       483: 1
       526: 1
       535: 1
       542: 1
       552: 1
       573: 1
       582: 1
       589: 1
       599: 1
       610: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       722: 1
       774: 1
       817: 1
       826: 1
       833: 1
       843: 1
      1033: 1

1034:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: q+1
       153: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       388: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       434: 1
       435: 1
       436: 1
       440: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       484: 1
       527: 1
       535: 1
       536: 1
       537: 1
       541: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       611: 1
       619: 1
       620: 1
       621: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       723: 1
       775: 1
       818: 1
       826: 1
       827: 1
       828: 1
       832: 1
      1034: 1

1035:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        62: q+1
        63: q+1
        64: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       146: q+1
       147: q+1
       148: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       191: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       300: q+1
       301: q+1
       302: 1
       321: 1
       329: 1
       331: 1
       332: 1
       358: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       397: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       485: 1
       528: 1
       536: 1
       538: 1
       539: 1
       575: 1
       583: 1
       585: 1
       586: 1
       612: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       724: 1
       776: 1
       819: 1
       827: 1
       829: 1
       830: 1
      1035: 1

1036:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       125: 1
       129: 1
       130: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       221: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       249: 1
       253: 1
       254: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       322: 1
       330: 1
       331: 1
       333: 1
       359: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       388: 1
       398: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       427: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       455: 1
       459: 1
       460: 1
       486: 1
       529: 1
       537: 1
       538: 1
       540: 1
       576: 1
       584: 1
       585: 1
       587: 1
       613: 1
       621: 1
       622: 1
       624: 1
       628: 1
       629: 1
       630: 1
       632: 1
       642: 1
       725: 1
       777: 1
       820: 1
       828: 1
       829: 1
       831: 1
      1036: 1

1037:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       193: 1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       323: 1
       331: 1
       332: 1
       360: 1
       368: 1
       369: 1
       375: 1
       376: 1
       377: 1
       399: 1
       407: 1
       408: 1
       414: 1
       415: 1
       416: 1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       487: 1
       530: 1
       538: 1
       539: 1
       577: 1
       585: 1
       586: 1
       614: 1
       622: 1
       623: 1
       629: 1
       630: 1
       631: 1
       726: 1
       778: 1
       821: 1
       829: 1
       830: 1
      1037: 1

1038:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        55: q+1
        57: 1
        58: 1
        59: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q+1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: q+1
       145: 1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: 1
       160: q+1
       162: 1
       163: 1
       164: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 1
       188: 1
       194: 1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: q+1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       324: 1
       331: 1
       333: 1
       346: 1
       349: 1
       361: 1
       368: 1
       370: 1
       375: 1
       376: 1
       378: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       400: 1
       407: 1
       409: 1
       414: 1
       415: 1
       417: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: q+1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       488: 1
       531: 1
       538: 1
       540: 1
       553: 1
       556: 1
       578: 1
       585: 1
       587: 1
       600: 1
       603: 1
       615: 1
       622: 1
       624: 1
       629: 1
       630: 1
       632: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       727: 1
       779: 1
       822: 1
       829: 1
       831: 1
       844: 1
       847: 1
      1038: 1

1039:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       325: 1
       332: 1
       333: 1
       334: 1
       362: 1
       369: 1
       370: 1
       371: 1
       376: 1
       377: 1
       378: 1
       379: 1
       388: 1
       401: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       438: 1
       439: 1
       440: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       489: 1
       532: 1
       539: 1
       540: 1
       541: 1
       579: 1
       586: 1
       587: 1
       588: 1
       616: 1
       623: 1
       624: 1
       625: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       728: 1
       780: 1
       823: 1
       830: 1
       831: 1
       832: 1
      1039: 1

1040:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: 1
        24: q+1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        54: 1
        55: q+1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        74: 1
        75: q+1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        86: q+1
        87: 1
        88: q+1
        90: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: 1
       139: q+1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       160: q+1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       179: 1
       180: q+1
       182: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       196: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       218: 1
       222: 1
       224: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       252: 1
       254: 1
       255: 1
       256: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       292: 1
       293: q+1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       326: 1
       334: 1
       335: 1
       349: 1
       363: 1
       371: 1
       372: 1
       377: 1
       378: 1
       379: 1
       385: 1
       389: 1
       391: 1
       402: 1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       424: 1
       428: 1
       430: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       461: 1
       462: 1
       490: 1
       533: 1
       541: 1
       542: 1
       556: 1
       580: 1
       588: 1
       589: 1
       603: 1
       617: 1
       625: 1
       626: 1
       631: 1
       632: 1
       633: 1
       639: 1
       643: 1
       645: 1
       729: 1
       781: 1
       824: 1
       832: 1
       833: 1
       847: 1
      1040: 1

1041:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: 1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: q+1
        27: q+1
        29: 1
        31: q+1
        32: 1
        35: q+1
        37: q+1
        38: 1
        39: q+1
        42: q+1
        44: q+1
        45: 1
        46: q+1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: q+1
        64: 1
        67: q+1
        69: 1
        70: 1
        74: 1
        75: q+1
        78: q+1
        80: 1
        82: q+1
        83: 1
        87: 1
        88: q+1
        91: q+1
        93: 1
        95: q+1
        96: 1
        99: q+1
       101: q+1
       102: 1
       103: q+1
       111: 1
       118: 1
       122: 1
       123: 1
       128: q+1
       131: 1
       133: 1
       140: 1
       144: 1
       145: q+1
       148: 1
       151: q+1
       153: 1
       154: 1
       161: 1
       165: 1
       166: q+1
       169: 1
       172: q+1
       174: 1
       175: 1
       179: 1
       180: q+1
       183: q+1
       185: 1
       187: q+1
       188: 1
       197: 1
       205: 1
       212: 1
       224: 1
       227: 1
       235: 1
       242: 1
       246: 1
       247: 1
       252: q+1
       255: 1
       257: 1
       265: 1
       272: 1
       276: 1
       277: 1
       282: q+1
       285: 1
       287: 1
       294: 1
       298: 1
       299: q+1
       302: 1
       305: q+1
       307: 1
       308: 1
       327: 1
       335: 1
       355: 1
       364: 1
       372: 1
       379: 1
       391: 1
       394: 1
       403: 1
       411: 1
       418: 1
       430: 1
       433: 1
       441: 1
       448: 1
       452: 1
       453: 1
       458: q+1
       461: 1
       463: 1
       491: 1
       534: 1
       542: 1
       562: 1
       581: 1
       589: 1
       609: 1
       618: 1
       626: 1
       633: 1
       645: 1
       648: 1
       730: 1
       782: 1
       825: 1
       833: 1
       853: 1
      1041: 1

1042:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: q+1
        24: 1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        40: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        74: q+1
        75: 1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: q+1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       179: q+1
       180: 1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: q+1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       319: 1
       336: 1
       343: 1
       344: 1
       356: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       395: 1
       404: 1
       411: 1
       412: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       492: 1
       526: 1
       543: 1
       550: 1
       551: 1
       573: 1
       590: 1
       597: 1
       598: 1
       610: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       731: 1
       783: 1
       817: 1
       834: 1
       841: 1
       842: 1
      1042: 1

1043:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       320: 1
       336: 1
       337: 1
       338: 1
       342: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       427: 1
       434: 1
       435: 1
       436: 1
       440: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       493: 1
       527: 1
       543: 1
       544: 1
       545: 1
       549: 1
       574: 1
       590: 1
       591: 1
       592: 1
       596: 1
       611: 1
       619: 1
       620: 1
       621: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       732: 1
       784: 1
       818: 1
       834: 1
       835: 1
       836: 1
       840: 1
      1043: 1

1044:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       199: 1
       201: 1
       202: 1
       213: 1
       215: 1
       216: 1
       217: 1
       221: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       321: 1
       337: 1
       339: 1
       340: 1
       358: 1
       366: 1
       368: 1
       369: 1
       380: 1
       382: 1
       383: 1
       384: 1
       388: 1
       397: 1
       405: 1
       407: 1
       408: 1
       419: 1
       421: 1
       422: 1
       423: 1
       427: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       494: 1
       528: 1
       544: 1
       546: 1
       547: 1
       575: 1
       591: 1
       593: 1
       594: 1
       612: 1
       620: 1
       622: 1
       623: 1
       634: 1
       636: 1
       637: 1
       638: 1
       642: 1
       733: 1
       785: 1
       819: 1
       835: 1
       837: 1
       838: 1
      1044: 1

1045:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        30: q+1
        31: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: q+1
        59: 1
        61: 1
        65: q+1
        66: q+1
        67: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        94: q+1
        95: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       103: q+1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       149: q+1
       150: q+1
       151: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: q+1
       164: 1
       166: 1
       170: q+1
       171: q+1
       172: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       186: q+1
       187: q+1
       192: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       216: 1
       218: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: q+1
       297: 1
       299: 1
       303: q+1
       304: q+1
       305: 1
       322: 1
       338: 1
       339: 1
       341: 1
       359: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       398: 1
       406: 1
       407: 1
       409: 1
       420: 1
       421: 1
       422: 1
       424: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       495: 1
       529: 1
       545: 1
       546: 1
       548: 1
       576: 1
       592: 1
       593: 1
       595: 1
       613: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       637: 1
       639: 1
       734: 1
       786: 1
       820: 1
       836: 1
       837: 1
       839: 1
      1045: 1

1046:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q+1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: q+1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: q+1
       137: 1
       138: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: q+1
       188: 1
       193: 1
       201: 1
       202: 1
       208: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: q+1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       323: 1
       339: 1
       340: 1
       346: 1
       348: 1
       360: 1
       368: 1
       369: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       399: 1
       407: 1
       408: 1
       414: 1
       416: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: q+1
       457: 1
       459: 1
       460: 1
       461: 1
       462: 1
       496: 1
       530: 1
       546: 1
       547: 1
       553: 1
       555: 1
       577: 1
       593: 1
       594: 1
       600: 1
       602: 1
       614: 1
       622: 1
       623: 1
       629: 1
       631: 1
       636: 1
       637: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       735: 1
       787: 1
       821: 1
       837: 1
       838: 1
       844: 1
       846: 1
      1046: 1

1047:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       194: 1
       201: 1
       203: 1
       215: 1
       216: 1
       218: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       324: 1
       339: 1
       341: 1
       361: 1
       368: 1
       370: 1
       382: 1
       383: 1
       385: 1
       400: 1
       407: 1
       409: 1
       421: 1
       422: 1
       424: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       497: 1
       531: 1
       546: 1
       548: 1
       578: 1
       593: 1
       595: 1
       615: 1
       622: 1
       624: 1
       636: 1
       637: 1
       639: 1
       736: 1
       788: 1
       822: 1
       837: 1
       839: 1
      1047: 1

1048:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       325: 1
       340: 1
       341: 1
       342: 1
       362: 1
       369: 1
       370: 1
       371: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       401: 1
       408: 1
       409: 1
       410: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       438: 1
       439: 1
       440: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       498: 1
       532: 1
       547: 1
       548: 1
       549: 1
       579: 1
       594: 1
       595: 1
       596: 1
       616: 1
       623: 1
       624: 1
       625: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       737: 1
       789: 1
       823: 1
       838: 1
       839: 1
       840: 1
      1048: 1

1049:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: q+1
        24: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        54: q+1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        74: q+1
        75: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        86: q+1
        87: q+1
        88: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       138: q+1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: q+1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       179: q+1
       180: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       196: 1
       204: 1
       205: 1
       210: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       280: 1
       281: 1
       282: 1
       284: 1
       285: 1
       286: 1
       292: q+1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       326: 1
       342: 1
       343: 1
       348: 1
       363: 1
       371: 1
       372: 1
       377: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       402: 1
       410: 1
       411: 1
       416: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       456: 1
       457: 1
       458: 1
       460: 1
       461: 1
       462: 1
       499: 1
       533: 1
       549: 1
       550: 1
       555: 1
       580: 1
       596: 1
       597: 1
       602: 1
       617: 1
       625: 1
       626: 1
       631: 1
       638: 1
       639: 1
       640: 1
       643: 1
       644: 1
       738: 1
       790: 1
       824: 1
       840: 1
       841: 1
       846: 1
      1049: 1

1050:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: q+1
        11: q+1
        12: 1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: q+1
        24: 1
        27: q+1
        29: q+1
        31: 1
        32: 1
        35: q+1
        37: q+1
        38: q+1
        39: 1
        42: q+1
        44: q+1
        45: q+1
        46: 1
        48: q+1
        49: q+1
        56: 1
        60: q+1
        61: 1
        64: q+1
        67: 1
        69: 1
        70: 1
        74: q+1
        75: 1
        78: q+1
        80: q+1
        82: 1
        83: 1
        87: q+1
        88: 1
        91: q+1
        93: q+1
        95: 1
        96: 1
        99: q+1
       101: q+1
       102: q+1
       103: 1
       111: 1
       118: 1
       122: q+1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: q+1
       145: 1
       148: q+1
       151: 1
       153: 1
       154: 1
       161: 1
       165: q+1
       166: 1
       169: q+1
       172: 1
       174: 1
       175: 1
       179: q+1
       180: 1
       183: q+1
       185: q+1
       187: 1
       188: 1
       197: 1
       205: 1
       219: 1
       223: 1
       227: 1
       235: 1
       242: 1
       246: q+1
       251: 1
       252: 1
       255: 1
       257: 1
       265: 1
       272: 1
       276: q+1
       281: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: q+1
       299: 1
       302: q+1
       305: 1
       307: 1
       308: 1
       327: 1
       343: 1
       354: 1
       364: 1
       372: 1
       386: 1
       390: 1
       394: 1
       403: 1
       411: 1
       425: 1
       429: 1
       433: 1
       441: 1
       448: 1
       452: q+1
       457: 1
       458: 1
       461: 1
       463: 1
       500: 1
       534: 1
       550: 1
       561: 1
       581: 1
       597: 1
       608: 1
       618: 1
       626: 1
       640: 1
       644: 1
       648: 1
       739: 1
       791: 1
       825: 1
       841: 1
       852: 1
      1050: 1

1051:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         8: q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        23: q+1
        24: q+1
        25: q+1
        27: 1
        28: 2q+1
        29: q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        33: q^2+2q+1
        35: q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        42: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        56: q+1
        57: 1
        60: 1
        61: 1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        74: q+1
        75: q+1
        76: q+1
        78: 1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        87: q+1
        88: q+1
        89: q+1
        91: 1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+2q+1
        99: q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       140: q+1
       141: 1
       144: 1
       145: 1
       146: q+1
       148: 1
       149: q+1
       151: 1
       152: 2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       161: q+1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       172: 1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       179: q+1
       180: q+1
       181: q+1
       183: 1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       198: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: q+1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       255: 1
       256: q+1
       258: q+1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: q+1
       302: 1
       303: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       328: 1
       336: 1
       344: 1
       345: 1
       350: 1
       365: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       404: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       501: 1
       535: 1
       543: 1
       551: 1
       552: 1
       557: 1
       582: 1
       590: 1
       598: 1
       599: 1
       604: 1
       619: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       740: 1
       792: 1
       826: 1
       834: 1
       842: 1
       843: 1
       848: 1
      1051: 1

1052:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: 1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        27: 1
        28: q^2+2q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: 1
        38: q^2+2q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: 1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: q+1
        52: q+1
        54: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        76: 1
        77: 1
        78: 1
        79: q^2+2q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: 1
        90: 1
        91: 1
        92: q^2+2q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: 1
       102: q^2+2q+1
       103: q+1
       105: q+1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       136: q+1
       138: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       159: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: 1
       182: 1
       183: 1
       184: q^2+2q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       199: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: q+1
       236: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       259: q+1
       266: 1
       268: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       290: q+1
       292: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       329: 1
       337: 1
       344: 1
       346: 1
       348: 1
       366: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       405: 1
       412: 1
       414: 1
       416: 1
       419: 1
       421: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       435: q+1
       442: 1
       444: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       502: 1
       536: 1
       544: 1
       551: 1
       553: 1
       555: 1
       583: 1
       591: 1
       598: 1
       600: 1
       602: 1
       620: 1
       627: 1
       629: 1
       631: 1
       634: 1
       636: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       741: 1
       793: 1
       827: 1
       835: 1
       842: 1
       844: 1
       846: 1
      1052: 1

1053:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: 1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: 1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: 1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        51: q+1
        52: q+1
        55: q+1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q^2+2q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: 1
       102: q+1
       103: q^2+2q+1
       106: q+1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: q+1
       136: q+1
       139: q+1
       141: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       156: q+1
       157: q+1
       160: q+1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q+1
       200: 1
       207: 1
       208: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: q+1
       237: 1
       238: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       260: q+1
       267: 1
       268: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       289: q+1
       290: q+1
       293: q+1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       330: 1
       338: 1
       345: 1
       346: 1
       349: 1
       367: 1
       374: 1
       375: 1
       378: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       406: 1
       413: 1
       414: 1
       417: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       436: q+1
       443: 1
       444: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       503: 1
       537: 1
       545: 1
       552: 1
       553: 1
       556: 1
       584: 1
       592: 1
       599: 1
       600: 1
       603: 1
       621: 1
       628: 1
       629: 1
       632: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       742: 1
       794: 1
       828: 1
       836: 1
       843: 1
       844: 1
       847: 1
      1053: 1

1054:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        25: 2q+1
        26: 1
        27: 2q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: 1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: q+1
        57: 2q+1
        58: 1
        59: 1
        62: q+1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 2q+1
        72: q+1
        73: q+1
        76: 2q+1
        77: 1
        78: 2q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: 1
        84: 2q+1
        85: q+1
        86: q+1
        89: 2q+1
        90: 1
        91: 2q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: 1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q+1
       107: q+1
       114: 1
       115: 1
       119: q+1
       120: 1
       121: 1
       124: q+1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       141: 2q+1
       142: 1
       143: 1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       162: 2q+1
       163: 1
       164: 1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: 2q+1
       177: q+1
       178: q+1
       181: 2q+1
       182: 1
       183: 2q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: 1
       201: 1
       208: 1
       209: 1
       215: 1
       216: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       231: q+1
       238: 1
       239: 1
       243: q+1
       244: 1
       245: 1
       248: q+1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       268: 1
       269: 1
       273: q+1
       274: 1
       275: 1
       278: q+1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       295: 2q+1
       296: 1
       297: 1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       331: 1
       339: 1
       346: 1
       347: 1
       351: 1
       368: 1
       375: 1
       376: 1
       382: 1
       383: 1
       387: 1
       388: 1
       389: 1
       392: 1
       394: 1
       407: 1
       414: 1
       415: 1
       421: 1
       422: 1
       426: 1
       427: 1
       428: 1
       431: 1
       433: 1
       437: q+1
       444: 1
       445: 1
       449: q+1
       450: 1
       451: 1
       454: q+1
       455: 1
       456: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       504: 1
       538: 1
       546: 1
       553: 1
       554: 1
       558: 1
       585: 1
       593: 1
       600: 1
       601: 1
       605: 1
       622: 1
       629: 1
       630: 1
       636: 1
       637: 1
       641: 1
       642: 1
       643: 1
       646: 1
       648: 1
       743: 1
       795: 1
       829: 1
       837: 1
       844: 1
       845: 1
       849: 1
      1054: 1

1055:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        21: q+1
        22: q+1
        23: 2q+1
        25: q+1
        26: 1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: 2q+1
        39: q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: 2q+1
        53: q+1
        54: q+1
        58: 1
        59: 1
        60: 2q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: q+1
        73: q+1
        74: 2q+1
        76: q+1
        77: 1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: 1
        82: q+1
        83: q+1
        85: q+1
        86: q+1
        87: 2q+1
        89: q+1
        90: 1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: 1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q+1
       101: 2q+1
       102: 2q+1
       103: q+1
       108: q+1
       115: 1
       116: 1
       120: 1
       121: 1
       122: q+1
       125: 1
       126: 1
       127: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: q+1
       142: 1
       143: 1
       144: 2q+1
       146: q+1
       147: 1
       148: q+1
       149: 1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: q+1
       159: q+1
       163: 1
       164: 1
       165: 2q+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: 1
       177: q+1
       178: q+1
       179: 2q+1
       181: q+1
       182: 1
       183: 2q+1
       184: q+1
       185: 2q+1
       186: 1
       187: q+1
       188: q+1
       202: 1
       209: 1
       210: 1
       216: 1
       217: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       232: q+1
       239: 1
       240: 1
       244: 1
       245: 1
       246: q+1
       249: 1
       250: 1
       251: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: q+1
       269: 1
       270: 1
       274: 1
       275: 1
       276: q+1
       279: 1
       280: 1
       281: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       292: q+1
       296: 1
       297: 1
       298: 2q+1
       300: q+1
       301: 1
       302: q+1
       303: 1
       304: 1
       305: q+1
       306: 1
       307: q+1
       308: 1
       332: 1
       340: 1
       347: 1
       348: 1
       354: 1
       369: 1
       376: 1
       377: 1
       383: 1
       384: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       408: 1
       415: 1
       416: 1
       422: 1
       423: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       438: q+1
       445: 1
       446: 1
       450: 1
       451: 1
       452: q+1
       455: 1
       456: 1
       457: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       505: 1
       539: 1
       547: 1
       554: 1
       555: 1
       561: 1
       586: 1
       594: 1
       601: 1
       602: 1
       608: 1
       623: 1
       630: 1
       631: 1
       637: 1
       638: 1
       642: 1
       643: 1
       644: 1
       646: 1
       648: 1
       744: 1
       796: 1
       830: 1
       838: 1
       845: 1
       846: 1
       852: 1
      1055: 1

1056:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        21: q+1
        22: q+1
        24: 2q+1
        25: q+1
        26: 1
        27: 2q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: q+1
        46: 2q+1
        47: q+1
        48: q^2+2q+1
        49: 2q+1
        53: q+1
        55: q+1
        58: 1
        59: 1
        61: 2q+1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: q+1
        73: q+1
        75: 2q+1
        76: q+1
        77: 1
        78: 2q+1
        79: 1
        80: q+1
        81: q+1
        82: 2q+1
        83: q+1
        85: q+1
        86: q+1
        88: 2q+1
        89: q+1
        90: 1
        91: 2q+1
        92: 1
        93: q+1
        94: q+1
        95: 2q+1
        96: q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       109: q+1
       115: 1
       117: 1
       120: 1
       121: 1
       123: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       139: q+1
       142: 1
       143: 1
       145: 2q+1
       146: 1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: q+1
       160: q+1
       163: 1
       164: 1
       166: 2q+1
       167: 1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: 1
       177: q+1
       178: q+1
       180: 2q+1
       181: q+1
       182: 1
       183: 2q+1
       184: 1
       185: q+1
       186: q+1
       187: 2q+1
       188: q+1
       203: 1
       209: 1
       211: 1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       233: q+1
       239: 1
       241: 1
       244: 1
       245: 1
       247: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       263: q+1
       269: 1
       271: 1
       274: 1
       275: 1
       277: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       293: q+1
       296: 1
       297: 1
       299: 2q+1
       300: 1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: q+1
       308: 1
       333: 1
       341: 1
       347: 1
       349: 1
       355: 1
       370: 1
       376: 1
       378: 1
       383: 1
       385: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       409: 1
       415: 1
       417: 1
       422: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       439: q+1
       445: 1
       447: 1
       450: 1
       451: 1
       453: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       506: 1
       540: 1
       548: 1
       554: 1
       556: 1
       562: 1
       587: 1
       595: 1
       601: 1
       603: 1
       609: 1
       624: 1
       630: 1
       632: 1
       637: 1
       639: 1
       642: 1
       643: 1
       645: 1
       646: 1
       648: 1
       745: 1
       797: 1
       831: 1
       839: 1
       845: 1
       847: 1
       853: 1
      1056: 1

1057:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        26: q+1
        27: 1
        28: 2q+1
        29: q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        34: q^2+2q+1
        35: q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        41: q^2+2q+1
        42: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        54: q+1
        55: q+1
        56: q+1
        59: 1
        60: 1
        61: 1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: 2q+1
        69: q+1
        70: q+1
        73: q+1
        74: q+1
        75: q+1
        77: q+1
        78: 1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        86: q+1
        87: q+1
        88: q+1
        90: q+1
        91: 1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        98: q^2+2q+1
        99: q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       110: q+1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: q+1
       138: q+1
       139: q+1
       140: q+1
       143: 1
       144: 1
       145: 1
       147: q+1
       148: 1
       150: q+1
       151: 1
       152: 2q+1
       153: q+1
       154: q+1
       159: q+1
       160: q+1
       161: q+1
       164: 1
       165: 1
       166: 1
       168: q+1
       169: 1
       171: q+1
       172: 1
       173: 2q+1
       174: q+1
       175: q+1
       178: q+1
       179: q+1
       180: q+1
       182: q+1
       183: 1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       204: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       234: q+1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       251: 1
       252: 1
       254: q+1
       255: 1
       256: q+1
       264: q+1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       281: 1
       282: 1
       284: q+1
       285: 1
       286: q+1
       292: q+1
       293: q+1
       294: q+1
       297: 1
       298: 1
       299: 1
       301: q+1
       302: 1
       304: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       334: 1
       342: 1
       348: 1
       349: 1
       350: 1
       371: 1
       377: 1
       378: 1
       379: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       391: 1
       410: 1
       416: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       440: q+1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       456: 1
       457: 1
       458: 1
       460: q+1
       461: 1
       462: q+1
       507: 1
       541: 1
       549: 1
       555: 1
       556: 1
       557: 1
       588: 1
       596: 1
       602: 1
       603: 1
       604: 1
       625: 1
       631: 1
       632: 1
       633: 1
       638: 1
       639: 1
       640: 1
       643: 1
       644: 1
       645: 1
       746: 1
       798: 1
       832: 1
       840: 1
       846: 1
       847: 1
       848: 1
      1057: 1

1058:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: q+1
        10: 1
        11: q+1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: q+1
        24: q+1
        27: 1
        29: 1
        31: 1
        32: q+1
        35: q+1
        37: 1
        38: q+1
        39: q+1
        42: q+1
        44: 1
        45: q+1
        46: q+1
        48: q+1
        49: q+1
        56: q+1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: q+1
        74: q+1
        75: q+1
        78: 1
        80: 1
        82: 1
        83: q+1
        87: q+1
        88: q+1
        91: 1
        93: 1
        95: 1
        96: q+1
        99: q+1
       101: 1
       102: q+1
       103: q+1
       111: q+1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       140: q+1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: q+1
       161: q+1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: q+1
       179: q+1
       180: q+1
       183: 1
       185: 1
       187: 1
       188: q+1
       205: 1
       212: 1
       219: 1
       223: 1
       224: 1
       235: q+1
       242: 1
       246: 1
       247: 1
       251: 1
       252: 1
       255: 1
       265: q+1
       272: 1
       276: 1
       277: 1
       281: 1
       282: 1
       285: 1
       294: q+1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: q+1
       335: 1
       343: 1
       350: 1
       372: 1
       379: 1
       386: 1
       390: 1
       391: 1
       411: 1
       418: 1
       425: 1
       429: 1
       430: 1
       441: q+1
       448: 1
       452: 1
       453: 1
       457: 1
       458: 1
       461: 1
       508: 1
       542: 1
       550: 1
       557: 1
       589: 1
       597: 1
       604: 1
       626: 1
       633: 1
       640: 1
       644: 1
       645: 1
       747: 1
       799: 1
       833: 1
       841: 1
       848: 1
      1058: 1

1059:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        57: 1
        60: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       112: 1
       119: 1
       122: 1
       124: 1
       127: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       162: 1
       165: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       206: 1
       213: 1
       220: 1
       223: 1
       225: 1
       227: 1
       236: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       257: 1
       266: 1
       273: 1
       276: 1
       278: 1
       281: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       344: 1
       351: 1
       354: 1
       373: 1
       380: 1
       387: 1
       390: 1
       392: 1
       394: 1
       412: 1
       419: 1
       426: 1
       429: 1
       431: 1
       433: 1
       442: 1
       449: 1
       452: 1
       454: 1
       457: 1
       459: 1
       461: 1
       462: 1
       463: 1
       509: 1
       551: 1
       558: 1
       561: 1
       598: 1
       605: 1
       608: 1
       627: 1
       634: 1
       641: 1
       644: 1
       646: 1
       648: 1
       748: 1
       800: 1
       842: 1
       849: 1
       852: 1
      1059: 1

1060:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        57: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       113: 1
       119: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       141: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       156: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       207: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       237: 1
       243: 1
       247: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       267: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       295: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       345: 1
       351: 1
       355: 1
       374: 1
       381: 1
       387: 1
       391: 1
       392: 1
       394: 1
       413: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       443: 1
       449: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       510: 1
       552: 1
       558: 1
       562: 1
       599: 1
       605: 1
       609: 1
       628: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       749: 1
       801: 1
       843: 1
       849: 1
       853: 1
      1060: 1

1061:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        52: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       114: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       136: 1
       141: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       157: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       208: 1
       215: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       238: 1
       243: 1
       244: 1
       245: 1
       248: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       268: 1
       273: 1
       274: 1
       275: 1
       278: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: 1
       295: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       346: 1
       351: 1
       352: 1
       353: 1
       375: 1
       382: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       414: 1
       421: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       444: 1
       449: 1
       450: 1
       451: 1
       454: 1
       455: 1
       456: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       511: 1
       553: 1
       558: 1
       559: 1
       560: 1
       600: 1
       605: 1
       606: 1
       607: 1
       629: 1
       636: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       750: 1
       802: 1
       844: 1
       849: 1
       850: 1
       851: 1
      1061: 1

1062:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       115: 1
       120: 1
       121: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       209: 1
       216: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       239: 1
       244: 1
       245: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       269: 1
       274: 1
       275: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       347: 1
       352: 1
       353: 1
       376: 1
       383: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       415: 1
       422: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       445: 1
       450: 1
       451: 1
       455: 1
       456: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       512: 1
       554: 1
       559: 1
       560: 1
       601: 1
       606: 1
       607: 1
       630: 1
       637: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       751: 1
       803: 1
       845: 1
       850: 1
       851: 1
      1062: 1

1063:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        59: 1
        60: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       116: 1
       121: 1
       122: 1
       126: 1
       127: 1
       130: 1
       131: 1
       132: 1
       133: 1
       138: 1
       143: 1
       144: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       164: 1
       165: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       210: 1
       217: 1
       222: 1
       223: 1
       226: 1
       227: 1
       240: 1
       245: 1
       246: 1
       250: 1
       251: 1
       254: 1
       255: 1
       256: 1
       257: 1
       270: 1
       275: 1
       276: 1
       280: 1
       281: 1
       284: 1
       285: 1
       286: 1
       287: 1
       292: 1
       297: 1
       298: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       348: 1
       353: 1
       354: 1
       377: 1
       384: 1
       389: 1
       390: 1
       393: 1
       394: 1
       416: 1
       423: 1
       428: 1
       429: 1
       432: 1
       433: 1
       446: 1
       451: 1
       452: 1
       456: 1
       457: 1
       460: 1
       461: 1
       462: 1
       463: 1
       513: 1
       555: 1
       560: 1
       561: 1
       602: 1
       607: 1
       608: 1
       631: 1
       638: 1
       643: 1
       644: 1
       647: 1
       648: 1
       752: 1
       804: 1
       846: 1
       851: 1
       852: 1
      1063: 1

1064:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        55: 1
        59: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       117: 1
       121: 1
       123: 1
       126: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       139: 1
       143: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       160: 1
       164: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       211: 1
       218: 1
       222: 1
       224: 1
       226: 1
       227: 1
       241: 1
       245: 1
       247: 1
       250: 1
       252: 1
       254: 1
       255: 1
       256: 1
       257: 1
       271: 1
       275: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       293: 1
       297: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       349: 1
       353: 1
       355: 1
       378: 1
       385: 1
       389: 1
       391: 1
       393: 1
       394: 1
       417: 1
       424: 1
       428: 1
       430: 1
       432: 1
       433: 1
       447: 1
       451: 1
       453: 1
       456: 1
       458: 1
       460: 1
       461: 1
       462: 1
       463: 1
       514: 1
       556: 1
       560: 1
       562: 1
       603: 1
       607: 1
       609: 1
       632: 1
       639: 1
       643: 1
       645: 1
       647: 1
       648: 1
       753: 1
       805: 1
       847: 1
       851: 1
       853: 1
      1064: 1

1065:    0: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         8: 1
        10: q+1
        11: q+1
        12: q+1
        14: q+1
        15: q+1
        17: q+1
        18: q+1
        19: q+1
        23: 1
        24: 1
        27: 1
        29: q+1
        31: q+1
        32: q+1
        35: 1
        37: q+1
        38: q+1
        39: q+1
        42: 1
        44: q+1
        45: q+1
        46: q+1
        48: q+1
        49: q+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: q+1
        70: q+1
        74: 1
        75: 1
        78: 1
        80: q+1
        82: q+1
        83: q+1
        87: 1
        88: 1
        91: 1
        93: q+1
        95: q+1
        96: q+1
        99: 1
       101: q+1
       102: q+1
       103: q+1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       133: q+1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: q+1
       154: q+1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: q+1
       175: q+1
       179: 1
       180: 1
       183: 1
       185: q+1
       187: q+1
       188: q+1
       212: 1
       219: 1
       223: 1
       224: 1
       227: 1
       242: 1
       246: 1
       247: 1
       251: 1
       252: 1
       255: 1
       257: q+1
       272: 1
       276: 1
       277: 1
       281: 1
       282: 1
       285: 1
       287: q+1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: q+1
       308: q+1
       350: 1
       354: 1
       355: 1
       379: 1
       386: 1
       390: 1
       391: 1
       394: 1
       418: 1
       425: 1
       429: 1
       430: 1
       433: 1
       448: 1
       452: 1
       453: 1
       457: 1
       458: 1
       461: 1
       463: q+1
       515: 1
       557: 1
       561: 1
       562: 1
       604: 1
       608: 1
       609: 1
       633: 1
       640: 1
       644: 1
       645: 1
       648: 1
       754: 1
       806: 1
       848: 1
       852: 1
       853: 1
      1065: 1

1066:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: 1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       189: q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       309: 1
       310: q+1
       311: q+1
       312: 1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       385: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       455: 1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: 1
       480: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       613: 1
       621: 1
       622: 1
       624: 1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: 1
       663: 1
       666: 1
       667: 1
       675: 1
       697: 1
       718: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       820: 1
       854: 1
       855: 1
       860: 1
       863: 1
       869: 1
       960: 1
       971: 1
      1066: 1

1067:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       189: q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       309: 1
       310: q+1
       311: q+1
       312: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       416: 1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       450: 1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       482: 1
       492: 1
       493: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       516: 1
       517: q+1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       566: 1
       575: 1
       577: 1
       583: 1
       612: 1
       620: 1
       622: 1
       623: 1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       662: 1
       676: 1
       677: 1
       685: 1
       696: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       767: 1
       819: 1
       854: 1
       856: 1
       859: 1
       864: 1
       878: 1
       906: 1
       918: 1
      1067: 1

1068:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       646: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       704: 1
       707: 1
       756: 1
       758: 1
       807: 1
       808: 1
       809: 1
       815: 1
       855: 1
       856: 1
       857: 1
       858: 1
       887: 1
      1015: 1
      1068: 1

1069:    0: q^3+7q^2+5q+1
         1: 3q^2+4q+1
         2: q^3+7q^2+5q+1
         3: q^3+7q^2+5q+1
         4: 5q^2+5q+1
         5: 5q^2+5q+1
         6: q^2+4q+1
         7: 3q^2+4q+1
         8: q^3+7q^2+5q+1
         9: 3q^2+4q+1
        10: q^3+5q^2+5q+1
        11: 3q^2+5q+1
        12: 3q^2+5q+1
        13: q^2+4q+1
        14: 5q^2+5q+1
        15: 5q^2+5q+1
        16: q^2+4q+1
        17: 5q^2+5q+1
        18: 5q^2+5q+1
        19: 4q^2+5q+1
        20: q^2+4q+1
        21: q^2+4q+1
        22: 3q^2+4q+1
        23: 3q^2+5q+1
        24: 3q^2+5q+1
        25: q^2+4q+1
        27: q^3+5q^2+5q+1
        28: q^2+4q+1
        29: 2q^2+5q+1
        30: q^2+4q+1
        31: 2q^2+5q+1
        32: q^2+5q+1
        33: 4q+1
        34: q^2+4q+1
        35: 5q^2+5q+1
        36: q^2+4q+1
        37: 2q^2+3q+1
        38: q^2+3q+1
        39: 3q^2+5q+1
        40: 4q+1
        41: q^2+4q+1
        42: 5q^2+5q+1
        43: q^2+4q+1
        44: 2q^2+3q+1
        45: 3q^2+5q+1
        46: q^2+3q+1
        47: 4q+1
        48: 4q^2+5q+1
        49: 4q^2+5q+1
        50: 2q+1
        51: 2q+1
        52: q^2+4q+1
        53: q^2+4q+1
        54: q^2+4q+1
        55: q^2+4q+1
        56: q^2+5q+1
        57: q^2+4q+1
        60: 2q^2+5q+1
        61: 2q^2+5q+1
        62: 4q+1
        64: 2q^2+5q+1
        65: 4q+1
        67: 2q^2+5q+1
        68: 4q+1
        69: q^2+5q+1
        70: q^2+5q+1
        71: 4q+1
        72: 4q+1
        73: q^2+4q+1
        74: q^2+3q+1
        75: 3q^2+5q+1
        76: 2q+1
        78: 2q^2+3q+1
        79: 2q+1
        80: 2q+1
        81: q^2+4q+1
        82: q^2+3q+1
        83: 3q+1
        84: 4q+1
        85: 4q+1
        86: q^2+4q+1
        87: 3q^2+5q+1
        88: q^2+3q+1
        89: 2q+1
        91: 2q^2+3q+1
        92: q^2+4q+1
        93: q^2+3q+1
        94: 2q+1
        95: 2q+1
        96: 3q+1
        97: 4q+1
        98: 4q+1
        99: 4q^2+5q+1
       100: 4q+1
       101: q^2+2q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: 2q+1
       106: 2q+1
       107: q^2+4q+1
       108: 4q+1
       109: 4q+1
       110: 4q+1
       111: q^2+5q+1
       112: 2q+1
       113: 2q+1
       118: q^2+5q+1
       119: 4q+1
       122: 2q^2+5q+1
       123: 2q+1
       124: 4q+1
       127: 2q+1
       128: 2q^2+5q+1
       129: 4q+1
       131: q^2+5q+1
       132: 4q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 4q+1
       137: 2q+1
       138: 2q+1
       139: q^2+4q+1
       140: 3q+1
       141: 2q+1
       144: 2q+1
       145: q^2+3q+1
       146: q+1
       148: 2q+1
       149: 2q+1
       151: q^2+3q+1
       152: 2q+1
       153: 2q+1
       154: 3q+1
       155: 2q+1
       156: q+1
       157: 4q+1
       158: 2q+1
       159: q^2+4q+1
       160: 2q+1
       161: 3q+1
       162: 2q+1
       165: q^2+3q+1
       166: 2q+1
       167: 2q+1
       169: q^2+3q+1
       170: q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 3q+1
       176: 4q+1
       177: 4q+1
       178: 4q+1
       179: q^2+3q+1
       180: q^2+3q+1
       181: q+1
       183: q^2+2q+1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: 2q+1
       193: 4q+1
       194: 4q+1
       195: 4q+1
       196: 4q+1
       197: q+1
       198: q+1
       205: q^2+5q+1
       206: 2q+1
       207: q+1
       212: 2q+1
       213: q+1
       214: 2q+1
       219: 2q+1
       220: 4q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       227: q+1
       228: 1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: 2q+1
       235: 3q+1
       236: 1
       237: q+1
       242: 2q+1
       243: q+1
       246: 2q+1
       248: 2q+1
       251: q+1
       252: q^2+3q+1
       253: q+1
       255: 2q+1
       256: 2q+1
       257: 1
       258: 1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: 2q+1
       265: 3q+1
       266: q+1
       267: 1
       272: 2q+1
       273: 2q+1
       276: q^2+3q+1
       277: q+1
       278: q+1
       282: 2q+1
       283: q+1
       285: 2q+1
       286: 2q+1
       287: 1
       288: q+1
       289: q+1
       290: 4q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       298: q+1
       299: q+1
       300: 1
       302: q+1
       303: 1
       305: q+1
       306: q+1
       307: q+1
       308: 2q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: 4q+1
       317: q+1
       319: q+1
       327: q+1
       328: 1
       335: 2q+1
       336: 1
       343: 2q+1
       344: q+1
       345: q+1
       350: q+1
       351: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: q+1
       361: 2q+1
       362: q+1
       363: 2q+1
       364: 1
       365: 1
       372: 2q+1
       373: 1
       380: 1
       381: q+1
       386: q+1
       387: q+1
       390: q+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: 2q+1
       400: q+1
       401: q+1
       402: 2q+1
       403: 1
       404: 1
       411: 2q+1
       412: q+1
       413: 1
       418: q+1
       420: 1
       426: q+1
       430: q+1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: q+1
       441: 2q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: q+1
       454: 1
       458: q+1
       459: 1
       461: q+1
       462: q+1
       463: 1
       466: q+1
       467: 1
       468: 1
       469: q+1
       470: q+1
       471: q+1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: q+1
       523: q+1
       524: 1
       526: 1
       534: 1
       543: 1
       550: q+1
       551: 1
       558: 1
       561: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       569: 1
       570: q+1
       571: 1
       573: 1
       581: 1
       582: 1
       589: q+1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       626: q+1
       627: 1
       635: 1
       641: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       686: 1
       694: 1
       695: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       731: 1
       739: 1
       748: 1
       757: 1
       758: 1
       761: 1
       762: 1
       774: 1
       782: 1
       801: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       849: 1
       857: 1
       858: 1
       897: 1
       905: 1
       909: 1
       911: 1
       962: 1
       966: 1
      1016: 1
      1021: 1
      1069: 1

1070:    0: 6q^2+5q+1
         1: 6q^2+5q+1
         2: 6q^2+5q+1
         3: 4q^2+5q+1
         4: 6q^2+5q+1
         5: 6q^2+5q+1
         6: 3q^2+4q+1
         7: 6q^2+5q+1
         8: 4q^2+5q+1
         9: 4q^2+5q+1
        10: q^2+4q+1
        11: 4q^2+5q+1
        12: 4q^2+5q+1
        13: 6q^2+5q+1
        14: 6q^2+5q+1
        15: q^2+3q+1
        16: 6q^2+5q+1
        17: 6q^2+5q+1
        18: q^2+3q+1
        19: 6q^2+5q+1
        20: q^2+2q+1
        21: 3q^2+4q+1
        22: 4q^2+5q+1
        23: 4q^2+5q+1
        24: 4q^2+5q+1
        25: 3q+1
        26: q^2+4q+1
        27: q^2+4q+1
        28: 4q^2+5q+1
        29: q^2+4q+1
        30: 4q^2+5q+1
        31: q^2+4q+1
        32: 4q^2+5q+1
        33: 3q^2+4q+1
        34: 6q^2+5q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: 3q^2+4q+1
        41: 6q^2+5q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 6q^2+5q+1
        48: 6q^2+5q+1
        49: 2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 3q+1
        54: 4q^2+5q+1
        55: 4q^2+5q+1
        56: 4q^2+5q+1
        57: q+1
        58: 3q+1
        59: q^2+4q+1
        60: q^2+4q+1
        61: q^2+4q+1
        62: 3q+1
        63: q^2+4q+1
        64: q+1
        65: 3q+1
        66: q^2+4q+1
        67: q+1
        68: 4q^2+5q+1
        69: q^2+4q+1
        70: q+1
        71: q+1
        72: 3q^2+4q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q+1
        85: 3q^2+4q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        94: q^2+3q+1
        95: 2q+1
        96: q^2+3q+1
        97: 3q^2+4q+1
        98: 6q^2+5q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: 3q+1
       109: 3q+1
       110: 4q^2+5q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 3q+1
       116: q^2+4q+1
       117: q^2+4q+1
       118: q^2+4q+1
       119: 1
       120: 3q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: 3q+1
       126: q+1
       127: q+1
       128: q+1
       129: 3q+1
       130: q^2+4q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q^2+3q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: 1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: 2q+1
       149: q+1
       150: 2q+1
       151: q+1
       152: q^2+3q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 1
       163: q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: 2q+1
       173: q^2+3q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: 3q^2+4q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 3q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: 3q+1
       203: 3q+1
       204: q^2+4q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 3q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: q^2+3q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       244: q+1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: 2q+1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: q^2+3q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       279: q+1
       283: q+1
       284: 2q+1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: q+1
       300: 1
       301: q+1
       303: 1
       304: q+1
       306: 2q+1
       307: q+1
       308: q+1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: 3q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: q+1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: 2q+1
       380: 1
       381: 1
       382: 1
       384: q+1
       385: q+1
       386: q+1
       388: q+1
       392: 1
       393: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: q+1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: 2q+1
       412: 1
       413: 1
       414: 1
       416: q+1
       417: q+1
       418: q+1
       427: q+1
       431: 1
       432: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: q+1
       447: q+1
       448: q+1
       450: 1
       455: 1
       459: 1
       460: q+1
       462: q+1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       482: 1
       484: 1
       490: 1
       491: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: q+1
       543: 1
       544: 1
       545: 1
       549: q+1
       559: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: q+1
       582: 1
       583: 1
       584: 1
       588: q+1
       606: 1
       611: q+1
       612: 1
       613: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: q+1
       642: 1
       646: 1
       647: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       675: 1
       685: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       809: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       823: 1
       850: 1
       858: 1
       859: 1
       860: 1
       865: 1
       896: 1
       898: 1
       918: 1
       971: 1
      1022: 1
      1025: 1
      1070: 1

1071:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: 1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       437: 1
       444: 1
       445: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       495: 1
       497: 1
       504: 1
       511: 1
       512: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       622: 1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       669: 1
       682: 1
       698: 1
       718: 1
       734: 1
       736: 1
       767: 1
       776: 1
       778: 1
       854: 1
       861: 1
       862: 1
       868: 1
       939: 1
       980: 1
      1071: 1

1072:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       436: 1
       437: 1
       439: 1
       443: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       613: 1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       682: 1
       689: 1
       756: 1
       758: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       872: 1
      1072: 1

1073:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       566: 1
       612: 1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       688: 1
       704: 1
       707: 1
       856: 1
       862: 1
       864: 1
       866: 1
       879: 1
       882: 1
      1073: 1

1074:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: 1
       564: 1
       610: 1
       611: 1
       617: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       808: 1
       857: 1
       863: 1
       864: 1
       865: 1
       888: 1
      1074: 1

1075:    0: q^2+3q+1
         1: 3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: 3q+1
         7: 3q+1
         8: q^2+3q+1
         9: 3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 3q+1
        14: q^2+3q+1
        15: q+1
        16: 3q+1
        17: q^2+3q+1
        18: q+1
        19: q^2+3q+1
        20: q+1
        21: 3q+1
        22: 3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: 3q+1
        26: 3q+1
        27: q^2+3q+1
        28: 3q+1
        29: q^2+3q+1
        30: 3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: 3q+1
        34: 3q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 3q+1
        41: 3q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: q^2+3q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: 3q+1
        54: 3q+1
        55: 3q+1
        56: q^2+3q+1
        57: q+1
        58: 3q+1
        59: 3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: 3q+1
        63: 3q+1
        64: q+1
        65: 3q+1
        66: 3q+1
        67: q+1
        68: 3q+1
        69: q^2+3q+1
        70: 1
        71: 1
        72: 3q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: 3q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 3q+1
        98: 3q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 3q+1
       109: 3q+1
       110: 3q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: 3q+1
       116: 3q+1
       117: 3q+1
       118: q^2+3q+1
       119: 1
       120: 3q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: 3q+1
       126: q+1
       127: q+1
       128: q+1
       129: 3q+1
       130: 3q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: q+1
       145: q+1
       146: q+1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: 3q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 3q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: 3q+1
       203: 3q+1
       204: 3q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 3q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       242: q+1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       283: q+1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: 3q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: q+1
       392: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: q+1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: q+1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       459: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       646: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       674: 1
       678: 1
       681: 1
       682: 1
       684: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       707: 1
       758: 1
       809: 1
       815: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       882: 1
       889: 1
       895: 1
      1075: 1

1076:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: q+1
        20: q+1
        21: 2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 2q+1
        41: 2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 2q+1
        86: q+1
        87: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       105: q+1
       107: q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 1
       120: 2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: q+1
       159: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       167: q+1
       168: q+1
       169: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       191: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       199: q+1
       201: q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: q+1
       266: 1
       268: 1
       269: q+1
       270: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       312: 1
       314: 1
       316: 1
       317: 1
       318: 1
       321: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       361: 1
       362: 1
       363: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: q+1
       412: 1
       414: 1
       415: q+1
       416: q+1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       450: 1
       469: 1
       471: 1
       472: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       521: 1
       524: 1
       525: 1
       528: 1
       531: 1
       532: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: q+1
       612: 1
       620: 1
       622: 1
       623: 1
       654: 1
       656: 1
       662: 1
       664: 1
       665: 1
       669: 1
       681: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       711: 1
       717: 1
       733: 1
       736: 1
       737: 1
       767: 1
       776: 1
       778: 1
       819: 1
       859: 1
       866: 1
       868: 1
       886: 1
       899: 1
       938: 1
       980: 1
      1076: 1

1077:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: q+1
        52: q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: 2q+1
        73: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       106: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       113: q+1
       114: q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: q+1
       139: q+1
       141: 1
       142: q+1
       143: q+1
       145: q+1
       149: q+1
       150: q+1
       151: q+1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       233: q+1
       237: 1
       238: 1
       239: q+1
       241: q+1
       248: 1
       249: q+1
       250: q+1
       252: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: q+1
       381: 1
       382: 1
       383: q+1
       385: q+1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       455: 1
       470: 1
       471: 1
       472: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: q+1
       567: 1
       571: 1
       572: 1
       576: 1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       613: 1
       621: 1
       622: 1
       624: 1
       655: 1
       656: 1
       663: 1
       664: 1
       665: 1
       670: 1
       674: 1
       675: 1
       682: 1
       689: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       763: 1
       768: 1
       777: 1
       778: 1
       780: 1
       820: 1
       860: 1
       867: 1
       868: 1
       877: 1
       900: 1
       939: 1
       981: 1
      1077: 1

1078:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: 1
        72: q^2+2q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q^2+2q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q^2+2q+1
       126: 1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       149: q+1
       150: q+1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q^2+2q+1
       178: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       186: q+1
       187: q+1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q^2+2q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       286: q+1
       287: q+1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: q+1
       297: 1
       299: 1
       303: q+1
       304: q+1
       309: 1
       310: 1
       311: q+1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       359: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       431: q+1
       432: q+1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       455: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       529: 1
       545: 1
       546: 1
       548: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: q+1
       613: 1
       621: 1
       622: 1
       624: 1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       689: 1
       697: 1
       698: 1
       700: 1
       734: 1
       755: 1
       756: 1
       763: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       820: 1
       861: 1
       869: 1
       870: 1
       877: 1
       900: 1
       960: 1
       979: 1
      1078: 1

1079:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: 2q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        75: q+1
        76: 2q+1
        78: 2q+1
        81: 2q+1
        82: 2q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       135: q+1
       136: q+1
       137: q+1
       139: 1
       141: 2q+1
       145: q+1
       149: 2q+1
       151: 2q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q+1
       177: q+1
       178: q+1
       180: 1
       181: 2q+1
       183: 2q+1
       186: q+1
       187: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       216: q+1
       218: 1
       220: 2q+1
       221: q+1
       222: q+1
       224: 1
       225: 2q+1
       227: 2q+1
       230: 1
       231: q+1
       233: 1
       237: q+1
       248: 2q+1
       252: q+1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: 2q+1
       276: q+1
       277: 1
       278: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       287: q+1
       289: 1
       290: q+1
       291: q+1
       293: 1
       295: 2q+1
       299: 1
       303: q+1
       305: q+1
       309: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: q+1
       341: 1
       345: 1
       346: q+1
       347: q+1
       349: 1
       351: 2q+1
       355: 1
       359: 1
       361: 1
       381: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: q+1
       430: 1
       431: q+1
       433: q+1
       436: 1
       437: q+1
       439: 1
       443: 1
       454: q+1
       458: 1
       465: 1
       466: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: q+1
       506: 1
       510: 1
       522: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: q+1
       609: 1
       613: 1
       615: 1
       635: 1
       650: 1
       658: 1
       659: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       756: 1
       757: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       813: 1
       862: 1
       870: 1
       871: 1
       876: 1
       893: 1
       961: 1
       977: 1
      1079: 1

1080:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: 1
       290: 1
       293: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       436: 1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       599: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       757: 1
       758: 1
       761: 1
       774: 1
       863: 1
       871: 1
       872: 1
       875: 1
       962: 1
      1080: 1

1081:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q^2+2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        75: q+1
        79: 2q+1
        81: 2q+1
        83: 2q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: 2q+1
        88: 1
        89: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       102: 2q+1
       103: q+1
       104: q+1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       134: 2q+1
       135: q+1
       136: q+1
       138: q+1
       139: 1
       140: q+1
       152: 2q+1
       154: 2q+1
       155: 2q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 1
       184: 2q+1
       186: q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 2q+1
       214: q+1
       215: q+1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       228: q+1
       229: q+1
       230: 1
       234: 1
       235: q+1
       256: 2q+1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       277: 1
       278: q+1
       281: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       288: 2q+1
       289: 1
       290: q+1
       292: q+1
       293: 1
       294: 1
       306: q+1
       308: q+1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 1
       346: q+1
       348: q+1
       349: 1
       350: 1
       356: q+1
       357: 1
       363: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       419: q+1
       420: 1
       425: 1
       426: q+1
       429: q+1
       430: 1
       434: 1
       435: q+1
       436: 1
       440: 1
       441: 1
       462: q+1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: q+1
       493: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       507: 1
       508: 1
       517: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: q+1
       599: 1
       604: 1
       610: 1
       611: 1
       617: 1
       652: 1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       686: 1
       687: 1
       693: 1
       757: 1
       759: 1
       760: 1
       774: 1
       783: 1
       792: 1
       799: 1
       808: 1
       864: 1
       871: 1
       873: 1
       874: 1
       888: 1
       963: 1
       997: 1
      1081: 1

1082:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q^2+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: 1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q^2+1
        36: 1
        38: q^2+1
        39: q^2+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q^2+q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q^2+1
        68: q+1
        69: q^2+q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: q^2+1
        75: q^2+1
        79: 1
        81: 1
        83: q^2+1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: q^2+1
       128: q^2+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: q^2+1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: q^2+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       363: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       611: 1
       617: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       687: 1
       693: 1
       758: 1
       759: 1
       760: 1
       761: 1
       792: 1
       799: 1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       964: 1
      1082: 1

1083:    0: 2q^2+2q+1
         1: q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: q^2+2q+1
         5: 2q^2+2q+1
         6: q+1
         7: q+1
         8: 2q^2+2q+1
         9: q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 2q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: 2q^2+2q+1
        28: q+1
        29: 2q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q^2+2q+1
        43: q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: 1
        58: q+1
        59: q+1
        60: 2q^2+2q+1
        61: q^2+2q+1
        62: q+1
        63: q+1
        64: q^2+2q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        91: q^2+2q+1
        92: q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+2q+1
       119: 1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: 1
       133: q+1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: 1
       144: q+1
       145: q+1
       146: 1
       149: 1
       151: q+1
       152: 1
       153: q+1
       154: q+1
       155: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: q^2+2q+1
       166: q+1
       167: q+1
       169: q^2+2q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: q+1
       199: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: 1
       227: q+1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: 1
       242: q+1
       248: 1
       251: q+1
       252: q+1
       253: 1
       256: 1
       257: q+1
       259: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       272: q+1
       273: 1
       276: q^2+2q+1
       277: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: q+1
       329: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: q+1
       355: 1
       358: 1
       361: 1
       362: 1
       363: 1
       364: q+1
       380: 1
       386: q+1
       392: 1
       397: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       403: 1
       411: 1
       412: 1
       418: q+1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       521: 1
       524: 1
       566: 1
       568: 1
       570: 1
       571: 1
       581: 1
       589: 1
       597: 1
       598: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       617: 1
       618: 1
       634: 1
       640: 1
       646: 1
       654: 1
       662: 1
       664: 1
       669: 1
       671: 1
       673: 1
       674: 1
       681: 1
       684: 1
       688: 1
       691: 1
       692: 1
       693: 1
       694: 1
       760: 1
       762: 1
       782: 1
       791: 1
       799: 1
       800: 1
       806: 1
       812: 1
       815: 1
       866: 1
       874: 1
       876: 1
       892: 1
       895: 1
       965: 1
      1005: 1
      1083: 1

1084:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: 1
        12: q^2+1
        13: 1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: q^2+1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        30: 1
        31: q^2+1
        32: 1
        33: 1
        34: 1
        35: q^2+1
        36: 1
        37: q^2+1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: q^2+1
        76: 1
        78: q^2+1
        81: 1
        82: q^2+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: q^2+1
       149: 1
       151: q^2+1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: q^2+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       313: 1
       315: 1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       567: 1
       569: 1
       570: 1
       571: 1
       581: 1
       589: 1
       599: 1
       605: 1
       609: 1
       613: 1
       615: 1
       635: 1
       655: 1
       663: 1
       664: 1
       670: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       761: 1
       762: 1
       782: 1
       801: 1
       813: 1
       867: 1
       875: 1
       876: 1
       893: 1
       966: 1
      1084: 1

1085:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        81: 2q+1
        82: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       103: q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       139: 2q+1
       141: 1
       142: 1
       143: q+1
       145: q+1
       149: 1
       150: q+1
       151: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       186: q+1
       187: 1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       208: q+1
       209: 1
       210: 2q+1
       211: q+1
       212: q+1
       215: q+1
       216: 1
       218: 2q+1
       220: q+1
       221: q+1
       222: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       233: 1
       238: 1
       239: 1
       241: q+1
       248: 1
       249: 1
       250: q+1
       252: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: q+1
       299: 1
       303: 1
       304: 1
       305: 1
       316: q+1
       317: 1
       318: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       339: 1
       341: 1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: q+1
       355: 1
       361: 1
       368: 1
       370: 1
       382: 1
       383: 1
       385: q+1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       471: 1
       472: 1
       480: q+1
       481: 1
       482: q+1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       497: 1
       504: 1
       506: 1
       511: 1
       512: 1
       514: 1
       531: 1
       546: 1
       548: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       615: 1
       622: 1
       624: 1
       636: 1
       639: 1
       656: 1
       664: 1
       665: 1
       673: 1
       674: 1
       675: 1
       691: 1
       698: 1
       700: 1
       736: 1
       762: 1
       763: 1
       771: 1
       773: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       802: 1
       805: 1
       822: 1
       868: 1
       876: 1
       877: 1
       902: 1
       967: 1
       984: 1
       986: 1
      1085: 1

1086:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: 1
        72: q^2+2q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q^2+2q+1
       121: 1
       122: 1
       124: 1
       125: q^2+2q+1
       126: 1
       127: 1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q^2+2q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       256: q+1
       257: q+1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       300: q+1
       301: q+1
       309: 1
       310: 1
       311: q+1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       392: q+1
       393: q+1
       397: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       450: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       481: 1
       482: 1
       485: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: q+1
       575: 1
       583: 1
       585: 1
       586: 1
       612: 1
       620: 1
       622: 1
       623: 1
       649: 1
       657: 1
       658: 1
       665: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       711: 1
       714: 1
       732: 1
       733: 1
       734: 1
       737: 1
       776: 1
       819: 1
       861: 1
       878: 1
       879: 1
       886: 1
       899: 1
       906: 1
       935: 1
      1086: 1

1087:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: 2q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       104: q+1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: 2q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       157: q+1
       158: q+1
       159: 1
       162: 2q+1
       165: q+1
       167: 2q+1
       169: 2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       181: 2q+1
       183: 2q+1
       184: q+1
       185: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       208: q+1
       209: q+1
       210: 1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       225: 2q+1
       227: 2q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       248: 2q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q+1
       257: q+1
       259: 1
       261: q+1
       262: 1
       266: q+1
       273: 2q+1
       276: q+1
       288: 1
       290: q+1
       291: q+1
       292: 1
       295: 2q+1
       298: 1
       300: q+1
       302: q+1
       309: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       329: 1
       331: q+1
       332: 1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       347: q+1
       348: 1
       351: 2q+1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       392: q+1
       394: q+1
       397: 1
       399: 1
       412: q+1
       435: 1
       437: q+1
       438: 1
       442: 1
       449: q+1
       452: 1
       465: 1
       466: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: q+1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: q+1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       650: 1
       658: 1
       659: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       688: 1
       690: 1
       704: 1
       705: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       810: 1
       862: 1
       879: 1
       880: 1
       885: 1
       890: 1
       907: 1
       933: 1
      1087: 1

1088:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q^2+2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: 2q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: 2q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        92: 2q+1
        94: 2q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       102: q+1
       103: 2q+1
       104: q+1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: 2q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       134: 1
       135: 2q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 2q+1
       157: q+1
       159: 1
       160: q+1
       161: q+1
       173: 2q+1
       175: 2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       180: 2q+1
       184: q+1
       186: 2q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 2q+1
       208: q+1
       210: 1
       211: q+1
       212: q+1
       213: 1
       214: 2q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       247: q+1
       248: q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q+1
       258: q+1
       259: 1
       260: q+1
       264: 1
       265: q+1
       286: 2q+1
       288: 1
       289: 2q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       306: q+1
       308: q+1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: q+1
       329: 1
       330: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 2q+1
       346: q+1
       348: 1
       349: q+1
       350: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       374: q+1
       379: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       391: q+1
       395: q+1
       396: 1
       402: 1
       434: 1
       435: 1
       436: q+1
       440: 1
       441: 1
       462: q+1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: q+1
       484: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       507: 1
       508: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: q+1
       557: 1
       564: 1
       610: 1
       611: 1
       617: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       709: 1
       722: 1
       731: 1
       740: 1
       747: 1
       808: 1
       863: 1
       880: 1
       881: 1
       884: 1
       888: 1
       908: 1
       943: 1
      1088: 1

1089:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       435: 1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       543: 1
       550: 1
       551: 1
       652: 1
       659: 1
       661: 1
       662: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       705: 1
       707: 1
       708: 1
       731: 1
       864: 1
       880: 1
       882: 1
       883: 1
       909: 1
      1089: 1

1090:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q+1
        16: q+1
        17: q^2+q+1
        18: q^2+1
        19: q^2+q+1
        20: 1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q^2+1
        43: 1
        45: q^2+1
        46: q^2+1
        47: q+1
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q^2+q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q^2+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q^2+q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: q^2+1
        88: q^2+1
        92: 1
        94: 1
        96: q^2+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+q+1
       119: 1
       120: q+1
       121: 1
       122: q^2+1
       123: q^2+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: q+1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: q^2+1
       173: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: q^2+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       490: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       611: 1
       617: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: 1
       693: 1
       706: 1
       707: 1
       708: 1
       709: 1
       740: 1
       747: 1
       865: 1
       881: 1
       882: 1
       883: 1
       884: 1
       910: 1
      1090: 1

1091:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: q^2+1
        18: q^2+1
        19: 1
        20: 1
        21: 1
        22: 1
        23: q^2+1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: q^2+1
        43: 1
        44: q^2+1
        45: q^2+1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: q^2+1
        61: 1
        62: 1
        63: 1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q^2+1
        89: 1
        91: q^2+1
        92: 1
        93: q^2+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: q^2+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: q^2+1
       167: 1
       169: q^2+1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: q^2+1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       312: 1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       373: 1
       380: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: 1
       521: 1
       523: 1
       524: 1
       534: 1
       550: 1
       551: 1
       558: 1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       654: 1
       662: 1
       664: 1
       669: 1
       679: 1
       681: 1
       683: 1
       684: 1
       688: 1
       690: 1
       708: 1
       710: 1
       739: 1
       748: 1
       810: 1
       866: 1
       883: 1
       885: 1
       890: 1
       911: 1
      1091: 1

1092:    0: 2q^2+2q+1
         1: q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q^2+2q+1
         9: q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: 2q^2+2q+1
        25: q+1
        26: q+1
        27: 2q^2+2q+1
        28: q+1
        29: q^2+2q+1
        30: q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: 2q^2+2q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q^2+2q+1
        68: q+1
        69: q^2+2q+1
        70: q+1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q^2+2q+1
        76: q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+2q+1
       119: 1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+2q+1
       129: q+1
       130: q+1
       131: q+1
       132: 1
       133: q+1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: q+1
       145: q^2+2q+1
       146: q+1
       148: 1
       149: q+1
       151: q^2+2q+1
       152: q+1
       153: q+1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: 1
       165: q+1
       166: q+1
       167: 1
       169: q+1
       170: 1
       173: 1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: q+1
       188: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: q+1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: 1
       227: q+1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       237: 1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       251: q+1
       252: q^2+2q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       283: 1
       286: 1
       287: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       372: 1
       374: 1
       379: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: q+1
       413: 1
       418: q+1
       431: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       534: 1
       542: 1
       550: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       571: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       628: 1
       633: 1
       646: 1
       655: 1
       663: 1
       664: 1
       670: 1
       674: 1
       680: 1
       682: 1
       683: 1
       684: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       709: 1
       710: 1
       730: 1
       739: 1
       747: 1
       749: 1
       754: 1
       811: 1
       815: 1
       867: 1
       884: 1
       885: 1
       891: 1
       895: 1
       912: 1
       951: 1
      1092: 1

1093:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       157: q+1
       158: 1
       159: 2q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       167: 1
       168: q+1
       169: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       208: q+1
       209: 1
       210: 2q+1
       215: q+1
       216: 1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: q+1
       273: 1
       274: 1
       275: q+1
       276: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       316: q+1
       317: 1
       318: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       331: 1
       332: 1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 1
       407: 1
       408: 1
       414: 1
       415: 1
       416: q+1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       471: 1
       472: 1
       480: q+1
       481: 1
       482: q+1
       487: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       504: 1
       505: 1
       511: 1
       512: 1
       513: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       577: 1
       585: 1
       586: 1
       614: 1
       622: 1
       623: 1
       629: 1
       631: 1
       656: 1
       664: 1
       665: 1
       683: 1
       684: 1
       685: 1
       690: 1
       698: 1
       699: 1
       710: 1
       711: 1
       719: 1
       721: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       750: 1
       752: 1
       778: 1
       821: 1
       868: 1
       885: 1
       886: 1
       901: 1
       913: 1
       940: 1
       942: 1
      1093: 1

1094:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       525: 1
       527: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       563: 1
       564: 1
       572: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       625: 1
       642: 1
       646: 1
       647: 1
       657: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       703: 1
       732: 1
       755: 1
       775: 1
       807: 1
       808: 1
       816: 1
       818: 1
       850: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       898: 1
      1014: 1
      1094: 1

1095:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       303: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       646: q+1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       676: 1
       677: 1
       678: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       756: 1
       807: 1
       808: 1
       809: 1
       815: 1
       870: 1
       879: 1
       887: 1
       888: 1
       889: 1
       895: 1
      1015: 1
      1095: 1

1096:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^2+4q+1
         3: 3q^2+4q+1
         4: q^2+4q+1
         5: q^2+4q+1
         6: q^2+4q+1
         7: 3q+1
         8: q^2+4q+1
         9: 3q^2+4q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^2+4q+1
        13: q^2+4q+1
        14: 4q+1
        15: q^2+4q+1
        16: q^2+4q+1
        17: 4q+1
        18: q^2+4q+1
        19: 4q+1
        20: q^2+4q+1
        21: 3q+1
        22: 3q+1
        23: 2q+1
        24: 2q+1
        25: q^2+4q+1
        26: 3q+1
        27: q^2+4q+1
        28: q^2+4q+1
        29: 4q+1
        30: q^2+4q+1
        31: 4q+1
        32: 4q+1
        33: 4q+1
        34: 3q+1
        35: 4q+1
        36: q^2+4q+1
        37: 2q+1
        38: 2q+1
        39: q^2+4q+1
        40: 4q+1
        41: 3q+1
        42: 4q+1
        43: q^2+4q+1
        44: 2q+1
        45: q^2+4q+1
        46: 2q+1
        47: 4q+1
        48: 4q+1
        49: 4q+1
        50: 2q+1
        51: 2q+1
        52: 3q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+4q+1
        58: 3q+1
        59: 3q+1
        60: 2q+1
        61: 2q+1
        62: 4q+1
        63: 3q+1
        64: 4q+1
        65: 4q+1
        66: 3q+1
        67: 4q+1
        68: 4q+1
        69: 4q+1
        70: 4q+1
        71: 4q+1
        72: 3q+1
        73: 3q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: 2q+1
        80: q+1
        81: q^2+4q+1
        82: 2q+1
        83: 2q+1
        84: 4q+1
        85: 3q+1
        86: 3q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        91: 2q+1
        92: q^2+4q+1
        93: 2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: 4q+1
        98: 3q+1
        99: 4q+1
       100: 4q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: 3q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 4q+1
       120: 3q+1
       121: 3q+1
       122: 2q+1
       123: q+1
       124: 4q+1
       125: 3q+1
       126: 3q+1
       127: q+1
       128: 2q+1
       129: 4q+1
       130: 3q+1
       131: 4q+1
       132: 4q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: 2q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       155: 2q+1
       156: q+1
       157: 3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: 4q+1
       177: 3q+1
       178: 3q+1
       179: q+1
       180: q+1
       181: q+1
       183: q+1
       184: 2q+1
       185: 1
       186: 2q+1
       187: 1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: q+1
       208: 3q+1
       209: q+1
       210: q+1
       211: q+1
       212: 1
       213: q+1
       214: 2q+1
       215: 3q+1
       216: q+1
       217: q+1
       218: q+1
       219: 1
       220: 4q+1
       221: 3q+1
       222: 3q+1
       223: q+1
       224: q+1
       225: q+1
       227: q+1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       248: 2q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: 2q+1
       257: 1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: 2q+1
       276: q+1
       277: 1
       278: q+1
       282: 1
       283: q+1
       285: q+1
       286: 2q+1
       287: 1
       288: q+1
       289: q+1
       290: 3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: q+1
       346: 3q+1
       347: q+1
       348: q+1
       349: q+1
       350: 1
       351: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: q+1
       430: 1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       646: 1
       648: 1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: 1
       731: 1
       748: 1
       757: 1
       774: 1
       801: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       849: 1
       871: 1
       880: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       897: 1
      1016: 1
      1096: 1

1097:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       148: 1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: q+1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       255: 1
       256: 1
       257: 1
       258: q+1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: q+1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       277: q+1
       283: q+1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: q+1
       412: q+1
       413: q+1
       418: q+1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: 1
       519: 1
       520: 1
       535: 1
       543: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       582: q+1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       660: 1
       668: 1
       669: 1
       670: 1
       678: 1
       679: 1
       680: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       695: 1
       706: 1
       740: 1
       748: 1
       749: 1
       754: 1
       758: 1
       809: 1
       810: 1
       811: 1
       826: 1
       872: 1
       881: 1
       889: 1
       890: 1
       891: 1
       952: 1
      1017: 1
      1097: 1

1098:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: 1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: q+1
       144: q+1
       145: q+1
       146: q+1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: q+1
       242: q+1
       248: q+1
       251: q+1
       252: q+1
       253: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: q+1
       380: q+1
       381: q+1
       386: q+1
       392: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       468: 1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: 1
       521: 1
       522: 1
       543: q+1
       565: 1
       568: 1
       569: 1
       582: 1
       590: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       661: 1
       668: 1
       671: 1
       672: 1
       678: 1
       681: 1
       682: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       695: 1
       707: 1
       759: 1
       792: 1
       800: 1
       801: 1
       806: 1
       809: 1
       812: 1
       813: 1
       834: 1
       873: 1
       882: 1
       889: 1
       892: 1
       893: 1
      1006: 1
      1018: 1
      1098: 1

1099:    0: q^3+3q^2+3q+1
         1: q^2+2q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 2q+1
         7: q+1
         8: 2q^2+3q+1
         9: q^2+2q+1
        10: 2q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^2+2q+1
        17: 2q^2+3q+1
        18: q^3+3q^2+3q+1
        19: q^2+3q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: 2q^2+3q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: 2q^2+3q+1
        28: q^2+2q+1
        29: 2q^2+3q+1
        30: 2q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: 2q+1
        34: q+1
        35: q^2+3q+1
        36: 2q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: 2q+1
        41: q+1
        42: 2q^2+3q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        50: 2q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q^2+3q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q^2+3q+1
        65: 2q+1
        66: q+1
        67: q^2+3q+1
        68: 2q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: q^2+3q+1
        75: q+1
        76: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q^2+3q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: 2q^2+3q+1
        88: 1
        89: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: q^2+3q+1
       103: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 2q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q^2+3q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: q^2+3q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: q^2+3q+1
       132: 2q+1
       133: q+1
       134: 2q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: q+1
       141: q+1
       144: 2q+1
       145: q+1
       146: q+1
       148: 2q+1
       149: q+1
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: q^2+3q+1
       155: 2q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       169: q^2+2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: q^2+3q+1
       180: 1
       181: 1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 2q+1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q^2+3q+1
       224: 1
       225: 1
       227: q+1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: q+1
       242: q+1
       243: q+1
       246: 2q+1
       248: q+1
       251: 2q+1
       252: q+1
       253: q+1
       255: 2q+1
       256: 2q+1
       257: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       272: 1
       273: q+1
       276: q^2+2q+1
       277: 1
       278: q+1
       281: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       287: 1
       288: 2q+1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: 1
       354: q+1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: q+1
       373: q+1
       380: q+1
       386: q+1
       387: q+1
       390: 2q+1
       392: 1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       412: q+1
       418: 1
       419: q+1
       425: 1
       426: q+1
       429: q+1
       430: 1
       431: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       449: 1
       452: q+1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       519: 1
       521: 1
       523: 1
       550: q+1
       551: q+1
       558: 1
       561: q+1
       566: 1
       568: 1
       570: 1
       589: 1
       597: 1
       598: q+1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       627: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       662: 1
       669: 1
       671: 1
       673: 1
       679: 1
       681: 1
       683: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       708: 1
       748: 1
       760: 1
       799: 1
       800: 1
       806: 1
       810: 1
       812: 1
       814: 1
       841: 1
       842: 1
       849: 1
       852: 1
       874: 1
       883: 1
       890: 1
       892: 1
       894: 1
      1013: 1
      1019: 1
      1059: 1
      1099: 1

1100:    0: q^3+3q^2+3q+1
         1: q^2+2q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^2+3q+1
         6: 2q+1
         7: q+1
         8: 2q^2+3q+1
         9: q^2+2q+1
        10: 2q^2+3q+1
        11: q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^2+2q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: 2q^2+3q+1
        25: 2q+1
        26: q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: q^2+3q+1
        33: 2q+1
        34: q+1
        35: 2q^2+3q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^3+3q^2+3q+1
        40: 2q+1
        41: q+1
        42: q^2+3q+1
        43: 2q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        51: 2q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q^2+3q+1
        62: 2q+1
        63: q+1
        64: q^2+3q+1
        65: 2q+1
        66: q+1
        67: 2q^2+3q+1
        68: 2q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: 2q^2+3q+1
        76: q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+3q+1
        89: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q^2+3q+1
        97: 2q+1
        98: q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q^2+3q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       113: 2q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: q^2+3q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q^2+3q+1
       129: 2q+1
       130: q+1
       131: q^2+3q+1
       132: 2q+1
       133: q+1
       135: 2q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: q^2+2q+1
       146: q+1
       148: q+1
       149: q+1
       151: q^2+2q+1
       152: q+1
       153: q+1
       154: q+1
       156: 2q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       165: q+1
       166: 2q+1
       167: q+1
       169: 2q+1
       170: q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: q^2+3q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       180: q^2+3q+1
       181: 1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       207: 2q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: q+1
       214: 2q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: q^2+3q+1
       225: 1
       227: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       247: q+1
       248: q+1
       251: 1
       252: q^2+2q+1
       253: q+1
       255: q+1
       256: q+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       277: 2q+1
       278: q+1
       282: 2q+1
       283: q+1
       285: 2q+1
       286: 2q+1
       287: q+1
       289: 2q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: 2q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: 1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       374: q+1
       379: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       391: q+1
       392: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: q+1
       413: q+1
       418: q+1
       420: q+1
       426: q+1
       430: 2q+1
       431: 1
       433: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: q+1
       459: 1
       461: 1
       462: q+1
       463: 1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: 1
       522: 1
       523: 1
       542: 1
       550: 1
       552: q+1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       589: q+1
       599: q+1
       605: 1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       663: 1
       670: 1
       672: 1
       673: 1
       680: 1
       682: 1
       683: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       709: 1
       747: 1
       749: 1
       754: 1
       761: 1
       801: 1
       811: 1
       813: 1
       814: 1
       833: 1
       843: 1
       849: 1
       853: 1
       875: 1
       884: 1
       891: 1
       893: 1
       894: 1
       959: 1
      1020: 1
      1060: 1
      1100: 1

1101:    0: q^2+q+1
         1: 1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q^2+q+1
         9: 1
        10: q^2+q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q^2+q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q+1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       418: 1
       426: 1
       430: 1
       431: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       471: 1
       480: 1
       481: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       523: 1
       524: 1
       534: 1
       550: 1
       558: 1
       561: 1
       570: 1
       571: 1
       581: 1
       589: 1
       605: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       641: 1
       646: 1
       648: 1
       664: 1
       673: 1
       674: 1
       683: 1
       684: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       710: 1
       739: 1
       762: 1
       782: 1
       814: 1
       815: 1
       825: 1
       849: 1
       876: 1
       885: 1
       894: 1
       895: 1
       905: 1
      1021: 1
      1101: 1

1102:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: q+1
       196: 1
       197: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: q+1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       438: 1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: 1
       524: 1
       525: 1
       532: 1
       547: 1
       548: 1
       549: 1
       559: 1
       571: 1
       572: 1
       579: 1
       586: 1
       587: 1
       588: 1
       606: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       642: 1
       646: 1
       647: 1
       665: 1
       674: 1
       675: 1
       684: 1
       685: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       711: 1
       737: 1
       763: 1
       780: 1
       815: 1
       816: 1
       823: 1
       850: 1
       877: 1
       886: 1
       895: 1
       896: 1
       903: 1
      1022: 1
      1102: 1

1103:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         6: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        56: q+1
        57: q^2+q+1
        60: q+1
        61: q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       104: q+1
       111: q+1
       112: q+1
       113: q+1
       118: q+1
       119: q+1
       122: q+1
       123: 1
       124: q+1
       127: 1
       128: q+1
       129: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       179: 1
       180: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       197: q+1
       198: q+1
       205: q+1
       206: q+1
       207: 1
       212: 1
       213: 1
       214: q+1
       219: 1
       220: q+1
       223: 1
       224: 1
       225: q+1
       227: q+1
       228: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: 1
       246: 1
       248: q+1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: q+1
       319: q+1
       327: q+1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: q+1
       354: 1
       355: 1
       356: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       403: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       473: q+1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       618: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       646: 1
       648: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       702: 1
       712: 1
       731: 1
       739: 1
       748: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       817: 1
       825: 1
       849: 1
       887: 1
       897: 1
       905: 1
       933: 1
       977: 1
      1023: 1
      1103: 1

1104:    0: 3q^3+6q^2+5q+1
         1: 3q^3+6q^2+5q+1
         2: q^2+4q+1
         3: 3q^3+6q^2+5q+1
         4: q^3+4q^2+5q+1
         5: q^3+4q^2+5q+1
         6: q^2+4q+1
         7: q^2+4q+1
         8: q^2+4q+1
         9: 3q^3+6q^2+5q+1
        10: q^2+4q+1
        11: q^3+4q^2+5q+1
        12: q^3+4q^2+5q+1
        13: q^3+4q^2+5q+1
        14: 4q+1
        15: q^3+4q^2+5q+1
        16: q^3+4q^2+5q+1
        17: 4q+1
        18: q^3+4q^2+5q+1
        19: 3q^2+5q+1
        20: q^2+4q+1
        21: q^2+4q+1
        22: q^2+4q+1
        23: 2q+1
        24: 2q+1
        25: q^2+4q+1
        26: q^2+4q+1
        27: q^2+4q+1
        28: q^3+4q^2+5q+1
        29: 4q+1
        30: q^3+4q^2+5q+1
        31: 4q+1
        32: 3q^2+5q+1
        33: 4q+1
        34: 4q+1
        35: 4q+1
        36: q^3+4q^2+5q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^3+4q^2+5q+1
        40: 4q+1
        41: 4q+1
        42: 4q+1
        43: q^3+4q^2+5q+1
        44: 2q+1
        45: q^3+4q^2+5q+1
        46: q^2+3q+1
        47: 3q^2+5q+1
        48: 4q+1
        49: 3q^2+5q+1
        50: 2q+1
        51: 2q+1
        52: q^2+4q+1
        54: 2q+1
        55: 2q+1
        56: q+1
        57: q^2+4q+1
        58: q^2+4q+1
        59: q^2+4q+1
        60: 2q+1
        61: 2q+1
        62: 4q+1
        63: 4q+1
        64: 4q+1
        65: 4q+1
        66: 4q+1
        67: 4q+1
        68: 3q^2+5q+1
        69: 4q+1
        70: 3q^2+5q+1
        71: 4q+1
        72: 4q+1
        73: 4q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+3q+1
        80: q+1
        81: q^3+4q^2+5q+1
        82: 2q+1
        83: q^2+3q+1
        84: 4q+1
        85: 4q+1
        86: 4q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: q^3+4q^2+5q+1
        93: 2q+1
        94: q^2+3q+1
        95: q+1
        96: q^2+3q+1
        97: 4q+1
        98: 4q+1
        99: 4q+1
       100: 3q^2+5q+1
       101: q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: 2q+1
       106: 2q+1
       110: q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q^2+4q+1
       116: 2q+1
       117: 2q+1
       118: q+1
       119: 4q+1
       120: 4q+1
       121: 4q+1
       122: 2q+1
       123: q+1
       124: 4q+1
       125: 4q+1
       126: 4q+1
       127: q+1
       128: 2q+1
       129: 4q+1
       130: 4q+1
       131: 4q+1
       132: 3q^2+5q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 4q+1
       138: q+1
       139: 2q+1
       140: 1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+3q+1
       153: q+1
       154: q^2+3q+1
       155: 2q+1
       156: q+1
       157: 4q+1
       159: 2q+1
       160: q+1
       161: 1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+3q+1
       174: q+1
       175: q^2+3q+1
       176: 4q+1
       177: 4q+1
       178: 4q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+3q+1
       185: 1
       186: q^2+3q+1
       187: 1
       188: 2q+1
       189: q+1
       190: q+1
       196: q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       204: q+1
       205: q+1
       206: 2q+1
       207: q+1
       208: 4q+1
       210: 2q+1
       211: q+1
       212: 1
       213: q+1
       214: 2q+1
       215: 4q+1
       217: q+1
       218: 2q+1
       219: 1
       220: 4q+1
       221: 4q+1
       222: 4q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: q+1
       230: 2q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: 2q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: 1
       258: 1
       259: 2q+1
       260: q+1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: 2q+1
       270: q+1
       271: 1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+3q+1
       287: 1
       288: q+1
       289: q+1
       290: 4q+1
       292: q+1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 2q+1
       307: 1
       308: 2q+1
       310: q+1
       319: q+1
       320: q+1
       326: q+1
       328: 1
       329: 2q+1
       330: q+1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 2q+1
       342: 1
       343: 1
       344: q+1
       345: q+1
       346: 4q+1
       348: q+1
       349: q+1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       371: 1
       372: 1
       373: 1
       375: q+1
       377: 1
       380: 1
       381: q+1
       382: 2q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: 2q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: q+1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 2q+1
       463: 1
       474: q+1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: q+1
       503: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       513: 1
       514: 1
       515: 1
       517: 1
       526: 1
       527: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       564: 1
       573: 1
       574: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: q+1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       617: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       713: 1
       731: 1
       732: 1
       738: 1
       741: 1
       748: 1
       750: 1
       752: 1
       765: 1
       774: 1
       775: 1
       781: 1
       794: 1
       801: 1
       802: 1
       805: 1
       808: 1
       817: 1
       818: 1
       824: 1
       827: 1
       836: 1
       844: 1
       849: 1
       850: 1
       851: 1
       888: 1
       897: 1
       898: 1
       904: 1
       934: 1
       953: 1
       978: 1
      1008: 1
      1024: 1
      1061: 1
      1104: 1

1105:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q+1
        19: q^2+3q+1
        20: q+1
        21: q^2+3q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+3q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: 1
        65: q^2+3q+1
        66: q^2+3q+1
        67: 1
        68: q^2+3q+1
        69: q^2+3q+1
        70: 1
        71: 1
        72: q^2+3q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q^2+3q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q^2+3q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q^2+3q+1
       126: 1
       127: 1
       128: 1
       129: q^2+3q+1
       130: q^2+3q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q^2+3q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: q+1
       191: q+1
       192: q+1
       195: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q^2+3q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       311: q+1
       320: q+1
       321: q+1
       322: q+1
       325: q+1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       392: 1
       393: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       475: q+1
       484: 1
       485: 1
       486: 1
       489: 1
       493: 1
       494: 1
       495: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       642: 1
       646: 1
       647: 1
       668: 1
       678: 1
       687: 1
       688: 1
       689: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       714: 1
       732: 1
       733: 1
       734: 1
       737: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       809: 1
       818: 1
       819: 1
       820: 1
       823: 1
       850: 1
       889: 1
       898: 1
       899: 1
       900: 1
       903: 1
       935: 1
       979: 1
      1025: 1
      1105: 1

1106:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 2q+1
        41: 2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        47: q+1
        48: q+1
        49: q+1
        50: 2q+1
        52: 2q+1
        53: q+1
        54: 2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        62: 2q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: 2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       105: 2q+1
       107: q+1
       108: q+1
       112: 2q+1
       114: 2q+1
       115: q+1
       116: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q+1
       122: 2q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 2q+1
       157: 2q+1
       158: 1
       159: 2q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       167: q+1
       168: q+1
       169: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       191: q+1
       193: q+1
       199: 2q+1
       201: q+1
       202: q+1
       206: 2q+1
       208: 2q+1
       209: 1
       210: 2q+1
       213: q+1
       215: q+1
       216: 1
       217: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: 2q+1
       261: 1
       262: 1
       266: q+1
       268: q+1
       269: 1
       270: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       312: q+1
       321: q+1
       323: q+1
       329: 2q+1
       331: 1
       332: 1
       337: q+1
       339: 1
       340: 1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: q+1
       407: 1
       408: 1
       412: q+1
       414: q+1
       415: 1
       416: q+1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       476: q+1
       485: 1
       487: 1
       494: 1
       496: 1
       502: q+1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: 1
       528: 1
       530: 1
       536: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: q+1
       585: 1
       586: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       631: 1
       669: 1
       679: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       715: 1
       733: 1
       735: 1
       741: 1
       748: 1
       750: 1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       890: 1
       899: 1
       901: 1
       936: 1
       953: 1
       980: 1
      1026: 1
      1106: 1

1107:    0: 4q^2+4q+1
         1: 4q^2+4q+1
         2: 3q^2+4q+1
         3: 4q^2+4q+1
         4: 4q^2+4q+1
         5: 3q^2+4q+1
         6: q^2+3q+1
         7: 3q^2+4q+1
         8: q^2+3q+1
         9: 4q^2+4q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: 4q^2+4q+1
        13: 4q^2+4q+1
        14: 3q^2+4q+1
        15: 2q^2+3q+1
        16: 3q^2+4q+1
        17: 2q^2+4q+1
        18: q^2+3q+1
        19: 3q^2+4q+1
        20: 2q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: 2q+1
        24: q^2+3q+1
        25: q^2+3q+1
        26: 3q^2+4q+1
        27: q^2+3q+1
        28: 3q^2+4q+1
        29: 2q^2+4q+1
        30: 4q^2+4q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+3q+1
        34: 3q^2+4q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^2+3q+1
        41: 2q^2+4q+1
        42: 3q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 3q^2+4q+1
        48: 2q^2+4q+1
        49: 2q+1
        51: 2q+1
        52: 2q+1
        53: q+1
        54: 2q+1
        55: q^2+3q+1
        56: 2q+1
        57: 2q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: 2q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: 2q^2+4q+1
        64: 3q+1
        65: q^2+3q+1
        66: 3q^2+4q+1
        67: 2q+1
        68: 3q^2+4q+1
        69: 2q^2+4q+1
        70: 2q+1
        71: q+1
        72: q^2+3q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: q+1
        77: q^2+2q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q+1
        85: q^2+3q+1
        86: 3q+1
        87: 2q+1
        88: 3q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        94: q^2+3q+1
        95: 2q+1
        96: q^2+3q+1
        97: q^2+3q+1
        98: 2q^2+4q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       116: 2q+1
       117: q^2+3q+1
       118: 2q+1
       119: 2q+1
       120: q^2+3q+1
       121: 3q+1
       122: 2q+1
       123: 3q+1
       124: q+1
       125: q^2+3q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q^2+3q+1
       130: 2q^2+4q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q^2+2q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       156: 2q+1
       157: 2q+1
       158: 1
       159: 2q+1
       160: 3q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: 2q+1
       173: q^2+3q+1
       174: 2q+1
       175: 2q+1
       176: q+1
       177: q^2+3q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: q+1
       193: q+1
       195: q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       207: 2q+1
       208: 2q+1
       209: 1
       210: 2q+1
       211: 3q+1
       212: 2q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: 1
       226: q+1
       227: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       260: 2q+1
       261: 1
       262: 1
       263: 1
       264: 2q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: 2q+1
       272: q+1
       273: q+1
       274: q+1
       275: 2q+1
       276: q+1
       277: 2q+1
       279: q+1
       283: q+1
       284: 2q+1
       286: 2q+1
       287: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       306: q+1
       307: 1
       308: q+1
       313: q+1
       322: q+1
       323: q+1
       325: q+1
       330: 2q+1
       331: 1
       332: 1
       333: 1
       334: 2q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: q+1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       401: 1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: 2q+1
       418: q+1
       427: q+1
       431: 1
       432: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       477: q+1
       486: 1
       487: 1
       489: 1
       495: 1
       496: 1
       498: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       541: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       606: 1
       613: 1
       614: 1
       616: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       670: 1
       680: 1
       689: 1
       690: 1
       692: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       716: 1
       734: 1
       735: 1
       737: 1
       742: 1
       746: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       768: 1
       777: 1
       778: 1
       780: 1
       811: 1
       820: 1
       821: 1
       823: 1
       828: 1
       832: 1
       850: 1
       891: 1
       900: 1
       901: 1
       903: 1
       937: 1
       954: 1
       958: 1
       981: 1
      1027: 1
      1107: 1

1108:    0: 4q^2+4q+1
         1: 4q^2+4q+1
         2: 3q^2+4q+1
         3: 4q^2+4q+1
         4: 3q^2+4q+1
         5: 4q^2+4q+1
         6: q^2+3q+1
         7: 3q^2+4q+1
         8: q^2+3q+1
         9: 4q^2+4q+1
        10: 3q^2+4q+1
        11: 4q^2+4q+1
        12: 3q^2+4q+1
        13: 3q^2+4q+1
        14: 2q^2+4q+1
        15: q^2+3q+1
        16: 4q^2+4q+1
        17: 3q^2+4q+1
        18: 2q^2+3q+1
        19: 3q^2+4q+1
        20: 2q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: 2q+1
        25: q^2+3q+1
        26: 3q^2+4q+1
        27: q^2+3q+1
        28: 4q^2+4q+1
        29: 3q^2+4q+1
        30: 3q^2+4q+1
        31: 2q^2+4q+1
        32: 3q^2+4q+1
        33: q^2+3q+1
        34: 2q^2+4q+1
        35: 3q+1
        36: q^2+3q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+3q+1
        41: 3q^2+4q+1
        42: 2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: 3q^2+4q+1
        48: 2q^2+4q+1
        49: 2q+1
        50: 2q+1
        52: 2q+1
        53: q+1
        54: q^2+3q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: 2q+1
        62: q^2+3q+1
        63: 3q^2+4q+1
        64: 2q+1
        65: q^2+3q+1
        66: 2q^2+4q+1
        67: 3q+1
        68: 3q^2+4q+1
        69: 2q^2+4q+1
        70: 2q+1
        71: 2q+1
        72: q^2+3q+1
        73: 3q+1
        74: 3q+1
        75: 2q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q+1
        85: q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q^2+2q+1
        91: q+1
        92: 2q^2+3q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: 2q^2+4q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       105: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       112: 2q+1
       114: 2q+1
       115: q+1
       116: q^2+3q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q^2+3q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: 2q+1
       125: q^2+3q+1
       126: 3q+1
       127: 3q+1
       128: 2q+1
       129: q^2+3q+1
       130: 2q^2+4q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       134: 2q+1
       136: 2q+1
       137: 1
       138: 3q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: q+1
       146: q+1
       147: 2q+1
       149: q+1
       150: 2q+1
       151: 2q+1
       152: q^2+3q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q^2+2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+3q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: q+1
       194: q+1
       195: q+1
       199: 2q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       206: q+1
       208: q+1
       209: 1
       210: 2q+1
       211: q+1
       212: q+1
       213: 2q+1
       215: 2q+1
       216: 1
       217: 3q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       229: 2q+1
       231: 1
       232: 1
       233: 1
       234: 2q+1
       236: q+1
       238: q+1
       239: 1
       240: 2q+1
       241: q+1
       242: q+1
       244: q+1
       248: q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q+1
       254: 2q+1
       256: 2q+1
       257: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       314: q+1
       321: q+1
       324: q+1
       325: q+1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       337: 2q+1
       339: 1
       340: 1
       341: 1
       342: 2q+1
       344: q+1
       346: q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: q+1
       355: 1
       358: 1
       361: 1
       362: 1
       366: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       380: q+1
       382: q+1
       383: 1
       384: 2q+1
       385: q+1
       386: q+1
       388: q+1
       392: 1
       393: q+1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       478: q+1
       485: 1
       488: 1
       489: 1
       494: 1
       497: 1
       498: 1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       509: 1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       521: 1
       528: 1
       531: 1
       532: 1
       544: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       559: 1
       568: 1
       575: 1
       578: 1
       579: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       591: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       671: 1
       681: 1
       688: 1
       691: 1
       692: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       717: 1
       733: 1
       736: 1
       737: 1
       769: 1
       776: 1
       779: 1
       780: 1
       793: 1
       798: 1
       800: 1
       802: 1
       804: 1
       805: 1
       806: 1
       812: 1
       819: 1
       822: 1
       823: 1
       835: 1
       840: 1
       850: 1
       892: 1
       899: 1
       902: 1
       903: 1
       938: 1
       982: 1
      1007: 1
      1012: 1
      1028: 1
      1108: 1

1109:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: 2q+1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: 2q+1
        52: 2q+1
        53: q+1
        55: 2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: 2q+1
        73: 2q+1
        75: 2q+1
        76: q+1
        77: q+1
        78: q+1
        81: q^2+2q+1
        82: q+1
        84: q+1
        85: q+1
        86: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       103: q+1
       106: 2q+1
       107: q+1
       109: q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       117: 2q+1
       119: q+1
       120: q+1
       121: q+1
       123: q+1
       124: 2q+1
       125: 2q+1
       126: 2q+1
       128: 2q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       135: 2q+1
       136: 2q+1
       137: 1
       139: 2q+1
       141: q+1
       142: q+1
       143: q+1
       145: q+1
       149: q+1
       150: q+1
       151: q+1
       156: q+1
       157: q+1
       158: 1
       160: q+1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       192: q+1
       194: q+1
       200: 2q+1
       201: q+1
       203: q+1
       207: q+1
       208: q+1
       209: 1
       211: q+1
       214: 2q+1
       215: 2q+1
       216: 1
       218: 2q+1
       220: q+1
       221: q+1
       222: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       230: 2q+1
       231: 1
       233: 1
       237: q+1
       238: q+1
       239: 1
       241: q+1
       248: q+1
       249: q+1
       250: q+1
       252: q+1
       260: q+1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       315: q+1
       322: q+1
       324: q+1
       330: q+1
       331: 1
       333: 1
       338: 2q+1
       339: 1
       341: 1
       345: q+1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: q+1
       368: 1
       370: 1
       381: q+1
       382: q+1
       383: 1
       385: q+1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       479: q+1
       486: 1
       488: 1
       495: 1
       497: 1
       503: q+1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: q+1
       546: 1
       548: 1
       569: 1
       576: 1
       578: 1
       584: 1
       585: 1
       587: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       639: 1
       672: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       770: 1
       777: 1
       779: 1
       794: 1
       801: 1
       802: 1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       893: 1
       900: 1
       902: 1
       939: 1
       983: 1
      1008: 1
      1029: 1
      1109: 1

1110:    0: 3q^2+4q+1
         1: 3q^2+4q+1
         2: q^2+4q+1
         3: 3q^2+4q+1
         4: q^2+4q+1
         5: q^2+4q+1
         6: 3q+1
         7: q^2+4q+1
         8: q^2+4q+1
         9: 3q^2+4q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^2+4q+1
        13: q^2+4q+1
        14: 4q+1
        15: q^2+4q+1
        16: q^2+4q+1
        17: 4q+1
        18: q^2+4q+1
        19: 4q+1
        20: 3q+1
        21: 3q+1
        22: q^2+4q+1
        23: 2q+1
        24: 2q+1
        25: 3q+1
        26: q^2+4q+1
        27: q^2+4q+1
        28: q^2+4q+1
        29: 4q+1
        30: q^2+4q+1
        31: 4q+1
        32: 4q+1
        33: 3q+1
        34: 4q+1
        35: 4q+1
        36: q^2+4q+1
        37: 2q+1
        38: 2q+1
        39: q^2+4q+1
        40: 3q+1
        41: 4q+1
        42: 4q+1
        43: q^2+4q+1
        44: 2q+1
        45: q^2+4q+1
        46: 2q+1
        47: 4q+1
        48: 4q+1
        49: 4q+1
        52: 3q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: q+1
        57: 3q+1
        58: 3q+1
        59: q^2+4q+1
        60: 2q+1
        61: 2q+1
        62: 3q+1
        63: 4q+1
        64: 4q+1
        65: 3q+1
        66: 4q+1
        67: 4q+1
        68: 4q+1
        69: 4q+1
        70: 4q+1
        71: 3q+1
        72: 3q+1
        73: 4q+1
        74: q+1
        75: 2q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: q+1
        81: q^2+4q+1
        82: 2q+1
        83: 2q+1
        84: 3q+1
        85: 3q+1
        86: 4q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+4q+1
        93: 2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: 3q+1
        98: 4q+1
        99: 4q+1
       100: 4q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       114: 3q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: q+1
       119: 3q+1
       120: 3q+1
       121: 4q+1
       122: 2q+1
       123: q+1
       124: 3q+1
       125: 3q+1
       126: 4q+1
       127: q+1
       128: 2q+1
       129: 3q+1
       130: 4q+1
       131: 4q+1
       132: 4q+1
       133: q+1
       136: 3q+1
       137: 1
       138: q+1
       139: 2q+1
       140: 1
       141: q+1
       142: q+1
       143: 2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: 2q+1
       151: 2q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       157: 3q+1
       158: 1
       159: 2q+1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: 2q+1
       165: q+1
       166: 1
       167: q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: 3q+1
       177: 3q+1
       178: 4q+1
       179: q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: 1
       186: 2q+1
       187: 1
       188: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       208: 3q+1
       209: 1
       210: 2q+1
       211: q+1
       212: 1
       215: 3q+1
       216: 1
       217: q+1
       218: 2q+1
       219: 1
       220: 3q+1
       221: 3q+1
       222: 4q+1
       223: q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: q+1
       249: q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q+1
       257: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: 2q+1
       287: 1
       290: 3q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       316: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 3q+1
       347: 1
       348: q+1
       349: q+1
       350: 1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: 1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: q+1
       377: 1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       421: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       480: q+1
       487: 1
       488: 1
       489: 1
       490: 1
       496: 1
       497: 1
       498: 1
       499: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: q+1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       600: q+1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       631: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       673: 1
       683: 1
       690: 1
       691: 1
       692: 1
       693: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       719: 1
       735: 1
       736: 1
       737: 1
       738: 1
       750: 1
       752: 1
       771: 1
       778: 1
       779: 1
       780: 1
       781: 1
       802: 1
       805: 1
       814: 1
       821: 1
       822: 1
       823: 1
       824: 1
       844: 1
       849: 1
       850: 1
       851: 1
       894: 1
       901: 1
       902: 1
       903: 1
       904: 1
       940: 1
       984: 1
      1030: 1
      1061: 1
      1110: 1

1111:    0: q^3+7q^2+5q+1
         1: 3q^2+4q+1
         2: q^3+7q^2+5q+1
         3: q^3+7q^2+5q+1
         4: 5q^2+5q+1
         5: 5q^2+5q+1
         6: 3q^2+4q+1
         7: q^2+4q+1
         8: q^3+5q^2+5q+1
         9: 3q^2+4q+1
        10: q^3+7q^2+5q+1
        11: 5q^2+5q+1
        12: 5q^2+5q+1
        13: q^2+4q+1
        14: 5q^2+5q+1
        15: 3q^2+5q+1
        16: q^2+4q+1
        17: 5q^2+5q+1
        18: 3q^2+5q+1
        19: 4q^2+5q+1
        21: q^2+4q+1
        22: q^2+4q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 3q^2+4q+1
        26: q^2+4q+1
        27: q^3+5q^2+5q+1
        28: q^2+4q+1
        29: 5q^2+5q+1
        30: q^2+4q+1
        31: 5q^2+5q+1
        32: 4q^2+5q+1
        33: q^2+4q+1
        34: 4q+1
        35: 2q^2+5q+1
        36: q^2+4q+1
        37: 3q^2+5q+1
        38: q^2+3q+1
        39: 3q^2+5q+1
        40: q^2+4q+1
        41: 4q+1
        42: 2q^2+5q+1
        43: q^2+4q+1
        44: 3q^2+5q+1
        45: 3q^2+5q+1
        46: q^2+3q+1
        47: 4q+1
        48: 4q^2+5q+1
        49: q^2+5q+1
        53: q^2+4q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        58: q^2+4q+1
        59: q^2+4q+1
        60: 2q^2+3q+1
        61: 2q^2+3q+1
        62: q^2+4q+1
        63: 4q+1
        64: 2q^2+5q+1
        65: q^2+4q+1
        66: 4q+1
        67: 2q^2+5q+1
        68: 4q+1
        69: 4q^2+5q+1
        70: q^2+5q+1
        72: 4q+1
        73: 4q+1
        74: 2q+1
        75: q^2+3q+1
        76: q^2+4q+1
        77: 2q+1
        78: 2q^2+5q+1
        79: 2q+1
        80: q^2+3q+1
        81: q^2+4q+1
        82: 3q^2+5q+1
        83: q^2+3q+1
        85: 4q+1
        86: 4q+1
        87: q^2+3q+1
        88: 2q+1
        89: q^2+4q+1
        90: 2q+1
        91: 2q^2+5q+1
        92: q^2+4q+1
        93: 3q^2+5q+1
        94: 2q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: 4q+1
        98: 4q+1
        99: q^2+5q+1
       100: 4q+1
       101: q^2+5q+1
       102: 3q+1
       103: 3q+1
       108: 2q+1
       109: 2q+1
       110: q+1
       111: q+1
       115: q^2+4q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       120: 4q+1
       121: 4q+1
       122: q^2+3q+1
       123: 2q+1
       125: 4q+1
       126: 4q+1
       127: 2q+1
       128: q^2+3q+1
       129: 4q+1
       130: 4q+1
       131: q^2+5q+1
       132: 4q+1
       133: q^2+5q+1
       137: 4q+1
       138: q+1
       139: 2q+1
       140: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: q^2+4q+1
       150: 2q+1
       151: 2q^2+5q+1
       152: 2q+1
       153: q^2+3q+1
       154: 3q+1
       158: 4q+1
       159: 2q+1
       160: q+1
       161: q+1
       163: 2q+1
       164: 2q+1
       165: q^2+3q+1
       166: 2q+1
       167: q^2+4q+1
       168: 2q+1
       169: 2q^2+5q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: 2q+1
       174: q^2+3q+1
       175: 3q+1
       177: 4q+1
       178: 4q+1
       179: 2q+1
       180: 2q+1
       181: 4q+1
       182: q+1
       183: q^2+5q+1
       184: 2q+1
       185: 3q+1
       186: 2q+1
       187: 3q+1
       188: 2q+1
       195: q+1
       196: q+1
       197: q+1
       202: 2q+1
       203: 2q+1
       204: q+1
       205: q+1
       209: 4q+1
       210: 2q+1
       211: q+1
       212: q+1
       216: 4q+1
       217: q+1
       218: 2q+1
       219: q+1
       221: 4q+1
       222: 4q+1
       223: 2q+1
       224: 2q+1
       225: 4q+1
       226: q+1
       227: q^2+5q+1
       232: q+1
       233: 2q+1
       234: 1
       235: 1
       239: 2q+1
       240: 1
       241: q+1
       242: q+1
       244: q+1
       245: q+1
       246: q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: q^2+3q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q+1
       257: 3q+1
       262: 2q+1
       263: q+1
       264: 1
       265: 1
       269: 2q+1
       270: q+1
       271: 1
       272: q+1
       274: 2q+1
       275: 2q+1
       276: q^2+3q+1
       277: 2q+1
       279: q+1
       280: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       287: 3q+1
       291: 4q+1
       292: q+1
       293: q+1
       294: q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 1
       302: 2q+1
       303: 2q+1
       304: 1
       305: 2q+1
       306: q+1
       307: 2q+1
       308: 2q+1
       317: q+1
       325: q+1
       326: q+1
       327: q+1
       332: 2q+1
       333: q+1
       334: 1
       335: 1
       340: q+1
       341: 2q+1
       342: 1
       343: 1
       347: 4q+1
       348: q+1
       349: q+1
       350: q+1
       352: q+1
       353: q+1
       354: 2q+1
       355: 2q+1
       362: 1
       363: 1
       364: 1
       369: 1
       370: q+1
       371: 1
       372: 1
       376: q+1
       377: 1
       383: 2q+1
       384: 1
       385: q+1
       386: q+1
       388: q+1
       389: q+1
       390: q+1
       392: 2q+1
       393: 1
       394: 2q+1
       401: 1
       402: 1
       403: 1
       408: q+1
       409: 1
       410: 1
       411: 1
       415: 2q+1
       416: q+1
       417: 1
       418: q+1
       422: q+1
       424: 1
       427: q+1
       428: q+1
       430: q+1
       431: 2q+1
       432: 1
       433: 2q+1
       438: q+1
       439: q+1
       440: 1
       441: 1
       445: q+1
       446: 1
       447: 1
       448: q+1
       450: 1
       451: 1
       452: q+1
       455: 1
       456: 1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: 2q+1
       481: q+1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: q+1
       506: q+1
       507: 1
       508: 1
       512: q+1
       513: 1
       514: 1
       515: q+1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       547: 1
       548: q+1
       549: 1
       550: 1
       554: q+1
       555: 1
       559: 1
       560: 1
       561: q+1
       571: 1
       579: 1
       580: 1
       581: 1
       586: q+1
       587: 1
       588: 1
       589: 1
       595: 1
       601: q+1
       603: 1
       606: 1
       607: 1
       609: q+1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       637: 1
       639: 1
       642: 1
       643: 1
       646: q+1
       647: 1
       648: q+1
       674: 1
       684: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       702: 1
       720: 1
       737: 1
       738: 1
       739: 1
       744: 1
       751: 1
       752: 1
       772: 1
       780: 1
       781: 1
       782: 1
       797: 1
       803: 1
       805: 1
       815: 1
       823: 1
       824: 1
       825: 1
       830: 1
       839: 1
       845: 1
       850: 1
       851: 1
       895: 1
       903: 1
       904: 1
       905: 1
       941: 1
       956: 1
       985: 1
      1011: 1
      1031: 1
      1062: 1
      1111: 1

1112:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q^2+q+1
        23: q+1
        24: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        54: q+1
        55: q+1
        56: q+1
        59: q^2+q+1
        60: q+1
        61: q+1
        63: q+1
        64: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        73: q+1
        74: 1
        75: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        86: q+1
        87: q+1
        88: 1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       110: q+1
       111: q+1
       116: q+1
       117: q+1
       118: q+1
       121: q+1
       122: q+1
       123: 1
       126: q+1
       127: 1
       128: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       138: 1
       139: q+1
       140: 1
       143: q+1
       144: 1
       145: q+1
       147: 1
       148: 1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       159: q+1
       160: 1
       161: 1
       164: q+1
       165: q+1
       166: 1
       168: q+1
       169: q+1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       179: 1
       180: 1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       196: q+1
       197: q+1
       204: q+1
       205: q+1
       210: q+1
       211: 1
       212: 1
       217: 1
       218: q+1
       219: 1
       222: q+1
       223: 1
       224: 1
       226: q+1
       227: q+1
       234: 1
       235: 1
       240: 1
       241: q+1
       242: 1
       245: 1
       246: 1
       250: q+1
       251: 1
       252: q+1
       254: 1
       255: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: q+1
       271: 1
       272: 1
       275: q+1
       276: q+1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: q+1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       318: q+1
       326: q+1
       327: q+1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       353: q+1
       354: 1
       355: 1
       363: 1
       364: 1
       371: 1
       372: 1
       377: 1
       384: 1
       385: q+1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       402: 1
       403: 1
       410: 1
       411: 1
       416: q+1
       417: 1
       418: 1
       424: 1
       428: 1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       456: 1
       458: 1
       460: 1
       461: 1
       462: 1
       463: 1
       482: q+1
       490: 1
       491: 1
       499: 1
       500: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       525: 1
       533: 1
       534: 1
       549: 1
       550: 1
       555: 1
       560: 1
       561: 1
       572: 1
       580: 1
       581: 1
       588: 1
       589: 1
       603: 1
       607: 1
       609: 1
       617: 1
       618: 1
       625: 1
       626: 1
       631: 1
       639: 1
       643: 1
       647: 1
       648: 1
       675: 1
       685: 1
       693: 1
       694: 1
       701: 1
       702: 1
       721: 1
       738: 1
       739: 1
       752: 1
       773: 1
       781: 1
       782: 1
       805: 1
       816: 1
       824: 1
       825: 1
       851: 1
       896: 1
       904: 1
       905: 1
       942: 1
       986: 1
      1032: 1
      1112: 1

1113:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q^2+2q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: q+1
       262: 1
       266: 1
       268: q+1
       269: q+1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       309: 1
       310: q+1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       338: 1
       346: 1
       351: 1
       352: 1
       353: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: q+1
       408: 1
       412: 1
       414: 1
       416: 1
       435: q+1
       437: q+1
       438: 1
       442: 1
       444: q+1
       445: q+1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       482: 1
       511: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       545: 1
       553: 1
       558: 1
       559: 1
       560: 1
       566: 1
       575: 1
       577: 1
       583: 1
       612: 1
       614: 1
       620: 1
       622: q+1
       623: 1
       627: 1
       629: 1
       631: 1
       649: 1
       650: 1
       656: 1
       657: 1
       659: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       721: 1
       750: 1
       767: 1
       810: 1
       819: 1
       821: 1
       827: 1
       854: 1
       906: 1
       907: 1
       913: 1
       914: 1
       916: 1
      1026: 1
      1113: 1

1114:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        64: 1
        65: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       104: q+1
       105: q+1
       106: 2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       112: q+1
       113: 2q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: q+1
       128: q+1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       148: 1
       149: 2q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: 2q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       207: 1
       212: 1
       214: q+1
       220: 1
       224: 1
       225: 1
       227: 1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: q+1
       252: q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 1
       345: 1
       351: 1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       372: 1
       373: 1
       374: 1
       379: 1
       381: q+1
       387: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       510: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       552: 1
       558: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       650: 1
       651: 1
       655: 1
       666: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       749: 1
       756: 1
       758: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       855: 1
       907: 1
       908: 1
       912: 1
       923: 1
      1015: 1
      1017: 1
      1114: 1

1115:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       309: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       336: 1
       343: 1
       344: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       492: 1
       500: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       650: 1
       652: 1
       654: 1
       676: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       810: 1
       856: 1
       907: 1
       909: 1
       911: 1
       933: 1
      1115: 1

1116:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       483: 1
       492: 1
       501: 1
       508: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       564: 1
       610: 1
       611: 1
       617: 1
       651: 1
       652: 1
       653: 1
       686: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       722: 1
       731: 1
       740: 1
       747: 1
       808: 1
       857: 1
       908: 1
       909: 1
       910: 1
       943: 1
      1116: 1

1117:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: 1
        60: 2q+1
        61: 2q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: q+1
        69: 2q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       118: 2q+1
       119: 1
       122: q+1
       123: q+1
       124: 1
       127: q+1
       128: q+1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: 2q+1
       141: 1
       144: 2q+1
       145: 2q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q+1
       153: 2q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: 1
       165: q+1
       166: q+1
       167: 1
       169: q+1
       170: 1
       173: 1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: q+1
       213: 1
       214: 1
       219: q+1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       242: 2q+1
       243: 1
       246: q+1
       247: q+1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: q+1
       295: 1
       298: q+1
       299: q+1
       300: 1
       302: q+1
       303: 1
       306: 1
       307: q+1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: q+1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: q+1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: q+1
       453: q+1
       459: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       491: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: q+1
       646: 1
       653: 1
       654: 1
       655: 1
       694: 1
       695: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       730: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       858: 1
       910: 1
       911: 1
       912: 1
       951: 1
       952: 1
      1017: 1
      1117: 1

1118:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       167: 1
       168: q+1
       169: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: q+1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: 1
       244: 1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: q+1
       273: 1
       274: 1
       275: q+1
       276: q+1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       300: 1
       301: q+1
       302: q+1
       312: 1
       314: 1
       316: 1
       317: 1
       318: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: q+1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       416: q+1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: q+1
       449: 1
       450: 1
       451: q+1
       452: q+1
       469: 1
       471: 1
       472: 1
       476: 1
       478: 1
       480: 1
       482: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       519: 1
       521: 1
       523: 1
       524: 1
       525: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       544: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       631: q+1
       654: 1
       656: 1
       662: 1
       685: 1
       696: 1
       708: 1
       710: 1
       711: 1
       715: 1
       717: 1
       719: 1
       721: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       767: 1
       810: 1
       819: 1
       821: 1
       827: 1
       859: 1
       911: 1
       913: 1
       919: 1
       942: 1
       953: 1
      1026: 1
      1118: 1

1119:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: q^2+3q+1
        23: q^2+2q+1
        24: q^2+3q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+3q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: q+1
        54: q^2+2q+1
        55: q^2+3q+1
        56: q^2+2q+1
        57: 1
        58: q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: 2q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q^2+3q+1
        74: q^2+2q+1
        75: q^2+3q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 2q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: q^2+2q+1
       111: q+1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+3q+1
       140: q^2+2q+1
       141: 1
       142: q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: 2q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: q^2+2q+1
       235: q+1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       306: q+1
       307: 1
       308: q+1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       401: 1
       402: q+1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       470: 1
       471: 1
       472: 1
       477: 1
       479: 1
       480: 1
       482: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       520: 1
       522: 1
       523: 1
       524: 1
       525: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       567: 1
       571: 1
       572: 1
       576: 1
       577: 1
       579: 1
       584: 1
       588: 1
       606: 1
       613: 1
       614: 1
       616: 1
       617: q+1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       655: 1
       656: 1
       663: 1
       675: 1
       697: 1
       709: 1
       710: 1
       711: 1
       716: 1
       718: 1
       719: 1
       721: 1
       729: 1
       730: 1
       742: 1
       749: 1
       750: 1
       753: 1
       763: 1
       768: 1
       811: 1
       815: 1
       816: 1
       820: 1
       821: 1
       823: 1
       828: 1
       832: 1
       850: 1
       860: 1
       912: 1
       913: 1
       920: 1
       932: 1
       954: 1
      1022: 1
      1027: 1
      1119: 1

1120:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: 1
        75: 1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: q+1
       158: q+1
       159: 1
       162: q+1
       163: q^2+2q+1
       164: q+1
       165: 1
       167: q+1
       168: q+1
       169: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q+1
       184: q+1
       185: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: 1
       261: q+1
       262: 1
       266: 1
       268: q+1
       269: q+1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       288: 1
       290: q+1
       291: q+1
       292: 1
       295: q+1
       296: q^2+2q+1
       297: q+1
       298: 1
       300: q+1
       301: q+1
       302: 1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: q+1
       353: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       381: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       392: q+1
       393: q+1
       394: 1
       397: 1
       405: 1
       407: q+1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: q+1
       438: 1
       442: 1
       444: q+1
       445: q+1
       446: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       485: 1
       495: 1
       504: 1
       511: 1
       512: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       545: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       559: q+1
       560: 1
       575: 1
       583: 1
       585: 1
       586: 1
       612: 1
       620: 1
       622: q+1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       649: 1
       657: 1
       658: 1
       665: 1
       698: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: 1
       720: 1
       721: 1
       724: 1
       734: 1
       743: 1
       750: 1
       751: 1
       776: 1
       819: 1
       827: 1
       829: 1
       830: 1
       861: 1
       906: 1
       914: 1
       915: 1
       922: 1
       955: 1
      1035: 1
      1120: 1

1121:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 1
        24: q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 2q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: 1
        55: q+1
        56: 1
        57: 2q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 2q+1
        72: 2q+1
        73: 2q+1
        74: 1
        75: q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        91: q+1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       104: 1
       105: 1
       106: q+1
       107: 2q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q+1
       136: 2q+1
       137: 2q+1
       138: 1
       139: q+1
       140: 1
       141: 2q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: 1
       157: q+1
       158: q+1
       159: 1
       162: q+1
       165: 1
       167: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: 2q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: q+1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: q+1
       291: q+1
       292: 1
       295: q+1
       298: 1
       300: 1
       302: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: q+1
       438: 1
       442: 1
       449: 1
       452: 1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       495: 1
       497: 1
       504: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       545: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       566: 1
       612: 1
       614: 1
       627: 1
       650: 1
       658: 1
       659: 1
       664: 1
       669: 1
       682: 1
       704: 1
       705: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       734: 1
       736: 1
       743: 1
       810: 1
       862: 1
       907: 1
       915: 1
       916: 1
       921: 1
       926: 1
       939: 1
      1121: 1

1122:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        92: 1
        94: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: 1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       157: q+1
       159: 1
       160: q+1
       161: 1
       173: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       184: 1
       186: q+1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       258: 1
       259: 1
       260: q+1
       264: 1
       265: 1
       286: 1
       288: 1
       289: q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: q+1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       503: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       564: 1
       610: 1
       611: 1
       617: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       742: 1
       808: 1
       863: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
      1122: 1

1123:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        92: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       159: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       184: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       259: q+1
       288: q+1
       290: q+1
       292: q+1
       310: q+1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       435: q+1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       492: 1
       493: 1
       499: 1
       502: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       652: 1
       659: 1
       661: 1
       662: 1
       677: 1
       705: 1
       707: 1
       708: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       731: 1
       732: 1
       738: 1
       741: 1
       864: 1
       909: 1
       916: 1
       918: 1
       919: 1
       934: 1
      1123: 1

1124:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+3q+1
        29: 2q+1
        30: q^2+3q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: 1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: q+1
        68: q^2+3q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        92: 2q+1
        94: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: q^2+3q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q^2+3q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: 1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: 2q+1
       151: q+1
       152: q^2+3q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       173: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       184: 2q+1
       186: 2q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: q^2+3q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: 2q+1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       264: 2q+1
       265: q+1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       306: 2q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: 2q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: q+1
       402: q+1
       434: q+1
       435: q+1
       436: q+1
       440: 2q+1
       441: q+1
       462: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       490: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       535: 1
       536: 1
       537: 1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       611: q+1
       617: q+1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       687: 1
       693: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: 1
       729: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       865: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       944: 1
       950: 1
      1124: 1

1125:    0: 2q^2+3q+1
         1: q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: 3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: 2q+1
        13: q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+3q+1
        22: 3q+1
        23: q^2+3q+1
        24: 2q+1
        25: 3q+1
        26: 2q+1
        27: q^2+3q+1
        28: 3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: 2q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        47: q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: 2q+1
        52: 2q+1
        53: 3q+1
        54: 3q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: q^2+3q+1
        61: 2q+1
        62: 3q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+3q+1
        73: 3q+1
        74: q^2+3q+1
        75: 2q+1
        76: 3q+1
        77: 2q+1
        78: q^2+3q+1
        79: 3q+1
        80: q^2+3q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+3q+1
        86: 2q+1
        87: 2q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       105: 2q+1
       107: 2q+1
       108: 3q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: 2q+1
       119: 1
       120: 2q+1
       121: q+1
       122: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       136: 2q+1
       137: 3q+1
       138: 3q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: q^2+3q+1
       145: 2q+1
       146: 3q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       162: q+1
       165: 2q+1
       167: 2q+1
       169: q+1
       176: q+1
       177: q^2+3q+1
       178: 2q+1
       179: 2q+1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       191: 2q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       199: q+1
       201: q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       213: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       229: 2q+1
       231: 2q+1
       232: 3q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: 2q+1
       243: 1
       244: 2q+1
       245: q+1
       246: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: 2q+1
       266: q+1
       273: 1
       276: q+1
       288: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       295: q+1
       298: 2q+1
       300: 2q+1
       302: q+1
       312: 1
       314: q+1
       316: 1
       317: q+1
       321: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 2q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       366: q+1
       368: q+1
       369: 2q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       375: 1
       376: q+1
       377: q+1
       380: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       394: 1
       397: q+1
       399: 1
       412: 1
       435: q+1
       437: q+1
       438: 2q+1
       442: q+1
       449: 1
       452: q+1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: 1
       521: q+1
       523: 1
       524: q+1
       528: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: q+1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       566: 1
       612: q+1
       614: 1
       627: 1
       654: 1
       662: 1
       664: 1
       669: 1
       681: 1
       684: 1
       688: 1
       708: 1
       710: 1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       733: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       810: 1
       866: 1
       911: 1
       919: 1
       921: 1
       926: 1
       938: 1
       941: 1
       945: 1
      1125: 1

1126:    0: q^3+3q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^2+2q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^2+3q+1
        10: 2q^2+3q+1
        11: q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 2q+1
        21: 2q^2+3q+1
        22: q^2+3q+1
        23: q+1
        24: 2q^2+3q+1
        25: q^2+3q+1
        26: 2q+1
        27: 2q^2+3q+1
        28: q+1
        29: q+1
        30: q^2+3q+1
        31: 2q^2+3q+1
        32: q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        38: q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        51: 2q+1
        52: 2q+1
        53: q^2+3q+1
        54: q+1
        55: q^2+3q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q^2+3q+1
        62: q+1
        63: q+1
        64: 1
        65: q^2+3q+1
        66: 2q+1
        67: q^2+2q+1
        68: q+1
        69: q+1
        70: 1
        71: 2q+1
        72: 2q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: 2q^2+3q+1
        76: q^2+3q+1
        77: 2q+1
        78: 2q^2+3q+1
        79: q+1
        80: q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       106: 2q+1
       107: 2q+1
       108: q+1
       109: q^2+3q+1
       110: q+1
       111: 1
       113: 2q+1
       114: q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 2q+1
       126: q+1
       128: q^2+2q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 2q+1
       136: 2q+1
       137: q^2+3q+1
       138: q+1
       139: q^2+3q+1
       140: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: 2q^2+3q+1
       146: q+1
       147: q+1
       148: 1
       149: q^2+3q+1
       150: 2q+1
       151: q^2+2q+1
       152: q+1
       153: q+1
       154: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       192: 2q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: 1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: q^2+3q+1
       234: q+1
       235: 1
       237: 2q+1
       238: q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 2q+1
       250: q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       267: q+1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: q+1
       306: 1
       307: 1
       308: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       367: q+1
       368: q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: 1
       383: q+1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       394: 1
       398: q+1
       399: 1
       401: 1
       402: 1
       403: 1
       413: 1
       418: 1
       431: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       443: q+1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       567: 1
       571: 1
       613: q+1
       614: 1
       616: 1
       617: 1
       618: 1
       628: 1
       633: 1
       646: 1
       655: 1
       663: 1
       664: 1
       670: 1
       674: 1
       682: 1
       689: 1
       709: 1
       710: 1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       811: 1
       815: 1
       867: 1
       912: 1
       920: 1
       921: 1
       927: 1
       931: 1
       939: 1
       946: 1
      1126: 1

1127:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: 1
       268: q+1
       269: q+1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: q+1
       291: q+1
       292: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       399: 1
       407: q+1
       408: 1
       414: 1
       415: 1
       416: 1
       437: q+1
       438: 1
       444: q+1
       445: q+1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: 1
       497: 1
       504: 1
       511: 1
       512: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       559: 1
       560: 1
       577: 1
       585: 1
       586: 1
       614: 1
       622: q+1
       623: 1
       629: 1
       630: 1
       631: 1
       656: 1
       664: 1
       665: 1
       698: 1
       710: 1
       711: 1
       719: 1
       720: 1
       721: 1
       726: 1
       736: 1
       743: 1
       750: 1
       751: 1
       778: 1
       821: 1
       829: 1
       830: 1
       868: 1
       913: 1
       921: 1
       922: 1
       955: 1
      1037: 1
      1127: 1

1128:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^2+2q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: q^2+2q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^3+3q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: q+1
        30: 2q^2+3q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+3q^2+3q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q^2+2q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: 2q+1
       110: q+1
       111: 1
       112: q+1
       113: 2q+1
       114: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: 2q+1
       136: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q^2+2q+1
       187: q+1
       188: q+1
       189: 1
       190: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: 2q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: 2q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       238: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 2q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: 1
       284: 1
       286: q+1
       287: 1
       288: 1
       289: q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: q+1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       356: 1
       357: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: 2q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: q+1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       545: q+1
       552: 1
       553: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       563: 1
       564: 1
       572: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       657: 1
       666: 1
       667: 1
       675: 1
       697: 1
       703: 1
       712: 1
       713: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       742: 1
       749: 1
       750: 1
       753: 1
       755: 1
       775: 1
       807: 1
       808: 1
       816: 1
       818: 1
       826: 1
       827: 1
       828: 1
       832: 1
       850: 1
       869: 1
       914: 1
       923: 1
       924: 1
       932: 1
       954: 1
      1014: 1
      1034: 1
      1128: 1

1129:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: 2q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: q^2+3q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: 2q+1
        39: q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+2q+1
        50: q+1
        51: 2q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: 1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 1
        65: q^2+3q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 2q+1
        76: q^2+3q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: q^2+2q+1
       104: q+1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: q+1
       113: 2q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 1
       144: q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 1
       149: q^2+3q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: q+1
       169: 1
       170: q^2+2q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q^2+2q+1
       183: q+1
       184: q+1
       185: q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: 2q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: 1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       272: 1
       273: 1
       276: 1
       277: 1
       283: q+1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: q+1
       302: 1
       303: q^2+2q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: q+1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: 1
       452: 1
       453: 1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       563: 1
       564: 1
       565: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: q+1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       689: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       734: 1
       742: 1
       743: 1
       745: 1
       749: 1
       756: 1
       807: 1
       808: 1
       809: 1
       815: 1
       826: 1
       870: 1
       915: 1
       923: 1
       924: 1
       925: 1
       931: 1
       946: 1
      1015: 1
      1129: 1

1130:    0: 4q^2+4q+1
         1: 4q^2+4q+1
         2: 3q^2+4q+1
         3: 4q^2+4q+1
         4: 4q^2+4q+1
         5: 3q^2+4q+1
         6: 3q^2+4q+1
         7: q^2+3q+1
         8: 3q^2+4q+1
         9: 4q^2+4q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: 2q^2+3q+1
        13: 4q^2+4q+1
        14: 3q^2+4q+1
        15: 4q^2+4q+1
        16: 3q^2+4q+1
        17: 2q^2+4q+1
        18: 3q^2+4q+1
        19: 3q^2+4q+1
        20: 3q^2+4q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: 2q+1
        24: q^2+2q+1
        25: q^2+3q+1
        26: 2q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: 3q+1
        30: 2q^2+3q+1
        31: 2q+1
        32: 2q+1
        33: 3q^2+4q+1
        34: q^2+3q+1
        35: 3q^2+4q+1
        36: 4q^2+4q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+4q+1
        41: q^2+3q+1
        42: 2q^2+4q+1
        43: 3q^2+4q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+2q+1
        47: 3q^2+4q+1
        48: 2q^2+4q+1
        49: 3q^2+4q+1
        50: 2q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+3q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 3q+1
        63: 2q+1
        64: 3q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 3q^2+4q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: 2q+1
        75: q^2+2q+1
        76: q^2+3q+1
        77: 2q+1
        78: q^2+3q+1
        79: q^2+3q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: 2q+1
        84: 2q^2+4q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q+1
        97: 2q^2+4q+1
        98: q^2+3q+1
        99: 2q^2+4q+1
       100: 3q^2+4q+1
       101: 2q+1
       102: q^2+3q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 2q+1
       113: q+1
       114: 2q+1
       115: q+1
       116: q+1
       117: 1
       118: q+1
       119: 3q+1
       120: 2q+1
       121: 2q+1
       122: 2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       134: 2q+1
       135: q^2+2q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q^2+3q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: q+1
       146: 3q+1
       147: 2q+1
       148: 3q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: 2q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q^2+4q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q+1
       180: q+1
       181: 2q+1
       183: 2q+1
       184: q^2+3q+1
       185: 2q+1
       186: q^2+2q+1
       187: q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: q+1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: 1
       208: 2q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       214: q+1
       215: q+1
       218: 1
       220: 2q+1
       221: q+1
       222: q+1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: 2q+1
       237: q+1
       238: 2q+1
       239: q+1
       240: q+1
       241: 1
       242: q+1
       243: 3q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 1
       248: 2q+1
       249: q+1
       250: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q+1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: 2q+1
       276: q+1
       277: 1
       278: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       288: 2q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: 2q+1
       298: q+1
       299: 1
       300: 2q+1
       302: 2q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: q+1
       349: 1
       356: q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: q+1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 2q+1
       374: 1
       375: 2q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       381: q+1
       382: q+1
       385: 1
       387: 2q+1
       388: q+1
       389: q+1
       391: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: q+1
       430: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       449: 2q+1
       452: q+1
       453: 1
       454: q+1
       458: 1
       459: q+1
       461: q+1
       462: q+1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: q+1
       556: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       599: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: q+1
       628: 1
       633: 1
       635: 1
       641: q+1
       645: 1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       742: 1
       757: 1
       774: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       843: 1
       871: 1
       916: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
      1016: 1
      1033: 1
      1130: 1

1131:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       388: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       565: 1
       566: 1
       567: 1
       582: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       660: 1
       668: 1
       669: 1
       670: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       758: 1
       809: 1
       810: 1
       811: 1
       826: 1
       872: 1
       917: 1
       925: 1
       926: 1
       927: 1
      1017: 1
      1131: 1

1132:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+3q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: q^2+3q+1
        29: 2q+1
        30: q^2+3q+1
        31: 2q+1
        32: q^2+3q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+3q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: q^2+3q+1
        69: 2q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 2q+1
        77: q+1
        78: q+1
        79: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: 1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q^2+2q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q^2+2q+1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       151: q+1
       152: q^2+3q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       172: 1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       183: 1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       194: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q^2+2q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: q+1
       302: 1
       303: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: q+1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: q+1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       468: 1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       518: 1
       521: 1
       522: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: q+1
       544: 1
       545: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       565: 1
       568: 1
       569: 1
       582: 1
       590: 1
       598: 1
       599: 1
       604: 1
       611: q+1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       661: 1
       668: 1
       671: 1
       672: 1
       687: 1
       707: 1
       714: 1
       717: 1
       718: 1
       723: 1
       724: 1
       725: 1
       727: 1
       728: 1
       732: 1
       740: 1
       741: 1
       742: 1
       746: 1
       759: 1
       792: 1
       809: 1
       812: 1
       813: 1
       826: 1
       834: 1
       842: 1
       843: 1
       848: 1
       873: 1
       918: 1
       925: 1
       928: 1
       929: 1
       944: 1
      1018: 1
      1051: 1
      1132: 1

1133:    0: q^2+3q+1
         1: 2q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q+1
         7: 2q+1
         8: q^2+3q+1
         9: 2q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+2q+1
        13: 2q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: 2q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q^2+3q+1
        24: q^2+2q+1
        25: 1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: 2q+1
        35: q^2+3q+1
        36: 2q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^2+2q+1
        40: q+1
        41: 2q+1
        42: q^2+3q+1
        43: 2q+1
        44: q+1
        45: q^2+3q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q^2+2q+1
        57: 1
        58: 1
        59: q+1
        60: 2q+1
        61: q+1
        62: 1
        63: q+1
        64: 2q+1
        65: 1
        66: 1
        67: q+1
        68: q+1
        69: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q^2+3q+1
        75: q^2+2q+1
        76: 1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q^2+3q+1
        88: q+1
        89: 1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: q^2+3q+1
       103: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q^2+2q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: q+1
       122: 2q+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: q+1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q^2+2q+1
       141: 1
       142: 1
       143: q+1
       144: 2q+1
       145: q+1
       146: 1
       147: q+1
       148: 2q+1
       149: 1
       150: 1
       151: q+1
       152: q+1
       153: q+1
       154: q^2+2q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q^2+3q+1
       180: q+1
       181: 1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q^2+2q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: q+1
       243: 1
       244: 1
       245: q+1
       246: 2q+1
       247: 1
       248: 1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: q+1
       256: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: q+1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       342: 1
       343: q+1
       344: 1
       346: 1
       348: 1
       349: 1
       350: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       375: 1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: 1
       382: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: 1
       389: 1
       390: q+1
       391: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       411: 1
       412: 1
       418: 1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       448: 1
       449: 1
       452: q+1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       499: 1
       502: 1
       507: 1
       508: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       544: 1
       549: 1
       550: q+1
       551: 1
       553: 1
       555: 1
       556: 1
       557: 1
       566: 1
       568: 1
       570: 1
       589: 1
       597: 1
       598: 1
       604: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       626: 1
       627: 1
       633: 1
       634: 1
       640: 1
       641: 1
       644: 1
       645: 1
       662: 1
       669: 1
       671: 1
       673: 1
       693: 1
       708: 1
       715: 1
       717: 1
       719: 1
       724: 1
       726: 1
       727: 1
       728: 1
       729: 1
       738: 1
       741: 1
       746: 1
       747: 1
       760: 1
       799: 1
       810: 1
       812: 1
       814: 1
       833: 1
       841: 1
       842: 1
       848: 1
       874: 1
       919: 1
       926: 1
       928: 1
       930: 1
       950: 1
      1019: 1
      1058: 1
      1133: 1

1134:    0: q^3+q^2+q+1
         1: q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q^3+q^2+q+1
         9: q+1
        10: q^2+1
        11: 1
        12: q^3+q^2+q+1
        13: q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q^3+q^2+q+1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        30: q+1
        31: q^2+1
        32: 1
        33: q+1
        34: q+1
        35: q^3+q^2+q+1
        36: q+1
        37: q^2+1
        38: 1
        39: q^3+q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q^3+q^2+q+1
        76: 1
        77: 1
        78: q^2+1
        79: 1
        80: 1
        81: q+1
        82: q^2+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       567: 1
       569: 1
       570: 1
       589: 1
       599: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       663: 1
       670: 1
       672: 1
       673: 1
       709: 1
       716: 1
       718: 1
       719: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       742: 1
       761: 1
       811: 1
       813: 1
       814: 1
       833: 1
       843: 1
       875: 1
       920: 1
       927: 1
       929: 1
       930: 1
      1020: 1
      1134: 1

1135:    0: 2q^2+2q+1
         1: q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q^2+2q+1
         9: q+1
        10: 2q^2+2q+1
        11: q+1
        12: q^2+2q+1
        13: q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q^2+2q+1
        25: q+1
        26: 1
        27: 2q^2+2q+1
        28: 1
        29: q+1
        30: q+1
        31: q^2+2q+1
        32: q+1
        33: q+1
        34: q+1
        35: 2q^2+2q+1
        36: q+1
        37: 2q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q^2+2q+1
        43: q+1
        44: q^2+2q+1
        45: q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q^2+2q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        59: 1
        60: q+1
        61: q^2+2q+1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q^2+2q+1
        68: 1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q^2+2q+1
        76: q+1
        77: 1
        78: 2q^2+2q+1
        79: 1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q^2+2q+1
        92: 1
        93: q+1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q^2+2q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       103: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q^2+2q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: q+1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: q^2+2q+1
       146: 1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q^2+2q+1
       152: 1
       153: q+1
       154: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: q+1
       166: q+1
       167: 1
       169: q+1
       170: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       183: q^2+2q+1
       184: 1
       185: q+1
       186: q+1
       187: q+1
       188: 1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q^2+2q+1
       253: 1
       254: 1
       255: q+1
       256: 1
       257: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: q+1
       282: q+1
       283: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: q+1
       299: q+1
       300: 1
       302: q+1
       303: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       411: 1
       418: 1
       426: 1
       430: 1
       431: 1
       433: 1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       448: 1
       449: 1
       452: q+1
       453: 1
       454: q+1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       471: 1
       480: 1
       481: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       497: 1
       504: 1
       506: 1
       523: 1
       524: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: 1
       548: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       570: 1
       571: 1
       581: 1
       589: 1
       605: 1
       609: 1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       626: 1
       633: 1
       641: 1
       645: 1
       646: 1
       648: 1
       664: 1
       673: 1
       674: 1
       691: 1
       710: 1
       719: 1
       720: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       736: 1
       743: 1
       745: 1
       762: 1
       782: 1
       814: 1
       815: 1
       825: 1
       833: 1
       849: 1
       853: 1
       876: 1
       921: 1
       930: 1
       931: 1
       948: 1
      1021: 1
      1041: 1
      1135: 1

1136:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       158: q+1
       159: 1
       160: q+1
       161: 1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       173: 1
       174: 1
       175: 1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       195: q+1
       196: 1
       197: 1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: q+1
       218: q+1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: q+1
       233: 2q+1
       234: q+1
       235: 1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       244: q+1
       245: 1
       246: 1
       247: 1
       249: 2q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       262: 1
       263: q+1
       264: 1
       265: 1
       269: q+1
       270: 1
       271: q+1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: 1
       284: 1
       286: 1
       287: 1
       291: q+1
       292: 1
       293: q+1
       294: 1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: q+1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       341: q+1
       347: 1
       349: 1
       352: 1
       353: 1
       355: 1
       362: q+1
       363: 1
       364: 1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: q+1
       385: q+1
       388: q+1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: q+1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       438: 1
       439: q+1
       440: 1
       441: 1
       445: q+1
       446: 1
       447: q+1
       448: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: q+1
       459: 1
       460: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       489: 1
       490: 1
       491: 1
       506: 1
       512: 1
       514: 1
       524: 1
       525: 1
       532: q+1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       548: q+1
       554: 1
       556: 1
       559: 1
       560: 1
       562: 1
       571: 1
       572: 1
       579: 1
       586: 1
       587: 1
       588: 1
       606: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: q+1
       625: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       665: 1
       674: 1
       675: 1
       700: 1
       711: 1
       720: 1
       721: 1
       728: 1
       729: 1
       730: 1
       745: 1
       751: 1
       753: 1
       763: 1
       780: 1
       815: 1
       816: 1
       823: 1
       830: 1
       831: 1
       832: 1
       850: 1
       877: 1
       922: 1
       931: 1
       932: 1
       957: 1
      1022: 1
      1039: 1
      1136: 1

1137:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       405: 1
       412: 1
       414: 1
       416: 1
       435: 1
       442: 1
       444: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       464: 1
       473: 1
       474: 1
       482: 1
       492: 1
       493: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       583: 1
       620: 1
       627: 1
       629: 1
       631: 1
       657: 1
       676: 1
       677: 1
       685: 1
       696: 1
       703: 1
       712: 1
       713: 1
       721: 1
       731: 1
       732: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       827: 1
       878: 1
       914: 1
       933: 1
       934: 1
       942: 1
       953: 1
      1137: 1

1138:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: q+1
       302: 1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       394: 1
       397: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       485: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       612: 1
       627: 1
       658: 1
       676: 1
       677: 1
       678: 1
       684: 1
       688: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       724: 1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       879: 1
       915: 1
       933: 1
       934: 1
       935: 1
       941: 1
       945: 1
      1138: 1

1139:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: 2q+1
        32: q+1
        33: 2q+1
        34: 2q+1
        35: 2q+1
        36: q^2+2q+1
        37: 2q+1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: 2q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q+1
        72: 2q+1
        73: 2q+1
        74: 1
        75: q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        92: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: 2q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       124: 2q+1
       125: 2q+1
       126: 2q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       134: 1
       135: q+1
       136: 2q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: q+1
       159: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       184: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: q+1
       210: 1
       213: 1
       214: q+1
       215: 2q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: 2q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       259: 1
       288: 1
       290: q+1
       292: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       348: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       377: 1
       380: 1
       381: q+1
       382: 2q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       435: 1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       659: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       880: 1
       916: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
      1139: 1

1140:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: 1
       434: 1
       435: 1
       436: 1
       440: 1
       462: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       507: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       611: 1
       660: 1
       678: 1
       679: 1
       680: 1
       687: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       732: 1
       733: 1
       734: 1
       735: 1
       737: 1
       740: 1
       741: 1
       742: 1
       746: 1
       881: 1
       917: 1
       935: 1
       936: 1
       937: 1
       944: 1
      1140: 1

1141:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       177: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       468: 1
       475: 1
       478: 1
       479: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       518: 1
       521: 1
       522: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       661: 1
       678: 1
       681: 1
       682: 1
       707: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       882: 1
       918: 1
       935: 1
       938: 1
       939: 1
      1141: 1

1142:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       435: 1
       469: 1
       476: 1
       478: 1
       480: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       662: 1
       679: 1
       681: 1
       683: 1
       708: 1
       715: 1
       717: 1
       719: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       883: 1
       919: 1
       936: 1
       938: 1
       940: 1
      1142: 1

1143:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: 1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: q+1
        74: 1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: q+1
       127: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       260: 1
       264: 1
       265: 1
       286: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       334: 1
       335: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       402: 1
       436: 1
       440: 1
       441: 1
       462: 1
       470: 1
       477: 1
       479: 1
       480: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: 1
       507: 1
       508: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       617: 1
       663: 1
       680: 1
       682: 1
       683: 1
       693: 1
       709: 1
       716: 1
       718: 1
       719: 1
       729: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       742: 1
       746: 1
       747: 1
       884: 1
       920: 1
       937: 1
       939: 1
       940: 1
       950: 1
      1143: 1

1144:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: 1
        12: q^2+1
        13: 1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: q^2+1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        30: 1
        31: q^2+1
        32: 1
        33: 1
        34: 1
        35: q^2+1
        36: 1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q^2+1
        76: 1
        77: 1
        78: q^2+1
        79: 1
        80: 1
        81: 1
        82: q^2+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       273: 1
       276: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       399: 1
       437: 1
       438: 1
       449: 1
       452: 1
       471: 1
       480: 1
       481: 1
       487: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       523: 1
       524: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       614: 1
       664: 1
       683: 1
       684: 1
       690: 1
       710: 1
       719: 1
       720: 1
       726: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       885: 1
       921: 1
       940: 1
       941: 1
       947: 1
      1144: 1

1145:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       245: 1
       246: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       269: 1
       270: 1
       274: 1
       275: 1
       276: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       408: 1
       415: 1
       416: 1
       438: 1
       445: 1
       446: 1
       450: 1
       451: 1
       452: 1
       472: 1
       481: 1
       482: 1
       498: 1
       499: 1
       500: 1
       505: 1
       512: 1
       513: 1
       524: 1
       525: 1
       532: 1
       533: 1
       534: 1
       539: 1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       559: 1
       560: 1
       561: 1
       586: 1
       623: 1
       630: 1
       631: 1
       665: 1
       684: 1
       685: 1
       699: 1
       711: 1
       720: 1
       721: 1
       737: 1
       738: 1
       739: 1
       744: 1
       751: 1
       752: 1
       830: 1
       886: 1
       922: 1
       941: 1
       942: 1
       956: 1
      1145: 1

1146:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: 1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: q+1
       127: q+1
       128: q+1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: q+1
       140: q+1
       141: q+1
       144: q+1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       207: 1
       212: 1
       213: q+1
       214: q+1
       219: q+1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: q+1
       235: 1
       236: q+1
       237: q+1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: q+1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: q+1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       364: 1
       365: q+1
       372: 1
       373: 1
       374: 1
       379: 1
       380: q+1
       381: q+1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: q+1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       582: 1
       610: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       807: 1
       826: 1
       887: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
      1146: 1

1147:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: q+1
        94: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: q+1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: q+1
       186: q+1
       188: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: q+1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: q+1
       308: q+1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: q+1
       474: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: 1
       526: 1
       527: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       564: 1
       610: 1
       611: 1
       617: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       713: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       808: 1
       888: 1
       924: 1
       934: 1
       943: 1
       944: 1
       950: 1
      1147: 1

1148:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: 2q+1
         8: q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q+1
        19: q^2+3q+1
        20: q+1
        21: 2q+1
        22: 1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: 2q+1
        27: q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: 2q+1
        35: q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+3q+1
        41: 2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: 2q+1
        59: 1
        60: q+1
        61: q+1
        62: q^2+3q+1
        63: 2q+1
        64: 1
        65: q^2+3q+1
        66: 2q+1
        67: q+1
        68: q^2+3q+1
        69: q^2+3q+1
        70: q+1
        71: q+1
        72: 2q+1
        73: 1
        74: q+1
        75: q+1
        76: q^2+3q+1
        77: 2q+1
        78: q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: 1
        85: 2q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+3q+1
        98: 2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 2q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 2q+1
       126: 1
       127: q+1
       128: q+1
       129: q^2+3q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: q+1
       142: 2q+1
       143: 1
       144: q+1
       145: q+1
       146: q^2+3q+1
       147: 2q+1
       148: 1
       149: q^2+3q+1
       150: 2q+1
       151: q+1
       152: q^2+3q+1
       153: q^2+3q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: 2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: 2q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 2q+1
       250: 1
       251: q+1
       252: q+1
       253: q^2+3q+1
       254: 2q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       302: 1
       303: q+1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: q+1
       462: q+1
       463: q+1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       493: 1
       494: 1
       495: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       582: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: q+1
       668: 1
       678: 1
       687: 1
       688: 1
       689: 1
       692: 1
       695: 1
       714: 1
       723: 1
       724: 1
       725: 1
       728: 1
       732: 1
       733: 1
       734: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       754: 1
       809: 1
       826: 1
       889: 1
       925: 1
       935: 1
       944: 1
       945: 1
       946: 1
       949: 1
       952: 1
      1148: 1

1149:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       312: 1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       476: 1
       485: 1
       487: 1
       494: 1
       496: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: 1
       528: 1
       530: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       669: 1
       679: 1
       688: 1
       690: 1
       715: 1
       724: 1
       726: 1
       733: 1
       735: 1
       741: 1
       743: 1
       744: 1
       748: 1
       810: 1
       890: 1
       926: 1
       936: 1
       945: 1
       947: 1
      1149: 1

1150:    0: q^3+q^2+q+1
         1: q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q^2+1
         9: q+1
        10: q^3+q^2+q+1
        11: q+1
        12: q^3+q^2+q+1
        13: q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: q^2+1
        25: q+1
        26: q+1
        27: q^2+1
        28: q+1
        29: q+1
        30: q+1
        31: q^3+q^2+q+1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+1
        36: q+1
        37: q^3+q^2+q+1
        38: q+1
        39: q^3+q^2+q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: q^2+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q^2+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: q^2+1
        76: q+1
        77: q+1
        78: q^2+1
        79: q+1
        80: q+1
        81: q+1
        82: q^3+q^2+q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: q^2+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: q^2+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q^2+1
       152: q+1
       153: q+1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: q^2+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       401: 1
       413: 1
       418: 1
       431: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       477: 1
       486: 1
       487: 1
       489: 1
       495: 1
       496: 1
       498: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       510: 1
       515: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       613: 1
       614: 1
       616: 1
       628: 1
       633: 1
       646: 1
       670: 1
       680: 1
       689: 1
       690: 1
       692: 1
       716: 1
       725: 1
       726: 1
       728: 1
       734: 1
       735: 1
       737: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       749: 1
       754: 1
       811: 1
       891: 1
       927: 1
       937: 1
       946: 1
       947: 1
       949: 1
      1150: 1

1151:    0: q^2+3q+1
         1: 2q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: 2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: 2q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: q^2+3q+1
        30: 2q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+2q+1
        50: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: q^2+3q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 1
        74: 2q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: q^2+3q+1
        81: 2q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: 1
        85: q+1
        86: 1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q+1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: q+1
       133: q^2+2q+1
       134: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: 2q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: 2q+1
       153: q^2+3q+1
       154: q^2+2q+1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q^2+2q+1
       186: q+1
       187: q+1
       188: q+1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       227: q+1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: q+1
       247: 1
       248: q+1
       249: q+1
       250: 1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: q+1
       256: q+1
       257: q^2+2q+1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: q+1
       302: q+1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       314: 1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: q+1
       355: 1
       358: 1
       361: 1
       362: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: q+1
       391: 1
       392: q+1
       394: q+1
       397: 1
       400: 1
       401: 1
       412: 1
       418: 1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       448: 1
       449: 1
       452: q+1
       453: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       463: q+1
       478: 1
       485: 1
       488: 1
       489: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       515: 1
       521: 1
       528: 1
       531: 1
       532: 1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: q+1
       562: 1
       568: 1
       598: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       627: 1
       633: 1
       634: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       671: 1
       681: 1
       688: 1
       691: 1
       692: 1
       717: 1
       724: 1
       727: 1
       728: 1
       733: 1
       736: 1
       737: 1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       754: 1
       800: 1
       806: 1
       812: 1
       842: 1
       848: 1
       849: 1
       852: 1
       853: 1
       892: 1
       928: 1
       938: 1
       945: 1
       948: 1
       949: 1
      1059: 1
      1065: 1
      1151: 1

1152:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: 1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q+1
        21: 1
        22: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: 1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: q+1
        52: 1
        53: 1
        55: 1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: 1
        73: 1
        75: q+1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: q+1
       136: 1
       137: 1
       139: 1
       141: q+1
       142: 1
       143: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: q+1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       263: 1
       267: 1
       273: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       315: 1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       398: 1
       400: 1
       413: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       449: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       479: 1
       486: 1
       488: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       529: 1
       531: 1
       537: 1
       538: 1
       540: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       569: 1
       599: 1
       605: 1
       609: 1
       613: 1
       615: 1
       628: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       672: 1
       682: 1
       689: 1
       691: 1
       718: 1
       725: 1
       727: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       801: 1
       813: 1
       843: 1
       849: 1
       853: 1
       893: 1
       929: 1
       939: 1
       946: 1
       948: 1
      1060: 1
      1152: 1

1153:    0: q^3+3q^2+3q+1
         1: q^2+2q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^2+3q+1
         6: q+1
         7: 2q+1
         8: 2q^2+3q+1
         9: q^2+2q+1
        10: 2q^2+3q+1
        11: q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^2+2q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q^2+2q+1
        25: q+1
        26: 2q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: q^2+3q+1
        30: q^2+2q+1
        31: 2q^2+3q+1
        32: q^2+3q+1
        33: q+1
        34: 2q+1
        35: 2q^2+3q+1
        36: q^2+2q+1
        37: 2q^2+3q+1
        38: q^2+3q+1
        39: q^3+3q^2+3q+1
        40: q+1
        41: 2q+1
        42: q^2+3q+1
        43: 2q+1
        44: q+1
        45: q^2+3q+1
        46: q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: q^2+2q+1
        62: q+1
        63: 2q+1
        64: q^2+3q+1
        65: q+1
        66: 2q+1
        67: 2q^2+3q+1
        68: 2q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: q^2+2q+1
        76: q+1
        77: 2q+1
        78: 2q^2+3q+1
        79: 2q+1
        80: q^2+3q+1
        81: q^2+2q+1
        82: 2q^2+3q+1
        83: q^2+3q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: q^2+3q+1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: 2q+1
       128: q^2+2q+1
       129: q+1
       130: 2q+1
       131: q^2+3q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: q^2+2q+1
       146: q+1
       147: 2q+1
       148: q^2+3q+1
       149: q+1
       150: 2q+1
       151: 2q^2+3q+1
       152: 2q+1
       153: q^2+3q+1
       154: q^2+3q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: 1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: 1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: 2q+1
       246: 2q+1
       247: q+1
       248: q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+2q+1
       253: q+1
       254: 2q+1
       255: q^2+3q+1
       256: 2q+1
       257: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: q+1
       287: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: 1
       351: 1
       354: q+1
       355: 1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: 1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: 1
       394: q+1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       418: 1
       426: 1
       430: 1
       431: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: q+1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       496: 1
       497: 1
       498: 1
       499: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: 1
       558: 1
       561: q+1
       562: 1
       570: 1
       589: 1
       605: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       633: 1
       641: 1
       645: 1
       646: 1
       648: 1
       673: 1
       683: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       719: 1
       726: 1
       727: 1
       728: 1
       729: 1
       735: 1
       736: 1
       737: 1
       738: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       754: 1
       814: 1
       833: 1
       849: 1
       853: 1
       894: 1
       930: 1
       940: 1
       947: 1
       948: 1
       949: 1
       950: 1
       959: 1
      1153: 1

1154:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: 1
        19: q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       142: 1
       143: 1
       144: q+1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       401: 1
       402: 1
       403: 1
       418: 1
       431: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       481: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       556: 1
       557: 1
       561: 1
       562: 1
       571: 1
       616: 1
       617: 1
       618: 1
       633: 1
       646: 1
       674: 1
       684: 1
       692: 1
       693: 1
       694: 1
       720: 1
       728: 1
       729: 1
       730: 1
       737: 1
       738: 1
       739: 1
       744: 1
       745: 1
       746: 1
       747: 1
       754: 1
       815: 1
       895: 1
       931: 1
       941: 1
       949: 1
       950: 1
       951: 1
      1154: 1

1155:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        22: q+1
        23: q+1
        24: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        54: q+1
        55: q+1
        56: q+1
        59: q+1
        60: q+1
        61: q+1
        63: q+1
        64: 1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        73: q+1
        74: q+1
        75: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: q+1
       111: 1
       116: q+1
       117: q+1
       118: q+1
       121: 1
       122: 1
       123: 1
       126: q+1
       127: q+1
       128: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: q+1
       139: q+1
       140: q+1
       143: q+1
       144: q+1
       145: q+1
       147: q+1
       148: 1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: q+1
       205: 1
       210: 1
       211: 1
       212: 1
       217: q+1
       218: q+1
       219: q+1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: q+1
       235: 1
       240: q+1
       241: q+1
       242: q+1
       245: 1
       246: 1
       247: 1
       250: q+1
       251: q+1
       252: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       284: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       334: 1
       335: 1
       342: q+1
       343: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       363: 1
       364: 1
       371: q+1
       372: 1
       377: 1
       378: 1
       379: 1
       384: q+1
       385: q+1
       386: q+1
       389: 1
       390: 1
       391: 1
       393: 1
       394: 1
       402: 1
       403: 1
       410: 1
       416: 1
       417: 1
       418: 1
       432: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       460: 1
       462: 1
       463: 1
       482: 1
       490: 1
       491: 1
       499: 1
       500: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       525: 1
       533: 1
       534: 1
       541: 1
       542: 1
       549: q+1
       550: 1
       555: 1
       556: 1
       557: 1
       560: 1
       561: 1
       562: 1
       572: 1
       588: 1
       617: 1
       618: 1
       625: 1
       631: 1
       632: 1
       633: 1
       647: 1
       675: 1
       685: 1
       693: 1
       694: 1
       701: 1
       721: 1
       729: 1
       730: 1
       738: 1
       739: 1
       746: 1
       747: 1
       752: 1
       753: 1
       754: 1
       816: 1
       832: 1
       896: 1
       932: 1
       942: 1
       950: 1
       951: 1
       958: 1
      1155: 1

1156:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: 1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        56: 1
        57: q+1
        60: 1
        61: q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q+1
        84: q+1
        87: 1
        88: q+1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       111: 1
       112: 1
       113: q+1
       118: 1
       119: q+1
       122: 1
       123: q+1
       124: q+1
       127: 1
       128: q+1
       129: q+1
       131: q+1
       132: q+1
       133: 1
       134: 1
       135: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       179: 1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       198: 1
       205: 1
       206: 1
       207: q+1
       212: 1
       213: 1
       214: q+1
       219: 1
       220: q+1
       223: 1
       224: q+1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       247: q+1
       248: q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q+1
       257: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: q+1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       365: 1
       372: 1
       373: 1
       374: q+1
       379: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       391: q+1
       392: 1
       394: 1
       395: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       483: 1
       492: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: q+1
       557: 1
       558: 1
       561: 1
       562: 1
       573: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       686: 1
       695: 1
       702: 1
       722: 1
       731: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       774: 1
       801: 1
       817: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       897: 1
       943: 1
       952: 1
       959: 1
      1033: 1
      1060: 1
      1156: 1

1157:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       440: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       484: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       527: 1
       535: 1
       536: 1
       537: 1
       541: 1
       543: 1
       544: 1
       545: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       611: 1
       619: 1
       620: 1
       621: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       687: 1
       695: 1
       696: 1
       697: 1
       701: 1
       723: 1
       732: 1
       740: 1
       741: 1
       742: 1
       746: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       775: 1
       818: 1
       826: 1
       827: 1
       828: 1
       832: 1
       850: 1
       898: 1
       944: 1
       952: 1
       953: 1
       954: 1
       958: 1
      1034: 1
      1157: 1

1158:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       191: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       300: q+1
       301: q+1
       302: 1
       321: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       358: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       397: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       485: 1
       494: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       528: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       575: 1
       583: 1
       585: 1
       586: 1
       612: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       688: 1
       696: 1
       698: 1
       699: 1
       724: 1
       733: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       776: 1
       819: 1
       827: 1
       829: 1
       830: 1
       899: 1
       945: 1
       953: 1
       955: 1
       956: 1
      1035: 1
      1158: 1

1159:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: q+1
        59: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: q+1
       121: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       243: 1
       244: q+1
       245: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       322: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       381: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       427: 1
       431: 1
       432: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       486: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       529: 1
       537: 1
       538: 1
       540: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       576: 1
       584: 1
       585: 1
       587: 1
       606: 1
       613: 1
       621: 1
       622: 1
       624: 1
       628: 1
       629: 1
       630: 1
       632: 1
       642: 1
       646: 1
       647: 1
       689: 1
       697: 1
       698: 1
       700: 1
       725: 1
       734: 1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       777: 1
       820: 1
       828: 1
       829: 1
       831: 1
       850: 1
       900: 1
       946: 1
       954: 1
       955: 1
       957: 1
      1036: 1
      1159: 1

1160:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       193: 1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       323: 1
       331: 1
       332: 1
       339: 1
       340: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       360: 1
       368: 1
       369: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 1
       407: 1
       408: 1
       414: 1
       415: 1
       416: 1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       487: 1
       496: 1
       504: 1
       505: 1
       511: 1
       512: 1
       513: 1
       530: 1
       538: 1
       539: 1
       546: 1
       547: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       577: 1
       585: 1
       586: 1
       614: 1
       622: 1
       623: 1
       629: 1
       630: 1
       631: 1
       690: 1
       698: 1
       699: 1
       726: 1
       735: 1
       743: 1
       744: 1
       750: 1
       751: 1
       752: 1
       778: 1
       821: 1
       829: 1
       830: 1
       901: 1
       947: 1
       955: 1
       956: 1
      1037: 1
      1160: 1

1161:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        24: q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q^2+2q+1
        37: 2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        55: q+1
        57: q+1
        58: q+1
        59: 2q+1
        61: q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        75: q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       107: 1
       109: 1
       114: q+1
       115: 1
       117: q+1
       119: q+1
       120: q+1
       121: 2q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       139: q+1
       141: q+1
       142: q+1
       143: 2q+1
       145: q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: q+1
       150: 2q+1
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       157: q+1
       158: 1
       160: q+1
       162: 1
       163: 1
       164: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       194: 1
       201: 1
       203: 1
       208: q+1
       209: 1
       211: q+1
       215: q+1
       216: 1
       218: q+1
       220: q+1
       221: q+1
       222: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       233: 1
       238: q+1
       239: 1
       241: q+1
       243: q+1
       244: q+1
       245: 2q+1
       247: q+1
       248: q+1
       249: q+1
       250: 2q+1
       252: q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: 2q+1
       257: q+1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       324: 1
       331: 1
       333: 1
       339: 1
       341: 1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: q+1
       355: 1
       361: 1
       368: 1
       370: 1
       375: q+1
       376: 1
       378: q+1
       382: q+1
       383: 1
       385: q+1
       387: q+1
       388: q+1
       389: 2q+1
       391: q+1
       392: 1
       393: q+1
       394: q+1
       400: 1
       407: 1
       409: 1
       414: 1
       415: 1
       417: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: q+1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       488: 1
       497: 1
       504: 1
       506: 1
       511: 1
       512: 1
       514: 1
       531: 1
       538: 1
       540: 1
       546: 1
       548: 1
       553: q+1
       554: 1
       556: q+1
       558: 1
       559: 1
       560: q+1
       562: 1
       578: 1
       585: 1
       587: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       615: 1
       622: 1
       624: 1
       629: 1
       630: 1
       632: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       691: 1
       698: 1
       700: 1
       727: 1
       736: 1
       743: 1
       745: 1
       750: 1
       751: 1
       753: 1
       779: 1
       802: 1
       805: 1
       822: 1
       829: 1
       831: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       902: 1
       948: 1
       955: 1
       957: 1
      1038: 1
      1061: 1
      1064: 1
      1161: 1

1162:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       325: 1
       332: 1
       333: 1
       334: 1
       340: 1
       341: 1
       342: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       362: 1
       369: 1
       370: 1
       371: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       401: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       438: 1
       439: 1
       440: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       489: 1
       498: 1
       505: 1
       506: 1
       507: 1
       512: 1
       513: 1
       514: 1
       515: 1
       532: 1
       539: 1
       540: 1
       541: 1
       547: 1
       548: 1
       549: 1
       554: 1
       555: 1
       556: 1
       557: 1
       559: 1
       560: 1
       561: 1
       562: 1
       579: 1
       586: 1
       587: 1
       588: 1
       606: 1
       616: 1
       623: 1
       624: 1
       625: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       692: 1
       699: 1
       700: 1
       701: 1
       728: 1
       737: 1
       744: 1
       745: 1
       746: 1
       751: 1
       752: 1
       753: 1
       754: 1
       780: 1
       823: 1
       830: 1
       831: 1
       832: 1
       850: 1
       903: 1
       949: 1
       956: 1
       957: 1
       958: 1
      1039: 1
      1162: 1

1163:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: 1
        24: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q+1
        39: q^2+q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        54: 1
        55: q+1
        56: 1
        59: q+1
        60: 1
        61: q+1
        63: q+1
        64: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        73: q+1
        74: 1
        75: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q+1
        86: q+1
        87: 1
        88: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       110: 1
       111: 1
       116: 1
       117: q+1
       118: 1
       121: q+1
       122: 1
       123: q+1
       126: q+1
       127: 1
       128: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       138: 1
       139: q+1
       140: 1
       143: q+1
       144: 1
       145: q+1
       147: q+1
       148: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       159: 1
       160: q+1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       178: q+1
       179: 1
       180: q+1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       196: 1
       204: 1
       205: 1
       210: 1
       211: q+1
       212: 1
       217: 1
       218: q+1
       219: 1
       222: q+1
       223: 1
       224: q+1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: q+1
       242: 1
       245: q+1
       246: 1
       247: q+1
       250: q+1
       251: 1
       252: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       292: 1
       293: q+1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       326: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: q+1
       350: 1
       353: 1
       354: 1
       355: 1
       363: 1
       371: 1
       372: 1
       377: 1
       378: q+1
       379: 1
       384: 1
       385: q+1
       386: 1
       389: q+1
       390: 1
       391: q+1
       393: 1
       394: 1
       402: 1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       424: 1
       428: 1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       490: 1
       499: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       533: 1
       541: 1
       542: 1
       549: 1
       550: 1
       555: 1
       556: q+1
       557: 1
       560: 1
       561: 1
       562: 1
       580: 1
       588: 1
       589: 1
       603: 1
       607: 1
       609: 1
       617: 1
       625: 1
       626: 1
       631: 1
       632: 1
       633: 1
       639: 1
       643: 1
       645: 1
       647: 1
       648: 1
       693: 1
       701: 1
       702: 1
       729: 1
       738: 1
       746: 1
       747: 1
       752: 1
       753: 1
       754: 1
       781: 1
       805: 1
       824: 1
       832: 1
       833: 1
       847: 1
       851: 1
       853: 1
       904: 1
       950: 1
       958: 1
       959: 1
      1040: 1
      1064: 1
      1163: 1

1164:    0: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         8: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        14: q^2+1
        15: q^2+1
        17: 1
        18: 1
        19: 1
        23: 1
        24: q^2+1
        27: q^2+1
        29: 1
        31: q^2+1
        32: 1
        35: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: q^2+1
        64: 1
        67: q^2+1
        69: 1
        70: 1
        74: 1
        75: q^2+1
        78: q^2+1
        80: 1
        82: q^2+1
        83: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       111: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: q^2+1
       131: 1
       133: 1
       140: 1
       144: 1
       145: q^2+1
       148: 1
       151: q^2+1
       153: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       197: 1
       205: 1
       212: 1
       219: 1
       223: 1
       224: 1
       227: 1
       235: 1
       242: 1
       246: 1
       247: 1
       251: 1
       252: q^2+1
       255: 1
       257: 1
       265: 1
       272: 1
       276: 1
       277: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       327: 1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       364: 1
       372: 1
       379: 1
       386: 1
       390: 1
       391: 1
       394: 1
       403: 1
       411: 1
       418: 1
       430: 1
       433: 1
       441: 1
       448: 1
       452: 1
       453: 1
       458: 1
       461: 1
       463: 1
       491: 1
       500: 1
       508: 1
       515: 1
       534: 1
       542: 1
       550: 1
       557: 1
       561: 1
       562: 1
       581: 1
       589: 1
       609: 1
       618: 1
       626: 1
       633: 1
       645: 1
       648: 1
       694: 1
       702: 1
       730: 1
       739: 1
       747: 1
       754: 1
       782: 1
       825: 1
       833: 1
       853: 1
       905: 1
       951: 1
       959: 1
      1041: 1
      1164: 1

1165:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q^2+2q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        81: q+1
        82: 1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: q+1
       136: q^2+2q+1
       137: q+1
       139: q+1
       141: q+1
       142: q+1
       143: q+1
       145: 1
       149: 1
       150: 1
       151: 1
       155: q+1
       156: q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       186: q+1
       187: 1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: q+1
       233: 1
       237: 1
       238: q+1
       239: q+1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q^2+2q+1
       291: q+1
       293: q+1
       295: q+1
       296: q+1
       297: q+1
       299: 1
       303: 1
       304: 1
       305: 1
       309: 1
       310: q+1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       338: 1
       346: 1
       351: 1
       352: 1
       353: 1
       359: 1
       361: 1
       367: 1
       368: q+1
       370: 1
       381: 1
       382: 1
       385: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: q+1
       439: 1
       443: 1
       444: q+1
       445: q+1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       482: 1
       511: 1
       522: 1
       529: 1
       531: 1
       545: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       592: 1
       600: 1
       605: 1
       606: 1
       607: 1
       613: 1
       615: 1
       621: 1
       622: q+1
       624: 1
       635: 1
       636: 1
       639: 1
       649: 1
       650: 1
       656: 1
       657: 1
       659: 1
       718: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       773: 1
       802: 1
       813: 1
       820: 1
       822: 1
       836: 1
       854: 1
       960: 1
       961: 1
       967: 1
       968: 1
       970: 1
      1029: 1
      1165: 1

1166:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 1
       345: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       510: 1
       522: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       613: 1
       615: 1
       635: 1
       650: 1
       651: 1
       655: 1
       666: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       813: 1
       855: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1166: 1

1167:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        64: q+1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: q+1
       105: 2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: 2q+1
       113: q+1
       118: q+1
       119: q+1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       205: 1
       206: q+1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: q+1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: 1
       266: 2q+1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       336: 1
       343: 1
       344: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       396: q+1
       397: 2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       411: 1
       412: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       492: 1
       500: 1
       509: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       590: 1
       597: 1
       598: 1
       605: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       650: 1
       652: 1
       654: 1
       676: 1
       704: 1
       707: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       783: 1
       791: 1
       800: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       856: 1
       961: 1
       963: 1
       965: 1
       987: 1
      1015: 1
      1018: 1
      1167: 1

1168:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       483: 1
       492: 1
       501: 1
       508: 1
       517: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       610: 1
       611: 1
       617: 1
       651: 1
       652: 1
       653: 1
       686: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       774: 1
       783: 1
       792: 1
       799: 1
       808: 1
       857: 1
       962: 1
       963: 1
       964: 1
       997: 1
      1168: 1

1169:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: q+1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: 1
        60: 2q+1
        61: 2q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: q+1
        69: 2q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: q+1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       118: 2q+1
       119: 1
       122: q+1
       123: q+1
       124: 1
       127: q+1
       128: q+1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: 1
       144: q+1
       145: q+1
       146: 1
       149: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: 2q+1
       162: 1
       165: 2q+1
       166: 2q+1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q+1
       174: 2q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: q+1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: q+1
       213: 1
       214: 1
       219: q+1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: q+1
       248: 1
       251: q+1
       252: q+1
       253: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       272: 2q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: q+1
       282: q+1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: q+1
       295: 1
       298: q+1
       299: q+1
       300: 1
       303: 1
       305: q+1
       306: 1
       307: q+1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: q+1
       392: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: q+1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: q+1
       454: 1
       457: q+1
       458: q+1
       459: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       491: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: q+1
       646: 1
       653: 1
       654: 1
       655: 1
       694: 1
       695: 1
       707: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       782: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       858: 1
       964: 1
       965: 1
       966: 1
      1005: 1
      1006: 1
      1018: 1
      1169: 1

1170:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+2q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+3q+1
        29: 2q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: q+1
        54: q^2+3q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q^2+2q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       105: q+1
       107: 1
       108: q+1
       109: q+1
       110: q^2+2q+1
       111: q+1
       112: 1
       114: 1
       115: q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q^2+3q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 1
       163: q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 1
       199: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       210: q+1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: q+1
       263: q+1
       264: q^2+2q+1
       265: q+1
       266: 1
       268: 1
       269: q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 1
       314: 1
       316: 1
       317: 1
       318: 1
       321: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       397: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: 1
       405: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       414: 1
       416: q+1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       469: 1
       471: 1
       472: 1
       476: 1
       478: 1
       480: 1
       482: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       521: 1
       524: 1
       525: 1
       528: 1
       531: 1
       532: 1
       544: 1
       549: 1
       559: 1
       566: 1
       568: 1
       570: 1
       571: 1
       572: 1
       575: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       612: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       654: 1
       656: 1
       662: 1
       685: 1
       696: 1
       711: 1
       717: 1
       760: 1
       762: 1
       763: 1
       767: 1
       769: 1
       771: 1
       773: 1
       790: 1
       791: 1
       793: 1
       800: 1
       802: 1
       804: 1
       812: 1
       815: 1
       816: 1
       819: 1
       822: 1
       823: 1
       835: 1
       840: 1
       850: 1
       859: 1
       965: 1
       967: 1
       973: 1
       996: 1
      1007: 1
      1022: 1
      1028: 1
      1170: 1

1171:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: 2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        81: 2q+1
        82: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 2q+1
        95: q+1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       103: 2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       139: 2q+1
       141: 1
       142: 1
       143: q+1
       145: q+1
       149: 1
       150: q+1
       151: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       186: 2q+1
       187: q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: q+1
       248: 1
       249: 1
       250: q+1
       252: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       293: 2q+1
       295: 1
       296: 1
       297: q+1
       299: q+1
       303: 1
       304: q+1
       305: q+1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       385: q+1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: q+1
       454: 1
       455: 1
       456: q+1
       458: q+1
       470: 1
       471: 1
       472: 1
       477: 1
       479: 1
       480: 1
       482: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       639: q+1
       655: 1
       656: 1
       663: 1
       675: 1
       697: 1
       718: 1
       761: 1
       762: 1
       763: 1
       768: 1
       770: 1
       771: 1
       773: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       860: 1
       966: 1
       967: 1
       974: 1
       986: 1
      1008: 1
      1029: 1
      1171: 1

1172:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        75: 1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q+1
        81: q+1
        82: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: 1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: q+1
       137: q+1
       139: 1
       141: q+1
       142: q^2+2q+1
       143: q+1
       145: 1
       149: q+1
       150: q+1
       151: 1
       155: 1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q^2+2q+1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       180: 1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q+1
       186: q+1
       187: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       225: q+1
       226: q+1
       227: 1
       230: 1
       231: q+1
       233: 1
       237: 1
       238: q+1
       239: q+1
       241: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 1
       290: q+1
       291: q+1
       293: 1
       295: q+1
       296: q^2+2q+1
       297: q+1
       299: 1
       303: q+1
       304: q+1
       305: 1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: q+1
       353: 1
       359: 1
       367: 1
       368: q+1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       431: q+1
       432: q+1
       433: 1
       436: 1
       437: q+1
       439: 1
       443: 1
       444: q+1
       445: q+1
       447: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       485: 1
       495: 1
       504: 1
       511: 1
       512: 1
       529: 1
       545: 1
       546: 1
       548: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       592: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       606: q+1
       607: 1
       613: 1
       621: 1
       622: q+1
       624: 1
       635: 1
       636: 1
       637: 1
       639: 1
       649: 1
       657: 1
       658: 1
       665: 1
       698: 1
       734: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: 1
       772: 1
       773: 1
       776: 1
       786: 1
       795: 1
       802: 1
       803: 1
       820: 1
       836: 1
       837: 1
       839: 1
       861: 1
       960: 1
       968: 1
       969: 1
       976: 1
      1009: 1
      1045: 1
      1172: 1

1173:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: 1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: 1
        40: 2q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 1
        56: 1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        78: q+1
        81: 1
        82: 1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: 2q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: q+1
       137: q+1
       139: 1
       141: q+1
       145: 1
       149: 1
       151: 1
       155: q+1
       156: 1
       157: 2q+1
       158: 2q+1
       159: q+1
       160: 1
       161: 1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       183: q+1
       186: 1
       187: 1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       230: 1
       231: q+1
       233: 1
       237: 1
       248: 1
       252: 1
       258: 1
       259: q+1
       260: 1
       261: 2q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: q+1
       291: q+1
       293: 1
       295: q+1
       299: 1
       303: 1
       305: 1
       309: 1
       310: 1
       311: 1
       312: q+1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       359: 1
       361: 1
       381: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       433: 1
       436: 1
       437: q+1
       439: 1
       443: 1
       454: 1
       458: 1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       495: 1
       497: 1
       504: 1
       522: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       592: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       613: 1
       615: 1
       635: 1
       650: 1
       658: 1
       659: 1
       664: 1
       669: 1
       682: 1
       756: 1
       757: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       776: 1
       778: 1
       786: 1
       788: 1
       795: 1
       813: 1
       862: 1
       961: 1
       969: 1
       970: 1
       975: 1
       980: 1
       993: 1
      1173: 1

1174:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        81: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: q+1
       136: q+1
       139: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       186: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       289: q+1
       290: q+1
       293: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       436: q+1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       503: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       757: 1
       758: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: 1
       775: 1
       781: 1
       794: 1
       863: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: 1
      1174: 1

1175:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        79: q+1
        81: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       139: 1
       140: 1
       152: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       184: q+1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: q+1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+1
       289: 1
       290: q+1
       292: q+1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       434: 1
       435: q+1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       492: 1
       493: 1
       499: 1
       502: 1
       517: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       610: 1
       611: 1
       617: 1
       652: 1
       659: 1
       661: 1
       662: 1
       677: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       783: 1
       784: 1
       790: 1
       793: 1
       808: 1
       864: 1
       963: 1
       970: 1
       972: 1
       973: 1
       988: 1
      1175: 1

1176:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+3q+1
        29: 2q+1
        30: q^2+3q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: 1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: q+1
        68: q^2+3q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        79: 2q+1
        81: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        94: q^2+3q+1
        95: 2q+1
        96: q^2+3q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: q^2+3q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       152: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 1
       163: q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: 2q+1
       172: q+1
       173: q^2+3q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       184: 2q+1
       186: 2q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       234: 2q+1
       235: q+1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: q^2+3q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: 2q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       306: 2q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       363: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: 2q+1
       411: 1
       412: 1
       413: 1
       414: 1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       440: 2q+1
       441: q+1
       462: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       490: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       582: 1
       583: 1
       584: 1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: q+1
       617: q+1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       687: 1
       693: 1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: 1
       781: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       865: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       998: 1
      1004: 1
      1176: 1

1177:    0: q^3+3q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^2+2q+1
         5: q^3+3q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: 2q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^2+2q+1
        20: 2q+1
        21: 2q^2+3q+1
        22: q^2+3q+1
        23: 2q^2+3q+1
        24: q+1
        25: q^2+3q+1
        26: 2q+1
        27: 2q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        52: 2q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q^2+3q+1
        61: q+1
        62: q^2+3q+1
        63: 2q+1
        64: q^2+2q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 2q+1
        85: 2q^2+3q+1
        86: q^2+3q+1
        87: 2q^2+3q+1
        88: q+1
        89: q^2+3q+1
        90: 2q+1
        91: 2q^2+3q+1
        92: q^2+3q+1
        93: 2q^2+3q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       105: 2q+1
       107: 2q+1
       108: q^2+3q+1
       109: q+1
       110: q+1
       111: 1
       112: 2q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q^2+2q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 2q+1
       157: 2q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q^2+3q+1
       166: q+1
       167: q^2+3q+1
       168: 2q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: 2q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       199: q+1
       201: q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       208: 1
       209: q+1
       210: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       227: 1
       229: q+1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       259: 2q+1
       261: 2q+1
       262: q^2+3q+1
       263: q+1
       264: q+1
       265: 1
       266: 2q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q^2+2q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: q+1
       314: 1
       316: 1
       317: 1
       321: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       380: 1
       386: 1
       392: 1
       397: 2q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       405: q+1
       407: q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: 1
       415: q+1
       416: q+1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       433: 1
       435: q+1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       521: 1
       524: 1
       566: q+1
       568: 1
       570: 1
       571: 1
       575: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       612: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       634: 1
       640: 1
       646: 1
       654: 1
       662: 1
       664: 1
       669: 1
       681: 1
       684: 1
       688: 1
       760: 1
       762: 1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       812: 1
       815: 1
       866: 1
       965: 1
       973: 1
       975: 1
       980: 1
       992: 1
       995: 1
       999: 1
      1177: 1

1178:    0: 2q^2+3q+1
         1: q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: 3q+1
        10: q^2+3q+1
        11: 2q+1
        12: q^2+3q+1
        13: q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+3q+1
        22: 3q+1
        23: 2q+1
        24: q^2+3q+1
        25: 3q+1
        26: 2q+1
        27: q^2+3q+1
        28: 2q+1
        29: 2q+1
        30: 3q+1
        31: q^2+3q+1
        32: 2q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        39: 2q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 3q+1
        44: q^2+3q+1
        45: 2q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        51: 2q+1
        52: 2q+1
        53: 3q+1
        54: 2q+1
        55: 3q+1
        56: 2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q^2+3q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 3q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+3q+1
        73: 2q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        81: 2q+1
        82: 2q+1
        84: 2q+1
        85: q^2+3q+1
        86: 3q+1
        87: 2q+1
        88: q^2+3q+1
        89: 3q+1
        90: 2q+1
        91: q^2+3q+1
        92: 2q+1
        93: 2q+1
        94: 3q+1
        95: q^2+3q+1
        96: 2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       103: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 3q+1
       110: 2q+1
       111: q+1
       113: 2q+1
       114: q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: 2q+1
       126: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: q+1
       136: q+1
       137: 2q+1
       139: 2q+1
       141: q+1
       145: 2q+1
       149: 2q+1
       151: q+1
       156: 2q+1
       157: 2q+1
       158: 3q+1
       159: 2q+1
       160: 3q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: q^2+3q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 3q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+3q+1
       178: 2q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       186: 2q+1
       187: 2q+1
       192: 2q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       230: q+1
       231: q+1
       233: 2q+1
       237: q+1
       248: 1
       252: q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 3q+1
       264: 2q+1
       265: q+1
       267: 2q+1
       268: q+1
       269: 2q+1
       270: q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: 2q+1
       280: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: 2q+1
       293: 2q+1
       295: q+1
       299: 2q+1
       303: 2q+1
       305: q+1
       313: q+1
       315: 1
       316: 1
       317: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: q+1
       361: 1
       381: 1
       398: 2q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       406: q+1
       407: q+1
       408: q+1
       409: 2q+1
       410: q+1
       411: 1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: 1
       421: 1
       422: q+1
       424: q+1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       433: 1
       436: q+1
       437: q+1
       439: 2q+1
       443: q+1
       454: 1
       458: q+1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       567: q+1
       569: 1
       570: 1
       571: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: q+1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: q+1
       615: 1
       635: 1
       655: 1
       663: 1
       664: 1
       670: 1
       674: 1
       682: 1
       689: 1
       761: 1
       762: 1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       813: 1
       867: 1
       966: 1
       974: 1
       975: 1
       981: 1
       985: 1
       993: 1
      1000: 1
      1178: 1

1179:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        81: 1
        82: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       139: 1
       141: q+1
       142: q+1
       143: q+1
       145: 1
       149: 1
       150: 1
       151: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       186: 1
       187: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: q+1
       233: 1
       238: q+1
       239: q+1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       293: 1
       295: q+1
       296: q+1
       297: q+1
       299: 1
       303: 1
       304: 1
       305: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       361: 1
       368: q+1
       370: 1
       382: 1
       383: 1
       385: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       437: q+1
       439: 1
       444: q+1
       445: q+1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: 1
       497: 1
       504: 1
       511: 1
       512: 1
       531: 1
       546: 1
       548: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       606: 1
       607: 1
       615: 1
       622: q+1
       624: 1
       636: 1
       637: 1
       639: 1
       656: 1
       664: 1
       665: 1
       698: 1
       736: 1
       762: 1
       763: 1
       771: 1
       772: 1
       773: 1
       778: 1
       788: 1
       795: 1
       802: 1
       803: 1
       822: 1
       837: 1
       839: 1
       868: 1
       967: 1
       975: 1
       976: 1
      1009: 1
      1047: 1
      1179: 1

1180:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       237: 1
       238: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       367: 1
       381: 1
       382: 1
       385: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: 1
       443: 1
       444: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       545: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       621: 1
       635: 1
       636: 1
       639: 1
       657: 1
       666: 1
       667: 1
       675: 1
       697: 1
       755: 1
       764: 1
       765: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       836: 1
       869: 1
       968: 1
       977: 1
       978: 1
       986: 1
      1008: 1
      1180: 1

1181:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        78: 1
        81: q+1
        82: q+1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: q+1
       151: 1
       155: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: q+1
       183: 1
       186: q+1
       187: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       258: q+1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: q+1
       305: 1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       381: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: 1
       635: 1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       689: 1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: 1
       870: 1
       969: 1
       977: 1
       978: 1
       979: 1
       985: 1
      1000: 1
      1181: 1

1182:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q+1
         5: q^2+2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: q+1
        24: 1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        39: q+1
        40: 2q+1
        41: 2q+1
        42: 2q+1
        43: q^2+2q+1
        44: 2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: 2q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 1
        62: 2q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        81: q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: q+1
        88: 1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: 2q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: 2q+1
       120: 2q+1
       121: 2q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       135: 1
       136: q+1
       139: 1
       155: q+1
       156: 1
       157: 2q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       186: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: 1
       208: 2q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       214: 1
       215: q+1
       218: 1
       220: q+1
       221: q+1
       222: q+1
       224: 1
       230: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: 2q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       289: 1
       290: q+1
       293: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: q+1
       349: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       436: 1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: q+1
       603: 1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       871: 1
       970: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
      1182: 1

1183:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        72: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       177: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       565: 1
       566: 1
       567: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       660: 1
       668: 1
       669: 1
       670: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       872: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1183: 1

1184:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       462: 1
       468: 1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: 1
       661: 1
       668: 1
       671: 1
       672: 1
       687: 1
       759: 1
       766: 1
       769: 1
       770: 1
       775: 1
       776: 1
       777: 1
       779: 1
       780: 1
       784: 1
       792: 1
       793: 1
       794: 1
       798: 1
       873: 1
       972: 1
       979: 1
       982: 1
       983: 1
       998: 1
      1184: 1

1185:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: 1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: 1
        21: 1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: q+1
        87: q+1
        88: 1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       229: 1
       234: 1
       235: 1
       256: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       349: 1
       350: 1
       363: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       435: 1
       440: 1
       441: 1
       462: 1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       499: 1
       502: 1
       507: 1
       508: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       617: 1
       662: 1
       669: 1
       671: 1
       673: 1
       693: 1
       760: 1
       767: 1
       769: 1
       771: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       790: 1
       793: 1
       798: 1
       799: 1
       874: 1
       973: 1
       980: 1
       982: 1
       984: 1
      1004: 1
      1185: 1

1186:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       289: 1
       290: 1
       293: 1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       436: 1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       663: 1
       670: 1
       672: 1
       673: 1
       761: 1
       768: 1
       770: 1
       771: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       875: 1
       974: 1
       981: 1
       983: 1
       984: 1
      1186: 1

1187:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: q^2+1
        18: q^2+1
        19: 1
        20: 1
        21: 1
        22: 1
        23: q^2+1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: q^2+1
        43: 1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: q^2+1
        61: 1
        62: 1
        63: 1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: 1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: q^2+1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: q^2+1
       166: 1
       167: 1
       168: 1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       231: 1
       233: 1
       248: 1
       252: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       361: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       437: 1
       439: 1
       454: 1
       458: 1
       471: 1
       480: 1
       481: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       497: 1
       504: 1
       506: 1
       570: 1
       571: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       615: 1
       664: 1
       673: 1
       674: 1
       691: 1
       762: 1
       771: 1
       772: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       788: 1
       795: 1
       797: 1
       876: 1
       975: 1
       984: 1
       985: 1
      1002: 1
      1187: 1

1188:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       233: 1
       239: 1
       241: 1
       249: 1
       250: 1
       252: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       341: 1
       347: 1
       349: 1
       352: 1
       353: 1
       355: 1
       370: 1
       383: 1
       385: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: 1
       422: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       439: 1
       445: 1
       447: 1
       455: 1
       456: 1
       458: 1
       472: 1
       481: 1
       482: 1
       489: 1
       490: 1
       491: 1
       506: 1
       512: 1
       514: 1
       548: 1
       571: 1
       572: 1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       595: 1
       601: 1
       603: 1
       606: 1
       607: 1
       609: 1
       624: 1
       637: 1
       639: 1
       665: 1
       674: 1
       675: 1
       700: 1
       763: 1
       772: 1
       773: 1
       780: 1
       781: 1
       782: 1
       797: 1
       803: 1
       805: 1
       839: 1
       877: 1
       976: 1
       985: 1
       986: 1
      1011: 1
      1188: 1

1189:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^2+2q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: 2q^2+3q+1
        12: q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^2+2q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q^2+3q+1
        29: 2q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: q^3+3q^2+3q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q+1
       104: q+1
       105: 2q+1
       106: q+1
       110: q+1
       111: 1
       112: 2q+1
       113: q+1
       114: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 2q+1
       156: q+1
       157: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: q+1
       196: 1
       197: 1
       198: q+1
       199: 2q+1
       200: q+1
       204: q+1
       205: 1
       206: q+1
       208: q+1
       210: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       240: q+1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       258: q+1
       259: 2q+1
       260: q+1
       264: q+1
       265: 1
       266: 2q+1
       267: q+1
       268: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: 1
       290: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: q+1
       326: 1
       327: 1
       329: q+1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: 1
       396: q+1
       402: 1
       403: 1
       404: q+1
       405: 2q+1
       406: q+1
       410: q+1
       411: 1
       412: q+1
       414: q+1
       416: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       446: q+1
       447: 1
       448: 1
       450: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       492: 1
       493: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       516: 1
       517: 1
       525: 1
       527: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: q+1
       580: 1
       581: 1
       583: q+1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       657: 1
       676: 1
       677: 1
       685: 1
       696: 1
       703: 1
       732: 1
       755: 1
       764: 1
       765: 1
       773: 1
       783: 1
       784: 1
       790: 1
       791: 1
       793: 1
       800: 1
       802: 1
       804: 1
       807: 1
       808: 1
       816: 1
       818: 1
       834: 1
       835: 1
       836: 1
       840: 1
       850: 1
       878: 1
       968: 1
       987: 1
       988: 1
       996: 1
      1007: 1
      1014: 1
      1043: 1
      1189: 1

1190:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: q^2+3q+1
        26: q+1
        27: 2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+2q+1
        50: 2q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        57: 2q+1
        58: q+1
        59: 1
        60: 2q+1
        61: q+1
        62: q^2+3q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q^2+2q+1
        78: q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q^2+2q+1
        86: q+1
        87: 2q+1
        88: q+1
        89: q^2+3q+1
        90: q+1
        91: 2q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q+1
       104: q+1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: 2q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q^2+2q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 2q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: q+1
       162: 2q+1
       163: q+1
       164: 1
       165: 2q+1
       166: q+1
       167: q^2+3q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q^2+2q+1
       183: q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: 2q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q^2+2q+1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: q+1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       485: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: q+1
       658: 1
       676: 1
       677: 1
       678: 1
       684: 1
       688: 1
       704: 1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       776: 1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       807: 1
       808: 1
       809: 1
       815: 1
       834: 1
       879: 1
       969: 1
       987: 1
       988: 1
       989: 1
       995: 1
       999: 1
      1015: 1
      1190: 1

1191:    0: 4q^2+4q+1
         1: 4q^2+4q+1
         2: 3q^2+4q+1
         3: 4q^2+4q+1
         4: 3q^2+4q+1
         5: 4q^2+4q+1
         6: 3q^2+4q+1
         7: q^2+3q+1
         8: 3q^2+4q+1
         9: 4q^2+4q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: q^2+3q+1
        13: 3q^2+4q+1
        14: 2q^2+4q+1
        15: 3q^2+4q+1
        16: 4q^2+4q+1
        17: 3q^2+4q+1
        18: 4q^2+4q+1
        19: 3q^2+4q+1
        20: 3q^2+4q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q^2+2q+1
        24: 2q+1
        25: q^2+3q+1
        26: 2q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: 2q+1
        30: q^2+3q+1
        31: 3q+1
        32: 2q+1
        33: 2q^2+4q+1
        34: q^2+3q+1
        35: 2q^2+4q+1
        36: 3q^2+4q+1
        37: 2q+1
        38: q^2+2q+1
        39: q^2+3q+1
        40: 3q^2+4q+1
        41: q^2+3q+1
        42: 3q^2+4q+1
        43: 4q^2+4q+1
        44: q^2+3q+1
        45: 2q^2+3q+1
        46: q^2+3q+1
        47: 3q^2+4q+1
        48: 2q^2+4q+1
        49: 3q^2+4q+1
        50: q^2+2q+1
        51: 2q+1
        52: q^2+3q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+3q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 3q+1
        66: 2q+1
        67: 3q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q^2+4q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+3q+1
        82: 2q+1
        83: q+1
        84: 3q^2+4q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: q^2+2q+1
        88: 2q+1
        89: q^2+3q+1
        90: 2q+1
        91: q^2+3q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^2+3q+1
        95: 3q+1
        96: 2q+1
        97: 2q^2+4q+1
        98: q^2+3q+1
        99: 2q^2+4q+1
       100: 3q^2+4q+1
       101: 2q+1
       102: q^2+2q+1
       103: q^2+3q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       124: 3q+1
       125: 2q+1
       126: 2q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       134: q+1
       135: 2q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: 2q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+2q+1
       156: 2q+1
       157: q^2+3q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q^2+3q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 3q+1
       171: 2q+1
       172: 3q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q^2+4q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+3q+1
       187: 2q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       208: q+1
       210: 1
       213: 1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       248: 2q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: q+1
       266: q+1
       267: 2q+1
       268: 2q+1
       269: q+1
       270: 1
       271: q+1
       272: q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: q+1
       278: 3q+1
       279: 2q+1
       280: 2q+1
       281: 1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       288: q+1
       289: 2q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: 2q+1
       298: 1
       299: q+1
       300: q+1
       302: q+1
       303: 2q+1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       348: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       395: q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: q+1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: q+1
       414: q+1
       416: 1
       419: 1
       420: 2q+1
       421: 2q+1
       422: q+1
       423: 1
       424: q+1
       425: 1
       426: 2q+1
       427: q+1
       428: q+1
       429: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: q+1
       452: 1
       454: 2q+1
       457: 1
       458: q+1
       459: q+1
       461: q+1
       462: q+1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       543: 1
       550: 1
       551: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: q+1
       602: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: q+1
       640: 1
       641: q+1
       644: 1
       659: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       705: 1
       731: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       834: 1
       841: 1
       842: 1
       880: 1
       970: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
      1016: 1
      1042: 1
      1191: 1

1192:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+3q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: q^2+3q+1
        29: 2q+1
        30: q^2+3q+1
        31: 2q+1
        32: q^2+3q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: q^2+3q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        78: 1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 2q+1
        90: q+1
        91: q+1
        92: q^2+3q+1
        93: 2q+1
        94: q^2+3q+1
        95: 2q+1
        96: q^2+3q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q^2+2q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: 1
       145: 1
       146: q+1
       148: 1
       149: q+1
       151: 1
       152: 2q+1
       153: q+1
       154: q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: q^2+3q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       183: 1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: q+1
       207: q+1
       208: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       255: 1
       256: q+1
       258: q^2+2q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: q+1
       302: 1
       303: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: q+1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: q+1
       413: q+1
       414: 1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       507: 1
       518: 1
       519: 1
       520: 1
       535: 1
       543: 1
       551: 1
       552: 1
       557: 1
       565: 1
       566: 1
       567: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: q+1
       583: 1
       584: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       660: 1
       678: 1
       679: 1
       680: 1
       687: 1
       706: 1
       740: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: 1
       784: 1
       785: 1
       786: 1
       787: 1
       789: 1
       792: 1
       793: 1
       794: 1
       798: 1
       809: 1
       810: 1
       811: 1
       826: 1
       834: 1
       842: 1
       843: 1
       848: 1
       881: 1
       971: 1
       989: 1
       990: 1
       991: 1
       998: 1
      1017: 1
      1051: 1
      1192: 1

1193:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       380: 1
       381: 1
       386: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       468: 1
       475: 1
       478: 1
       479: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       518: 1
       521: 1
       522: 1
       543: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       634: 1
       635: 1
       640: 1
       661: 1
       678: 1
       681: 1
       682: 1
       707: 1
       759: 1
       766: 1
       769: 1
       770: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       809: 1
       812: 1
       813: 1
       834: 1
       882: 1
       972: 1
       989: 1
       992: 1
       993: 1
      1018: 1
      1193: 1

1194:    0: q^3+q^2+q+1
         1: q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q+1
         5: q^3+q^2+q+1
         6: q+1
         7: q+1
         8: q^3+q^2+q+1
         9: q+1
        10: q^2+1
        11: q^3+q^2+q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q^3+q^2+q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q^3+q^2+q+1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        28: q+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q^3+q^2+q+1
        43: q+1
        44: q^2+1
        45: q^3+q^2+q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: q^2+1
        61: 1
        62: 1
        63: 1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q^3+q^2+q+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: q+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: q^2+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: q^2+1
       166: 1
       167: 1
       168: 1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: q^2+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       373: 1
       380: 1
       386: 1
       387: 1
       390: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       469: 1
       476: 1
       478: 1
       480: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       519: 1
       521: 1
       523: 1
       550: 1
       551: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       627: 1
       634: 1
       640: 1
       641: 1
       644: 1
       662: 1
       679: 1
       681: 1
       683: 1
       708: 1
       760: 1
       767: 1
       769: 1
       771: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: 1
       810: 1
       812: 1
       814: 1
       841: 1
       842: 1
       883: 1
       973: 1
       990: 1
       992: 1
       994: 1
      1019: 1
      1194: 1

1195:    0: q^2+3q+1
         1: 2q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q+1
         7: 2q+1
         8: q^2+3q+1
         9: 2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+3q+1
        13: 2q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: 2q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+3q+1
        25: 1
        26: q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q+1
        34: 2q+1
        35: q^2+3q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: q^2+3q+1
        40: q+1
        41: 2q+1
        42: q^2+3q+1
        43: 2q+1
        44: 2q+1
        45: q^2+2q+1
        46: q^2+3q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q^2+2q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 2q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: q+1
        67: 2q+1
        68: q+1
        69: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: q^2+3q+1
        76: 1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+3q+1
        89: 1
        90: q+1
        91: 2q+1
        92: q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q+1
        98: 2q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q^2+3q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q^2+2q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: 1
       126: q+1
       127: 1
       128: 2q+1
       129: 1
       130: 1
       131: q+1
       132: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q^2+2q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 2q+1
       167: 1
       168: 1
       169: q+1
       170: 1
       171: q+1
       172: 2q+1
       173: q+1
       174: q+1
       175: q^2+2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q^2+3q+1
       181: 1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       207: 1
       208: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q^2+2q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: q+1
       273: 1
       274: 1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: 1
       280: q+1
       281: 1
       282: 2q+1
       283: 1
       284: 1
       285: q+1
       286: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       334: 1
       335: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       372: 1
       374: 1
       379: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       413: 1
       414: 1
       416: 1
       417: 1
       418: q+1
       420: 1
       421: 1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: q+1
       459: 1
       461: 1
       462: q+1
       470: 1
       477: 1
       479: 1
       480: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: 1
       507: 1
       508: 1
       520: 1
       522: 1
       523: 1
       542: 1
       550: 1
       552: 1
       557: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: 1
       588: 1
       589: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       626: 1
       628: 1
       633: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       663: 1
       680: 1
       682: 1
       683: 1
       693: 1
       709: 1
       747: 1
       761: 1
       768: 1
       770: 1
       771: 1
       781: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       794: 1
       798: 1
       799: 1
       811: 1
       813: 1
       814: 1
       833: 1
       841: 1
       843: 1
       848: 1
       884: 1
       974: 1
       991: 1
       993: 1
       994: 1
      1004: 1
      1020: 1
      1058: 1
      1195: 1

1196:    0: 2q^2+2q+1
         1: q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: q^2+2q+1
         5: 2q^2+2q+1
         6: q+1
         7: q+1
         8: 2q^2+2q+1
         9: q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: q+1
        26: 1
        27: 2q^2+2q+1
        28: q+1
        29: q^2+2q+1
        30: 1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q+1
        37: q^2+2q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 2q^2+2q+1
        43: q+1
        44: 2q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        57: q+1
        58: 1
        59: 1
        60: q^2+2q+1
        61: q+1
        62: q+1
        63: 1
        64: q^2+2q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: 1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: 1
        91: 2q^2+2q+1
        92: q+1
        93: q^2+2q+1
        94: 1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q^2+2q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       103: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: 1
       121: 1
       122: q^2+2q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: q+1
       146: q+1
       148: q+1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: 1
       169: q^2+2q+1
       170: 1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       183: q^2+2q+1
       184: q+1
       185: q+1
       186: 1
       187: q+1
       188: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: q+1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       242: 1
       243: q+1
       246: q+1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: 1
       275: 1
       276: q^2+2q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: q+1
       283: 1
       284: 1
       285: q+1
       286: 1
       287: q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: q+1
       300: q+1
       302: q+1
       303: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       331: 1
       332: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       414: 1
       415: 1
       416: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: q+1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       448: 1
       449: q+1
       452: q+1
       454: 1
       457: 1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       471: 1
       480: 1
       481: 1
       487: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       523: 1
       524: 1
       534: 1
       550: 1
       558: 1
       561: 1
       570: 1
       571: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q+1
       585: 1
       586: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       664: 1
       683: 1
       684: 1
       690: 1
       710: 1
       739: 1
       762: 1
       771: 1
       772: 1
       778: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       795: 1
       796: 1
       814: 1
       815: 1
       825: 1
       841: 1
       849: 1
       852: 1
       885: 1
       975: 1
       994: 1
       995: 1
      1001: 1
      1021: 1
      1050: 1
      1196: 1

1197:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       120: 2q+1
       121: q+1
       122: q+1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: q+1
       139: 1
       140: 1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       195: q+1
       196: 1
       197: 1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       209: q+1
       210: q+1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       232: q+1
       233: 1
       234: 1
       235: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       244: q+1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 2q+1
       263: q+1
       264: q+1
       265: 1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       274: 2q+1
       275: q+1
       276: q+1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       291: q+1
       292: q+1
       293: 1
       294: 1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: q+1
       326: 1
       327: 1
       332: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       362: 1
       363: 1
       364: 1
       369: q+1
       370: 1
       371: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       401: q+1
       402: 1
       403: 1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       415: q+1
       416: q+1
       422: 1
       423: 1
       424: 1
       425: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       438: q+1
       439: 1
       440: 1
       441: 1
       445: q+1
       446: q+1
       447: 1
       448: 1
       450: q+1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       498: 1
       499: 1
       500: 1
       505: 1
       512: 1
       513: 1
       524: 1
       525: 1
       532: 1
       547: 1
       548: 1
       549: 1
       559: 1
       571: 1
       572: 1
       579: q+1
       580: 1
       581: 1
       586: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       606: 1
       607: 1
       608: 1
       616: 1
       617: 1
       618: 1
       623: q+1
       624: 1
       625: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       665: 1
       684: 1
       685: 1
       699: 1
       711: 1
       737: 1
       763: 1
       772: 1
       773: 1
       789: 1
       790: 1
       791: 1
       796: 1
       803: 1
       804: 1
       815: 1
       816: 1
       823: 1
       838: 1
       839: 1
       840: 1
       850: 1
       886: 1
       976: 1
       995: 1
       996: 1
      1010: 1
      1022: 1
      1048: 1
      1197: 1

1198:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: q+1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: q+1
       122: q+1
       123: q+1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       161: q+1
       162: q+1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: q+1
       205: 1
       206: q+1
       207: q+1
       212: q+1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: q+1
       265: 1
       266: q+1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       277: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       328: q+1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       403: 1
       404: q+1
       411: 1
       412: q+1
       413: q+1
       418: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       543: 1
       563: 1
       573: 1
       581: 1
       582: q+1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       834: 1
       887: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1198: 1

1199:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: q+1
       186: q+1
       188: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: q+1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: q+1
       308: q+1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: q+1
       474: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: 1
       564: 1
       573: 1
       574: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       610: 1
       611: 1
       617: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       765: 1
       774: 1
       775: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       808: 1
       888: 1
       978: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1199: 1

1200:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: 2q+1
         8: q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: 2q+1
        22: 1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: 2q+1
        27: q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: 2q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+3q+1
        41: 2q+1
        42: q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: 2q+1
        59: 1
        60: q+1
        61: q+1
        62: q^2+3q+1
        63: 2q+1
        64: q+1
        65: q^2+3q+1
        66: 2q+1
        67: 1
        68: q^2+3q+1
        69: q^2+3q+1
        70: q+1
        71: 1
        72: 2q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: 2q+1
        86: 1
        87: q+1
        88: q+1
        89: q^2+3q+1
        90: 2q+1
        91: q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: q^2+3q+1
        98: 2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: 2q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: 2q+1
       126: 1
       127: 1
       128: 1
       129: q^2+3q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: q+1
       163: 2q+1
       164: 1
       165: q+1
       166: q+1
       167: q^2+3q+1
       168: 2q+1
       169: q+1
       170: q^2+3q+1
       171: 2q+1
       172: 1
       173: q^2+3q+1
       174: q^2+3q+1
       175: q+1
       176: 1
       177: 2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: 2q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: 2q+1
       280: 1
       281: 1
       282: 1
       283: q^2+3q+1
       284: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: q+1
       396: 1
       397: 1
       398: 1
       401: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       462: q+1
       463: q+1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       493: 1
       494: 1
       495: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: 1
       543: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: q+1
       668: 1
       678: 1
       687: 1
       688: 1
       689: 1
       692: 1
       695: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       784: 1
       785: 1
       786: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       806: 1
       809: 1
       834: 1
       889: 1
       979: 1
       989: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1006: 1
      1200: 1

1201:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: 1
         5: q+1
         6: q+1
         7: 1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: 1
        20: q+1
        21: 1
        22: 1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: 1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: q+1
        52: 1
        53: 1
        54: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: 1
        86: 1
        87: q+1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       144: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: 1
       158: 1
       159: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       243: 1
       246: 1
       248: 1
       251: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: q+1
       268: 1
       269: 1
       270: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 1
       360: 1
       373: 1
       380: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       454: 1
       457: 1
       459: 1
       461: 1
       462: 1
       463: 1
       476: 1
       485: 1
       487: 1
       494: 1
       496: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: 1
       551: 1
       558: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       591: 1
       593: 1
       594: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       612: 1
       614: 1
       627: 1
       634: 1
       641: 1
       644: 1
       646: 1
       648: 1
       669: 1
       679: 1
       688: 1
       690: 1
       748: 1
       767: 1
       776: 1
       778: 1
       785: 1
       787: 1
       793: 1
       795: 1
       796: 1
       800: 1
       810: 1
       842: 1
       849: 1
       852: 1
       890: 1
       980: 1
       990: 1
       999: 1
      1001: 1
      1059: 1
      1201: 1

1202:    0: q^2+3q+1
         1: 2q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: 2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: q^2+3q+1
        15: q^2+2q+1
        16: 2q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: q^2+3q+1
        30: 2q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+2q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: q^2+3q+1
        70: q^2+2q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: q^2+3q+1
        94: 2q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: 2q+1
        98: q+1
        99: q+1
       100: q+1
       101: q^2+2q+1
       102: q+1
       103: q^2+2q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: 2q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: q+1
       133: q^2+2q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: q^2+3q+1
       175: q^2+2q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q^2+2q+1
       188: q+1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       227: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: q+1
       253: q+1
       255: 1
       256: q+1
       257: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: 2q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: q+1
       283: 2q+1
       284: q+1
       285: q+1
       286: q+1
       287: q^2+2q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: q+1
       302: 1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: q+1
       359: 1
       360: 1
       362: 1
       374: 1
       379: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       398: 1
       399: 1
       401: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: q+1
       431: q+1
       433: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: q+1
       459: q+1
       461: 1
       462: q+1
       463: q+1
       477: 1
       486: 1
       487: 1
       489: 1
       495: 1
       496: 1
       498: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       510: 1
       515: 1
       520: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: q+1
       613: 1
       614: 1
       616: 1
       628: 1
       633: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       670: 1
       680: 1
       689: 1
       690: 1
       692: 1
       749: 1
       754: 1
       768: 1
       777: 1
       778: 1
       780: 1
       786: 1
       787: 1
       789: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       801: 1
       806: 1
       811: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       891: 1
       981: 1
       991: 1
      1000: 1
      1001: 1
      1003: 1
      1060: 1
      1065: 1
      1202: 1

1203:    0: q^3+q^2+q+1
         1: q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q+1
         5: q^3+q^2+q+1
         6: q+1
         7: q+1
         8: q^2+1
         9: q+1
        10: q^3+q^2+q+1
        11: q^3+q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q^3+q^2+q+1
        18: q^3+q^2+q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: q^2+1
        24: 1
        25: q+1
        26: q+1
        27: q^2+1
        28: q+1
        29: q^3+q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q^2+1
        43: q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: q^2+1
        61: 1
        62: q+1
        63: q+1
        64: q^2+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: q^2+1
        88: 1
        89: q+1
        90: q+1
        91: q^2+1
        92: q+1
        93: q^3+q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: q^2+1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: q^2+1
       166: 1
       167: q+1
       168: q+1
       169: q^2+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: q^2+1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       314: 1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       358: 1
       361: 1
       362: 1
       380: 1
       386: 1
       392: 1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       478: 1
       485: 1
       488: 1
       489: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       515: 1
       521: 1
       568: 1
       575: 1
       578: 1
       579: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       634: 1
       640: 1
       646: 1
       671: 1
       681: 1
       688: 1
       691: 1
       692: 1
       769: 1
       776: 1
       779: 1
       780: 1
       785: 1
       788: 1
       789: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       806: 1
       812: 1
       892: 1
       982: 1
       992: 1
       999: 1
      1002: 1
      1003: 1
      1203: 1

1204:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       315: 1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       479: 1
       486: 1
       488: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       569: 1
       576: 1
       578: 1
       584: 1
       585: 1
       587: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: 1
       615: 1
       635: 1
       672: 1
       682: 1
       689: 1
       691: 1
       770: 1
       777: 1
       779: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       813: 1
       893: 1
       983: 1
       993: 1
      1000: 1
      1002: 1
      1204: 1

1205:    0: q^3+3q^2+3q+1
         1: q^2+2q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q+1
         7: 2q+1
         8: 2q^2+3q+1
         9: q^2+2q+1
        10: 2q^2+3q+1
        11: q^3+3q^2+3q+1
        12: q^2+3q+1
        13: 2q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^2+2q+1
        17: 2q^2+3q+1
        18: q^3+3q^2+3q+1
        19: q^2+3q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q+1
        25: q+1
        26: 2q+1
        27: 2q^2+3q+1
        28: q^2+2q+1
        29: 2q^2+3q+1
        30: 2q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: q+1
        34: 2q+1
        35: q^2+3q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: q^2+3q+1
        40: q+1
        41: 2q+1
        42: 2q^2+3q+1
        43: q^2+2q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: q^2+3q+1
        47: 2q+1
        48: q^2+3q+1
        49: q^2+3q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: 2q+1
        60: q^2+2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: 2q^2+3q+1
        65: q+1
        66: 2q+1
        67: q^2+3q+1
        68: 2q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q^2+2q+1
        88: 2q+1
        89: q+1
        90: 2q+1
        91: 2q^2+3q+1
        92: q^2+2q+1
        93: 2q^2+3q+1
        94: 2q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: q+1
        98: 2q+1
        99: q^2+3q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q^2+3q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: q^2+2q+1
       123: 2q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: q^2+3q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: 2q+1
       165: q^2+2q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: 2q^2+3q+1
       170: q+1
       171: 2q+1
       172: q^2+3q+1
       173: 2q+1
       174: q^2+3q+1
       175: q^2+3q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: 1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: q+1
       257: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: 2q+1
       276: q^2+2q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: 2q+1
       281: q+1
       282: 2q+1
       283: q+1
       284: 2q+1
       285: q^2+3q+1
       286: 2q+1
       287: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: 1
       351: 1
       354: 1
       355: q+1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: 1
       433: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: q+1
       459: 1
       461: 1
       462: q+1
       463: 1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       496: 1
       497: 1
       498: 1
       499: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       523: 1
       550: 1
       558: 1
       561: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: 1
       605: 1
       608: 1
       609: q+1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       673: 1
       683: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       771: 1
       778: 1
       779: 1
       780: 1
       781: 1
       787: 1
       788: 1
       789: 1
       790: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       806: 1
       814: 1
       841: 1
       849: 1
       852: 1
       894: 1
       984: 1
       994: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1013: 1
      1205: 1

1206:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: 1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: q+1
        47: 1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: q+1
        70: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: q+1
       123: q+1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       163: 1
       164: 1
       165: q+1
       166: q+1
       167: 1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: q+1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       362: 1
       363: 1
       364: 1
       386: 1
       392: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       433: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       481: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       524: 1
       571: 1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       603: 1
       604: 1
       608: 1
       609: 1
       616: 1
       617: 1
       618: 1
       640: 1
       646: 1
       674: 1
       684: 1
       692: 1
       693: 1
       694: 1
       772: 1
       780: 1
       781: 1
       782: 1
       789: 1
       790: 1
       791: 1
       796: 1
       797: 1
       798: 1
       799: 1
       806: 1
       815: 1
       895: 1
       985: 1
       995: 1
      1003: 1
      1004: 1
      1005: 1
      1206: 1

1207:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: q+1
        24: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        54: q+1
        55: q+1
        56: q+1
        59: q+1
        60: q+1
        61: q+1
        63: q+1
        64: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: q+1
        87: q+1
        88: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: q+1
       111: 1
       116: q+1
       117: q+1
       118: q+1
       121: q+1
       122: q+1
       123: q+1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: q+1
       160: q+1
       161: q+1
       164: q+1
       165: q+1
       166: q+1
       168: q+1
       169: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: q+1
       205: 1
       210: q+1
       211: q+1
       212: q+1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       250: 1
       251: 1
       252: 1
       254: 1
       256: 1
       257: 1
       264: q+1
       265: 1
       270: q+1
       271: q+1
       272: q+1
       275: q+1
       276: q+1
       277: q+1
       280: 1
       281: 1
       282: 1
       284: q+1
       285: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       334: q+1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       363: 1
       364: 1
       371: 1
       384: 1
       385: 1
       386: 1
       393: 1
       402: 1
       403: 1
       410: q+1
       411: 1
       416: q+1
       417: q+1
       418: q+1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       456: 1
       457: 1
       458: 1
       460: 1
       462: 1
       463: 1
       482: 1
       490: 1
       491: 1
       499: 1
       500: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       525: 1
       549: 1
       572: 1
       580: 1
       581: 1
       588: q+1
       589: 1
       596: 1
       597: 1
       602: 1
       603: 1
       604: 1
       607: 1
       608: 1
       609: 1
       617: 1
       618: 1
       625: 1
       638: 1
       639: 1
       640: 1
       647: 1
       675: 1
       685: 1
       693: 1
       694: 1
       701: 1
       773: 1
       781: 1
       782: 1
       790: 1
       791: 1
       798: 1
       799: 1
       804: 1
       805: 1
       806: 1
       816: 1
       840: 1
       896: 1
       986: 1
       996: 1
      1004: 1
      1005: 1
      1012: 1
      1207: 1

1208:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        23: q+1
        24: 1
        25: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        56: 1
        57: q+1
        60: q+1
        61: 1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        74: q+1
        75: 1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       111: 1
       112: q+1
       113: 1
       118: 1
       119: q+1
       122: q+1
       123: 1
       124: q+1
       127: q+1
       128: 1
       129: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: 1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       179: q+1
       180: 1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       198: 1
       205: 1
       206: q+1
       207: 1
       212: 1
       213: q+1
       214: 1
       219: 1
       220: q+1
       223: q+1
       224: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       277: 1
       278: q+1
       281: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: q+1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       419: q+1
       420: 1
       425: 1
       426: q+1
       429: q+1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       483: 1
       492: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       526: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: q+1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       686: 1
       695: 1
       702: 1
       731: 1
       748: 1
       774: 1
       783: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       817: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       897: 1
       997: 1
      1006: 1
      1013: 1
      1042: 1
      1059: 1
      1208: 1

1209:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       440: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       484: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       527: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       590: 1
       591: 1
       592: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       611: 1
       619: 1
       620: 1
       621: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       687: 1
       695: 1
       696: 1
       697: 1
       701: 1
       732: 1
       775: 1
       784: 1
       792: 1
       793: 1
       794: 1
       798: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       818: 1
       834: 1
       835: 1
       836: 1
       840: 1
       850: 1
       898: 1
       998: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1043: 1
      1209: 1

1210:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       321: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       366: 1
       368: 1
       369: 1
       380: 1
       382: 1
       383: 1
       384: 1
       388: 1
       392: 1
       393: 1
       397: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       462: 1
       463: 1
       485: 1
       494: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       528: 1
       544: 1
       546: 1
       547: 1
       559: 1
       575: 1
       583: 1
       585: 1
       586: 1
       591: 1
       593: 1
       594: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       612: 1
       620: 1
       622: 1
       623: 1
       634: 1
       636: 1
       637: 1
       638: 1
       642: 1
       646: 1
       647: 1
       688: 1
       696: 1
       698: 1
       699: 1
       733: 1
       776: 1
       785: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       819: 1
       835: 1
       837: 1
       838: 1
       850: 1
       899: 1
       999: 1
      1007: 1
      1009: 1
      1010: 1
      1044: 1
      1210: 1

1211:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: q+1
        59: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       103: q+1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: q+1
       121: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       149: q+1
       150: q+1
       151: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: q+1
       164: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       186: q+1
       187: q+1
       192: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: q+1
       275: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: q+1
       297: 1
       299: 1
       303: q+1
       304: q+1
       305: 1
       322: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       359: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       398: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       486: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       529: 1
       545: 1
       546: 1
       548: 1
       576: 1
       584: 1
       585: 1
       587: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       613: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       637: 1
       639: 1
       689: 1
       697: 1
       698: 1
       700: 1
       734: 1
       777: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       820: 1
       836: 1
       837: 1
       839: 1
       900: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1045: 1
      1211: 1

1212:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q^2+2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: q^2+2q+1
        44: 2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        57: q+1
        58: q+1
        59: 2q+1
        60: q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       107: 1
       108: 1
       114: q+1
       115: 1
       116: q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       157: q+1
       158: 1
       159: q+1
       162: q+1
       163: q+1
       164: 2q+1
       165: q+1
       167: q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       193: 1
       201: 1
       202: 1
       208: q+1
       209: 1
       210: q+1
       215: q+1
       216: 1
       217: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       261: 1
       262: 1
       268: q+1
       269: 1
       270: q+1
       273: q+1
       274: q+1
       275: 2q+1
       276: q+1
       278: q+1
       279: q+1
       280: 2q+1
       281: q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       323: 1
       331: 1
       332: 1
       339: 1
       340: 1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       360: 1
       368: 1
       369: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 1
       407: 1
       408: 1
       414: q+1
       415: 1
       416: q+1
       421: q+1
       422: 1
       423: q+1
       426: q+1
       427: q+1
       428: 2q+1
       429: q+1
       431: 1
       432: q+1
       433: q+1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: q+1
       457: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       487: 1
       496: 1
       504: 1
       505: 1
       511: 1
       512: 1
       513: 1
       530: 1
       546: 1
       547: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       577: 1
       585: 1
       586: 1
       593: 1
       594: 1
       600: q+1
       601: 1
       602: q+1
       605: 1
       606: 1
       607: q+1
       608: 1
       614: 1
       622: 1
       623: 1
       629: 1
       631: 1
       636: 1
       637: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       690: 1
       698: 1
       699: 1
       735: 1
       750: 1
       752: 1
       778: 1
       787: 1
       795: 1
       796: 1
       802: 1
       803: 1
       804: 1
       821: 1
       837: 1
       838: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       901: 1
      1001: 1
      1009: 1
      1010: 1
      1046: 1
      1061: 1
      1063: 1
      1212: 1

1213:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       194: 1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       324: 1
       331: 1
       333: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       361: 1
       368: 1
       370: 1
       382: 1
       383: 1
       385: 1
       400: 1
       407: 1
       409: 1
       414: 1
       415: 1
       417: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       488: 1
       497: 1
       504: 1
       506: 1
       511: 1
       512: 1
       514: 1
       531: 1
       546: 1
       548: 1
       578: 1
       585: 1
       587: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       615: 1
       622: 1
       624: 1
       636: 1
       637: 1
       639: 1
       691: 1
       698: 1
       700: 1
       736: 1
       779: 1
       788: 1
       795: 1
       797: 1
       802: 1
       803: 1
       805: 1
       822: 1
       837: 1
       839: 1
       902: 1
      1002: 1
      1009: 1
      1011: 1
      1047: 1
      1213: 1

1214:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       325: 1
       332: 1
       333: 1
       334: 1
       340: 1
       341: 1
       342: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       362: 1
       369: 1
       370: 1
       371: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       401: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       438: 1
       439: 1
       440: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       489: 1
       498: 1
       505: 1
       506: 1
       507: 1
       512: 1
       513: 1
       514: 1
       515: 1
       532: 1
       547: 1
       548: 1
       549: 1
       559: 1
       579: 1
       586: 1
       587: 1
       588: 1
       594: 1
       595: 1
       596: 1
       601: 1
       602: 1
       603: 1
       604: 1
       606: 1
       607: 1
       608: 1
       609: 1
       616: 1
       623: 1
       624: 1
       625: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       692: 1
       699: 1
       700: 1
       701: 1
       737: 1
       780: 1
       789: 1
       796: 1
       797: 1
       798: 1
       803: 1
       804: 1
       805: 1
       806: 1
       823: 1
       838: 1
       839: 1
       840: 1
       850: 1
       903: 1
      1003: 1
      1010: 1
      1011: 1
      1012: 1
      1048: 1
      1214: 1

1215:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q+1
        22: q+1
        23: q+1
        24: 1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        54: q+1
        55: 1
        56: 1
        59: q+1
        60: q+1
        61: 1
        63: q+1
        64: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        73: q+1
        74: q+1
        75: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        86: q+1
        87: q+1
        88: 1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       110: 1
       111: 1
       116: q+1
       117: 1
       118: 1
       121: q+1
       122: q+1
       123: 1
       126: q+1
       127: q+1
       128: 1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       138: q+1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       159: q+1
       160: 1
       161: 1
       164: q+1
       165: q+1
       166: 1
       168: q+1
       169: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       178: q+1
       179: q+1
       180: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       196: 1
       204: 1
       205: 1
       210: q+1
       211: 1
       212: 1
       217: q+1
       218: 1
       219: 1
       222: q+1
       223: q+1
       224: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       264: 1
       265: 1
       270: q+1
       271: 1
       272: 1
       275: q+1
       276: q+1
       277: 1
       280: q+1
       281: q+1
       282: 1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       292: q+1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       326: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: q+1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       363: 1
       371: 1
       372: 1
       377: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       402: 1
       410: 1
       411: 1
       416: q+1
       417: 1
       418: 1
       423: q+1
       424: 1
       425: 1
       428: q+1
       429: q+1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       456: 1
       457: 1
       458: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       490: 1
       499: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       533: 1
       549: 1
       550: 1
       555: 1
       560: 1
       561: 1
       580: 1
       588: 1
       589: 1
       596: 1
       597: 1
       602: q+1
       603: 1
       604: 1
       607: 1
       608: 1
       609: 1
       617: 1
       625: 1
       626: 1
       631: 1
       638: 1
       639: 1
       640: 1
       643: 1
       644: 1
       647: 1
       648: 1
       693: 1
       701: 1
       702: 1
       738: 1
       752: 1
       781: 1
       790: 1
       798: 1
       799: 1
       804: 1
       805: 1
       806: 1
       824: 1
       840: 1
       841: 1
       846: 1
       851: 1
       852: 1
       904: 1
      1004: 1
      1012: 1
      1013: 1
      1049: 1
      1063: 1
      1215: 1

1216:    0: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         8: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        14: 1
        15: 1
        17: q^2+1
        18: q^2+1
        19: 1
        23: q^2+1
        24: 1
        27: q^2+1
        29: q^2+1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        48: 1
        49: 1
        56: 1
        60: q^2+1
        61: 1
        64: q^2+1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: q^2+1
        88: 1
        91: q^2+1
        93: q^2+1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       111: 1
       118: 1
       122: q^2+1
       123: 1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       161: 1
       165: q^2+1
       166: 1
       169: q^2+1
       172: 1
       174: 1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       197: 1
       205: 1
       212: 1
       219: 1
       223: 1
       224: 1
       227: 1
       235: 1
       242: 1
       246: 1
       251: 1
       252: 1
       255: 1
       257: 1
       265: 1
       272: 1
       276: q^2+1
       277: 1
       281: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       327: 1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       364: 1
       372: 1
       386: 1
       390: 1
       394: 1
       403: 1
       411: 1
       418: 1
       425: 1
       429: 1
       430: 1
       433: 1
       441: 1
       448: 1
       452: 1
       457: 1
       458: 1
       461: 1
       463: 1
       491: 1
       500: 1
       508: 1
       515: 1
       534: 1
       550: 1
       561: 1
       581: 1
       589: 1
       597: 1
       604: 1
       608: 1
       609: 1
       618: 1
       626: 1
       640: 1
       644: 1
       648: 1
       694: 1
       702: 1
       739: 1
       782: 1
       791: 1
       799: 1
       806: 1
       825: 1
       841: 1
       852: 1
       905: 1
      1005: 1
      1013: 1
      1050: 1
      1216: 1

1217:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: 1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: 1
        16: q^2+q+1
        17: q^2+q+1
        18: 1
        19: q^2+q+1
        20: 1
        21: q^2+q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q^2+q+1
        34: q^2+q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+q+1
        41: q^2+q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q^2+q+1
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: q^2+q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q^2+q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       125: 1
       129: 1
       130: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q^2+q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       221: 1
       225: 1
       226: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       253: 1
       254: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       320: 1
       321: 1
       322: 1
       325: 1
       352: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       388: 1
       392: 1
       393: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       464: 1
       465: 1
       472: 1
       475: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       532: 1
       559: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       579: 1
       606: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       642: 1
       646: 1
       647: 1
       649: 1
       703: 1
       704: 1
       711: 1
       714: 1
       755: 1
       756: 1
       763: 1
       766: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       823: 1
       850: 1
       906: 1
       960: 1
      1014: 1
      1015: 1
      1022: 1
      1025: 1
      1217: 1

1218:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       214: 1
       220: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       351: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       381: 1
       387: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       420: 1
       426: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       471: 1
       473: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       558: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       605: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       646: 1
       648: 1
       650: 1
       704: 1
       705: 1
       710: 1
       712: 1
       756: 1
       757: 1
       762: 1
       764: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       849: 1
       907: 1
       961: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1218: 1

1219:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       328: 1
       335: 1
       345: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       381: 1
       387: 1
       391: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       466: 1
       467: 1
       470: 1
       483: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       552: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       599: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       651: 1
       705: 1
       706: 1
       709: 1
       722: 1
       757: 1
       758: 1
       761: 1
       774: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       843: 1
       908: 1
       962: 1
      1016: 1
      1017: 1
      1020: 1
      1033: 1
      1219: 1

1220:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       205: 1
       206: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       336: 1
       343: 1
       344: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       466: 1
       468: 1
       469: 1
       492: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       543: 1
       550: 1
       551: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       590: 1
       597: 1
       598: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       652: 1
       705: 1
       707: 1
       708: 1
       731: 1
       757: 1
       759: 1
       760: 1
       783: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       834: 1
       841: 1
       842: 1
       909: 1
       963: 1
      1016: 1
      1018: 1
      1019: 1
      1042: 1
      1220: 1

1221:    0: q^3+3q^2+3q+1
         1: q^2+2q+1
         2: q^3+3q^2+3q+1
         3: q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+3q+1
         9: 2q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: q^2+2q+1
        14: q^3+3q^2+3q+1
        15: q^2+3q+1
        16: q^2+2q+1
        17: q^3+3q^2+3q+1
        18: q^2+3q+1
        19: q^3+3q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+3q+1
        36: 2q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+3q+1
        43: 2q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+2q+1
        48: q^3+3q^2+3q+1
        49: q^2+3q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: q^2+3q+1
        57: 1
        60: 2q+1
        61: 2q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: q^2+3q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: q^2+3q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+3q+1
       100: 2q+1
       101: 2q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: 1
       113: 1
       118: 2q+1
       119: 1
       122: q+1
       123: q+1
       124: 1
       127: q+1
       128: q+1
       129: q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: q^2+3q+1
       141: 1
       144: 2q+1
       145: 2q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: q^2+3q+1
       162: 1
       165: 2q+1
       166: 2q+1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q^2+3q+1
       180: q^2+3q+1
       181: q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: q^2+3q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 1
       205: 1
       206: 1
       207: 1
       212: q+1
       213: 1
       214: 1
       219: q+1
       220: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       242: 2q+1
       243: 1
       246: q+1
       247: q+1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: 1
       267: 1
       272: 2q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: q+1
       282: q+1
       283: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: q^2+3q+1
       295: 1
       298: 2q+1
       299: 2q+1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: 1
       372: 1
       373: 1
       374: 1
       379: q+1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: 1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: q+1
       426: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       448: 2q+1
       449: 1
       452: q+1
       453: q+1
       454: 1
       457: q+1
       458: q+1
       459: q+1
       461: 1
       462: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       501: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: q+1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: 1
       645: 1
       653: 1
       706: 1
       707: 1
       708: 1
       709: 1
       740: 1
       747: 1
       758: 1
       759: 1
       760: 1
       761: 1
       792: 1
       799: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       910: 1
       964: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1051: 1
      1058: 1
      1221: 1

1222:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: 1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: 1
        25: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: 1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: q+1
        61: 1
        62: 1
        64: q+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: 1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q+1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       118: 1
       119: 1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: q+1
       145: 1
       146: 1
       148: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: q+1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       205: 1
       206: 1
       213: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       243: 1
       246: q+1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       272: 1
       273: 1
       276: q+1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       327: 1
       343: 1
       344: 1
       351: 1
       354: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       373: 1
       380: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       412: 1
       419: 1
       425: 1
       426: 1
       429: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       449: 1
       452: q+1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       469: 1
       471: 1
       500: 1
       509: 1
       519: 1
       521: 1
       523: 1
       524: 1
       534: 1
       550: 1
       551: 1
       558: 1
       561: 1
       566: 1
       568: 1
       570: 1
       571: 1
       581: 1
       597: 1
       598: 1
       605: 1
       608: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       627: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       654: 1
       708: 1
       710: 1
       739: 1
       748: 1
       760: 1
       762: 1
       791: 1
       800: 1
       810: 1
       812: 1
       814: 1
       815: 1
       825: 1
       841: 1
       842: 1
       849: 1
       852: 1
       911: 1
       965: 1
      1019: 1
      1021: 1
      1050: 1
      1059: 1
      1222: 1

1223:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: 1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: q+1
        25: 1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: q+1
        32: 1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: 1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: q+1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       128: q+1
       129: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: q+1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       205: 1
       207: 1
       212: 1
       214: 1
       220: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: q+1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       317: 1
       327: 1
       335: 1
       345: 1
       351: 1
       355: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       374: 1
       379: 1
       381: 1
       387: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       470: 1
       471: 1
       491: 1
       510: 1
       520: 1
       522: 1
       523: 1
       524: 1
       534: 1
       542: 1
       552: 1
       558: 1
       562: 1
       567: 1
       569: 1
       570: 1
       571: 1
       581: 1
       589: 1
       599: 1
       605: 1
       609: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       655: 1
       709: 1
       710: 1
       730: 1
       749: 1
       761: 1
       762: 1
       782: 1
       801: 1
       811: 1
       813: 1
       814: 1
       815: 1
       825: 1
       833: 1
       843: 1
       849: 1
       853: 1
       912: 1
       966: 1
      1020: 1
      1021: 1
      1041: 1
      1060: 1
      1223: 1

1224:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       346: 1
       351: 1
       352: 1
       353: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       416: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       471: 1
       472: 1
       480: 1
       482: 1
       511: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       553: 1
       558: 1
       559: 1
       560: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       600: 1
       605: 1
       606: 1
       607: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       631: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       656: 1
       710: 1
       711: 1
       719: 1
       721: 1
       750: 1
       762: 1
       763: 1
       771: 1
       773: 1
       802: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       844: 1
       849: 1
       850: 1
       851: 1
       913: 1
       967: 1
      1021: 1
      1022: 1
      1030: 1
      1032: 1
      1061: 1
      1224: 1

1225:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: 1
        51: 1
        52: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: 1
       157: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       329: 1
       338: 1
       346: 1
       351: 1
       352: 1
       353: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       511: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: 1
       533: 1
       534: 1
       536: 1
       545: 1
       553: 1
       558: 1
       559: 1
       560: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: 1
       580: 1
       581: 1
       583: 1
       592: 1
       600: 1
       605: 1
       606: 1
       607: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       657: 1
       703: 1
       712: 1
       713: 1
       721: 1
       750: 1
       755: 1
       764: 1
       765: 1
       773: 1
       802: 1
       807: 1
       808: 1
       816: 1
       817: 1
       818: 1
       824: 1
       825: 1
       827: 1
       836: 1
       844: 1
       849: 1
       850: 1
       851: 1
       914: 1
       968: 1
      1014: 1
      1023: 1
      1024: 1
      1032: 1
      1061: 1
      1225: 1

1226:    0: 6q^2+5q+1
         1: 6q^2+5q+1
         2: 6q^2+5q+1
         3: 4q^2+5q+1
         4: 6q^2+5q+1
         5: 6q^2+5q+1
         6: 6q^2+5q+1
         7: 3q^2+4q+1
         8: q^2+4q+1
         9: 4q^2+5q+1
        10: 4q^2+5q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 6q^2+5q+1
        14: 6q^2+5q+1
        15: 4q^2+5q+1
        16: 6q^2+5q+1
        17: 6q^2+5q+1
        18: 4q^2+5q+1
        19: 6q^2+5q+1
        20: q^2+4q+1
        21: 3q^2+4q+1
        22: 3q+1
        23: 2q+1
        24: 2q+1
        25: 4q^2+5q+1
        26: q^2+2q+1
        27: q^2+4q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: 2q+1
        33: 6q^2+5q+1
        34: 3q^2+4q+1
        35: q^2+4q+1
        36: 4q^2+5q+1
        37: 4q^2+5q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: 6q^2+5q+1
        41: 3q^2+4q+1
        42: q^2+4q+1
        43: 4q^2+5q+1
        44: 4q^2+5q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 6q^2+5q+1
        48: 6q^2+5q+1
        49: 4q^2+5q+1
        50: 2q+1
        51: 2q+1
        52: 3q+1
        53: 3q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+4q+1
        58: q^2+2q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+1
        63: q+1
        64: q+1
        65: q^2+3q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q^2+4q+1
        72: 3q^2+4q+1
        73: 3q+1
        74: 2q+1
        75: 2q+1
        76: 4q^2+5q+1
        77: q^2+2q+1
        78: q^2+4q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: 2q+1
        84: q^2+4q+1
        85: 3q^2+4q+1
        86: 3q+1
        87: 2q+1
        88: 2q+1
        89: 4q^2+5q+1
        90: q^2+2q+1
        91: q^2+4q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q+1
        97: 6q^2+5q+1
        98: 3q^2+4q+1
        99: q^2+4q+1
       100: 4q^2+5q+1
       101: 4q^2+5q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: q+1
       106: q+1
       107: 3q+1
       108: q+1
       109: q+1
       110: 1
       111: 1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       124: q+1
       125: q+1
       126: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 3q+1
       137: 3q+1
       138: q+1
       139: q+1
       140: q+1
       141: q^2+4q+1
       142: q^2+2q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: q^2+3q+1
       147: q+1
       148: q+1
       149: q^2+3q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 3q+1
       158: 3q+1
       159: q+1
       160: q+1
       161: q+1
       162: q^2+4q+1
       163: q^2+2q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: q+1
       170: q^2+3q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q^2+4q+1
       177: 3q^2+4q+1
       178: 3q+1
       179: 2q+1
       180: 2q+1
       181: 4q^2+5q+1
       182: q^2+2q+1
       183: q^2+4q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: 2q+1
       189: 1
       190: 1
       191: q+1
       192: q+1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 3q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       248: q+1
       249: q+1
       250: 1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 3q+1
       262: q+1
       263: q+1
       264: 1
       265: 1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       278: q+1
       279: q+1
       280: 1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       290: 3q+1
       291: 3q+1
       292: q+1
       293: q+1
       294: q+1
       295: q^2+4q+1
       296: q^2+2q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: q^2+3q+1
       301: q+1
       302: q+1
       303: q^2+3q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       356: 1
       357: 1
       358: q+1
       359: q+1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       392: q+1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: q+1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 3q+1
       438: q+1
       439: q+1
       440: 1
       441: 1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       454: q+1
       455: q+1
       456: 1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       485: 1
       495: 1
       504: 1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       545: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       592: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       610: 1
       611: 1
       612: q+1
       613: q+1
       616: 1
       617: 1
       618: 1
       619: q+1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       646: q+1
       648: 1
       658: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       724: 1
       734: 1
       743: 1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       776: 1
       786: 1
       795: 1
       807: 1
       808: 1
       809: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       915: 1
       969: 1
      1015: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1035: 1
      1045: 1
      1054: 1
      1226: 1

1227:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^2+3q+1
        50: q+1
        51: q+1
        52: q^2+3q+1
        53: q+1
        54: q+1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+1
       135: q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       338: 1
       346: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       545: 1
       553: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       592: 1
       600: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       659: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       836: 1
       844: 1
       916: 1
       970: 1
      1016: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1227: 1

1228:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: q+1
        69: 1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: q+1
       153: 1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       221: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       334: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       388: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       541: 1
       565: 1
       566: 1
       567: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       588: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       660: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: 1
       809: 1
       810: 1
       811: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       832: 1
       917: 1
       971: 1
      1017: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1228: 1

1229:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: q+1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       336: 1
       337: 1
       338: 1
       342: 1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       396: q+1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       427: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       468: 1
       475: 1
       478: 1
       479: 1
       493: 1
       518: 1
       521: 1
       522: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       549: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       590: 1
       591: 1
       592: 1
       596: 1
       611: q+1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       661: 1
       707: 1
       714: 1
       717: 1
       718: 1
       732: 1
       759: 1
       766: 1
       769: 1
       770: 1
       784: 1
       809: 1
       812: 1
       813: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       840: 1
       918: 1
       972: 1
      1018: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1229: 1

1230:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: 2q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q+1
        11: q^2+3q+1
        12: q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: 2q+1
        21: 2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: q^2+3q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: 2q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q+1
        38: q^2+3q+1
        39: q+1
        40: 2q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q+1
        45: q^2+3q+1
        46: q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^2+3q+1
        50: 2q+1
        52: 2q+1
        53: 1
        54: q^2+3q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 2q+1
        72: 2q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: q^2+3q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: q^2+3q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: q+1
       102: q^2+3q+1
       103: q+1
       105: 2q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 2q+1
       136: 2q+1
       137: 1
       138: q^2+3q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 2q+1
       157: 2q+1
       158: 1
       159: q^2+3q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 2q+1
       177: 2q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: q^2+3q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: q+1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: 2q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: 1
       244: 1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       259: 2q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: 2q+1
       290: 2q+1
       291: 1
       292: q^2+3q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: q+1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: q+1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       435: 2q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       469: 1
       476: 1
       478: 1
       480: 1
       499: 1
       502: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       544: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: q+1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       662: 1
       708: 1
       715: 1
       717: 1
       719: 1
       738: 1
       741: 1
       760: 1
       767: 1
       769: 1
       771: 1
       790: 1
       793: 1
       810: 1
       812: 1
       814: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       835: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       919: 1
       973: 1
      1019: 1
      1026: 1
      1028: 1
      1030: 1
      1049: 1
      1052: 1
      1230: 1

1231:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: 2q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q+1
        11: q+1
        12: q^2+3q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: 2q+1
        21: 2q+1
        22: q^2+3q+1
        23: q+1
        24: q^2+3q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q^2+3q+1
        31: q+1
        32: q+1
        33: 2q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q+1
        38: q+1
        39: q^2+3q+1
        40: 2q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q+1
        45: q+1
        46: q^2+3q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^2+3q+1
        51: 2q+1
        52: 2q+1
        53: 1
        54: q+1
        55: q^2+3q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: q+1
        69: 1
        70: q+1
        71: 2q+1
        72: 2q+1
        73: q^2+3q+1
        74: q+1
        75: q^2+3q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q^2+3q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: 2q+1
        86: q^2+3q+1
        87: q+1
        88: q^2+3q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q^2+3q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: q+1
       102: q+1
       103: q^2+3q+1
       106: 2q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: 2q+1
       136: 2q+1
       137: 1
       138: q+1
       139: q^2+3q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       156: 2q+1
       157: 2q+1
       158: 1
       159: q+1
       160: q^2+3q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: 2q+1
       177: 2q+1
       178: q^2+3q+1
       179: q+1
       180: q^2+3q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q^2+3q+1
       187: q+1
       188: q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 2q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       260: 2q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       289: 2q+1
       290: 2q+1
       291: 1
       292: q+1
       293: q^2+3q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: q+1
       387: 1
       388: 1
       389: 1
       391: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       436: 2q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       470: 1
       477: 1
       479: 1
       480: 1
       490: 1
       503: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       663: 1
       709: 1
       716: 1
       718: 1
       719: 1
       729: 1
       742: 1
       761: 1
       768: 1
       770: 1
       771: 1
       781: 1
       794: 1
       811: 1
       813: 1
       814: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       920: 1
       974: 1
      1020: 1
      1027: 1
      1029: 1
      1030: 1
      1040: 1
      1053: 1
      1231: 1

1232:    0: q^2+3q+1
         1: 3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: 3q+1
         7: 3q+1
         8: q^2+3q+1
         9: 3q+1
        10: q^2+3q+1
        11: q+1
        12: q+1
        13: 3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: 3q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: 3q+1
        21: 3q+1
        22: 3q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: q+1
        27: q^2+3q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: 1
        33: 3q+1
        34: 3q+1
        35: q^2+3q+1
        36: 3q+1
        37: q^2+3q+1
        38: q+1
        39: q+1
        40: 3q+1
        41: 3q+1
        42: q^2+3q+1
        43: 3q+1
        44: q^2+3q+1
        45: q+1
        46: q+1
        47: 3q+1
        48: q^2+3q+1
        49: q^2+3q+1
        52: 3q+1
        53: 3q+1
        54: q+1
        55: q+1
        56: 1
        57: 3q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: 3q+1
        72: 3q+1
        73: 3q+1
        74: q+1
        75: q+1
        76: 3q+1
        77: q+1
        78: q^2+3q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: 1
        84: 3q+1
        85: 3q+1
        86: 3q+1
        87: q+1
        88: q+1
        89: 3q+1
        90: q+1
        91: q^2+3q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: 1
        97: 3q+1
        98: 3q+1
        99: q^2+3q+1
       100: 3q+1
       101: q^2+3q+1
       102: q+1
       103: q+1
       107: 3q+1
       108: q+1
       109: q+1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 3q+1
       137: 3q+1
       138: q+1
       139: q+1
       140: 1
       141: 3q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 3q+1
       158: 3q+1
       159: q+1
       160: q+1
       161: 1
       162: 3q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: 3q+1
       177: 3q+1
       178: 3q+1
       179: q+1
       180: q+1
       181: 3q+1
       182: q+1
       183: q^2+3q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: 1
       193: q+1
       194: q+1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       231: 3q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 3q+1
       262: q+1
       263: q+1
       264: 1
       265: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 3q+1
       291: 3q+1
       292: q+1
       293: q+1
       294: 1
       295: 3q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       360: q+1
       361: q+1
       362: 1
       363: 1
       364: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       394: 1
       399: q+1
       400: q+1
       401: 1
       402: 1
       403: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       433: 1
       437: 3q+1
       438: q+1
       439: q+1
       440: 1
       441: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: 1
       480: 1
       481: 1
       487: 1
       497: 1
       504: 1
       523: 1
       524: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       570: 1
       571: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       614: q+1
       615: q+1
       616: 1
       617: 1
       618: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       648: 1
       664: 1
       710: 1
       719: 1
       720: 1
       726: 1
       736: 1
       743: 1
       762: 1
       771: 1
       772: 1
       778: 1
       788: 1
       795: 1
       814: 1
       815: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       921: 1
       975: 1
      1021: 1
      1030: 1
      1031: 1
      1037: 1
      1047: 1
      1054: 1
      1232: 1

1233:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: 1
       118: 1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: 1
       139: 1
       140: 1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: q+1
       159: 1
       160: 1
       161: 1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       218: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: q+1
       240: 1
       241: 1
       242: 1
       244: 1
       245: 1
       246: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: q+1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       292: 1
       293: 1
       294: 1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: 1
       341: 1
       347: 1
       352: 1
       353: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       383: 1
       385: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       422: 1
       424: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       438: 1
       439: 1
       440: 1
       441: 1
       445: q+1
       446: 1
       447: 1
       448: 1
       450: 1
       451: 1
       452: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       512: 1
       524: 1
       525: 1
       532: 1
       533: 1
       534: 1
       539: 1
       548: 1
       554: 1
       559: 1
       560: 1
       571: 1
       572: 1
       579: 1
       580: 1
       581: 1
       586: 1
       595: 1
       601: 1
       606: 1
       607: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       637: 1
       639: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       665: 1
       711: 1
       720: 1
       721: 1
       751: 1
       763: 1
       772: 1
       773: 1
       803: 1
       815: 1
       816: 1
       823: 1
       824: 1
       825: 1
       830: 1
       839: 1
       845: 1
       850: 1
       851: 1
       922: 1
       976: 1
      1022: 1
      1031: 1
      1032: 1
      1062: 1
      1233: 1

1234:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: 1
        24: q+1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        56: 1
        57: q+1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       104: 1
       111: 1
       112: 1
       113: q+1
       118: 1
       119: 1
       122: 1
       123: 1
       124: q+1
       128: q+1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: q+1
       220: 1
       224: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: 1
       246: 1
       247: 1
       248: q+1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       267: q+1
       272: 1
       273: 1
       276: 1
       277: 1
       278: q+1
       282: q+1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       328: 1
       335: 1
       345: 1
       351: 1
       355: 1
       356: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       381: q+1
       387: 1
       391: 1
       392: 1
       394: 1
       395: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: q+1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: 1
       452: 1
       453: 1
       454: q+1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       473: 1
       483: 1
       491: 1
       510: 1
       516: 1
       526: 1
       534: 1
       535: 1
       542: 1
       552: 1
       558: 1
       562: 1
       563: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: q+1
       641: 1
       645: 1
       646: 1
       648: 1
       666: 1
       712: 1
       722: 1
       730: 1
       749: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       923: 1
       977: 1
      1023: 1
      1033: 1
      1041: 1
      1060: 1
      1234: 1

1235:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: 1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: 1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: 1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: 1
        51: q+1
        52: q+1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q^2+2q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: 1
       102: q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: q+1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: 1
       135: q+1
       136: q+1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       159: 1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       228: 1
       229: 1
       230: q+1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: 1
       259: 1
       260: q+1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: 1
       289: q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       434: 1
       435: 1
       436: q+1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       474: 1
       483: 1
       484: 1
       490: 1
       503: 1
       517: 1
       526: 1
       527: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       564: 1
       573: 1
       574: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       610: 1
       611: 1
       617: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       667: 1
       713: 1
       722: 1
       723: 1
       729: 1
       742: 1
       765: 1
       774: 1
       775: 1
       781: 1
       794: 1
       808: 1
       817: 1
       818: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       924: 1
       978: 1
      1024: 1
      1033: 1
      1034: 1
      1040: 1
      1053: 1
      1235: 1

1236:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q^2+2q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        68: q+1
        69: q+1
        71: 1
        72: q^2+2q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       129: q+1
       130: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       152: q+1
       153: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       249: q+1
       253: q+1
       254: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       306: q+1
       307: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       388: q+1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       455: q+1
       459: q+1
       460: q+1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: q+1
       668: 1
       714: 1
       723: 1
       724: 1
       725: 1
       728: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       809: 1
       818: 1
       819: 1
       820: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       925: 1
       979: 1
      1025: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1236: 1

1237:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       312: 1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       476: 1
       485: 1
       487: 1
       519: 1
       528: 1
       530: 1
       536: 1
       538: 1
       539: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       669: 1
       715: 1
       724: 1
       726: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       829: 1
       830: 1
       926: 1
       980: 1
      1026: 1
      1035: 1
      1037: 1
      1237: 1

1238:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       388: 1
       398: 1
       399: 1
       401: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       477: 1
       486: 1
       487: 1
       489: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       613: 1
       614: 1
       616: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       670: 1
       716: 1
       725: 1
       726: 1
       728: 1
       768: 1
       777: 1
       778: 1
       780: 1
       811: 1
       820: 1
       821: 1
       823: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       927: 1
       981: 1
      1027: 1
      1036: 1
      1037: 1
      1039: 1
      1238: 1

1239:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: 2q+1
         9: q^2+3q+1
        10: q^2+2q+1
        11: q^2+3q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: q^2+3q+1
        29: q^2+2q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+2q+1
        38: q^2+3q+1
        39: 2q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: q^2+3q+1
        44: q^2+2q+1
        45: q^2+3q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q^2+2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: q+1
        77: q^2+2q+1
        78: q+1
        79: q^2+3q+1
        80: q^2+2q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+3q+1
        93: q^2+2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: q^2+3q+1
       101: q^2+2q+1
       102: q^2+3q+1
       103: 2q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       151: 1
       152: 2q+1
       153: q+1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q^2+2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: q+1
       182: q^2+2q+1
       183: q+1
       184: q^2+3q+1
       185: q^2+2q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q^2+2q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       314: 1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       342: 1
       344: 1
       346: 1
       348: 1
       349: 1
       350: 1
       358: 1
       361: 1
       362: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       375: 1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       478: 1
       485: 1
       488: 1
       489: 1
       502: 1
       507: 1
       521: 1
       528: 1
       531: 1
       532: 1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       544: 1
       549: 1
       551: 1
       553: 1
       555: 1
       556: 1
       557: 1
       568: 1
       575: 1
       578: 1
       579: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       591: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       612: 1
       615: 1
       616: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       629: 1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       671: 1
       717: 1
       724: 1
       727: 1
       728: 1
       741: 1
       746: 1
       769: 1
       776: 1
       779: 1
       780: 1
       793: 1
       798: 1
       812: 1
       819: 1
       822: 1
       823: 1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       835: 1
       840: 1
       842: 1
       844: 1
       846: 1
       847: 1
       848: 1
       928: 1
       982: 1
      1028: 1
      1035: 1
      1038: 1
      1039: 1
      1052: 1
      1057: 1
      1239: 1

1240:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: 1
        55: q+1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       106: q+1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: q+1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       158: 1
       160: q+1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: q+1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       260: q+1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       289: q+1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       315: 1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       345: 1
       346: 1
       349: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       479: 1
       486: 1
       488: 1
       503: 1
       522: 1
       529: 1
       531: 1
       537: 1
       538: 1
       540: 1
       545: 1
       552: 1
       553: 1
       556: 1
       569: 1
       576: 1
       578: 1
       584: 1
       585: 1
       587: 1
       592: 1
       599: 1
       600: 1
       603: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       628: 1
       629: 1
       630: 1
       632: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       672: 1
       718: 1
       725: 1
       727: 1
       742: 1
       770: 1
       777: 1
       779: 1
       794: 1
       813: 1
       820: 1
       822: 1
       828: 1
       829: 1
       831: 1
       836: 1
       843: 1
       844: 1
       847: 1
       929: 1
       983: 1
      1029: 1
      1036: 1
      1038: 1
      1053: 1
      1240: 1

1241:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: 1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: 1
       244: 1
       245: q+1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       346: 1
       349: 1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: q+1
       378: 1
       379: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       553: 1
       556: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       600: 1
       603: 1
       614: 1
       615: 1
       616: 1
       617: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: q+1
       632: 1
       633: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       673: 1
       719: 1
       726: 1
       727: 1
       728: 1
       729: 1
       771: 1
       778: 1
       779: 1
       780: 1
       781: 1
       814: 1
       821: 1
       822: 1
       823: 1
       824: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       844: 1
       847: 1
       930: 1
       984: 1
      1030: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1241: 1

1242:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: q+1
        26: 1
        27: 2q+1
        28: 1
        29: q+1
        30: q+1
        31: 2q+1
        32: q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: q+1
        46: 2q+1
        47: q+1
        48: q^2+2q+1
        49: 2q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: 2q+1
        62: 1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: q+1
        73: q+1
        74: q+1
        75: 2q+1
        76: q+1
        77: 1
        78: 2q+1
        79: 1
        80: q+1
        81: q+1
        82: 2q+1
        83: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: q+1
        90: 1
        91: 2q+1
        92: 1
        93: q+1
        94: q+1
        95: 2q+1
        96: q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: q+1
       123: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: 1
       139: q+1
       140: q+1
       142: 1
       143: 1
       144: q+1
       145: 2q+1
       146: 1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: q+1
       159: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       165: q+1
       166: 2q+1
       167: 1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: 1
       177: q+1
       178: q+1
       179: q+1
       180: 2q+1
       181: q+1
       182: 1
       183: 2q+1
       184: 1
       185: q+1
       186: q+1
       187: 2q+1
       188: q+1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       232: 1
       233: q+1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       263: q+1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       292: 1
       293: q+1
       294: q+1
       296: 1
       297: 1
       298: q+1
       299: 2q+1
       300: 1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: q+1
       308: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       341: 1
       347: 1
       349: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       383: 1
       385: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       422: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       438: 1
       439: q+1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       450: 1
       451: 1
       452: q+1
       453: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       481: 1
       489: 1
       490: 1
       491: 1
       506: 1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       548: 1
       554: 1
       556: 1
       562: 1
       571: 1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       595: 1
       601: 1
       603: 1
       609: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       637: 1
       639: 1
       642: 1
       643: 1
       645: 1
       646: 1
       648: 1
       674: 1
       720: 1
       728: 1
       729: 1
       730: 1
       745: 1
       772: 1
       780: 1
       781: 1
       782: 1
       797: 1
       815: 1
       823: 1
       824: 1
       825: 1
       830: 1
       831: 1
       832: 1
       833: 1
       839: 1
       845: 1
       847: 1
       853: 1
       931: 1
       985: 1
      1031: 1
      1039: 1
      1040: 1
      1041: 1
      1056: 1
      1242: 1

1243:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: 1
        24: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        54: 1
        55: q+1
        56: 1
        59: q+1
        60: 1
        61: q+1
        63: 1
        64: 1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        73: q+1
        74: 1
        75: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        86: q+1
        87: 1
        88: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       110: 1
       111: 1
       116: 1
       117: q+1
       118: 1
       121: 1
       122: 1
       123: 1
       126: q+1
       128: q+1
       130: 1
       131: 1
       132: 1
       133: 1
       138: 1
       139: q+1
       140: 1
       143: q+1
       144: 1
       145: q+1
       147: 1
       148: 1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       159: 1
       160: q+1
       161: 1
       164: q+1
       165: 1
       166: q+1
       168: 1
       169: 1
       171: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       178: q+1
       179: 1
       180: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       218: q+1
       222: 1
       224: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: q+1
       242: 1
       245: 1
       246: 1
       247: 1
       250: q+1
       252: q+1
       254: 1
       255: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: 1
       271: q+1
       272: 1
       275: 1
       276: 1
       277: 1
       280: q+1
       282: q+1
       284: 1
       285: 1
       286: 1
       287: 1
       292: 1
       293: q+1
       294: 1
       297: q+1
       298: 1
       299: q+1
       301: 1
       302: 1
       304: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       334: 1
       335: 1
       349: 1
       353: 1
       355: 1
       363: 1
       364: 1
       371: 1
       372: 1
       377: 1
       378: 1
       379: 1
       385: q+1
       389: 1
       391: 1
       393: 1
       394: 1
       402: 1
       403: 1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       424: q+1
       428: 1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: q+1
       448: 1
       451: 1
       452: 1
       453: 1
       456: q+1
       458: q+1
       460: 1
       461: 1
       462: 1
       463: 1
       482: 1
       490: 1
       491: 1
       514: 1
       525: 1
       533: 1
       534: 1
       541: 1
       542: 1
       556: 1
       560: 1
       562: 1
       572: 1
       580: 1
       581: 1
       588: 1
       589: 1
       603: 1
       607: 1
       609: 1
       617: 1
       618: 1
       625: 1
       626: 1
       631: 1
       632: 1
       633: 1
       639: q+1
       643: 1
       645: 1
       647: 1
       648: 1
       675: 1
       721: 1
       729: 1
       730: 1
       753: 1
       773: 1
       781: 1
       782: 1
       805: 1
       816: 1
       824: 1
       825: 1
       832: 1
       833: 1
       847: 1
       851: 1
       853: 1
       932: 1
       986: 1
      1032: 1
      1040: 1
      1041: 1
      1064: 1
      1243: 1

1244:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: q+1
        24: 1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        56: 1
        57: q+1
        60: q+1
        61: 1
        62: q+1
        64: q+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: 1
       111: 1
       112: q+1
       113: 1
       118: 1
       119: q+1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       148: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: q+1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: q+1
       237: 1
       242: 1
       243: q+1
       246: q+1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       336: 1
       343: 1
       344: 1
       351: 1
       354: 1
       356: 1
       364: 1
       365: 1
       372: 1
       373: q+1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       403: 1
       404: 1
       411: 1
       412: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       449: q+1
       452: q+1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       473: 1
       492: 1
       500: 1
       509: 1
       516: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       573: 1
       581: 1
       590: 1
       597: 1
       598: 1
       605: 1
       608: 1
       610: 1
       618: 1
       619: 1
       626: 1
       627: q+1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       676: 1
       712: 1
       731: 1
       739: 1
       748: 1
       764: 1
       783: 1
       791: 1
       800: 1
       807: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       933: 1
       987: 1
      1023: 1
      1042: 1
      1050: 1
      1059: 1
      1244: 1

1245:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: 1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q^2+2q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: 1
        38: q^2+2q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: 1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: q+1
        51: 1
        52: q+1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q^2+2q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q^2+2q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: 1
       102: q^2+2q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q^2+2q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: q+1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: 1
       259: q+1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       289: 1
       290: q+1
       292: q+1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       319: 1
       320: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       434: 1
       435: q+1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       474: 1
       492: 1
       493: 1
       499: 1
       502: 1
       517: 1
       526: 1
       527: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       564: 1
       573: 1
       574: 1
       580: 1
       583: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       610: 1
       611: 1
       617: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       677: 1
       713: 1
       731: 1
       732: 1
       738: 1
       741: 1
       765: 1
       783: 1
       784: 1
       790: 1
       793: 1
       808: 1
       817: 1
       818: 1
       824: 1
       827: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       934: 1
       988: 1
      1024: 1
      1042: 1
      1043: 1
      1049: 1
      1052: 1
      1245: 1

1246:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q^2+2q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        71: 1
        72: q^2+2q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       475: 1
       493: 1
       494: 1
       495: 1
       498: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: q+1
       678: 1
       714: 1
       732: 1
       733: 1
       734: 1
       737: 1
       766: 1
       784: 1
       785: 1
       786: 1
       789: 1
       809: 1
       818: 1
       819: 1
       820: 1
       823: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       935: 1
       989: 1
      1025: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1246: 1

1247:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       105: q+1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: q+1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       259: q+1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       321: 1
       323: 1
       329: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       461: 1
       462: 1
       476: 1
       494: 1
       496: 1
       502: 1
       519: 1
       528: 1
       530: 1
       536: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       555: 1
       566: 1
       575: 1
       577: 1
       583: 1
       591: 1
       593: 1
       594: 1
       598: 1
       600: 1
       602: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       679: 1
       715: 1
       733: 1
       735: 1
       741: 1
       767: 1
       785: 1
       787: 1
       793: 1
       810: 1
       819: 1
       821: 1
       827: 1
       835: 1
       837: 1
       838: 1
       842: 1
       844: 1
       846: 1
       936: 1
       990: 1
      1026: 1
      1044: 1
      1046: 1
      1052: 1
      1247: 1

1248:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: 2q+1
         9: q^2+3q+1
        10: q^2+2q+1
        11: 2q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q^2+3q+1
        31: q^2+2q+1
        32: 2q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+2q+1
        38: 2q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: q^2+3q+1
        44: q^2+2q+1
        45: 2q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q^2+2q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: q+1
        77: q^2+2q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q^2+3q+1
        82: q^2+2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: q+1
        90: q^2+2q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q^2+3q+1
        95: q^2+2q+1
        96: 2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: q^2+3q+1
       101: q^2+2q+1
       102: 2q+1
       103: q^2+3q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q^2+2q+1
       151: q+1
       152: 2q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q^2+2q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: q+1
       182: q^2+2q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q^2+3q+1
       187: q^2+2q+1
       188: 2q+1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: q+1
       281: 1
       282: q+1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q^2+2q+1
       305: q+1
       306: 2q+1
       307: q+1
       308: q+1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       398: 1
       399: 1
       401: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       477: 1
       495: 1
       496: 1
       498: 1
       503: 1
       507: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       541: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: 1
       588: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       613: 1
       614: 1
       616: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       680: 1
       716: 1
       734: 1
       735: 1
       737: 1
       742: 1
       746: 1
       768: 1
       786: 1
       787: 1
       789: 1
       794: 1
       798: 1
       811: 1
       820: 1
       821: 1
       823: 1
       828: 1
       832: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       937: 1
       991: 1
      1027: 1
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1057: 1
      1248: 1

1249:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       314: 1
       321: 1
       324: 1
       325: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       358: 1
       361: 1
       362: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       478: 1
       494: 1
       497: 1
       498: 1
       521: 1
       528: 1
       531: 1
       532: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       568: 1
       575: 1
       578: 1
       579: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       612: 1
       615: 1
       616: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       681: 1
       717: 1
       733: 1
       736: 1
       737: 1
       769: 1
       785: 1
       788: 1
       789: 1
       812: 1
       819: 1
       822: 1
       823: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       938: 1
       992: 1
      1028: 1
      1044: 1
      1047: 1
      1048: 1
      1249: 1

1250:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        30: 1
        31: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        65: 1
        66: 1
        67: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        94: 1
        95: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       124: 1
       125: 1
       126: 1
       128: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       170: 1
       171: 1
       172: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       214: 1
       215: 1
       216: 1
       218: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       278: 1
       279: 1
       280: 1
       282: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       315: 1
       322: 1
       324: 1
       338: 1
       339: 1
       341: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       420: 1
       421: 1
       422: 1
       424: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       479: 1
       495: 1
       497: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       569: 1
       576: 1
       578: 1
       592: 1
       593: 1
       595: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       637: 1
       639: 1
       682: 1
       718: 1
       734: 1
       736: 1
       770: 1
       786: 1
       788: 1
       813: 1
       820: 1
       822: 1
       836: 1
       837: 1
       839: 1
       939: 1
       993: 1
      1029: 1
      1045: 1
      1047: 1
      1250: 1

1251:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: q+1
       127: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: q+1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       210: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: q+1
       281: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       348: 1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       416: 1
       421: 1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: q+1
       457: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       480: 1
       496: 1
       497: 1
       498: 1
       499: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       555: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: 1
       602: 1
       614: 1
       615: 1
       616: 1
       617: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       631: 1
       636: 1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       683: 1
       719: 1
       735: 1
       736: 1
       737: 1
       738: 1
       771: 1
       787: 1
       788: 1
       789: 1
       790: 1
       814: 1
       821: 1
       822: 1
       823: 1
       824: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       846: 1
       940: 1
       994: 1
      1030: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1251: 1

1252:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: q+1
        26: 1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: 1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: 2q+1
        39: q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q+1
        48: q^2+2q+1
        49: 2q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: 2q+1
        61: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: 1
        72: q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: q+1
        77: 1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: 1
        82: q+1
        83: q+1
        85: q+1
        86: q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: 1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: 1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q+1
       101: 2q+1
       102: 2q+1
       103: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: q+1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: q+1
       139: 1
       140: q+1
       142: 1
       143: 1
       144: 2q+1
       145: q+1
       146: q+1
       147: 1
       148: q+1
       149: 1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: 1
       158: q+1
       159: q+1
       160: 1
       161: q+1
       163: 1
       164: 1
       165: 2q+1
       166: q+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: 1
       177: q+1
       178: q+1
       179: 2q+1
       180: q+1
       181: q+1
       182: 1
       183: 2q+1
       184: q+1
       185: 2q+1
       186: 1
       187: q+1
       188: q+1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       232: q+1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: q+1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: q+1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: 1
       275: 1
       276: q+1
       279: 1
       280: 1
       281: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       292: q+1
       293: 1
       294: q+1
       296: 1
       297: 1
       298: 2q+1
       299: q+1
       300: q+1
       301: 1
       302: q+1
       303: 1
       304: 1
       305: q+1
       306: 1
       307: q+1
       308: 1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       354: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       438: q+1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       450: 1
       451: 1
       452: q+1
       455: 1
       456: 1
       457: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       481: 1
       498: 1
       499: 1
       500: 1
       505: 1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       561: 1
       571: 1
       579: 1
       580: 1
       581: 1
       586: 1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       608: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       642: 1
       643: 1
       644: 1
       646: 1
       648: 1
       684: 1
       720: 1
       737: 1
       738: 1
       739: 1
       744: 1
       772: 1
       789: 1
       790: 1
       791: 1
       796: 1
       815: 1
       823: 1
       824: 1
       825: 1
       830: 1
       838: 1
       839: 1
       840: 1
       841: 1
       845: 1
       846: 1
       852: 1
       941: 1
       995: 1
      1031: 1
      1048: 1
      1049: 1
      1050: 1
      1055: 1
      1252: 1

1253:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: q+1
        24: 1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        54: q+1
        55: 1
        56: 1
        59: q+1
        60: q+1
        61: 1
        63: q+1
        64: q+1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: q+1
        74: q+1
        75: 1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        86: q+1
        87: q+1
        88: 1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       110: 1
       111: 1
       116: q+1
       117: 1
       118: 1
       121: q+1
       122: q+1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       138: q+1
       139: 1
       140: 1
       143: q+1
       144: q+1
       145: 1
       147: q+1
       148: q+1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: q+1
       160: 1
       161: 1
       164: q+1
       165: q+1
       166: 1
       168: q+1
       169: q+1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: q+1
       179: q+1
       180: 1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: q+1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: q+1
       241: 1
       242: 1
       245: q+1
       246: q+1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: q+1
       271: 1
       272: 1
       275: q+1
       276: q+1
       280: 1
       281: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       292: q+1
       293: 1
       294: 1
       297: q+1
       298: q+1
       299: 1
       301: q+1
       302: q+1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       342: 1
       343: 1
       348: 1
       353: 1
       354: 1
       363: 1
       364: 1
       371: 1
       372: 1
       377: q+1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       402: 1
       403: 1
       410: 1
       411: 1
       416: q+1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: q+1
       447: 1
       448: 1
       451: q+1
       452: q+1
       456: 1
       457: 1
       458: 1
       460: 1
       461: 1
       462: 1
       463: 1
       482: 1
       499: 1
       500: 1
       513: 1
       525: 1
       533: 1
       534: 1
       549: 1
       550: 1
       555: 1
       560: 1
       561: 1
       572: 1
       580: 1
       581: 1
       596: 1
       597: 1
       602: 1
       607: 1
       608: 1
       617: 1
       618: 1
       625: 1
       626: 1
       631: q+1
       638: 1
       639: 1
       640: 1
       643: 1
       644: 1
       647: 1
       648: 1
       685: 1
       721: 1
       738: 1
       739: 1
       752: 1
       773: 1
       790: 1
       791: 1
       804: 1
       816: 1
       824: 1
       825: 1
       840: 1
       841: 1
       846: 1
       851: 1
       852: 1
       942: 1
       996: 1
      1032: 1
      1049: 1
      1050: 1
      1063: 1
      1253: 1

1254:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        23: q+1
        24: q+1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        56: q+1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        74: q+1
        75: q+1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        87: q+1
        88: q+1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       111: q+1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       140: q+1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       161: q+1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       179: q+1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: q+1
       235: q+1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q+1
       258: q+1
       265: q+1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       356: q+1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       395: q+1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       483: 1
       492: 1
       501: 1
       508: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       610: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       686: 1
       722: 1
       731: 1
       740: 1
       747: 1
       774: 1
       783: 1
       792: 1
       799: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       943: 1
       997: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1254: 1

1255:    0: q^3+2q^2+3q+1
         1: q^3+2q^2+3q+1
         2: q^2+2q+1
         3: q^2+3q+1
         4: q^3+2q^2+3q+1
         5: q^3+2q^2+3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+3q+1
        10: q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: q^3+2q^2+3q+1
        14: q^2+2q+1
        15: q^2+3q+1
        16: q^3+2q^2+3q+1
        17: q^2+2q+1
        18: q^2+3q+1
        19: q^3+2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: 1
        28: q^2+3q+1
        29: q+1
        30: q^2+3q+1
        31: q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+3q+1
        37: q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+3q+1
        44: q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^3+2q^2+3q+1
        48: q^2+2q+1
        49: q^2+3q+1
        50: q+1
        51: q+1
        52: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+3q+1
        69: q+1
        70: 2q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: 1
        79: q^2+3q+1
        80: q+1
        81: q^2+3q+1
        82: q+1
        83: q^2+3q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q^2+3q+1
        93: q+1
        94: q^2+3q+1
        95: q+1
        96: q^2+3q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+3q+1
       101: q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: q+1
       106: q+1
       110: q+1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 2q+1
       134: q+1
       135: q+1
       136: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q^2+3q+1
       153: q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q^2+3q+1
       174: q+1
       175: 2q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: 1
       184: q^2+3q+1
       185: q+1
       186: q^2+3q+1
       187: q+1
       188: q^2+3q+1
       190: q+1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       234: q+1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: 2q+1
       258: q+1
       259: q+1
       260: q+1
       264: q+1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 2q+1
       288: q+1
       289: q+1
       290: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q^2+3q+1
       307: q+1
       308: 2q+1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       365: 1
       366: 1
       367: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: q+1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       440: q+1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: 2q+1
       484: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       527: 1
       535: 1
       536: 1
       537: 1
       541: 1
       543: 1
       544: 1
       545: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       590: 1
       591: 1
       592: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: q+1
       619: 1
       620: 1
       621: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       687: 1
       723: 1
       732: 1
       740: 1
       741: 1
       742: 1
       746: 1
       775: 1
       784: 1
       792: 1
       793: 1
       794: 1
       798: 1
       818: 1
       826: 1
       827: 1
       828: 1
       832: 1
       834: 1
       835: 1
       836: 1
       840: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       944: 1
       998: 1
      1034: 1
      1043: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1255: 1

1256:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: q+1
        23: 2q+1
        25: q^2+3q+1
        26: q+1
        27: 2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: 2q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        50: 2q+1
        52: q+1
        53: q+1
        54: q+1
        57: 2q+1
        58: q+1
        59: 1
        60: 2q+1
        62: q^2+3q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: q+1
        74: 2q+1
        76: q^2+3q+1
        77: q+1
        78: 2q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: q+1
        87: 2q+1
        89: q^2+3q+1
        90: q+1
        91: 2q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+3q+1
       103: 2q+1
       105: q+1
       107: q+1
       108: q+1
       112: 2q+1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       136: q+1
       137: q+1
       138: q+1
       141: 2q+1
       142: q+1
       143: 1
       144: 2q+1
       146: q^2+3q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       157: q+1
       158: q+1
       159: q+1
       162: 2q+1
       163: q+1
       164: 1
       165: 2q+1
       167: q^2+3q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: q+1
       179: 2q+1
       181: q^2+3q+1
       182: q+1
       183: 2q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       191: q+1
       199: 1
       201: 1
       202: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: q+1
       215: 1
       216: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       229: q+1
       231: q+1
       232: q+1
       236: 2q+1
       238: 1
       239: 1
       240: 1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: q+1
       266: 2q+1
       268: 1
       269: 1
       270: 1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       290: q+1
       291: q+1
       292: q+1
       295: 2q+1
       296: q+1
       297: 1
       298: 2q+1
       300: q^2+3q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       321: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: q+1
       366: 1
       368: 1
       369: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: q+1
       382: 1
       383: 1
       384: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       394: 1
       397: q+1
       405: 1
       407: 1
       408: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: q+1
       421: 1
       422: 1
       423: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: q+1
       433: 1
       435: q+1
       437: q+1
       438: q+1
       442: 2q+1
       444: 1
       445: 1
       446: 1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       485: 1
       494: 1
       502: 1
       504: 1
       505: 1
       509: 1
       528: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       575: 1
       583: 1
       585: 1
       586: 1
       591: 1
       593: 1
       594: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       612: q+1
       620: 1
       622: 1
       623: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: q+1
       636: 1
       637: 1
       638: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       648: 1
       688: 1
       724: 1
       733: 1
       741: 1
       743: 1
       744: 1
       748: 1
       776: 1
       785: 1
       793: 1
       795: 1
       796: 1
       800: 1
       819: 1
       827: 1
       829: 1
       830: 1
       835: 1
       837: 1
       838: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       852: 1
       945: 1
       999: 1
      1035: 1
      1044: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1256: 1

1257:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: 2q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: q+1
        24: 2q+1
        25: q^2+3q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: 2q+1
        39: q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: 2q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        51: 2q+1
        52: q+1
        53: q+1
        55: q+1
        57: 2q+1
        58: q+1
        59: 1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: q^2+3q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: q+1
        75: 2q+1
        76: q^2+3q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: q+1
        88: 2q+1
        89: q^2+3q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: 2q+1
       103: q^2+3q+1
       106: q+1
       107: q+1
       109: q+1
       113: 2q+1
       114: 1
       115: 1
       117: 1
       119: q+1
       120: q+1
       121: 1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 2q+1
       136: q+1
       137: q+1
       139: q+1
       141: 2q+1
       142: q+1
       143: 1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: q^2+3q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       156: 2q+1
       157: q+1
       158: q+1
       160: q+1
       162: 2q+1
       163: q+1
       164: 1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: q^2+3q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: q+1
       180: 2q+1
       181: q^2+3q+1
       182: q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: 2q+1
       192: q+1
       200: 1
       201: 1
       203: 1
       207: q+1
       208: 1
       209: 1
       211: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       230: q+1
       231: q+1
       233: q+1
       237: 2q+1
       238: 1
       239: 1
       241: 1
       243: q+1
       244: q+1
       245: 1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       260: q+1
       261: q+1
       263: q+1
       267: 2q+1
       268: 1
       269: 1
       271: 1
       273: q+1
       274: q+1
       275: 1
       277: q+1
       278: q+1
       279: q+1
       280: 1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 2q+1
       290: q+1
       291: q+1
       293: q+1
       295: 2q+1
       296: q+1
       297: 1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: q^2+3q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       322: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: q+1
       367: 1
       368: 1
       370: 1
       374: q+1
       375: 1
       376: 1
       378: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: q+1
       394: 1
       398: q+1
       406: 1
       407: 1
       409: 1
       413: q+1
       414: 1
       415: 1
       417: 1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       433: 1
       436: q+1
       437: q+1
       439: q+1
       443: 2q+1
       444: 1
       445: 1
       447: 1
       449: q+1
       450: q+1
       451: 1
       453: q+1
       454: q+1
       455: q+1
       456: 1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       486: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       529: 1
       537: 1
       538: 1
       540: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       576: 1
       584: 1
       585: 1
       587: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: q+1
       621: 1
       622: 1
       624: 1
       628: q+1
       629: 1
       630: 1
       632: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       648: 1
       689: 1
       725: 1
       734: 1
       742: 1
       743: 1
       745: 1
       749: 1
       777: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: 1
       820: 1
       828: 1
       829: 1
       831: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       853: 1
       946: 1
      1000: 1
      1036: 1
      1045: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1257: 1

1258:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q+1
        12: q^2+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        25: q+1
        26: 1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: 1
        31: q^2+1
        32: 1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: q+1
        39: q^2+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q+1
        46: q^2+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        77: 1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: 1
        82: q^2+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: q+1
        90: 1
        91: q^2+q+1
        92: q+1
        93: q+1
        94: 1
        95: q^2+1
        96: 1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: q^2+q+1
       102: q+1
       103: q^2+1
       107: q+1
       108: q+1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       138: q+1
       141: q+1
       142: 1
       143: 1
       144: q+1
       146: q+1
       147: 1
       148: q+1
       149: 1
       150: 1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: q+1
       162: q+1
       163: 1
       164: 1
       165: q+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: q^2+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: q+1
       182: 1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: 1
       187: q^2+1
       188: 1
       193: q+1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       231: q+1
       232: q+1
       238: 1
       239: 1
       240: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: q+1
       268: 1
       269: 1
       270: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       292: q+1
       295: q+1
       296: 1
       297: 1
       298: q+1
       300: q+1
       301: 1
       302: q+1
       303: 1
       304: 1
       305: q^2+1
       306: 1
       307: 1
       308: 1
       323: 1
       331: 1
       332: 1
       339: 1
       340: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       360: q+1
       368: 1
       369: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       399: q+1
       407: 1
       408: 1
       414: 1
       415: 1
       416: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       437: q+1
       438: q+1
       444: 1
       445: 1
       446: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       487: 1
       496: 1
       504: 1
       505: 1
       530: 1
       538: 1
       539: 1
       546: 1
       547: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       577: 1
       585: 1
       586: 1
       593: 1
       594: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       614: q+1
       622: 1
       623: 1
       629: 1
       630: 1
       631: 1
       636: 1
       637: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       648: 1
       690: 1
       726: 1
       735: 1
       743: 1
       744: 1
       778: 1
       787: 1
       795: 1
       796: 1
       821: 1
       829: 1
       830: 1
       837: 1
       838: 1
       844: 1
       845: 1
       846: 1
       849: 1
       852: 1
       947: 1
      1001: 1
      1037: 1
      1046: 1
      1054: 1
      1055: 1
      1258: 1

1259:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+1
        12: q+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        24: q+1
        25: q+1
        26: 1
        27: q^2+q+1
        28: 1
        29: q^2+1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: q^2+1
        39: q+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q^2+1
        46: q+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        52: q+1
        53: q+1
        55: q+1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: q^2+1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: q+1
        77: 1
        78: q^2+q+1
        79: 1
        80: q^2+1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        88: q+1
        89: q+1
        90: 1
        91: q^2+q+1
        92: 1
        93: q^2+1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: q^2+q+1
       102: q^2+1
       103: q+1
       107: q+1
       109: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       139: q+1
       141: q+1
       142: 1
       143: 1
       145: q+1
       146: 1
       147: 1
       148: q^2+1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       160: q+1
       162: q+1
       163: 1
       164: 1
       166: q+1
       167: 1
       168: 1
       169: q^2+1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: q+1
       182: 1
       183: q^2+q+1
       184: 1
       185: q^2+1
       186: q+1
       187: q+1
       188: 1
       194: q+1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       231: q+1
       233: q+1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       263: q+1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       293: q+1
       295: q+1
       296: 1
       297: 1
       299: q+1
       300: 1
       301: 1
       302: q^2+1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       324: 1
       331: 1
       333: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       361: q+1
       368: 1
       370: 1
       375: 1
       376: 1
       378: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       400: q+1
       407: 1
       409: 1
       414: 1
       415: 1
       417: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       437: q+1
       439: q+1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       488: 1
       497: 1
       504: 1
       506: 1
       531: 1
       538: 1
       540: 1
       546: 1
       548: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       578: 1
       585: 1
       587: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       615: q+1
       622: 1
       624: 1
       629: 1
       630: 1
       632: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       648: 1
       691: 1
       727: 1
       736: 1
       743: 1
       745: 1
       779: 1
       788: 1
       795: 1
       797: 1
       822: 1
       829: 1
       831: 1
       837: 1
       839: 1
       844: 1
       845: 1
       847: 1
       849: 1
       853: 1
       948: 1
      1002: 1
      1038: 1
      1047: 1
      1054: 1
      1056: 1
      1259: 1

1260:    0: q^3+3q^2+3q+1
         1: q^2+2q+1
         2: q^3+3q^2+3q+1
         3: q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: q^2+2q+1
        14: q^3+3q^2+3q+1
        15: q^2+3q+1
        16: q^2+2q+1
        17: q^3+3q^2+3q+1
        18: q^2+3q+1
        19: q^3+3q^2+3q+1
        21: q^2+2q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: q^2+3q+1
        30: 2q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^2+2q+1
        48: q^3+3q^2+3q+1
        49: q^2+3q+1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        58: q+1
        59: 1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: q^2+3q+1
        70: q+1
        72: q^2+2q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: q^2+3q+1
        81: 2q+1
        82: q^2+3q+1
        83: q^2+3q+1
        85: q^2+2q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: q^2+3q+1
        94: 2q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: q^2+3q+1
       102: q^2+3q+1
       103: q^2+3q+1
       108: q+1
       109: q+1
       110: q+1
       115: 1
       116: 1
       117: 1
       118: 2q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 2q+1
       142: q+1
       143: 1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: q^2+3q+1
       154: q+1
       158: q+1
       159: q+1
       160: q+1
       161: 2q+1
       163: q+1
       164: 1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: q^2+3q+1
       175: q+1
       177: q^2+2q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: q+1
       183: 2q+1
       184: 2q+1
       185: q^2+3q+1
       186: 2q+1
       187: q^2+3q+1
       188: q^2+3q+1
       195: q+1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       216: 1
       217: 1
       218: 1
       219: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       232: q+1
       233: q+1
       234: q+1
       239: 1
       240: 1
       241: 1
       242: 2q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       262: q+1
       263: q+1
       264: q+1
       269: 1
       270: 1
       271: 1
       272: 2q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       291: q+1
       292: q+1
       293: q+1
       294: 2q+1
       296: q+1
       297: 1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: q^2+3q+1
       308: q+1
       325: 1
       332: 1
       333: 1
       334: 1
       340: 1
       341: 1
       342: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       362: q+1
       369: 1
       370: 1
       371: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       383: 1
       384: 1
       385: 1
       386: q+1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       401: q+1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       422: 1
       423: 1
       424: 1
       425: q+1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       438: q+1
       439: q+1
       440: q+1
       445: 1
       446: 1
       447: 1
       448: 2q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       489: 1
       498: 1
       505: 1
       506: 1
       507: 1
       515: 1
       532: 1
       539: 1
       540: 1
       541: 1
       547: 1
       548: 1
       549: 1
       554: 1
       555: 1
       556: 1
       557: 1
       561: 1
       562: 1
       579: 1
       586: 1
       587: 1
       588: 1
       594: 1
       595: 1
       596: 1
       601: 1
       602: 1
       603: 1
       604: 1
       608: 1
       609: 1
       616: q+1
       623: 1
       624: 1
       625: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       637: 1
       638: 1
       639: 1
       640: q+1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       692: 1
       728: 1
       737: 1
       744: 1
       745: 1
       746: 1
       754: 1
       780: 1
       789: 1
       796: 1
       797: 1
       798: 1
       806: 1
       823: 1
       830: 1
       831: 1
       832: 1
       838: 1
       839: 1
       840: 1
       845: 1
       846: 1
       847: 1
       848: 1
       852: 1
       853: 1
       949: 1
      1003: 1
      1039: 1
      1048: 1
      1055: 1
      1056: 1
      1057: 1
      1065: 1
      1260: 1

1261:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: q+1
        23: q+1
        24: q+1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        54: q+1
        55: q+1
        56: q+1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        73: q+1
        74: q+1
        75: q+1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        86: q+1
        87: q+1
        88: q+1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       110: q+1
       111: q+1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: q+1
       138: q+1
       139: q+1
       140: q+1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       159: q+1
       160: q+1
       161: q+1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       178: q+1
       179: q+1
       180: q+1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       196: q+1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       234: q+1
       235: q+1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: q+1
       264: q+1
       265: q+1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       281: 1
       282: 1
       284: 1
       285: 1
       286: q+1
       292: q+1
       293: q+1
       294: q+1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       326: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       363: q+1
       371: 1
       372: 1
       377: 1
       378: 1
       379: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       391: 1
       402: q+1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       440: q+1
       441: q+1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       456: 1
       457: 1
       458: 1
       460: 1
       461: 1
       462: q+1
       490: 1
       499: 1
       507: 1
       508: 1
       533: 1
       541: 1
       542: 1
       549: 1
       550: 1
       555: 1
       556: 1
       557: 1
       580: 1
       588: 1
       589: 1
       596: 1
       597: 1
       602: 1
       603: 1
       604: 1
       617: q+1
       625: 1
       626: 1
       631: 1
       632: 1
       633: 1
       638: 1
       639: 1
       640: 1
       643: 1
       644: 1
       645: 1
       693: 1
       729: 1
       738: 1
       746: 1
       747: 1
       781: 1
       790: 1
       798: 1
       799: 1
       824: 1
       832: 1
       833: 1
       840: 1
       841: 1
       846: 1
       847: 1
       848: 1
       950: 1
      1004: 1
      1040: 1
      1049: 1
      1057: 1
      1058: 1
      1261: 1

1262:    0: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         8: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        14: q^2+2q+1
        15: 2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        23: 2q+1
        24: 2q+1
        27: 2q+1
        29: 2q+1
        31: 2q+1
        32: 2q+1
        35: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        42: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        48: q^2+2q+1
        49: 2q+1
        56: 2q+1
        60: 2q+1
        61: 2q+1
        64: q+1
        67: q+1
        69: 2q+1
        70: q+1
        74: 2q+1
        75: 2q+1
        78: 2q+1
        80: 2q+1
        82: 2q+1
        83: 2q+1
        87: 2q+1
        88: 2q+1
        91: 2q+1
        93: 2q+1
        95: 2q+1
        96: 2q+1
        99: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       111: q+1
       118: 2q+1
       122: q+1
       123: q+1
       127: q+1
       128: q+1
       131: 1
       133: q+1
       140: 2q+1
       144: 2q+1
       145: 2q+1
       148: q+1
       151: q+1
       153: 2q+1
       154: q+1
       161: 2q+1
       165: 2q+1
       166: 2q+1
       169: q+1
       172: q+1
       174: 2q+1
       175: q+1
       179: 2q+1
       180: 2q+1
       183: 2q+1
       185: 2q+1
       187: 2q+1
       188: 2q+1
       197: q+1
       205: 1
       212: q+1
       219: q+1
       223: 1
       224: 1
       227: 1
       235: q+1
       242: 2q+1
       246: q+1
       247: q+1
       251: q+1
       252: q+1
       255: 1
       257: q+1
       265: q+1
       272: 2q+1
       276: q+1
       277: q+1
       281: q+1
       282: q+1
       285: 1
       287: q+1
       294: 2q+1
       298: 2q+1
       299: 2q+1
       302: q+1
       305: q+1
       307: 2q+1
       308: q+1
       327: 1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       364: q+1
       372: 1
       379: q+1
       386: q+1
       390: 1
       391: 1
       394: 1
       403: q+1
       411: 1
       418: q+1
       425: q+1
       429: 1
       430: 1
       433: 1
       441: q+1
       448: 2q+1
       452: q+1
       453: q+1
       457: q+1
       458: q+1
       461: 1
       463: q+1
       491: 1
       500: 1
       508: 1
       515: 1
       534: 1
       542: 1
       550: 1
       557: 1
       561: 1
       562: 1
       581: 1
       589: 1
       597: 1
       604: 1
       608: 1
       609: 1
       618: q+1
       626: 1
       633: q+1
       640: q+1
       644: 1
       645: 1
       648: 1
       694: 1
       730: 1
       739: 1
       747: 1
       754: 1
       782: 1
       791: 1
       799: 1
       806: 1
       825: 1
       833: 1
       841: 1
       848: 1
       852: 1
       853: 1
       951: 1
      1005: 1
      1041: 1
      1050: 1
      1058: 1
      1065: 1
      1262: 1

1263:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        23: 1
        24: 1
        25: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: q+1
        64: 1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       148: 1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       198: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       302: 1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       328: 1
       336: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       365: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       404: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       463: q+1
       501: 1
       509: 1
       510: 1
       515: 1
       535: 1
       543: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       582: 1
       590: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       619: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       695: 1
       740: 1
       748: 1
       749: 1
       754: 1
       792: 1
       800: 1
       801: 1
       806: 1
       826: 1
       834: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       952: 1
      1006: 1
      1051: 1
      1059: 1
      1060: 1
      1065: 1
      1263: 1

1264:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        52: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       105: 1
       112: 1
       114: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: 1
       136: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       157: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       199: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       236: 1
       238: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: 1
       266: 1
       268: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       290: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       329: 1
       337: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       366: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       405: 1
       412: 1
       414: 1
       416: 1
       419: 1
       421: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       435: 1
       442: 1
       444: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       502: 1
       509: 1
       511: 1
       513: 1
       536: 1
       544: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       583: 1
       591: 1
       598: 1
       600: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       620: 1
       627: 1
       629: 1
       631: 1
       634: 1
       636: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       696: 1
       741: 1
       748: 1
       750: 1
       752: 1
       793: 1
       800: 1
       802: 1
       804: 1
       827: 1
       835: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       953: 1
      1007: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1264: 1

1265:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        51: 1
        52: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       106: 1
       113: 1
       114: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: 1
       136: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       156: 1
       157: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       200: 1
       207: 1
       208: 1
       211: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       237: 1
       238: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       260: 1
       267: 1
       268: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: 1
       290: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       330: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       367: 1
       374: 1
       375: 1
       378: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       406: 1
       413: 1
       414: 1
       417: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: 1
       443: 1
       444: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       503: 1
       510: 1
       511: 1
       514: 1
       537: 1
       545: 1
       552: 1
       553: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       584: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       621: 1
       628: 1
       629: 1
       632: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       697: 1
       742: 1
       749: 1
       750: 1
       753: 1
       794: 1
       801: 1
       802: 1
       805: 1
       828: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       954: 1
      1008: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1265: 1

1266:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        57: 1
        58: 1
        59: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       114: 1
       115: 1
       119: 1
       120: 1
       121: 1
       124: 1
       125: 1
       126: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       141: 1
       142: 1
       143: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       162: 1
       163: 1
       164: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       201: 1
       208: 1
       209: 1
       215: 1
       216: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: 1
       238: 1
       239: 1
       243: 1
       244: 1
       245: 1
       248: 1
       249: 1
       250: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       268: 1
       269: 1
       273: 1
       274: 1
       275: 1
       278: 1
       279: 1
       280: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       295: 1
       296: 1
       297: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       331: 1
       339: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       368: 1
       375: 1
       376: 1
       382: 1
       383: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       407: 1
       414: 1
       415: 1
       421: 1
       422: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       437: 1
       444: 1
       445: 1
       449: 1
       450: 1
       451: 1
       454: 1
       455: 1
       456: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       504: 1
       511: 1
       512: 1
       538: 1
       546: 1
       553: 1
       554: 1
       558: 1
       559: 1
       560: 1
       585: 1
       593: 1
       600: 1
       601: 1
       605: 1
       606: 1
       607: 1
       622: 1
       629: 1
       630: 1
       636: 1
       637: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       698: 1
       743: 1
       750: 1
       751: 1
       795: 1
       802: 1
       803: 1
       829: 1
       837: 1
       844: 1
       845: 1
       849: 1
       850: 1
       851: 1
       955: 1
      1009: 1
      1054: 1
      1061: 1
      1062: 1
      1266: 1

1267:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: 1
        54: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       115: 1
       116: 1
       120: 1
       121: 1
       122: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       202: 1
       209: 1
       210: 1
       216: 1
       217: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       232: 1
       239: 1
       240: 1
       244: 1
       245: 1
       246: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       269: 1
       270: 1
       274: 1
       275: 1
       276: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       332: 1
       340: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       369: 1
       376: 1
       377: 1
       383: 1
       384: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       408: 1
       415: 1
       416: 1
       422: 1
       423: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       438: 1
       445: 1
       446: 1
       450: 1
       451: 1
       452: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       505: 1
       512: 1
       513: 1
       539: 1
       547: 1
       554: 1
       555: 1
       559: 1
       560: 1
       561: 1
       586: 1
       594: 1
       601: 1
       602: 1
       606: 1
       607: 1
       608: 1
       623: 1
       630: 1
       631: 1
       637: 1
       638: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       699: 1
       744: 1
       751: 1
       752: 1
       796: 1
       803: 1
       804: 1
       830: 1
       838: 1
       845: 1
       846: 1
       850: 1
       851: 1
       852: 1
       956: 1
      1010: 1
      1055: 1
      1062: 1
      1063: 1
      1267: 1

1268:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: 1
        55: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       109: 1
       115: 1
       117: 1
       120: 1
       121: 1
       123: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       139: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       160: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       203: 1
       209: 1
       211: 1
       216: 1
       218: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       233: 1
       239: 1
       241: 1
       244: 1
       245: 1
       247: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       263: 1
       269: 1
       271: 1
       274: 1
       275: 1
       277: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       293: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       333: 1
       341: 1
       347: 1
       349: 1
       352: 1
       353: 1
       355: 1
       370: 1
       376: 1
       378: 1
       383: 1
       385: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       409: 1
       415: 1
       417: 1
       422: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       439: 1
       445: 1
       447: 1
       450: 1
       451: 1
       453: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       506: 1
       512: 1
       514: 1
       540: 1
       548: 1
       554: 1
       556: 1
       559: 1
       560: 1
       562: 1
       587: 1
       595: 1
       601: 1
       603: 1
       606: 1
       607: 1
       609: 1
       624: 1
       630: 1
       632: 1
       637: 1
       639: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       700: 1
       745: 1
       751: 1
       753: 1
       797: 1
       803: 1
       805: 1
       831: 1
       839: 1
       845: 1
       847: 1
       850: 1
       851: 1
       853: 1
       957: 1
      1011: 1
      1056: 1
      1062: 1
      1064: 1
      1268: 1

1269:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        22: 1
        23: 1
        24: 1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: q+1
        64: 1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        73: 1
        74: 1
        75: 1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        86: 1
        87: 1
        88: 1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       110: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: q+1
       148: 1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: q+1
       169: 1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       178: 1
       179: 1
       180: 1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       204: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       226: q+1
       227: 1
       234: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       251: 1
       252: 1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       264: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       281: 1
       282: 1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: q+1
       302: 1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       334: 1
       342: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       371: 1
       377: 1
       378: 1
       379: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       391: 1
       393: q+1
       394: 1
       410: 1
       416: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       432: q+1
       433: 1
       440: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       456: 1
       457: 1
       458: 1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       507: 1
       513: 1
       514: 1
       515: 1
       541: 1
       549: 1
       555: 1
       556: 1
       557: 1
       560: 1
       561: 1
       562: 1
       588: 1
       596: 1
       602: 1
       603: 1
       604: 1
       607: 1
       608: 1
       609: 1
       625: 1
       631: 1
       632: 1
       633: 1
       638: 1
       639: 1
       640: 1
       643: 1
       644: 1
       645: 1
       647: q+1
       648: 1
       701: 1
       746: 1
       752: 1
       753: 1
       754: 1
       798: 1
       804: 1
       805: 1
       806: 1
       832: 1
       840: 1
       846: 1
       847: 1
       848: 1
       851: 1
       852: 1
       853: 1
       958: 1
      1012: 1
      1057: 1
      1063: 1
      1064: 1
      1065: 1
      1269: 1

1270:    0: q^2+1
         2: 1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         8: 1
        10: 1
        11: q^2+1
        12: q^2+1
        14: 1
        15: q^2+1
        17: 1
        18: q^2+1
        19: q^2+1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: q^2+1
        35: 1
        37: 1
        38: q^2+1
        39: q^2+1
        42: 1
        44: 1
        45: q^2+1
        46: q^2+1
        48: 1
        49: q^2+1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: q^2+1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: q^2+1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: q^2+1
        99: 1
       101: 1
       102: q^2+1
       103: q^2+1
       111: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: q^2+1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: q^2+1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: q^2+1
       205: 1
       212: 1
       219: 1
       223: 1
       224: 1
       227: 1
       235: 1
       242: 1
       246: 1
       247: 1
       251: 1
       252: 1
       255: 1
       257: 1
       265: 1
       272: 1
       276: 1
       277: 1
       281: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: q^2+1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       372: 1
       379: 1
       386: 1
       390: 1
       391: 1
       394: 1
       411: 1
       418: 1
       425: 1
       429: 1
       430: 1
       433: 1
       441: 1
       448: 1
       452: 1
       453: 1
       457: 1
       458: 1
       461: 1
       463: 1
       508: 1
       515: 1
       542: 1
       550: 1
       557: 1
       561: 1
       562: 1
       589: 1
       597: 1
       604: 1
       608: 1
       609: 1
       626: 1
       633: 1
       640: 1
       644: 1
       645: 1
       648: 1
       702: 1
       747: 1
       754: 1
       799: 1
       806: 1
       833: 1
       841: 1
       848: 1
       852: 1
       853: 1
       959: 1
      1013: 1
      1058: 1
      1065: 1
      1270: 1

1271:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       807: 1
       808: q+1
       809: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       823: 1
       850: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       898: 1
       906: 1
       918: 1
       960: 1
       971: 1
      1014: 1
      1015: 1
      1022: 1
      1025: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1074: 1
      1094: 1
      1217: 1
      1271: 1

1272:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        60: q+1
        61: q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q^2+q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       118: q+1
       119: q+1
       122: q+1
       123: 1
       124: q+1
       127: 1
       128: q+1
       129: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       205: q+1
       206: q+1
       207: 1
       212: 1
       213: 1
       214: q+1
       219: 1
       220: q+1
       223: 1
       224: 1
       225: q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: 1
       246: 1
       248: q+1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       319: q+1
       327: q+1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: q+1
       473: q+1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       646: 1
       648: 1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       849: 1
       855: 1
       856: 1
       857: 1
       858: 1
       887: 1
       897: 1
       905: 1
       907: 1
       909: 1
       911: 1
       933: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1068: 1
      1069: 1
      1103: 1
      1115: 1
      1166: 1
      1218: 1
      1272: 1

1273:    0: 4q^3+10q^2+6q+1
         1: 4q^3+10q^2+6q+1
         2: 4q^3+10q^2+6q+1
         3: 4q^3+10q^2+6q+1
         4: q^3+8q^2+6q+1
         5: q^3+8q^2+6q+1
         6: q^3+5q^2+5q+1
         7: 4q^3+10q^2+6q+1
         8: 4q^3+10q^2+6q+1
         9: 4q^3+10q^2+6q+1
        10: q^3+5q^2+5q+1
        11: q^3+6q^2+6q+1
        12: q^3+6q^2+6q+1
        13: q^3+8q^2+6q+1
        14: q^3+8q^2+6q+1
        15: q^3+8q^2+6q+1
        16: q^3+8q^2+6q+1
        17: q^3+8q^2+6q+1
        18: q^3+8q^2+6q+1
        19: 7q^2+6q+1
        20: q^3+5q^2+5q+1
        21: q^3+5q^2+5q+1
        22: 4q^3+10q^2+6q+1
        23: q^3+6q^2+6q+1
        24: q^3+6q^2+6q+1
        25: q^2+4q+1
        26: q^3+5q^2+5q+1
        27: q^3+5q^2+5q+1
        28: q^3+6q^2+6q+1
        29: 2q^2+5q+1
        30: q^3+6q^2+6q+1
        31: 2q^2+5q+1
        32: 4q^2+6q+1
        33: 4q^2+5q+1
        34: q^3+8q^2+6q+1
        35: q^3+8q^2+6q+1
        36: q^3+8q^2+6q+1
        37: 2q^2+3q+1
        38: 2q^2+4q+1
        39: q^3+6q^2+6q+1
        40: 4q^2+5q+1
        41: q^3+8q^2+6q+1
        42: q^3+8q^2+6q+1
        43: q^3+8q^2+6q+1
        44: 2q^2+3q+1
        45: q^3+6q^2+6q+1
        46: 2q^2+4q+1
        47: 7q^2+6q+1
        48: 7q^2+6q+1
        49: 7q^2+6q+1
        50: 2q^2+3q+1
        51: 2q^2+3q+1
        52: q^3+5q^2+5q+1
        53: q^2+4q+1
        54: q^3+6q^2+6q+1
        55: q^3+6q^2+6q+1
        56: 4q^2+6q+1
        57: q^2+4q+1
        58: q^2+4q+1
        59: q^3+5q^2+5q+1
        60: 2q^2+5q+1
        61: 2q^2+5q+1
        62: 4q+1
        63: 2q^2+5q+1
        64: 2q^2+5q+1
        65: 4q+1
        66: 2q^2+5q+1
        67: 2q^2+5q+1
        68: 4q^2+6q+1
        69: q^2+5q+1
        70: 4q^2+6q+1
        71: 4q^2+5q+1
        72: 4q^2+5q+1
        73: q^3+8q^2+6q+1
        74: 2q^2+4q+1
        75: q^3+6q^2+6q+1
        76: 2q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+4q+1
        80: 2q+1
        81: q^3+6q^2+6q+1
        82: q^2+3q+1
        83: q^2+4q+1
        84: 4q^2+5q+1
        85: 4q^2+5q+1
        86: q^3+8q^2+6q+1
        87: q^3+6q^2+6q+1
        88: 2q^2+4q+1
        89: 2q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+6q^2+6q+1
        93: q^2+3q+1
        94: 2q^2+4q+1
        95: 2q+1
        96: q^2+4q+1
        97: 4q^2+5q+1
        98: 7q^2+6q+1
        99: 7q^2+6q+1
       100: 7q^2+6q+1
       101: q^2+2q+1
       102: 2q^2+4q+1
       103: 2q^2+4q+1
       104: q^2+2q+1
       105: 2q^2+3q+1
       106: 2q^2+3q+1
       107: q^2+4q+1
       108: 4q+1
       109: 4q+1
       110: 4q^2+6q+1
       111: 4q^2+6q+1
       112: 2q+1
       113: 2q+1
       114: q^2+4q+1
       115: q^2+4q+1
       116: 2q^2+5q+1
       117: 2q^2+5q+1
       118: q^2+5q+1
       119: 4q+1
       120: 4q+1
       121: 2q^2+5q+1
       122: 2q^2+5q+1
       123: 2q+1
       124: 4q+1
       125: 4q+1
       126: 2q^2+5q+1
       127: 2q+1
       128: 2q^2+5q+1
       129: 4q+1
       130: q^2+5q+1
       131: q^2+5q+1
       132: 4q^2+6q+1
       133: q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: 4q^2+5q+1
       137: 2q+1
       138: 2q^2+4q+1
       139: q^3+6q^2+6q+1
       140: q^2+4q+1
       141: 2q+1
       142: 2q+1
       143: 2q^2+3q+1
       144: 2q+1
       145: q^2+3q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: 2q+1
       150: q^2+3q+1
       151: q^2+3q+1
       152: q^2+4q+1
       153: 2q+1
       154: q^2+4q+1
       155: 2q^2+3q+1
       156: q^2+2q+1
       157: 4q^2+5q+1
       158: 2q+1
       159: q^3+6q^2+6q+1
       160: 2q^2+4q+1
       161: q^2+4q+1
       162: 2q+1
       163: 2q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: 2q+1
       167: 2q+1
       168: q^2+3q+1
       169: q^2+3q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: q^2+4q+1
       174: 2q+1
       175: q^2+4q+1
       176: 4q^2+5q+1
       177: 4q^2+5q+1
       178: 7q^2+6q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: 2q^2+4q+1
       185: q+1
       186: 2q^2+4q+1
       187: q+1
       188: 3q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: 2q+1
       192: 2q+1
       193: 4q+1
       194: 4q+1
       195: 4q+1
       196: 4q^2+6q+1
       197: q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       201: q^2+4q+1
       202: 4q+1
       203: 4q+1
       204: q^2+5q+1
       205: q^2+5q+1
       206: 2q+1
       207: q+1
       208: 4q+1
       210: 2q^2+5q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: 2q+1
       215: 4q+1
       217: 2q+1
       218: 2q^2+5q+1
       219: 2q+1
       220: 4q+1
       221: 4q+1
       222: q^2+5q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q^2+2q+1
       230: 2q^2+3q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q^2+4q+1
       235: q^2+4q+1
       236: 1
       237: q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+3q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 2q+1
       246: 2q+1
       248: 2q+1
       249: 2q+1
       250: q^2+3q+1
       251: q+1
       252: q^2+3q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: q^2+4q+1
       257: 1
       258: q+1
       259: 2q^2+3q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q^2+4q+1
       265: q^2+4q+1
       266: q+1
       267: 1
       268: 2q+1
       269: 2q+1
       270: q^2+3q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: q+1
       278: q+1
       279: q+1
       280: 2q+1
       282: 2q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: q^2+4q+1
       287: 1
       288: q^2+2q+1
       289: q^2+2q+1
       290: 4q^2+5q+1
       291: q+1
       292: 2q^2+4q+1
       293: 2q^2+4q+1
       294: 3q+1
       295: q+1
       296: q+1
       297: q^2+2q+1
       298: q+1
       299: q+1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: q+1
       305: q+1
       306: 3q+1
       307: q+1
       308: 3q+1
       310: q^2+2q+1
       311: q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: 4q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: 4q+1
       324: 4q+1
       325: 4q+1
       326: q^2+5q+1
       327: q+1
       328: 1
       329: 2q+1
       330: q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: q+1
       338: 2q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: q+1
       346: 4q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: q+1
       361: 2q+1
       362: q+1
       363: q^2+4q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: 1
       375: q+1
       377: 2q+1
       380: 1
       381: q+1
       382: 2q+1
       384: q+1
       385: q^2+3q+1
       386: q+1
       387: q+1
       388: q+1
       389: 2q+1
       390: q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: 1
       399: 2q+1
       400: q+1
       401: q+1
       402: q^2+4q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: 2q+1
       411: 2q+1
       412: q+1
       413: 1
       414: 2q+1
       416: q^2+3q+1
       417: q+1
       418: q+1
       420: 1
       421: q+1
       424: 2q+1
       426: q+1
       427: q+1
       428: 2q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q+1
       438: 1
       439: 1
       440: 3q+1
       441: 3q+1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: q+1
       458: q+1
       459: 1
       460: q+1
       461: q+1
       462: 3q+1
       463: 1
       466: q+1
       467: 1
       468: 1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 4q+1
       482: q+1
       483: 1
       484: 1
       490: 2q+1
       491: 1
       492: 1
       493: 1
       499: 2q+1
       500: 1
       501: 1
       502: q+1
       503: q+1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: q+1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: q+1
       523: q+1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: 2q+1
       532: q+1
       533: 2q+1
       534: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       549: q+1
       550: q+1
       551: 1
       553: q+1
       555: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       564: q+1
       565: 1
       566: q+1
       567: 1
       569: 1
       570: q+1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: 2q+1
       578: q+1
       579: q+1
       580: 2q+1
       581: 1
       582: 1
       583: q+1
       584: 1
       588: q+1
       589: q+1
       592: 1
       599: 1
       600: q+1
       603: q+1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 3q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: q+1
       626: q+1
       627: 1
       629: 1
       631: q+1
       635: 1
       636: 1
       639: q+1
       641: 1
       642: 1
       643: q+1
       646: 1
       647: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       667: 1
       675: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: q+1
       719: q+1
       721: 1
       731: 1
       732: 1
       738: q+1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       770: 1
       771: q+1
       773: 1
       774: 1
       775: 1
       781: q+1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       808: q+1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: q+1
       825: 1
       827: 1
       836: 1
       844: 1
       849: 1
       850: 1
       851: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       909: 1
       911: 1
       913: 1
       916: 1
       918: 1
       919: 1
       934: 1
       942: 1
       953: 1
       962: 1
       966: 1
       967: 1
       970: 1
       971: 1
       974: 1
       978: 1
       986: 1
      1008: 1
      1016: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1032: 1
      1061: 1
      1069: 1
      1070: 1
      1074: 1
      1104: 1
      1112: 1
      1118: 1
      1123: 1
      1171: 1
      1174: 1
      1224: 1
      1227: 1
      1273: 1

1274:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       455: 1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       613: 1
       621: 1
       622: 1
       624: 1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       682: 1
       689: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       820: 1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       900: 1
       939: 1
       960: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1183: 1
      1274: 1

1275:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       450: 1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       612: 1
       620: 1
       622: 1
       623: 1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       665: 1
       669: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       767: 1
       776: 1
       778: 1
       819: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       878: 1
       879: 1
       882: 1
       886: 1
       899: 1
       906: 1
       918: 1
       935: 1
       938: 1
       939: 1
       980: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1086: 1
      1141: 1
      1275: 1

1276:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       646: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       707: 1
       756: 1
       758: 1
       807: 1
       808: 1
       809: 1
       815: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       872: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       895: 1
      1015: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1095: 1
      1276: 1

1277:    0: q^3+4q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: 2q^2+4q+1
         5: 2q^2+4q+1
         6: q^2+4q+1
         7: 3q^2+4q+1
         8: q^3+4q^2+4q+1
         9: 3q^2+4q+1
        10: q^3+4q^2+4q+1
        11: 2q^2+4q+1
        12: 2q^2+4q+1
        13: q^2+4q+1
        14: 2q^2+4q+1
        15: 2q^2+4q+1
        16: q^2+4q+1
        17: 2q^2+4q+1
        18: 2q^2+4q+1
        19: q^2+4q+1
        20: q^2+4q+1
        21: q^2+4q+1
        22: 3q^2+4q+1
        23: 2q^2+4q+1
        24: 2q^2+4q+1
        25: q^2+4q+1
        26: 3q^2+4q+1
        27: q^3+4q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+4q+1
        30: q^2+4q+1
        31: 2q^2+4q+1
        32: q^2+4q+1
        33: 4q+1
        34: q^2+4q+1
        35: 2q^2+4q+1
        36: q^2+4q+1
        37: q^2+2q+1
        38: 2q+1
        39: 2q^2+4q+1
        40: 4q+1
        41: q^2+4q+1
        42: 2q^2+4q+1
        43: q^2+4q+1
        44: q^2+2q+1
        45: 2q^2+4q+1
        46: 2q+1
        47: 4q+1
        48: q^2+4q+1
        49: q^2+4q+1
        50: 2q+1
        51: 2q+1
        52: q^2+4q+1
        53: q^2+4q+1
        54: q^2+4q+1
        55: q^2+4q+1
        56: q^2+4q+1
        57: q^2+4q+1
        58: q^2+4q+1
        59: 3q^2+4q+1
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: 4q+1
        63: q^2+4q+1
        64: 2q^2+4q+1
        65: 4q+1
        66: q^2+4q+1
        67: 2q^2+4q+1
        68: 4q+1
        69: q^2+4q+1
        70: q^2+4q+1
        71: 4q+1
        72: 4q+1
        73: q^2+4q+1
        74: 2q+1
        75: 2q^2+4q+1
        76: 2q+1
        78: q^2+2q+1
        79: 2q+1
        80: q+1
        81: q^2+4q+1
        82: q^2+2q+1
        83: 2q+1
        84: 4q+1
        85: 4q+1
        86: q^2+4q+1
        87: 2q^2+4q+1
        88: 2q+1
        89: 2q+1
        91: q^2+2q+1
        92: q^2+4q+1
        93: q^2+2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: 4q+1
        98: 4q+1
        99: q^2+4q+1
       100: 4q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: 2q+1
       106: 2q+1
       107: q^2+4q+1
       108: 4q+1
       109: 4q+1
       110: 4q+1
       111: q^2+4q+1
       112: 2q+1
       113: 2q+1
       114: q^2+4q+1
       115: q^2+4q+1
       116: q^2+4q+1
       117: q^2+4q+1
       118: q^2+4q+1
       119: 4q+1
       120: 4q+1
       121: q^2+4q+1
       122: 2q^2+4q+1
       123: 2q+1
       124: 4q+1
       125: 4q+1
       126: q^2+4q+1
       127: 2q+1
       128: 2q^2+4q+1
       129: 4q+1
       130: 4q+1
       131: q^2+4q+1
       132: 4q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 4q+1
       137: 2q+1
       138: 2q+1
       139: q^2+4q+1
       140: 2q+1
       141: 2q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: q^2+2q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       155: 2q+1
       156: q+1
       157: 4q+1
       158: 2q+1
       159: q^2+4q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       165: q^2+2q+1
       166: q+1
       167: 2q+1
       169: q^2+2q+1
       170: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: 4q+1
       177: 4q+1
       178: 4q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       183: q+1
       184: 2q+1
       185: 1
       186: 2q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: 2q+1
       193: 4q+1
       194: 4q+1
       195: 4q+1
       196: 4q+1
       197: q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       201: q^2+4q+1
       202: 4q+1
       203: 4q+1
       204: 4q+1
       205: q^2+4q+1
       206: 2q+1
       207: q+1
       208: 4q+1
       209: 2q+1
       210: q^2+4q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: 2q+1
       215: 4q+1
       216: 2q+1
       217: 2q+1
       218: q^2+4q+1
       219: 2q+1
       220: 4q+1
       221: 4q+1
       222: 4q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       227: q+1
       228: 1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 1
       237: q+1
       242: q+1
       243: q+1
       246: q+1
       248: 2q+1
       251: q+1
       252: q^2+2q+1
       253: q+1
       255: q+1
       256: 2q+1
       257: 1
       258: 1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: 2q+1
       265: 2q+1
       266: q+1
       267: 1
       272: q+1
       273: 2q+1
       276: q^2+2q+1
       277: q+1
       278: q+1
       282: q+1
       283: q+1
       285: q+1
       286: 2q+1
       287: 1
       288: q+1
       289: q+1
       290: 4q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: q+1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: 4q+1
       317: q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: 4q+1
       324: 4q+1
       325: 4q+1
       326: 4q+1
       327: q+1
       328: 1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: q+1
       346: 4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: q+1
       361: 2q+1
       362: q+1
       363: 2q+1
       364: 1
       365: 1
       372: q+1
       373: 1
       380: 1
       381: q+1
       386: q+1
       387: q+1
       390: q+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: 2q+1
       400: q+1
       401: q+1
       402: 2q+1
       403: 1
       404: 1
       411: q+1
       412: q+1
       413: 1
       418: q+1
       420: 1
       426: q+1
       430: q+1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: q+1
       467: 1
       468: 1
       469: q+1
       470: q+1
       471: q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 4q+1
       481: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: 2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: 2q+1
       498: q+1
       499: 2q+1
       500: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: q+1
       523: q+1
       524: 1
       526: 1
       534: 1
       543: 1
       550: q+1
       551: 1
       558: 1
       561: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       569: 1
       570: q+1
       571: 1
       573: 1
       581: 1
       582: 1
       589: q+1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: q+1
       674: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: q+1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       731: 1
       739: 1
       748: 1
       757: 1
       758: 1
       761: 1
       762: 1
       774: 1
       782: 1
       801: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       849: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       875: 1
       876: 1
       880: 1
       882: 1
       883: 1
       885: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       909: 1
       911: 1
       962: 1
       966: 1
      1016: 1
      1021: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1084: 1
      1089: 1
      1091: 1
      1096: 1
      1101: 1
      1277: 1

1278:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q+1
        19: q^2+3q+1
        20: q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q+1
        68: q^2+3q+1
        69: q^2+3q+1
        70: 1
        71: 1
        72: q^2+3q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q^2+3q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q^2+3q+1
       118: q^2+3q+1
       119: 1
       120: q^2+3q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q^2+3q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q^2+3q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q^2+3q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q^2+3q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       244: q+1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       279: q+1
       283: q+1
       284: q+1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q^2+3q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       388: q+1
       392: 1
       393: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: q+1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       427: q+1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       559: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: q+1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       606: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       642: 1
       646: 1
       647: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: q+1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: q+1
       809: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       823: 1
       850: 1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: 1
       877: 1
       882: 1
       886: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       918: 1
       935: 1
       938: 1
       939: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1022: 1
      1025: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1102: 1
      1105: 1
      1141: 1
      1183: 1
      1278: 1

1279:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 2q^2+3q+1
        23: 2q+1
        24: 2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        39: 2q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: 2q+1
        52: 2q^2+3q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q^2+3q+1
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        81: 2q^2+3q+1
        82: 2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       103: q^2+2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q^2+2q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q^2+3q+1
       115: q^2+2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: 2q+1
       123: q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       135: 2q+1
       136: q^2+3q+1
       137: q+1
       139: 2q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       145: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       155: 2q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       186: q^2+2q+1
       187: q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: q^2+2q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: q+1
       208: q^2+3q+1
       209: q+1
       210: 2q+1
       211: q+1
       212: q+1
       214: 2q+1
       215: q^2+3q+1
       216: q+1
       218: 2q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       230: 2q+1
       231: q+1
       233: 1
       237: q+1
       238: 2q+1
       239: q+1
       241: q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       252: q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: 2q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       293: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       299: 1
       303: q+1
       304: q+1
       305: q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: q+1
       335: q+1
       338: 2q+1
       339: q+1
       341: 1
       345: q+1
       346: q^2+3q+1
       347: q+1
       349: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       355: 1
       359: 1
       361: 1
       367: q+1
       368: q+1
       370: 1
       381: q+1
       382: 2q+1
       383: q+1
       385: q+1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       436: q+1
       437: q+1
       439: 1
       443: 1
       444: 2q+1
       445: q+1
       447: 1
       454: q+1
       455: q+1
       456: q+1
       458: 1
       464: q+1
       465: 1
       466: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       495: 1
       497: 1
       503: q+1
       504: q+1
       506: 1
       510: 1
       511: 2q+1
       512: q+1
       514: 1
       522: 1
       529: 1
       531: 1
       545: q+1
       546: q+1
       548: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       613: 1
       615: 1
       621: 1
       622: q+1
       624: 1
       635: 1
       636: q+1
       639: 1
       649: 1
       650: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: q+1
       700: 1
       718: 1
       734: 1
       736: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: q+1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       854: 1
       861: 1
       862: 1
       868: 1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       939: 1
       960: 1
       961: 1
       967: 1
       968: 1
       970: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1029: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1109: 1
      1165: 1
      1180: 1
      1182: 1
      1279: 1

1280:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       613: 1
       615: 1
       635: 1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       813: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       893: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1166: 1
      1280: 1

1281:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 2q^2+3q+1
         5: 3q^2+3q+1
         6: 3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: q^2+2q+1
        25: 3q^2+3q+1
        26: q^2+2q+1
        27: 2q^2+3q+1
        28: 3q^2+3q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 3q^2+3q+1
        41: q^2+2q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q^2+2q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q^2+3q+1
        61: q^2+2q+1
        62: 3q^2+3q+1
        63: q^2+2q+1
        64: q^2+3q+1
        65: 2q^2+3q+1
        66: q^2+2q+1
        67: 2q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q^2+3q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+3q+1
        88: q+1
        89: 2q^2+3q+1
        91: q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: q+1
       104: q^2+2q+1
       105: 2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: q+1
       112: 2q^2+3q+1
       113: q^2+2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q^2+2q+1
       119: q^2+3q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+3q+1
       123: q+1
       124: 2q+1
       125: q^2+2q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q^2+3q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: 2q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: q+1
       141: 2q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       149: 2q+1
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q^2+3q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q^2+3q+1
       165: q^2+3q+1
       166: q+1
       167: 2q^2+3q+1
       169: q^2+3q+1
       170: q^2+2q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: q+1
       179: 2q+1
       180: 1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: q+1
       198: q^2+2q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: q+1
       206: q^2+3q+1
       207: q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: 2q+1
       224: 1
       225: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: q+1
       236: 2q+1
       237: q+1
       242: q+1
       248: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: 1
       266: q^2+3q+1
       267: q+1
       272: q+1
       273: q^2+3q+1
       276: q^2+3q+1
       277: q+1
       278: q+1
       281: q+1
       282: 1
       283: q^2+2q+1
       285: q+1
       286: q+1
       287: q+1
       288: 2q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: 2q+1
       298: 2q+1
       299: 1
       300: 2q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: q+1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: q+1
       320: q+1
       321: 2q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: 2q+1
       354: 2q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       359: 1
       361: 1
       362: 1
       363: 1
       364: q+1
       365: q+1
       380: 2q+1
       381: q+1
       386: q+1
       392: 2q+1
       395: 1
       396: q+1
       397: 2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       411: 1
       412: q^2+3q+1
       413: q+1
       418: q+1
       419: q+1
       420: 1
       425: 1
       426: q+1
       429: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: 2q+1
       443: 1
       448: 1
       454: q+1
       457: q+1
       458: 1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: q+1
       474: 1
       475: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: q+1
       485: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: 2q+1
       510: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: q+1
       563: 1
       564: 1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: q+1
       589: 1
       590: 1
       597: 1
       598: q+1
       599: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: q+1
       635: 1
       640: 1
       646: q+1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       707: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       856: 1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       961: 1
       963: 1
       965: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1015: 1
      1018: 1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1095: 1
      1098: 1
      1167: 1
      1198: 1
      1281: 1

1282:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       610: 1
       611: 1
       617: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: 1
       686: 1
       687: 1
       693: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       774: 1
       783: 1
       792: 1
       799: 1
       808: 1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       888: 1
       962: 1
       963: 1
       964: 1
       997: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1168: 1
      1282: 1

1283:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q^2+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: 1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q^2+1
        36: 1
        37: q^2+1
        38: q^2+1
        39: q^2+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q^2+q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q^2+1
        68: q+1
        69: q^2+q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: q^2+1
        75: q^2+1
        76: 1
        78: q^2+1
        79: 1
        80: q^2+1
        81: 1
        82: q^2+1
        83: q^2+1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: q^2+1
       128: q^2+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q^2+1
       141: 1
       144: q^2+1
       145: q^2+1
       146: 1
       149: 1
       151: q^2+1
       152: 1
       153: q^2+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q^2+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: q^2+1
       248: 1
       251: q^2+1
       252: q^2+1
       253: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: q^2+1
       392: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       678: 1
       681: 1
       682: 1
       684: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       707: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       782: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       882: 1
       889: 1
       892: 1
       893: 1
       895: 1
       964: 1
       965: 1
       966: 1
      1005: 1
      1006: 1
      1018: 1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1098: 1
      1169: 1
      1283: 1

1284:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 2q^2+3q+1
         5: 3q^2+3q+1
         6: q^2+2q+1
         7: 3q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+2q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: 3q^2+3q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: 3q^2+3q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: q^2+2q+1
        54: 3q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q+1
        58: q^2+2q+1
        59: 3q^2+3q+1
        60: 3q^2+3q+1
        61: 2q^2+3q+1
        62: q^2+2q+1
        63: 3q^2+3q+1
        64: 2q^2+3q+1
        65: q^2+2q+1
        66: 2q^2+3q+1
        67: 2q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+2q+1
        89: q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+3q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       105: q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+3q+1
       111: 2q+1
       112: q+1
       114: q+1
       115: q^2+2q+1
       116: 3q^2+3q+1
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: q+1
       120: q^2+2q+1
       121: 2q^2+3q+1
       122: 2q^2+3q+1
       123: q^2+2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: 2q^2+3q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q+1
       146: 1
       147: q+1
       149: 1
       150: q+1
       151: q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       155: q+1
       157: q+1
       158: q+1
       159: 2q^2+3q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: 2q+1
       197: q+1
       199: q+1
       201: q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 2q^2+3q+1
       205: 2q+1
       206: q+1
       208: q+1
       209: q+1
       210: 2q^2+3q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q+1
       215: q+1
       216: 1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 2q+1
       235: 2q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       244: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: q+1
       256: 2q+1
       257: q+1
       259: q+1
       261: 1
       262: q+1
       263: q+1
       264: q^2+2q+1
       265: q+1
       266: 1
       268: 1
       269: q+1
       270: q^2+2q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: q+1
       314: q+1
       316: q+1
       317: 1
       318: q+1
       321: q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: 2q+1
       327: q+1
       329: q+1
       331: 1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q+1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: 2q+1
       343: 2q+1
       344: q+1
       346: q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: q+1
       355: 1
       358: 1
       361: 1
       362: 1
       363: 2q+1
       364: q+1
       366: 1
       368: 1
       369: 1
       370: 1
       371: q+1
       380: 1
       382: 1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       388: 1
       392: 1
       393: q+1
       397: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: 1
       405: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       414: 1
       415: q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       469: q+1
       471: 1
       472: 1
       476: q+1
       478: q+1
       480: q+1
       481: 1
       482: q+1
       485: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: 1
       494: 1
       497: 1
       498: 1
       499: 2q+1
       500: q+1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       521: 1
       524: 1
       525: q+1
       528: 1
       531: 1
       532: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: q+1
       559: 1
       566: 1
       568: 1
       570: 1
       571: 1
       572: 1
       575: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       654: 1
       656: 1
       662: q+1
       664: 1
       665: 1
       669: 1
       671: 1
       673: 1
       674: 1
       675: 1
       681: 1
       684: 1
       685: q+1
       688: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       711: 1
       717: 1
       733: 1
       736: 1
       737: 1
       760: 1
       762: 1
       763: 1
       767: 1
       769: 1
       771: 1
       773: 1
       776: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       790: 1
       791: 1
       793: 1
       798: 1
       799: 1
       800: 1
       802: 1
       804: 1
       805: 1
       806: 1
       812: 1
       815: 1
       816: 1
       819: 1
       822: 1
       823: 1
       835: 1
       840: 1
       850: 1
       859: 1
       866: 1
       868: 1
       874: 1
       876: 1
       877: 1
       886: 1
       892: 1
       895: 1
       896: 1
       899: 1
       902: 1
       903: 1
       938: 1
       965: 1
       967: 1
       973: 1
       980: 1
       982: 1
       984: 1
       986: 1
       996: 1
      1004: 1
      1005: 1
      1007: 1
      1012: 1
      1022: 1
      1028: 1
      1076: 1
      1083: 1
      1085: 1
      1102: 1
      1108: 1
      1170: 1
      1185: 1
      1207: 1
      1284: 1

1285:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q+1
        24: q^2+q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q^2+q+1
        75: q^2+q+1
        76: 1
        77: q^2+1
        78: q^2+1
        81: q^2+q+1
        82: q^2+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q^2+q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q^2+q+1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       139: q^2+q+1
       141: 1
       142: 1
       143: q^2+1
       145: q^2+1
       149: 1
       150: q^2+1
       151: q^2+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       214: q+1
       215: q+1
       216: 1
       218: q^2+q+1
       220: q+1
       221: q+1
       222: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: q^2+1
       248: 1
       249: 1
       250: q^2+1
       252: q^2+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       313: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       338: q+1
       339: 1
       341: 1
       345: q+1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: q^2+1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       470: q+1
       471: 1
       472: 1
       477: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       495: 1
       497: 1
       503: q+1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       639: 1
       655: 1
       656: 1
       663: q+1
       664: 1
       665: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       761: 1
       762: 1
       763: 1
       768: 1
       770: 1
       771: 1
       773: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       860: 1
       867: 1
       868: 1
       875: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       939: 1
       966: 1
       967: 1
       974: 1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1029: 1
      1077: 1
      1084: 1
      1085: 1
      1109: 1
      1171: 1
      1186: 1
      1285: 1

1286:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 2q^2+3q+1
        23: 2q+1
        24: 2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: 2q+1
        52: 2q^2+3q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q^2+3q+1
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: q^2+2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q^2+2q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q^2+3q+1
       115: q^2+2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: 2q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q+1
       135: 2q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 2q+1
       157: q^2+3q+1
       158: q+1
       159: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: q^2+2q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       208: q^2+3q+1
       209: q+1
       210: 2q+1
       213: q+1
       214: 2q+1
       215: q^2+3q+1
       216: q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q+1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: 2q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       259: 2q+1
       261: q+1
       262: 1
       266: q+1
       268: 2q+1
       269: q+1
       270: q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       288: q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 1
       300: q+1
       301: q+1
       302: q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       329: 2q+1
       331: q+1
       332: 1
       336: q+1
       337: q+1
       338: 2q+1
       339: q+1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       377: 1
       380: 1
       381: q+1
       382: 2q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       397: 1
       399: 1
       405: q+1
       407: q+1
       408: 1
       412: q+1
       414: 2q+1
       415: q+1
       416: q+1
       435: q+1
       437: q+1
       438: 1
       442: 1
       444: 2q+1
       445: q+1
       446: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       464: q+1
       465: 1
       466: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       485: 1
       487: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       502: q+1
       504: q+1
       505: 1
       509: 1
       511: 2q+1
       512: q+1
       513: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       566: 1
       575: 1
       577: 1
       583: q+1
       585: q+1
       586: 1
       612: 1
       614: 1
       620: 1
       622: q+1
       623: 1
       627: 1
       629: q+1
       631: 1
       649: 1
       650: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       664: 1
       665: 1
       669: 1
       676: 1
       677: q+1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: q+1
       699: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: q+1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       854: 1
       861: 1
       862: 1
       868: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       906: 1
       907: 1
       913: 1
       914: 1
       916: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       942: 1
       953: 1
       980: 1
      1026: 1
      1071: 1
      1086: 1
      1087: 1
      1093: 1
      1106: 1
      1113: 1
      1137: 1
      1139: 1
      1286: 1

1287:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 2q^2+3q+1
         6: 3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 2q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q^2+3q+1
        25: 3q^2+3q+1
        26: q^2+2q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+3q+1
        31: 3q^2+3q+1
        32: 2q^2+3q+1
        33: 3q^2+3q+1
        34: q^2+2q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+3q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q^2+2q+1
        51: 2q^2+3q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q^2+2q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: 2q^2+3q+1
        62: 2q^2+3q+1
        63: q^2+2q+1
        64: 2q+1
        65: 3q^2+3q+1
        66: q^2+2q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: q^2+3q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: q^2+3q+1
        76: 2q^2+3q+1
        78: q^2+3q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: 2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       104: q^2+2q+1
       105: q+1
       106: 2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: q+1
       112: q^2+2q+1
       113: 2q^2+3q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q^2+2q+1
       119: 2q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: q^2+3q+1
       125: q^2+2q+1
       126: 2q+1
       127: q+1
       128: q^2+3q+1
       129: 2q^2+3q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: q+1
       135: q^2+3q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^2+3q+1
       144: q+1
       145: q^2+3q+1
       146: q^2+2q+1
       148: q+1
       149: 2q^2+3q+1
       151: q^2+3q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q+1
       155: q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: q+1
       162: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       169: 2q+1
       170: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: q+1
       185: q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: 2q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: q+1
       198: q^2+2q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: q+1
       206: q+1
       207: 2q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: q+1
       213: q+1
       214: q^2+3q+1
       215: 2q+1
       216: 2q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: 1
       224: 2q+1
       225: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: 1
       236: q+1
       237: q^2+3q+1
       242: q+1
       243: q+1
       246: 1
       247: q+1
       248: q^2+3q+1
       251: q+1
       252: q^2+3q+1
       253: q^2+2q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: q+1
       266: q+1
       267: 2q+1
       272: q+1
       273: 2q+1
       276: q+1
       277: 2q+1
       283: 2q+1
       286: 2q+1
       287: 2q+1
       288: 1
       289: 2q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: 2q+1
       298: 1
       299: 2q+1
       300: q+1
       302: q+1
       303: 2q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: q+1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: q+1
       320: q+1
       321: q+1
       322: 2q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: q+1
       328: q+1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: q+1
       336: q+1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q+1
       343: 1
       344: 1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: 2q+1
       354: 1
       355: 2q+1
       356: 1
       357: q+1
       358: q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       372: 1
       373: 1
       374: q+1
       379: 1
       380: q+1
       381: q^2+3q+1
       386: q+1
       387: q+1
       390: 1
       391: q+1
       392: q+1
       394: q+1
       395: q+1
       396: 1
       397: 1
       398: q+1
       399: 1
       401: 1
       402: 1
       403: q+1
       404: q+1
       412: q+1
       413: 2q+1
       418: q+1
       431: 2q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: 2q+1
       448: 1
       449: q+1
       452: 1
       453: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: q+1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: q+1
       487: 1
       489: 1
       490: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: 2q+1
       515: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: q+1
       550: 1
       551: 1
       552: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       563: q+1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: q+1
       633: 1
       646: q+1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       756: 1
       758: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       872: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       907: 1
       908: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
      1015: 1
      1017: 1
      1072: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1097: 1
      1114: 1
      1146: 1
      1287: 1

1288:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       309: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       688: 1
       690: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       810: 1
       856: 1
       862: 1
       864: 1
       866: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       890: 1
       907: 1
       909: 1
       911: 1
       933: 1
      1073: 1
      1087: 1
      1089: 1
      1091: 1
      1115: 1
      1288: 1

1289:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       564: 1
       610: 1
       611: 1
       617: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       722: 1
       731: 1
       740: 1
       747: 1
       808: 1
       857: 1
       863: 1
       864: 1
       865: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: 1
       908: 1
       909: 1
       910: 1
       943: 1
      1074: 1
      1088: 1
      1089: 1
      1090: 1
      1116: 1
      1289: 1

1290:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q+1
        16: q+1
        17: q^2+q+1
        18: q^2+1
        19: q^2+q+1
        20: 1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q^2+1
        43: 1
        44: q^2+1
        45: q^2+1
        46: q^2+1
        47: q+1
        48: q^2+q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q^2+q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q^2+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q^2+q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: q^2+1
        88: q^2+1
        89: 1
        91: q^2+1
        92: 1
        93: q^2+1
        94: 1
        95: q^2+1
        96: q^2+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+q+1
       119: 1
       120: q+1
       121: 1
       122: q^2+1
       123: q^2+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: q+1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q^2+1
       162: 1
       165: q^2+1
       166: q^2+1
       167: 1
       169: q^2+1
       170: 1
       173: 1
       174: q^2+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q^2+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: q^2+1
       273: 1
       276: q^2+1
       277: q^2+1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: q^2+1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       674: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       730: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       889: 1
       890: 1
       891: 1
       895: 1
       910: 1
       911: 1
       912: 1
       951: 1
       952: 1
      1017: 1
      1075: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1117: 1
      1290: 1

1291:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+1
        45: q^2+q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q+1
        62: q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q^2+q+1
        87: q^2+q+1
        89: 1
        90: q^2+1
        91: q^2+1
        92: q^2+q+1
        93: q^2+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       114: q+1
       115: q+1
       116: q^2+q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^2+q+1
       122: q^2+q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: q^2+q+1
       162: 1
       163: 1
       164: q^2+1
       165: q^2+1
       167: 1
       168: q^2+1
       169: q^2+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       191: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       199: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       208: q+1
       209: 1
       210: q^2+q+1
       213: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: q^2+1
       273: 1
       274: 1
       275: q^2+1
       276: q^2+1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       312: q+1
       314: q+1
       316: q+1
       317: 1
       318: 1
       321: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       329: q+1
       331: 1
       332: 1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: q^2+1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       469: q+1
       471: 1
       472: 1
       476: q+1
       478: q+1
       480: q+1
       481: 1
       482: 1
       485: 1
       487: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       502: q+1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: 1
       521: 1
       523: 1
       524: 1
       525: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       631: 1
       654: 1
       656: 1
       662: q+1
       664: 1
       665: 1
       669: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       708: 1
       710: 1
       711: 1
       715: 1
       717: 1
       719: 1
       721: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       859: 1
       866: 1
       868: 1
       883: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       911: 1
       913: 1
       919: 1
       936: 1
       938: 1
       940: 1
       942: 1
       953: 1
       980: 1
      1026: 1
      1076: 1
      1091: 1
      1093: 1
      1106: 1
      1118: 1
      1142: 1
      1291: 1

1292:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 3q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 2q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 3q^2+3q+1
        23: 2q^2+3q+1
        24: 3q^2+3q+1
        25: q^2+2q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+3q+1
        31: 3q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+2q+1
        34: 3q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: 2q^2+3q+1
        55: 3q^2+3q+1
        56: 2q^2+3q+1
        57: q+1
        58: q^2+2q+1
        59: 3q^2+3q+1
        60: 2q^2+3q+1
        61: 3q^2+3q+1
        62: q^2+2q+1
        63: 2q^2+3q+1
        64: 2q+1
        65: q^2+2q+1
        66: 3q^2+3q+1
        67: 2q^2+3q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: 2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q^2+3q+1
        74: q^2+2q+1
        75: 2q^2+3q+1
        76: q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       106: q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+3q+1
       111: 2q+1
       113: q+1
       114: q+1
       115: q^2+2q+1
       116: 2q^2+3q+1
       117: 3q^2+3q+1
       118: 2q^2+3q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       127: q^2+2q+1
       128: 2q^2+3q+1
       129: q^2+2q+1
       130: 2q^2+3q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q^2+2q+1
       141: 1
       142: q+1
       143: q^2+2q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: q+1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: 2q+1
       197: q+1
       200: q+1
       201: q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 2q^2+3q+1
       205: 2q+1
       207: q+1
       208: q+1
       209: 1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       214: q+1
       215: q+1
       216: q+1
       217: q^2+2q+1
       218: 2q^2+3q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: 1
       226: q+1
       227: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: q^2+2q+1
       235: q+1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q^2+2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 2q+1
       265: 2q+1
       267: 1
       268: 1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       279: 1
       283: 1
       284: q+1
       286: 2q+1
       287: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       306: q+1
       307: 1
       308: q+1
       313: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: 2q+1
       327: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 2q+1
       335: 2q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       401: 1
       402: 2q+1
       403: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q+1
       413: 1
       414: 1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       427: 1
       431: 1
       432: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       470: q+1
       471: 1
       472: 1
       477: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       486: 1
       487: 1
       489: 1
       490: 2q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       525: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       571: 1
       572: q+1
       576: 1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: q+1
       606: 1
       613: 1
       614: 1
       616: 1
       617: q+1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       655: 1
       656: 1
       663: q+1
       664: 1
       665: 1
       670: 1
       674: 1
       675: q+1
       680: 1
       682: 1
       683: 1
       684: 1
       685: 1
       689: 1
       690: 1
       692: 1
       693: q+1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       709: 1
       710: 1
       711: 1
       716: 1
       718: 1
       719: 1
       721: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       742: 1
       746: 1
       747: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       763: 1
       768: 1
       777: 1
       778: 1
       780: 1
       811: 1
       815: 1
       816: 1
       820: 1
       821: 1
       823: 1
       828: 1
       832: 1
       850: 1
       860: 1
       867: 1
       868: 1
       877: 1
       884: 1
       885: 1
       886: 1
       891: 1
       895: 1
       896: 1
       900: 1
       901: 1
       903: 1
       912: 1
       913: 1
       920: 1
       932: 1
       937: 1
       939: 1
       940: 1
       942: 1
       950: 1
       951: 1
       954: 1
       958: 1
       981: 1
      1022: 1
      1027: 1
      1077: 1
      1092: 1
      1093: 1
      1102: 1
      1107: 1
      1119: 1
      1143: 1
      1155: 1
      1292: 1

1293:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: 1
        72: q^2+2q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q^2+2q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q^2+2q+1
       126: 1
       127: 1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q^2+2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       303: q+1
       304: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       392: q+1
       393: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       431: q+1
       432: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: q+1
       455: q+1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: q+1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: q+1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       642: q+1
       646: q+1
       647: q+1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: 1
       704: 1
       711: 1
       714: 1
       732: 1
       733: 1
       734: 1
       737: 1
       755: 1
       756: 1
       763: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       823: 1
       850: q+1
       861: 1
       869: 1
       870: 1
       877: 1
       878: 1
       879: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       906: 1
       935: 1
       960: 1
       979: 1
      1014: 1
      1015: 1
      1022: 1
      1025: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1105: 1
      1217: 1
      1293: 1

1294:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: 2q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: 2q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: 2q+1
       183: 2q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: 2q+1
       227: 2q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       248: 2q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: 2q+1
       276: q+1
       277: 1
       278: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: 2q+1
       298: 1
       299: 1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: 2q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       392: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: q+1
       452: 1
       454: q+1
       458: 1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: q+1
       561: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: q+1
       646: q+1
       648: q+1
       650: 1
       658: 1
       659: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       849: q+1
       862: 1
       870: 1
       871: 1
       876: 1
       879: 1
       880: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       933: 1
       961: 1
       977: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1079: 1
      1087: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1218: 1
      1294: 1

1295:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q^2+2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: 2q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: 2q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 1
       102: q+1
       103: 2q+1
       104: q+1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: 2q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 1
       134: 1
       135: 2q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 2q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       180: 2q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: 2q+1
       187: 1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 2q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: q+1
       213: 1
       214: 2q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       247: q+1
       248: q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q+1
       257: 1
       258: q+1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       266: q+1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       277: q+1
       278: q+1
       282: q+1
       283: q+1
       285: q+1
       286: 2q+1
       287: 1
       288: 1
       289: 2q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: q+1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 2q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       374: q+1
       379: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       391: q+1
       392: 1
       394: 1
       395: q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: q+1
       411: q+1
       412: q+1
       413: q+1
       418: q+1
       420: q+1
       426: q+1
       430: q+1
       431: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: q+1
       557: 1
       558: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: q+1
       582: q+1
       589: q+1
       599: q+1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: 1
       706: 1
       709: 1
       722: 1
       731: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       761: 1
       774: q+1
       801: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       863: 1
       871: 1
       872: 1
       875: 1
       880: 1
       881: 1
       884: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       897: 1
       908: 1
       943: 1
       952: 1
       959: 1
       962: 1
      1016: 1
      1017: 1
      1020: 1
      1033: 1
      1060: 1
      1080: 1
      1088: 1
      1096: 1
      1097: 1
      1100: 1
      1156: 1
      1219: 1
      1295: 1

1296:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q^2+2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: 2q+1
        88: 1
        89: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 1
       102: 2q+1
       103: q+1
       104: q+1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 1
       134: 2q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: q+1
       141: q+1
       144: q+1
       145: q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       155: 2q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 1
       181: 1
       183: 1
       184: 2q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 2q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: 1
       227: 1
       228: q+1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: q+1
       237: q+1
       242: q+1
       243: q+1
       246: q+1
       248: q+1
       251: q+1
       252: q+1
       253: q+1
       255: q+1
       256: 2q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       277: 1
       278: q+1
       281: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       287: 1
       288: 2q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: q+1
       372: q+1
       373: q+1
       380: q+1
       381: q+1
       386: q+1
       387: q+1
       390: q+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       419: q+1
       420: 1
       425: 1
       426: q+1
       429: q+1
       430: 1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       543: q+1
       550: q+1
       551: q+1
       558: 1
       561: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: q+1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       652: 1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: 1
       707: 1
       708: 1
       731: q+1
       748: 1
       757: 1
       759: 1
       760: 1
       774: 1
       783: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       864: 1
       871: 1
       873: 1
       874: 1
       880: 1
       882: 1
       883: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       897: 1
       909: 1
       963: 1
       997: 1
      1006: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1042: 1
      1059: 1
      1081: 1
      1089: 1
      1096: 1
      1098: 1
      1099: 1
      1208: 1
      1220: 1
      1296: 1

1297:    0: 2q^3+6q^2+4q+1
         1: 3q^2+3q+1
         2: q^3+5q^2+4q+1
         3: 2q^3+6q^2+4q+1
         4: 2q^3+6q^2+4q+1
         5: 2q^3+6q^2+4q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 3q^2+4q+1
         9: 3q^2+3q+1
        10: q^3+5q^2+4q+1
        11: 2q^3+6q^2+4q+1
        12: 2q^3+6q^2+4q+1
        13: 3q^2+3q+1
        14: q^3+5q^2+4q+1
        15: q^3+4q^2+4q+1
        16: 3q^2+3q+1
        17: q^3+5q^2+4q+1
        18: q^3+4q^2+4q+1
        19: 2q^3+6q^2+4q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 2q^2+3q+1
        26: q^2+2q+1
        27: 3q^2+4q+1
        28: 3q^2+3q+1
        29: q^3+5q^2+4q+1
        30: 3q^2+3q+1
        31: q^3+5q^2+4q+1
        32: 2q^3+6q^2+4q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q^2+4q+1
        36: 2q^2+3q+1
        37: 2q^2+3q+1
        38: q^3+4q^2+4q+1
        39: q^3+4q^2+4q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q^2+4q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+4q^2+4q+1
        46: q^3+4q^2+4q+1
        47: 3q^2+3q+1
        48: q^3+5q^2+4q+1
        49: 2q^2+4q+1
        50: 2q+1
        51: 2q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 3q^2+4q+1
        57: 2q+1
        58: q^2+2q+1
        59: 2q+1
        60: 3q^2+4q+1
        61: 3q^2+4q+1
        62: 2q^2+3q+1
        63: q^2+2q+1
        64: 2q^2+4q+1
        65: 2q^2+3q+1
        66: q^2+2q+1
        67: 2q^2+4q+1
        68: 3q^2+3q+1
        69: q^3+5q^2+4q+1
        70: 2q^2+4q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: q^2+2q+1
        78: q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+4q^2+4q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q^2+4q+1
        88: 2q^2+4q+1
        89: q^2+2q+1
        91: q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+4q^2+4q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: q^2+4q+1
       100: q^2+3q+1
       101: 2q+1
       102: 2q^2+4q+1
       103: 2q^2+4q+1
       104: 2q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 3q^2+4q+1
       119: 2q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q^2+4q+1
       123: 2q^2+4q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 2q^2+3q+1
       130: q^2+2q+1
       131: q^2+4q+1
       132: q^2+3q+1
       133: 2q+1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: 2q^2+4q+1
       141: q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: q^2+2q+1
       148: 2q+1
       149: q^2+2q+1
       151: q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+4q+1
       155: 2q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: 2q^2+4q+1
       162: q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: q^2+2q+1
       169: q^2+3q+1
       170: q^2+2q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: 2q^2+4q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: q^2+4q+1
       180: q^2+4q+1
       181: q+1
       183: 2q+1
       184: q^2+3q+1
       185: 2q+1
       186: q^2+3q+1
       187: 2q+1
       188: 2q^2+4q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q^2+4q+1
       213: 2q+1
       214: 2q+1
       215: q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q^2+4q+1
       220: 2q+1
       221: q^2+2q+1
       222: 2q+1
       223: q^2+4q+1
       224: q^2+4q+1
       225: q+1
       227: 2q+1
       228: 2q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: 2q+1
       236: q+1
       237: q+1
       242: q^2+3q+1
       243: q+1
       246: 2q+1
       247: 2q+1
       248: q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+2q+1
       255: 2q+1
       256: q^2+3q+1
       257: 2q+1
       258: 2q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: 2q+1
       266: q+1
       267: q+1
       272: q^2+3q+1
       273: q+1
       276: q^2+3q+1
       277: q^2+3q+1
       278: q+1
       281: 2q+1
       282: 2q+1
       283: q^2+2q+1
       285: 2q+1
       286: q^2+3q+1
       287: 2q+1
       288: 2q+1
       289: 2q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: q^2+4q+1
       295: 1
       298: 2q+1
       299: 2q+1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q^2+3q+1
       307: 2q+1
       308: 2q^2+4q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       328: 2q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q^2+4q+1
       351: 1
       354: 2q+1
       355: 2q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: q+1
       372: q+1
       373: q+1
       374: q+1
       379: 2q+1
       380: q+1
       381: q+1
       386: q^2+3q+1
       387: q+1
       390: 2q+1
       391: 2q+1
       392: q+1
       394: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: q+1
       411: q+1
       412: q+1
       413: q+1
       418: q^2+3q+1
       419: q+1
       420: q+1
       425: 2q+1
       426: q+1
       429: 2q+1
       430: 2q+1
       431: q+1
       433: q+1
       434: 2q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: 2q+1
       442: 1
       443: 1
       448: 2q+1
       449: 1
       452: q+1
       453: q+1
       454: 1
       457: q+1
       458: q+1
       459: q+1
       461: 1
       462: q^2+3q+1
       463: 2q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       501: 2q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: 2q+1
       508: 2q+1
       509: 1
       510: 1
       515: 2q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       535: q+1
       542: q+1
       543: q+1
       550: q+1
       551: q+1
       552: q+1
       557: 2q+1
       558: 1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       582: q+1
       589: q+1
       590: q+1
       597: q+1
       598: q+1
       599: q+1
       604: 2q+1
       605: 1
       608: q+1
       609: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: q+1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       695: 1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       740: q+1
       747: q+1
       748: 1
       749: 1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       792: q+1
       799: q+1
       800: 1
       801: 1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       910: 1
       952: 1
       959: 1
       964: 1
      1006: 1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1082: 1
      1090: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1221: 1
      1263: 1
      1270: 1
      1297: 1

1298:    0: q^2+q+1
         1: 1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: 1
         7: 1
         8: q^2+q+1
         9: 1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q^2+q+1
        24: q+1
        25: 1
        26: 1
        27: q^2+q+1
        28: 1
        29: q^2+q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: q^2+q+1
        43: 1
        44: q^2+q+1
        45: q^2+q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: q^2+q+1
        61: q+1
        62: 1
        63: 1
        64: q^2+q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: q^2+q+1
        88: 1
        89: 1
        91: q^2+q+1
        92: 1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q^2+q+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: 1
       144: q+1
       145: q+1
       146: 1
       148: q+1
       149: 1
       151: q+1
       152: 1
       153: q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: q^2+q+1
       166: 1
       167: 1
       169: q^2+q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: q+1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: 1
       227: q+1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: 1
       242: q+1
       243: 1
       246: q+1
       248: 1
       251: q+1
       252: q+1
       253: 1
       255: q+1
       256: 1
       257: q+1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       272: 1
       273: 1
       276: q^2+q+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: q+1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: q+1
       372: q+1
       373: 1
       380: 1
       386: q+1
       387: 1
       390: q+1
       392: 1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       412: 1
       418: 1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       449: 1
       452: q+1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       519: 1
       521: 1
       523: 1
       524: 1
       534: q+1
       550: q+1
       551: 1
       558: 1
       561: q+1
       566: 1
       568: 1
       570: 1
       571: 1
       581: 1
       589: 1
       597: 1
       598: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       627: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       654: 1
       662: 1
       664: 1
       669: 1
       671: 1
       673: 1
       674: 1
       679: 1
       681: 1
       683: 1
       684: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       708: 1
       710: 1
       739: q+1
       748: 1
       760: 1
       762: 1
       782: 1
       791: 1
       799: 1
       800: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: 1
       825: 1
       841: 1
       842: 1
       849: 1
       852: 1
       866: 1
       874: 1
       876: 1
       883: 1
       885: 1
       890: 1
       892: 1
       894: 1
       895: 1
       905: 1
       911: 1
       965: 1
      1005: 1
      1013: 1
      1019: 1
      1021: 1
      1050: 1
      1059: 1
      1083: 1
      1091: 1
      1099: 1
      1101: 1
      1216: 1
      1222: 1
      1298: 1

1299:    0: q^2+q+1
         1: 1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: 1
         7: 1
         8: q^2+q+1
         9: 1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: 1
        14: q^2+q+1
        15: q^2+q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: q^2+q+1
        28: 1
        29: q+1
        30: 1
        31: q^2+q+1
        32: q+1
        33: 1
        34: 1
        35: q^2+q+1
        36: 1
        37: q^2+q+1
        38: 1
        39: q^2+q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: q+1
        61: q^2+q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q^2+q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q^2+q+1
        76: 1
        78: q^2+q+1
        79: 1
        80: 1
        81: 1
        82: q^2+q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q+1
        88: q+1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: q^2+q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: q^2+q+1
       146: 1
       148: 1
       149: 1
       151: q^2+q+1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: 1
       165: q+1
       166: q+1
       167: 1
       169: q+1
       170: 1
       172: q+1
       173: 1
       174: q+1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: q+1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: q+1
       225: 1
       227: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: q^2+q+1
       253: 1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       282: q+1
       283: 1
       285: q+1
       286: 1
       287: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       374: 1
       379: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: q+1
       411: q+1
       413: 1
       418: q+1
       420: 1
       426: 1
       430: q+1
       431: 1
       433: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       534: 1
       542: 1
       550: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       571: 1
       581: q+1
       589: q+1
       599: 1
       605: 1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       655: 1
       663: 1
       664: 1
       670: 1
       672: 1
       673: 1
       674: 1
       680: 1
       682: 1
       683: 1
       684: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       709: 1
       710: 1
       730: 1
       739: 1
       747: 1
       749: 1
       754: 1
       761: 1
       762: 1
       782: q+1
       801: 1
       811: 1
       813: 1
       814: 1
       815: 1
       825: 1
       833: 1
       843: 1
       849: 1
       853: 1
       867: 1
       875: 1
       876: 1
       884: 1
       885: 1
       891: 1
       893: 1
       894: 1
       895: 1
       905: 1
       912: 1
       951: 1
       959: 1
       966: 1
      1020: 1
      1021: 1
      1041: 1
      1060: 1
      1084: 1
      1092: 1
      1100: 1
      1101: 1
      1164: 1
      1223: 1
      1299: 1

1300:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       208: q+1
       209: 1
       210: 2q+1
       211: q+1
       212: q+1
       215: q+1
       216: 1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       316: q+1
       317: 1
       318: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       471: 1
       472: 1
       480: q+1
       481: 1
       482: q+1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       631: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       673: 1
       674: 1
       675: 1
       683: 1
       684: 1
       685: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       711: 1
       719: 1
       721: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       750: 1
       752: 1
       762: 1
       763: 1
       771: 1
       773: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       802: 1
       805: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       844: 1
       849: 1
       850: 1
       851: 1
       868: 1
       876: 1
       877: 1
       885: 1
       886: 1
       894: 1
       895: 1
       896: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       913: 1
       940: 1
       942: 1
       967: 1
       984: 1
       986: 1
      1021: 1
      1022: 1
      1030: 1
      1032: 1
      1061: 1
      1085: 1
      1093: 1
      1101: 1
      1102: 1
      1110: 1
      1112: 1
      1224: 1
      1300: 1

1301:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+q+1
         3: q^3+2q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^3+2q^2+2q+1
        10: q^2+q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q^2+q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q^2+q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+2q+1
       133: q+1
       134: 1
       135: q+1
       136: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       210: q+1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: q+1
       310: q+1
       318: q+1
       319: q+1
       320: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: q+1
       382: q+1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: q+1
       473: q+1
       474: q+1
       482: q+1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       657: q+1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       703: 1
       712: 1
       713: 1
       721: 1
       731: 1
       732: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       764: 1
       765: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: 1
       816: 1
       817: 1
       818: 1
       824: 1
       825: 1
       827: 1
       836: 1
       844: 1
       849: 1
       850: 1
       851: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       914: 1
       933: 1
       934: 1
       942: 1
       953: 1
       968: 1
       977: 1
       978: 1
       986: 1
      1008: 1
      1014: 1
      1023: 1
      1024: 1
      1032: 1
      1061: 1
      1094: 1
      1103: 1
      1104: 1
      1112: 1
      1137: 1
      1180: 1
      1225: 1
      1301: 1

1302:    0: 4q^3+10q^2+6q+1
         1: 4q^3+10q^2+6q+1
         2: 4q^3+10q^2+6q+1
         3: 4q^3+10q^2+6q+1
         4: q^3+8q^2+6q+1
         5: q^3+8q^2+6q+1
         6: 4q^3+10q^2+6q+1
         7: q^3+5q^2+5q+1
         8: q^3+5q^2+5q+1
         9: 4q^3+10q^2+6q+1
        10: 4q^3+10q^2+6q+1
        11: q^3+8q^2+6q+1
        12: q^3+8q^2+6q+1
        13: q^3+8q^2+6q+1
        14: q^3+8q^2+6q+1
        15: q^3+6q^2+6q+1
        16: q^3+8q^2+6q+1
        17: q^3+8q^2+6q+1
        18: q^3+6q^2+6q+1
        19: 7q^2+6q+1
        20: q^3+5q^2+5q+1
        21: q^3+5q^2+5q+1
        22: q^2+4q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 4q^3+10q^2+6q+1
        26: q^3+5q^2+5q+1
        27: q^3+5q^2+5q+1
        28: q^3+8q^2+6q+1
        29: q^3+8q^2+6q+1
        30: q^3+8q^2+6q+1
        31: q^3+8q^2+6q+1
        32: 7q^2+6q+1
        33: q^3+8q^2+6q+1
        34: 4q^2+5q+1
        35: 2q^2+5q+1
        36: q^3+6q^2+6q+1
        37: q^3+6q^2+6q+1
        38: 2q^2+4q+1
        39: q^3+6q^2+6q+1
        40: q^3+8q^2+6q+1
        41: 4q^2+5q+1
        42: 2q^2+5q+1
        43: q^3+6q^2+6q+1
        44: q^3+6q^2+6q+1
        45: q^3+6q^2+6q+1
        46: 2q^2+4q+1
        47: 7q^2+6q+1
        48: 7q^2+6q+1
        49: 4q^2+6q+1
        50: 2q^2+3q+1
        51: 2q^2+3q+1
        52: q^2+4q+1
        53: q^2+4q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^3+5q^2+5q+1
        58: q^3+5q^2+5q+1
        59: q^2+4q+1
        60: 2q^2+3q+1
        61: 2q^2+3q+1
        62: q^3+8q^2+6q+1
        63: 4q^2+5q+1
        64: 2q^2+5q+1
        65: q^3+8q^2+6q+1
        66: 4q^2+5q+1
        67: 2q^2+5q+1
        68: 7q^2+6q+1
        69: 7q^2+6q+1
        70: 4q^2+6q+1
        71: 2q^2+5q+1
        72: 4q^2+5q+1
        73: 4q+1
        74: 2q+1
        75: q^2+3q+1
        76: q^3+6q^2+6q+1
        77: 2q^2+3q+1
        78: 2q^2+5q+1
        79: 2q^2+4q+1
        80: 2q^2+4q+1
        81: q^3+6q^2+6q+1
        82: q^3+6q^2+6q+1
        83: 2q^2+4q+1
        84: 2q^2+5q+1
        85: 4q^2+5q+1
        86: 4q+1
        87: q^2+3q+1
        88: 2q+1
        89: q^3+6q^2+6q+1
        90: 2q^2+3q+1
        91: 2q^2+5q+1
        92: q^3+6q^2+6q+1
        93: q^3+6q^2+6q+1
        94: 2q^2+4q+1
        95: 2q^2+4q+1
        96: 2q^2+4q+1
        97: 7q^2+6q+1
        98: 4q^2+5q+1
        99: q^2+5q+1
       100: 4q^2+6q+1
       101: 4q^2+6q+1
       102: q^2+4q+1
       103: q^2+4q+1
       104: q^2+2q+1
       105: 2q+1
       106: 2q+1
       107: q^2+4q+1
       108: 2q+1
       109: 2q+1
       110: q+1
       111: q+1
       112: 2q^2+3q+1
       113: 2q^2+3q+1
       114: q^2+4q+1
       115: q^2+4q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: 2q^2+5q+1
       120: 4q^2+5q+1
       121: 4q+1
       122: q^2+3q+1
       123: 2q+1
       124: 2q^2+5q+1
       125: 4q^2+5q+1
       126: 4q+1
       127: 2q+1
       128: q^2+3q+1
       129: 7q^2+6q+1
       130: 4q^2+5q+1
       131: q^2+5q+1
       132: 4q^2+6q+1
       133: 4q^2+6q+1
       134: 2q+1
       135: q^2+3q+1
       136: 4q+1
       137: 4q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q^2+5q+1
       142: 2q^2+3q+1
       143: 2q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q^2+4q+1
       147: q^2+2q+1
       148: 2q+1
       149: q^3+6q^2+6q+1
       150: 2q^2+3q+1
       151: 2q^2+5q+1
       152: 2q^2+4q+1
       153: 2q^2+4q+1
       154: q^2+4q+1
       155: q^2+3q+1
       156: 2q+1
       157: 4q+1
       158: 4q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q^2+5q+1
       163: 2q^2+3q+1
       164: 2q+1
       165: q^2+3q+1
       166: 2q+1
       167: q^3+6q^2+6q+1
       168: 2q^2+3q+1
       169: 2q^2+5q+1
       170: 2q^2+4q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+4q+1
       174: 2q^2+4q+1
       175: q^2+4q+1
       176: q^2+5q+1
       177: 4q^2+5q+1
       178: 4q+1
       179: 2q+1
       180: 2q+1
       181: 4q^2+6q+1
       182: q^2+2q+1
       183: q^2+5q+1
       184: q^2+4q+1
       185: q^2+4q+1
       186: q^2+4q+1
       187: q^2+4q+1
       188: 3q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: 2q+1
       195: q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: 2q+1
       200: 2q+1
       201: q^2+4q+1
       202: 2q+1
       203: 2q+1
       204: q+1
       205: q+1
       206: q^2+3q+1
       207: 2q+1
       208: 4q+1
       209: 4q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: q^2+3q+1
       215: 4q+1
       216: 4q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: q^2+5q+1
       221: 4q^2+5q+1
       222: 4q+1
       223: 2q+1
       224: 2q+1
       225: 4q^2+6q+1
       226: q^2+2q+1
       227: q^2+5q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 4q+1
       232: q+1
       233: 2q+1
       234: 1
       235: 1
       236: 2q+1
       237: q^2+3q+1
       238: 2q+1
       239: 2q+1
       240: 1
       241: q+1
       242: q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       248: 2q^2+5q+1
       249: 2q^2+3q+1
       250: 2q+1
       251: 2q+1
       252: q^2+3q+1
       253: 2q^2+4q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: 4q+1
       262: 2q+1
       263: q+1
       264: 1
       265: 1
       266: q^2+3q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: q+1
       271: 1
       272: q+1
       273: 2q^2+5q+1
       274: 2q^2+3q+1
       275: 2q+1
       276: q^2+3q+1
       277: 2q+1
       278: 2q+1
       279: q^2+2q+1
       280: q+1
       282: q+1
       283: 2q^2+4q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+4q+1
       287: q^2+4q+1
       288: 2q+1
       289: 2q+1
       290: 4q+1
       291: 4q+1
       292: q+1
       293: q+1
       294: q+1
       295: q^2+5q+1
       296: q^2+2q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: q^2+4q+1
       301: q+1
       302: 2q+1
       303: q^2+4q+1
       304: q+1
       305: 2q+1
       306: 3q+1
       307: 3q+1
       308: 3q+1
       309: q+1
       310: q+1
       311: q+1
       317: q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       325: q+1
       326: q+1
       327: q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: 4q+1
       332: 2q+1
       333: q+1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 2q+1
       339: 4q+1
       340: q+1
       341: 2q+1
       342: 1
       343: 1
       344: 2q+1
       345: 2q+1
       346: 4q+1
       347: 4q+1
       348: q+1
       349: q+1
       350: q+1
       351: q^2+5q+1
       352: q^2+2q+1
       353: q+1
       354: 2q+1
       355: 2q+1
       356: 1
       357: 1
       358: q+1
       359: 2q+1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: q+1
       368: 2q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: q+1
       375: q+1
       376: q+1
       377: 1
       380: 2q+1
       381: q^2+3q+1
       382: 2q+1
       383: 2q+1
       384: 1
       385: q+1
       386: q+1
       387: 2q+1
       388: q^2+2q+1
       389: q+1
       390: q+1
       392: q^2+4q+1
       393: q+1
       394: 2q+1
       395: 1
       396: 1
       397: 2q+1
       398: q+1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: q+1
       406: 1
       407: 2q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q^2+3q+1
       413: 2q+1
       414: 2q+1
       415: 2q+1
       416: q+1
       417: 1
       418: q+1
       420: q+1
       421: q+1
       422: q+1
       424: 1
       426: 2q+1
       427: q^2+2q+1
       428: q+1
       430: q+1
       431: q^2+4q+1
       432: q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: q+1
       437: 4q+1
       438: q+1
       439: q+1
       440: 1
       441: 1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: q+1
       449: 2q+1
       450: q+1
       451: 1
       452: q+1
       454: 2q+1
       455: q+1
       456: 1
       458: q+1
       459: 3q+1
       460: q+1
       461: q+1
       462: 3q+1
       463: 3q+1
       465: q+1
       473: q+1
       474: q+1
       475: q+1
       481: q+1
       483: 1
       484: 1
       485: 2q+1
       486: q+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 2q+1
       498: 1
       499: 1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 4q+1
       505: q+1
       506: q+1
       507: 1
       508: 1
       509: 2q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       532: 1
       533: 1
       534: 1
       536: 1
       538: q+1
       539: 1
       543: q+1
       544: 1
       545: q+1
       546: 2q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: q+1
       553: q+1
       554: q+1
       555: 1
       558: 2q+1
       559: q+1
       560: 1
       561: q+1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       579: 1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: 1
       585: 2q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       592: 1
       593: q+1
       595: 1
       599: q+1
       600: q+1
       601: q+1
       603: 1
       605: 2q+1
       606: q+1
       607: 1
       609: q+1
       610: 1
       611: 1
       612: q+1
       613: q+1
       616: 1
       617: 1
       618: 1
       619: q+1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: q+1
       643: 1
       646: 3q+1
       647: q+1
       648: q+1
       658: q+1
       666: 1
       667: 1
       668: 1
       674: 1
       676: 1
       677: 1
       678: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: q+1
       692: 1
       693: 1
       694: 1
       695: q+1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       724: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: q+1
       750: 1
       751: 1
       752: 1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       780: 1
       781: 1
       782: 1
       786: 1
       794: 1
       795: q+1
       797: 1
       801: q+1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: q+1
       850: q+1
       851: 1
       870: 1
       879: 1
       887: 1
       888: 1
       889: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       915: 1
       933: 1
       934: 1
       935: 1
       941: 1
       945: 1
       953: 1
       955: 1
       956: 1
       969: 1
       977: 1
       978: 1
       979: 1
       985: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1015: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1035: 1
      1045: 1
      1054: 1
      1061: 1
      1062: 1
      1095: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1138: 1
      1158: 1
      1181: 1
      1211: 1
      1226: 1
      1266: 1
      1302: 1

1303:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: 2q^2+4q+1
         3: q^3+4q^2+4q+1
         4: 2q^2+4q+1
         5: 2q^2+4q+1
         6: 2q^2+4q+1
         7: 2q^2+4q+1
         8: 2q^2+4q+1
         9: q^3+4q^2+4q+1
        10: 2q^2+4q+1
        11: 2q^2+4q+1
        12: 2q^2+4q+1
        13: 2q^2+4q+1
        14: q^2+4q+1
        15: 2q^2+4q+1
        16: 2q^2+4q+1
        17: q^2+4q+1
        18: 2q^2+4q+1
        19: q^2+4q+1
        20: 2q^2+4q+1
        21: 2q^2+4q+1
        22: 2q^2+4q+1
        23: 2q+1
        24: 2q+1
        25: 2q^2+4q+1
        26: 2q^2+4q+1
        27: 2q^2+4q+1
        28: 2q^2+4q+1
        29: q^2+4q+1
        30: 2q^2+4q+1
        31: q^2+4q+1
        32: q^2+4q+1
        33: q^2+4q+1
        34: q^2+4q+1
        35: q^2+4q+1
        36: 2q^2+4q+1
        37: 2q+1
        38: 2q+1
        39: 2q^2+4q+1
        40: q^2+4q+1
        41: q^2+4q+1
        42: q^2+4q+1
        43: 2q^2+4q+1
        44: 2q+1
        45: 2q^2+4q+1
        46: 2q+1
        47: q^2+4q+1
        48: q^2+4q+1
        49: q^2+4q+1
        50: 2q+1
        51: 2q+1
        52: 2q^2+4q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: q+1
        57: 2q^2+4q+1
        58: 2q^2+4q+1
        59: 2q^2+4q+1
        60: 2q+1
        61: 2q+1
        62: q^2+4q+1
        63: q^2+4q+1
        64: q^2+4q+1
        65: q^2+4q+1
        66: q^2+4q+1
        67: q^2+4q+1
        68: q^2+4q+1
        69: q^2+4q+1
        70: q^2+4q+1
        71: q^2+4q+1
        72: q^2+4q+1
        73: q^2+4q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: q+1
        81: 2q^2+4q+1
        82: 2q+1
        83: 2q+1
        84: q^2+4q+1
        85: q^2+4q+1
        86: q^2+4q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+4q+1
        93: 2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+4q+1
       100: q^2+4q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: 2q+1
       106: 2q+1
       107: q^2+2q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: 2q^2+4q+1
       115: q^2+2q+1
       116: 2q+1
       117: 2q+1
       118: q+1
       119: q^2+4q+1
       120: q^2+4q+1
       121: q^2+4q+1
       122: 2q+1
       123: q+1
       124: q^2+4q+1
       125: q^2+4q+1
       126: q^2+4q+1
       127: q+1
       128: 2q+1
       129: q^2+4q+1
       130: q^2+4q+1
       131: q^2+4q+1
       132: q^2+4q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: q^2+4q+1
       137: q+1
       138: q+1
       139: 2q+1
       140: 1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       155: 2q+1
       156: q+1
       157: q^2+4q+1
       158: q+1
       159: 2q+1
       160: q+1
       161: 1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: q^2+4q+1
       177: q^2+4q+1
       178: q^2+4q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: 2q+1
       185: 1
       186: 2q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       201: q^2+2q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: 2q+1
       207: q+1
       208: q^2+4q+1
       209: q+1
       210: 2q+1
       211: q+1
       212: 1
       213: q+1
       214: 2q+1
       215: q^2+4q+1
       216: q+1
       217: q+1
       218: 2q+1
       219: 1
       220: q^2+4q+1
       221: q^2+4q+1
       222: q^2+4q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: q+1
       230: 2q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: 2q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q+1
       257: 1
       258: 1
       259: 2q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: 2q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: 2q+1
       287: 1
       288: q+1
       289: q+1
       290: q^2+4q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: q+1
       312: q+1
       315: q+1
       316: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       328: 1
       329: 2q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 2q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: q+1
       346: q^2+4q+1
       347: q+1
       348: q+1
       349: q+1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       377: 1
       380: 1
       381: q+1
       382: 2q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       466: q+1
       474: q+1
       475: q+1
       476: q+1
       479: q+1
       480: q+1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: q+1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       659: q+1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       748: 1
       750: 1
       752: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       801: 1
       802: 1
       805: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       836: 1
       844: 1
       849: 1
       850: 1
       851: 1
       871: 1
       880: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       916: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       953: 1
       970: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
      1008: 1
      1016: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1061: 1
      1096: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1139: 1
      1182: 1
      1227: 1
      1303: 1

1304:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+3q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: 2q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: 2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q^2+3q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: q+1
        71: q+1
        72: q^2+3q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: 1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 2q+1
        85: q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: q^2+3q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: q^2+3q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+3q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: q+1
       195: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: 1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+3q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 1
       262: 1
       263: 1
       264: 2q+1
       266: q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       279: q+1
       283: q+1
       284: q+1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       311: q+1
       312: q+1
       313: q+1
       320: 2q+1
       321: q+1
       322: q+1
       323: q+1
       325: q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: 1
       332: 1
       333: 1
       334: 2q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       396: 2q+1
       397: 1
       398: 1
       399: 1
       401: 1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       412: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       427: q+1
       431: 1
       432: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       467: q+1
       475: q+1
       476: q+1
       477: q+1
       484: 2q+1
       485: 1
       486: 1
       487: 1
       489: 1
       493: q+1
       494: 1
       495: 1
       496: 1
       498: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       574: q+1
       575: 1
       576: 1
       577: 1
       579: 1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       606: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       660: q+1
       668: 1
       669: 1
       670: 1
       678: 1
       679: 1
       680: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       732: 1
       733: 1
       734: 1
       735: 1
       737: 1
       740: 1
       741: 1
       742: 1
       746: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: q+1
       776: 1
       777: 1
       778: 1
       780: 1
       809: 1
       810: 1
       811: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       832: 1
       850: 1
       872: 1
       881: 1
       889: 1
       890: 1
       891: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       917: 1
       935: 1
       936: 1
       937: 1
       944: 1
       952: 1
       953: 1
       954: 1
       958: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1017: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1097: 1
      1105: 1
      1106: 1
      1107: 1
      1140: 1
      1157: 1
      1183: 1
      1228: 1
      1304: 1

1305:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: q^2+2q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: q^2+2q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+3q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: 2q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: 2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q^2+3q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: 2q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: q+1
        71: 2q+1
        72: q^2+3q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+3q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q^2+3q+1
       121: q+1
       122: q+1
       123: q+1
       124: 2q+1
       125: q^2+3q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q+1
       132: q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+3q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: 2q+1
       191: q+1
       192: q+1
       194: q+1
       195: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+3q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 1
       232: 1
       233: 1
       234: 2q+1
       236: q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       244: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       311: q+1
       314: q+1
       315: q+1
       320: 2q+1
       321: q+1
       322: q+1
       324: q+1
       325: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: 1
       340: 1
       341: 1
       342: 2q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 2q+1
       358: 1
       359: 1
       361: 1
       362: 1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       380: q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       388: q+1
       392: 1
       393: 1
       396: q+1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       468: q+1
       475: q+1
       478: q+1
       479: q+1
       484: q+1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 2q+1
       494: 1
       495: 1
       497: 1
       498: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       521: 1
       522: 1
       527: q+1
       528: 1
       529: 1
       531: 1
       532: 1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       559: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       661: q+1
       668: 1
       671: 1
       672: 1
       678: 1
       681: 1
       682: 1
       687: q+1
       688: 1
       689: 1
       691: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       707: 1
       714: 1
       717: 1
       718: 1
       732: q+1
       733: 1
       734: 1
       736: 1
       737: 1
       759: 1
       766: 1
       769: 1
       770: 1
       775: 1
       776: 1
       777: 1
       779: 1
       780: 1
       784: 1
       792: 1
       793: 1
       794: 1
       798: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       809: 1
       812: 1
       813: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       840: 1
       850: 1
       873: 1
       882: 1
       889: 1
       892: 1
       893: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       918: 1
       935: 1
       938: 1
       939: 1
       972: 1
       979: 1
       982: 1
       983: 1
       998: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1018: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1098: 1
      1105: 1
      1108: 1
      1109: 1
      1141: 1
      1184: 1
      1209: 1
      1229: 1
      1305: 1

1306:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: 2q^2+4q+1
         3: q^3+4q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+4q^2+4q+1
         6: 3q+1
         7: 2q^2+4q+1
         8: 2q^2+4q+1
         9: q^3+4q^2+4q+1
        10: 2q^2+4q+1
        11: q^3+4q^2+4q+1
        12: 2q^2+4q+1
        13: 2q^2+4q+1
        14: q^2+4q+1
        15: 2q^2+4q+1
        16: q^3+4q^2+4q+1
        17: 2q^2+4q+1
        18: q^3+4q^2+4q+1
        19: 2q^2+4q+1
        20: 3q+1
        21: 3q+1
        22: 2q^2+4q+1
        23: 2q^2+4q+1
        24: 2q+1
        25: 3q+1
        26: 2q^2+4q+1
        27: 2q^2+4q+1
        28: q^3+4q^2+4q+1
        29: 2q^2+4q+1
        30: 2q^2+4q+1
        31: q^2+4q+1
        32: 2q^2+4q+1
        33: 3q+1
        34: q^2+4q+1
        35: q^2+4q+1
        36: 2q^2+4q+1
        37: 2q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 3q+1
        41: 2q^2+4q+1
        42: 2q^2+4q+1
        43: q^3+4q^2+4q+1
        44: q^2+2q+1
        45: q^3+4q^2+4q+1
        46: q^2+2q+1
        47: 2q^2+4q+1
        48: q^2+4q+1
        49: 2q^2+4q+1
        50: 3q+1
        52: 3q+1
        53: q+1
        54: 2q^2+4q+1
        55: 2q+1
        56: 2q+1
        57: 3q+1
        58: 3q+1
        59: 2q^2+4q+1
        60: 2q^2+4q+1
        61: 2q+1
        62: 3q+1
        63: 2q^2+4q+1
        64: 2q^2+4q+1
        65: 3q+1
        66: q^2+4q+1
        67: q^2+4q+1
        68: 2q^2+4q+1
        69: q^2+4q+1
        70: 2q^2+4q+1
        71: 3q+1
        72: 3q+1
        73: q^2+4q+1
        74: q^2+4q+1
        75: 2q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: 2q^2+4q+1
        80: 2q+1
        81: 2q^2+4q+1
        82: 2q+1
        83: 2q^2+4q+1
        84: 3q+1
        85: 3q+1
        86: 2q^2+4q+1
        87: 2q^2+4q+1
        88: q+1
        89: q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^3+4q^2+4q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: 3q+1
        98: q^2+4q+1
        99: q^2+4q+1
       100: 2q^2+4q+1
       101: q+1
       102: 2q^2+4q+1
       103: q^2+2q+1
       105: 3q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: 3q+1
       114: 3q+1
       115: q+1
       116: 2q^2+4q+1
       117: 2q+1
       118: 2q+1
       119: 3q+1
       120: 3q+1
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: q+1
       124: 3q+1
       125: 3q+1
       126: q^2+4q+1
       127: q^2+4q+1
       128: 2q+1
       129: 3q+1
       130: q^2+4q+1
       131: q^2+4q+1
       132: 2q^2+4q+1
       133: q+1
       134: 3q+1
       136: 3q+1
       137: 1
       138: q^2+4q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: q+1
       150: 2q+1
       151: 2q+1
       152: 2q^2+4q+1
       153: 2q+1
       154: 2q^2+4q+1
       155: 3q+1
       157: 3q+1
       158: 1
       159: 2q^2+4q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 1
       167: q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: 3q+1
       177: 3q+1
       178: q^2+4q+1
       179: q^2+4q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q^2+4q+1
       185: q+1
       186: q^2+2q+1
       187: 1
       188: q^2+2q+1
       191: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       199: 3q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 3q+1
       208: 3q+1
       209: 1
       210: 2q^2+4q+1
       211: q+1
       212: q+1
       213: 3q+1
       215: 3q+1
       216: 1
       217: q^2+4q+1
       218: 2q+1
       219: 2q+1
       220: 3q+1
       221: 3q+1
       222: q^2+4q+1
       223: q^2+4q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       229: 3q+1
       231: 1
       232: 1
       233: 1
       234: 2q+1
       235: 2q+1
       236: q+1
       238: q+1
       239: 1
       240: 2q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: 2q+1
       246: 2q+1
       248: q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: 2q^2+4q+1
       257: q+1
       259: 3q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       268: q+1
       269: 1
       270: q^2+2q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: 1
       288: 3q+1
       290: 3q+1
       291: 1
       292: q^2+4q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       312: q+1
       314: q+1
       316: q+1
       321: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       329: 3q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       337: 3q+1
       339: 1
       340: 1
       341: 1
       342: 2q+1
       343: 2q+1
       344: 3q+1
       346: 3q+1
       347: 1
       348: q^2+4q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: q+1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 2q+1
       366: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       375: q+1
       377: 2q+1
       380: q+1
       382: q+1
       383: 1
       384: 2q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: 2q+1
       390: 2q+1
       392: 1
       393: q+1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       405: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       415: 1
       416: q^2+2q+1
       417: 1
       418: 1
       419: q+1
       421: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: 1
       432: 1
       433: 1
       435: 3q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+2q+1
       463: 1
       469: q+1
       476: q+1
       478: q+1
       480: q+1
       485: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 2q+1
       502: 3q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       536: q+1
       544: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q+1
       551: q+1
       553: q+1
       555: 2q+1
       558: 1
       559: 1
       560: q+1
       561: q+1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: q+1
       596: 1
       597: 1
       598: q+1
       600: q+1
       602: q+1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: q+1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       662: q+1
       669: 1
       671: 1
       673: 1
       679: 1
       681: 1
       683: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 1
       715: 1
       717: 1
       719: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       741: q+1
       748: 1
       750: 1
       752: q+1
       760: 1
       767: 1
       769: 1
       771: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       790: 1
       793: q+1
       798: 1
       799: 1
       800: 1
       802: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       835: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       874: 1
       883: 1
       890: 1
       892: 1
       894: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       919: 1
       936: 1
       938: 1
       940: 1
       953: 1
       973: 1
       980: 1
       982: 1
       984: 1
      1004: 1
      1007: 1
      1012: 1
      1013: 1
      1019: 1
      1026: 1
      1028: 1
      1030: 1
      1049: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1099: 1
      1106: 1
      1108: 1
      1110: 1
      1142: 1
      1185: 1
      1215: 1
      1230: 1
      1264: 1
      1306: 1

1307:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: 2q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: 2q^2+4q+1
         6: 3q+1
         7: 2q^2+4q+1
         8: 2q^2+4q+1
         9: q^3+4q^2+4q+1
        10: 2q^2+4q+1
        11: 2q^2+4q+1
        12: q^3+4q^2+4q+1
        13: q^3+4q^2+4q+1
        14: 2q^2+4q+1
        15: q^3+4q^2+4q+1
        16: 2q^2+4q+1
        17: q^2+4q+1
        18: 2q^2+4q+1
        19: 2q^2+4q+1
        20: 3q+1
        21: 3q+1
        22: 2q^2+4q+1
        23: 2q+1
        24: 2q^2+4q+1
        25: 3q+1
        26: 2q^2+4q+1
        27: 2q^2+4q+1
        28: 2q^2+4q+1
        29: q^2+4q+1
        30: q^3+4q^2+4q+1
        31: 2q^2+4q+1
        32: 2q^2+4q+1
        33: 3q+1
        34: 2q^2+4q+1
        35: 2q^2+4q+1
        36: q^3+4q^2+4q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^3+4q^2+4q+1
        40: 3q+1
        41: q^2+4q+1
        42: q^2+4q+1
        43: 2q^2+4q+1
        44: 2q+1
        45: 2q^2+4q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: q^2+4q+1
        49: 2q^2+4q+1
        51: 3q+1
        52: 3q+1
        53: q+1
        54: 2q+1
        55: 2q^2+4q+1
        56: 2q+1
        57: 3q+1
        58: 3q+1
        59: 2q^2+4q+1
        60: 2q+1
        61: 2q^2+4q+1
        62: 3q+1
        63: q^2+4q+1
        64: q^2+4q+1
        65: 3q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: 2q^2+4q+1
        69: q^2+4q+1
        70: 2q^2+4q+1
        71: 3q+1
        72: 3q+1
        73: 2q^2+4q+1
        74: q+1
        75: 2q^2+4q+1
        76: q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q+1
        81: q^3+4q^2+4q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 3q+1
        85: 3q+1
        86: q^2+4q+1
        87: 2q+1
        88: q^2+4q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+4q+1
        93: 2q+1
        94: 2q^2+4q+1
        95: 2q+1
        96: 2q^2+4q+1
        97: 3q+1
        98: q^2+4q+1
        99: q^2+4q+1
       100: 2q^2+4q+1
       101: q+1
       102: q^2+2q+1
       103: 2q^2+4q+1
       106: 3q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       113: 3q+1
       114: 3q+1
       115: q+1
       116: 2q+1
       117: 2q^2+4q+1
       118: 2q+1
       119: 3q+1
       120: 3q+1
       121: q^2+4q+1
       122: 2q+1
       123: q^2+4q+1
       124: 3q+1
       125: 3q+1
       126: 2q^2+4q+1
       127: q+1
       128: 2q^2+4q+1
       129: 3q+1
       130: q^2+4q+1
       131: q^2+4q+1
       132: 2q^2+4q+1
       133: q+1
       135: 3q+1
       136: 3q+1
       137: 1
       138: q+1
       139: 2q^2+4q+1
       140: q+1
       141: q+1
       142: q+1
       143: q^2+2q+1
       144: 1
       145: q^2+2q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       156: 3q+1
       157: 3q+1
       158: 1
       159: 2q+1
       160: q^2+4q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: 2q^2+4q+1
       174: 2q+1
       175: 2q^2+4q+1
       176: 3q+1
       177: 3q+1
       178: q^2+4q+1
       179: q+1
       180: q^2+4q+1
       181: 1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: 1
       186: 2q^2+4q+1
       187: q+1
       188: q^2+2q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       200: 3q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       207: 3q+1
       208: 3q+1
       209: 1
       210: 2q+1
       211: q^2+4q+1
       212: 2q+1
       214: 3q+1
       215: 3q+1
       216: 1
       217: q+1
       218: 2q^2+4q+1
       219: q+1
       220: 3q+1
       221: 3q+1
       222: q^2+4q+1
       223: q+1
       224: q^2+4q+1
       225: 1
       226: q+1
       227: q+1
       230: 3q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q^2+2q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: 1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: 1
       260: 3q+1
       261: 1
       262: 1
       263: 1
       264: 2q+1
       265: 2q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: 2q+1
       272: q+1
       273: q+1
       274: q+1
       275: 2q+1
       276: q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: 2q+1
       282: 2q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: 2q^2+4q+1
       287: q+1
       289: 3q+1
       290: 3q+1
       291: 1
       292: q+1
       293: q^2+4q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       313: q+1
       315: q+1
       316: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       330: 3q+1
       331: 1
       332: 1
       333: 1
       334: 2q+1
       335: 2q+1
       338: 3q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       345: 3q+1
       346: 3q+1
       347: 1
       348: q+1
       349: q^2+4q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       377: 1
       378: q+1
       379: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q^2+2q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 2q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: 2q+1
       418: q+1
       420: q+1
       421: q+1
       424: 2q+1
       426: q+1
       427: q+1
       428: 2q+1
       430: 2q+1
       431: 1
       432: q+1
       433: q+1
       436: 3q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q^2+2q+1
       463: 1
       470: q+1
       477: q+1
       479: q+1
       480: q+1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 2q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       503: 3q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: q+1
       541: 1
       542: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q+1
       592: q+1
       599: q+1
       600: q+1
       603: 2q+1
       605: 1
       606: 1
       607: q+1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       663: q+1
       670: 1
       672: 1
       673: 1
       680: 1
       682: 1
       683: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 1
       716: 1
       718: 1
       719: 1
       729: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       742: q+1
       746: 1
       747: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       761: 1
       768: 1
       770: 1
       771: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       794: q+1
       801: 1
       802: 1
       805: q+1
       811: 1
       813: 1
       814: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       875: 1
       884: 1
       891: 1
       893: 1
       894: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       920: 1
       937: 1
       939: 1
       940: 1
       950: 1
       954: 1
       958: 1
       959: 1
       974: 1
       981: 1
       983: 1
       984: 1
      1008: 1
      1020: 1
      1027: 1
      1029: 1
      1030: 1
      1040: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1100: 1
      1107: 1
      1109: 1
      1110: 1
      1143: 1
      1163: 1
      1186: 1
      1231: 1
      1265: 1
      1307: 1

1308:    0: q^3+4q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: 2q^2+4q+1
         5: 2q^2+4q+1
         6: 3q^2+4q+1
         7: q^2+4q+1
         8: q^3+4q^2+4q+1
         9: 3q^2+4q+1
        10: q^3+4q^2+4q+1
        11: 2q^2+4q+1
        12: 2q^2+4q+1
        13: q^2+4q+1
        14: 2q^2+4q+1
        15: 2q^2+4q+1
        16: q^2+4q+1
        17: 2q^2+4q+1
        18: 2q^2+4q+1
        19: q^2+4q+1
        20: 3q^2+4q+1
        21: q^2+4q+1
        22: q^2+4q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 3q^2+4q+1
        26: q^2+4q+1
        27: q^3+4q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+4q+1
        30: q^2+4q+1
        31: 2q^2+4q+1
        32: q^2+4q+1
        33: q^2+4q+1
        34: 4q+1
        35: 2q^2+4q+1
        36: q^2+4q+1
        37: 2q^2+4q+1
        38: 2q+1
        39: 2q^2+4q+1
        40: q^2+4q+1
        41: 4q+1
        42: 2q^2+4q+1
        43: q^2+4q+1
        44: 2q^2+4q+1
        45: 2q^2+4q+1
        46: 2q+1
        47: 4q+1
        48: q^2+4q+1
        49: q^2+4q+1
        52: q^2+4q+1
        53: q^2+4q+1
        54: 2q+1
        55: 2q+1
        56: q+1
        57: 3q^2+4q+1
        58: q^2+4q+1
        59: q^2+4q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+4q+1
        63: 4q+1
        64: 2q^2+4q+1
        65: q^2+4q+1
        66: 4q+1
        67: 2q^2+4q+1
        68: 4q+1
        69: q^2+4q+1
        70: q^2+4q+1
        71: q^2+4q+1
        72: 4q+1
        73: 4q+1
        74: q+1
        75: q^2+2q+1
        76: q^2+4q+1
        77: 2q+1
        78: 2q^2+4q+1
        79: 2q+1
        80: 2q+1
        81: q^2+4q+1
        82: 2q^2+4q+1
        83: 2q+1
        84: q^2+4q+1
        85: 4q+1
        86: 4q+1
        87: q^2+2q+1
        88: q+1
        89: q^2+4q+1
        90: 2q+1
        91: 2q^2+4q+1
        92: q^2+4q+1
        93: 2q^2+4q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 4q+1
        98: 4q+1
        99: q^2+4q+1
       100: 4q+1
       101: q^2+4q+1
       102: 2q+1
       103: 2q+1
       107: q^2+4q+1
       108: 2q+1
       109: 2q+1
       110: q+1
       111: q+1
       114: q^2+4q+1
       115: q^2+4q+1
       116: 2q+1
       117: 2q+1
       118: q+1
       119: q^2+4q+1
       120: 4q+1
       121: 4q+1
       122: q^2+2q+1
       123: q+1
       124: q^2+4q+1
       125: 4q+1
       126: 4q+1
       127: q+1
       128: q^2+2q+1
       129: 4q+1
       130: 4q+1
       131: q^2+4q+1
       132: 4q+1
       133: q^2+4q+1
       136: 4q+1
       137: 4q+1
       138: q+1
       139: 2q+1
       140: 1
       141: q^2+4q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: q^2+2q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: q^2+4q+1
       150: 2q+1
       151: 2q^2+4q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       157: 4q+1
       158: 4q+1
       159: 2q+1
       160: q+1
       161: 1
       162: q^2+4q+1
       163: 2q+1
       164: 2q+1
       165: q^2+2q+1
       166: q+1
       167: q^2+4q+1
       168: 2q+1
       169: 2q^2+4q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 4q+1
       177: 4q+1
       178: 4q+1
       179: q+1
       180: q+1
       181: 4q+1
       182: q+1
       183: q^2+4q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       193: 2q+1
       194: 2q+1
       195: q+1
       196: q+1
       197: q+1
       201: q^2+4q+1
       202: 2q+1
       203: 2q+1
       204: q+1
       205: q+1
       208: 4q+1
       209: 4q+1
       210: 2q+1
       211: q+1
       212: 1
       215: 4q+1
       216: 4q+1
       217: q+1
       218: 2q+1
       219: 1
       220: 4q+1
       221: 4q+1
       222: 4q+1
       223: q+1
       224: q+1
       225: 4q+1
       226: q+1
       227: q^2+4q+1
       231: 4q+1
       232: q+1
       233: 2q+1
       234: 1
       235: 1
       238: 2q+1
       239: 2q+1
       240: 1
       241: q+1
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       248: q^2+4q+1
       249: 2q+1
       250: 2q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       261: 4q+1
       262: 2q+1
       263: q+1
       264: 1
       265: 1
       268: 2q+1
       269: 2q+1
       270: q+1
       271: 1
       272: 1
       273: q^2+4q+1
       274: 2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       279: q+1
       280: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       287: 2q+1
       290: 4q+1
       291: 4q+1
       292: q+1
       293: q+1
       294: 1
       295: 4q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: 2q+1
       301: 1
       302: 2q+1
       303: 2q+1
       304: 1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       316: q+1
       317: q+1
       323: 2q+1
       324: 2q+1
       325: q+1
       326: q+1
       327: q+1
       331: 4q+1
       332: 2q+1
       333: q+1
       334: 1
       335: 1
       339: 4q+1
       340: q+1
       341: 2q+1
       342: 1
       343: 1
       346: 4q+1
       347: 4q+1
       348: q+1
       349: q+1
       350: 1
       351: 4q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       360: q+1
       361: 2q+1
       362: 1
       363: 1
       364: 1
       368: 2q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       375: q+1
       376: q+1
       377: 1
       382: 2q+1
       383: 2q+1
       384: 1
       385: q+1
       386: 1
       387: 2q+1
       388: q+1
       389: q+1
       390: q+1
       392: 2q+1
       393: 1
       394: 2q+1
       399: 2q+1
       400: q+1
       401: 1
       402: 1
       403: 1
       407: 2q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       414: 2q+1
       415: 2q+1
       416: q+1
       417: 1
       418: 1
       421: q+1
       422: q+1
       424: 1
       426: 2q+1
       427: q+1
       428: q+1
       430: q+1
       431: 2q+1
       432: 1
       433: 2q+1
       437: 4q+1
       438: q+1
       439: q+1
       440: 1
       441: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 2q+1
       450: 1
       451: 1
       452: q+1
       454: 2q+1
       455: 1
       456: 1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       471: q+1
       480: q+1
       481: q+1
       487: 2q+1
       488: q+1
       489: 1
       490: 1
       491: 1
       496: q+1
       497: 2q+1
       498: 1
       499: 1
       500: 1
       504: 4q+1
       505: q+1
       506: q+1
       507: 1
       508: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       523: 1
       524: 1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       538: q+1
       539: 1
       546: 2q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       553: q+1
       554: q+1
       555: 1
       558: 2q+1
       559: 1
       560: 1
       561: q+1
       570: 1
       571: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 2q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       593: q+1
       595: 1
       600: q+1
       601: q+1
       603: 1
       605: 2q+1
       606: 1
       607: 1
       609: q+1
       614: q+1
       615: q+1
       616: 1
       617: 1
       618: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: 1
       643: 1
       646: q+1
       647: 1
       648: q+1
       664: q+1
       673: 1
       674: 1
       683: 1
       684: 1
       690: q+1
       691: q+1
       692: 1
       693: 1
       694: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       719: 1
       720: 1
       726: 1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       743: q+1
       744: 1
       750: 1
       751: 1
       752: 1
       762: 1
       771: 1
       772: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       788: 1
       795: q+1
       797: 1
       802: 1
       803: 1
       805: 1
       814: 1
       815: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: q+1
       850: 1
       851: 1
       876: 1
       885: 1
       894: 1
       895: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       921: 1
       940: 1
       941: 1
       947: 1
       955: 1
       956: 1
       975: 1
       984: 1
       985: 1
      1002: 1
      1009: 1
      1011: 1
      1021: 1
      1030: 1
      1031: 1
      1037: 1
      1047: 1
      1054: 1
      1061: 1
      1062: 1
      1101: 1
      1110: 1
      1111: 1
      1144: 1
      1160: 1
      1187: 1
      1213: 1
      1232: 1
      1266: 1
      1308: 1

1309:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        53: q^2+q+1
        54: q+1
        55: q+1
        56: q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       115: q^2+q+1
       116: q+1
       117: q+1
       118: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       158: q+1
       159: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: q+1
       196: q+1
       197: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       216: q+1
       217: 1
       218: q+1
       219: 1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       239: q+1
       240: 1
       241: q+1
       242: 1
       244: 1
       245: 1
       246: 1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: q+1
       263: 1
       264: 1
       265: 1
       269: q+1
       270: q+1
       271: 1
       272: 1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       292: 1
       293: 1
       294: 1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: q+1
       318: q+1
       325: q+1
       326: q+1
       327: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       340: 1
       341: q+1
       342: 1
       343: 1
       347: q+1
       348: 1
       349: 1
       350: 1
       352: q+1
       353: q+1
       354: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: q+1
       371: 1
       372: 1
       376: 1
       377: 1
       383: q+1
       384: 1
       385: q+1
       386: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: q+1
       409: 1
       410: 1
       411: 1
       415: q+1
       416: q+1
       417: 1
       418: 1
       422: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       438: 1
       439: 1
       440: 1
       441: 1
       445: q+1
       446: 1
       447: 1
       448: 1
       450: 1
       451: 1
       452: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       472: q+1
       481: q+1
       482: q+1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       512: q+1
       513: 1
       514: 1
       515: 1
       524: 1
       525: 1
       532: 1
       533: 1
       534: 1
       539: 1
       547: 1
       548: q+1
       549: 1
       550: 1
       554: 1
       555: 1
       559: 1
       560: 1
       561: 1
       571: 1
       572: 1
       579: 1
       580: 1
       581: 1
       586: q+1
       587: 1
       588: 1
       589: 1
       595: 1
       601: 1
       603: 1
       606: 1
       607: 1
       609: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       637: 1
       639: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       665: q+1
       674: 1
       675: 1
       684: 1
       685: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       702: 1
       711: 1
       720: 1
       721: 1
       737: 1
       738: 1
       739: 1
       744: 1
       751: 1
       752: 1
       763: 1
       772: 1
       773: 1
       780: 1
       781: 1
       782: 1
       797: 1
       803: 1
       805: 1
       815: 1
       816: 1
       823: 1
       824: 1
       825: 1
       830: 1
       839: 1
       845: 1
       850: 1
       851: 1
       877: 1
       886: 1
       895: 1
       896: 1
       903: 1
       904: 1
       905: 1
       922: 1
       941: 1
       942: 1
       956: 1
       976: 1
       985: 1
       986: 1
      1011: 1
      1022: 1
      1031: 1
      1032: 1
      1062: 1
      1102: 1
      1111: 1
      1112: 1
      1145: 1
      1188: 1
      1233: 1
      1309: 1

1310:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q^2+3q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: q^2+2q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^2+2q+1
        19: q^3+3q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: q^2+2q+1
        24: 2q^2+3q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: q+1
        30: 2q^2+3q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: 2q+1
        54: q^2+2q+1
        55: 2q^2+3q+1
        56: q^2+2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 2q^2+3q+1
        72: q^3+3q^2+3q+1
        73: 2q^2+3q+1
        74: q^2+2q+1
        75: 2q^2+3q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^3+3q^2+3q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q^2+2q+1
        95: q+1
        96: q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: 2q^2+3q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q^2+2q+1
       111: q+1
       112: q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q^2+2q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^3+3q^2+3q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q^2+2q+1
       187: q+1
       188: q+1
       189: q+1
       190: q^2+2q+1
       191: q+1
       192: 2q+1
       193: 1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+3q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q^2+2q+1
       235: q+1
       236: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 2q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: q+1
       262: 1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: 1
       284: 1
       286: q+1
       287: 1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: 2q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: q+1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       356: q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       365: q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: q+1
       399: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: q+1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: q+1
       480: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       516: 1
       517: q+1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       545: q+1
       552: 1
       553: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       610: q+1
       611: q+1
       612: 1
       613: q+1
       614: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: 1
       663: 1
       666: 1
       667: 1
       675: 1
       697: 1
       703: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       742: 1
       749: 1
       750: 1
       753: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       832: 1
       850: 1
       854: 1
       855: 1
       860: 1
       863: 1
       869: 1
       906: 1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       920: 1
       923: 1
       924: 1
       932: 1
       954: 1
       960: 1
       971: 1
      1014: 1
      1015: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1066: 1
      1113: 1
      1114: 1
      1119: 1
      1122: 1
      1128: 1
      1217: 1
      1228: 1
      1310: 1

1311:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       309: 1
       310: q+1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       416: 1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       482: 1
       492: 1
       493: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       631: 1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       662: 1
       676: 1
       677: 1
       685: 1
       696: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       767: 1
       810: 1
       819: 1
       821: 1
       827: 1
       854: 1
       856: 1
       859: 1
       864: 1
       878: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       942: 1
       953: 1
      1026: 1
      1067: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1311: 1

1312:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: 1
        65: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: 1
       122: 1
       123: 1
       124: q+1
       127: q+1
       128: q+1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       144: q+1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       205: 1
       206: 1
       207: 1
       212: 1
       213: q+1
       214: q+1
       219: q+1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: q+1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: q+1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       372: 1
       373: 1
       374: 1
       379: 1
       380: q+1
       381: q+1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: q+1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       704: 1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       758: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       855: 1
       856: 1
       857: 1
       858: 1
       887: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
      1015: 1
      1017: 1
      1068: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1312: 1

1313:    0: 2q^2+2q+1
         1: q^2+q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q^2+q+1
         8: 2q^2+2q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: 2q+1
        12: 2q^2+2q+1
        13: q^2+q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: 2q+1
        24: 2q^2+2q+1
        25: q+1
        27: q^2+2q+1
        28: q+1
        29: 2q+1
        30: q^2+q+1
        31: q^2+2q+1
        32: 2q+1
        33: q+1
        34: q^2+q+1
        35: 2q^2+2q+1
        36: q^2+q+1
        37: q^2+2q+1
        38: 2q+1
        39: 2q^2+2q+1
        40: q+1
        41: q+1
        42: q^2+2q+1
        43: q+1
        44: q+1
        45: 2q+1
        46: q^2+2q+1
        47: q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: 2q+1
        57: q+1
        60: 2q+1
        61: q^2+2q+1
        62: q+1
        64: 2q+1
        65: q+1
        67: q^2+2q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: q^2+q+1
        74: 2q+1
        75: 2q^2+2q+1
        76: q+1
        78: q^2+2q+1
        79: q+1
        80: 2q+1
        81: q^2+q+1
        82: q^2+2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: q+1
        87: 2q+1
        88: q^2+2q+1
        89: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: 2q+1
        97: q+1
        98: q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: 2q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+1
       112: 1
       113: q+1
       118: 2q+1
       119: q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       127: q+1
       128: q^2+2q+1
       129: q+1
       131: 2q+1
       132: q+1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+q+1
       140: 2q+1
       141: q+1
       144: 2q+1
       145: q^2+2q+1
       146: q+1
       148: 2q+1
       149: q+1
       151: q^2+2q+1
       152: q+1
       153: 2q+1
       154: 2q+1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 2q+1
       162: 1
       165: q+1
       166: q+1
       167: 1
       169: q+1
       170: 1
       172: q+1
       173: q+1
       174: q+1
       175: 2q+1
       176: q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: q^2+2q+1
       181: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: 2q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: 1
       205: 2q+1
       206: 1
       207: q+1
       212: 2q+1
       213: 1
       214: q+1
       219: q+1
       220: q+1
       223: q+1
       224: 2q+1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 2q+1
       236: 1
       237: q+1
       242: 2q+1
       243: q+1
       246: 2q+1
       247: 2q+1
       248: q+1
       251: q+1
       252: q^2+2q+1
       253: q+1
       255: 2q+1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: 2q+1
       266: 1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       282: q+1
       283: 1
       285: q+1
       286: q+1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 2q+1
       295: 1
       298: q+1
       299: q+1
       300: 1
       302: q+1
       303: 1
       305: q+1
       306: q+1
       307: q+1
       308: 2q+1
       310: 1
       311: 1
       312: 1
       313: q+1
       314: 1
       315: q+1
       316: q+1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 2q+1
       336: 1
       343: q+1
       344: 1
       345: q+1
       350: q+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       365: 1
       372: 2q+1
       373: 1
       374: q+1
       379: 2q+1
       380: 1
       381: q+1
       386: q+1
       387: q+1
       390: q+1
       391: 2q+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       411: q+1
       412: 1
       413: 1
       418: q+1
       420: 1
       426: 1
       430: q+1
       431: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: 2q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: q+1
       453: q+1
       454: 1
       458: q+1
       459: 1
       461: q+1
       462: q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: q+1
       471: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: q+1
       521: 1
       522: q+1
       523: q+1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 2q+1
       543: 1
       550: q+1
       551: 1
       552: q+1
       557: q+1
       558: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: q+1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       626: q+1
       627: 1
       628: 1
       633: q+1
       635: 1
       641: 1
       645: q+1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       686: 1
       694: 1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: q+1
       710: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: q+1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       761: 1
       762: 1
       774: 1
       782: 1
       801: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: q+1
       843: 1
       849: 1
       853: 1
       857: 1
       858: 1
       897: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       943: 1
       951: 1
       952: 1
       959: 1
       962: 1
       966: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1033: 1
      1041: 1
      1060: 1
      1069: 1
      1116: 1
      1117: 1
      1156: 1
      1164: 1
      1219: 1
      1223: 1
      1313: 1

1314:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+3q+1
        29: 2q+1
        30: q^2+3q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: 1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: q+1
        68: q^2+3q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: q^2+3q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q^2+3q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: 1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: 2q+1
       151: q+1
       152: q^2+3q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: q+1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: q+1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: q^2+3q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: 2q+1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 2q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       279: 1
       283: 1
       284: q+1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: q+1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: q+1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: 2q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q+1
       412: 1
       413: 1
       414: 1
       416: q+1
       417: q+1
       418: q+1
       427: 1
       431: 1
       432: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: q+1
       455: 1
       459: 1
       460: q+1
       462: q+1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       482: 1
       484: 1
       490: 1
       491: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       588: q+1
       606: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: q+1
       627: 1
       628: 1
       629: 1
       631: q+1
       632: q+1
       633: q+1
       642: 1
       646: 1
       647: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       675: 1
       685: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       723: 1
       729: 1
       730: 1
       732: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       832: q+1
       850: 1
       858: 1
       859: 1
       860: 1
       865: 1
       896: 1
       898: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       932: 1
       942: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       971: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1070: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1155: 1
      1157: 1
      1228: 1
      1314: 1

1315:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: q+1
       158: q+1
       159: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: q+1
       262: 1
       266: 1
       268: q+1
       269: q+1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: q+1
       291: q+1
       292: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       300: 1
       301: 1
       302: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       381: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: q+1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: q+1
       438: 1
       442: 1
       444: q+1
       445: q+1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       495: 1
       497: 1
       504: 1
       511: 1
       512: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       545: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       559: 1
       560: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       612: 1
       614: 1
       620: 1
       622: q+1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       669: 1
       682: 1
       698: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       734: 1
       736: 1
       743: 1
       750: 1
       751: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       829: 1
       830: 1
       854: 1
       861: 1
       862: 1
       868: 1
       906: 1
       907: 1
       913: 1
       914: 1
       915: 1
       916: 1
       921: 1
       922: 1
       926: 1
       939: 1
       955: 1
       980: 1
      1026: 1
      1035: 1
      1037: 1
      1071: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1237: 1
      1315: 1

1316:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       104: q+1
       105: q+1
       106: 2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       112: q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: 2q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       227: 1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: 1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       682: 1
       689: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       756: 1
       758: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       872: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       939: 1
       946: 1
      1015: 1
      1017: 1
      1072: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1131: 1
      1316: 1

1317:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       162: q+1
       165: q+1
       167: q+1
       169: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: q+1
       266: q+1
       273: 1
       276: 1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       295: q+1
       298: q+1
       300: q+1
       302: 1
       309: q+1
       310: q+1
       311: 2q+1
       312: 1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       394: 1
       397: q+1
       399: 1
       412: 1
       435: q+1
       437: q+1
       438: q+1
       442: q+1
       449: 1
       452: 1
       465: q+1
       466: 1
       468: q+1
       469: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       566: 1
       612: q+1
       614: 1
       627: 1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       688: 1
       704: q+1
       705: 1
       707: q+1
       708: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       810: 1
       856: 1
       862: 1
       864: 1
       866: 1
       879: 1
       882: 1
       907: 1
       909: 1
       911: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       926: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       945: 1
      1073: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1138: 1
      1141: 1
      1317: 1

1318:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        92: q+1
        94: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       159: q+1
       160: q+1
       161: q+1
       173: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       184: q+1
       186: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       264: q+1
       265: q+1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       292: q+1
       293: q+1
       294: q+1
       306: q+1
       308: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       395: q+1
       396: q+1
       402: q+1
       434: q+1
       435: q+1
       436: q+1
       440: q+1
       441: q+1
       462: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       564: q+1
       610: q+1
       611: q+1
       617: q+1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       808: q+1
       857: 1
       863: 1
       864: 1
       865: 1
       888: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       934: 1
       943: 1
       944: 1
       950: 1
      1074: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1147: 1
      1318: 1

1319:    0: q^3+4q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+4q^2+4q+1
         3: 2q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: 3q^2+4q+1
         7: 3q^2+4q+1
         8: 2q^2+4q+1
         9: q^2+4q+1
        10: 2q^2+4q+1
        11: 2q^2+4q+1
        12: 2q^2+4q+1
        13: 3q^2+4q+1
        14: q^3+4q^2+4q+1
        15: 2q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q+1
        19: q^3+4q^2+4q+1
        20: 2q+1
        21: 3q^2+4q+1
        22: q^2+4q+1
        23: 2q^2+4q+1
        24: 2q^2+4q+1
        25: q^2+4q+1
        26: 3q+1
        27: 2q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+4q+1
        30: q^2+4q+1
        31: 2q^2+4q+1
        32: 2q^2+4q+1
        33: 3q^2+4q+1
        34: 3q^2+4q+1
        35: 2q^2+4q+1
        36: q^2+4q+1
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q^2+4q+1
        40: 3q^2+4q+1
        41: 3q^2+4q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 3q^2+4q+1
        48: q^3+4q^2+4q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: q^2+4q+1
        54: q^2+4q+1
        55: q^2+4q+1
        56: 2q^2+4q+1
        57: 2q+1
        58: 3q+1
        59: 3q+1
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: q^2+4q+1
        63: 3q+1
        64: q+1
        65: q^2+4q+1
        66: 3q+1
        67: q^2+2q+1
        68: q^2+4q+1
        69: 2q^2+4q+1
        70: q+1
        71: 2q+1
        72: 3q^2+4q+1
        73: q^2+4q+1
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: q^2+4q+1
        77: 3q+1
        78: 2q^2+4q+1
        79: q^2+4q+1
        80: 2q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+4q+1
        83: 2q^2+4q+1
        84: q+1
        85: 3q^2+4q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 3q^2+4q+1
        98: 3q^2+4q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: q^2+4q+1
       109: q^2+4q+1
       110: q^2+4q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: 3q+1
       116: 3q+1
       117: 3q+1
       118: 2q^2+4q+1
       119: 1
       120: 3q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 3q+1
       126: q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+4q+1
       130: 3q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+4q+1
       138: q^2+4q+1
       139: q^2+4q+1
       140: 2q^2+4q+1
       141: 2q+1
       142: 3q+1
       143: 3q+1
       144: 2q^2+4q+1
       145: 2q^2+4q+1
       146: q^2+4q+1
       147: 3q+1
       148: q+1
       149: q^2+4q+1
       150: 3q+1
       151: q^2+2q+1
       152: q^2+4q+1
       153: 2q^2+4q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       169: q+1
       170: 2q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: 3q^2+4q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: 1
       194: q+1
       195: q^2+4q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: 3q+1
       203: 3q+1
       204: 3q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+2q+1
       220: 1
       221: 3q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: q^2+4q+1
       233: q^2+4q+1
       234: q^2+4q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: 3q+1
       240: 3q+1
       241: 3q+1
       242: 2q^2+4q+1
       243: 1
       244: 3q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: 3q+1
       250: q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+4q+1
       254: 3q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       272: 2q+1
       273: 1
       276: q+1
       277: q+1
       283: 2q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: 2q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: 3q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q^2+4q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: 3q+1
       370: 3q+1
       371: 3q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q^2+2q+1
       387: 1
       388: 3q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       401: 2q+1
       402: q+1
       403: q+1
       404: q+1
       412: 1
       413: 1
       418: q+1
       431: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       448: 2q+1
       449: 1
       452: q+1
       453: q+1
       459: 2q+1
       462: q+1
       463: q+1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 2q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: 3q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: q+1
       566: 1
       567: 1
       571: q+1
       582: 1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       627: 1
       628: 1
       633: q+1
       646: q+1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       674: 1
       678: 1
       681: 1
       682: 1
       684: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       714: q+1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: q+1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: 1
       809: q+1
       810: 1
       811: 1
       815: q+1
       826: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       882: 1
       889: 1
       895: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       931: 1
       935: 1
       938: 1
       939: 1
       941: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
      1017: 1
      1075: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1141: 1
      1148: 1
      1154: 1
      1319: 1

1320:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       105: q+1
       107: q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 1
       120: 2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: q+1
       140: q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       191: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       199: q+1
       201: q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       229: q+1
       231: q+1
       232: 2q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 1
       244: 2q+1
       245: q+1
       246: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: 2q+1
       266: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       273: 1
       274: 2q+1
       275: q+1
       276: q+1
       288: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       312: 1
       314: 1
       316: 1
       317: q+1
       318: q+1
       321: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       358: q+1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       366: q+1
       368: q+1
       369: 2q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       375: 1
       376: q+1
       377: q+1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       397: q+1
       399: 1
       405: q+1
       407: q+1
       408: 2q+1
       412: 1
       414: 1
       415: q+1
       416: q+1
       435: q+1
       437: q+1
       438: 2q+1
       442: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       449: 1
       450: 2q+1
       451: q+1
       452: q+1
       469: 1
       471: 1
       472: q+1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: 1
       521: 1
       523: 1
       524: q+1
       525: q+1
       528: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: q+1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       566: 1
       575: q+1
       577: 1
       583: 1
       585: 1
       586: q+1
       612: q+1
       614: 1
       620: q+1
       622: q+1
       623: 2q+1
       627: 1
       629: 1
       630: q+1
       631: q+1
       654: 1
       656: 1
       662: 1
       664: 1
       665: 1
       669: 1
       681: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       708: 1
       710: 1
       711: q+1
       715: 1
       717: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       733: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: q+1
       821: 1
       827: 1
       829: 1
       830: q+1
       859: 1
       866: 1
       868: 1
       886: 1
       899: 1
       911: 1
       913: 1
       919: 1
       921: 1
       922: 1
       926: 1
       938: 1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       980: 1
      1026: 1
      1035: 1
      1037: 1
      1076: 1
      1118: 1
      1125: 1
      1127: 1
      1145: 1
      1158: 1
      1237: 1
      1320: 1

1321:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       113: q+1
       114: q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: q+1
       136: q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: 1
       237: q+1
       238: q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 2q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: 1
       284: 1
       286: 1
       287: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: q+1
       360: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       367: q+1
       368: q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: q+1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: q+1
       399: 1
       401: 1
       402: 1
       403: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: q+1
       459: 1
       460: 1
       462: 1
       463: 1
       470: 1
       471: 1
       472: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       520: 1
       522: 1
       523: 1
       524: 1
       525: 1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       567: 1
       571: 1
       572: 1
       576: q+1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       613: q+1
       614: 1
       616: 1
       617: 1
       618: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       655: 1
       656: 1
       663: 1
       664: 1
       665: 1
       670: 1
       674: 1
       675: 1
       682: 1
       689: 1
       697: 1
       698: 1
       700: 1
       709: 1
       710: 1
       711: 1
       716: 1
       718: 1
       719: 1
       720: 1
       721: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       763: 1
       768: 1
       777: 1
       778: 1
       780: 1
       811: 1
       815: 1
       816: 1
       820: q+1
       821: 1
       823: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: 1
       860: 1
       867: 1
       868: 1
       877: 1
       900: 1
       912: 1
       913: 1
       920: 1
       921: 1
       922: 1
       927: 1
       931: 1
       932: 1
       939: 1
       946: 1
       954: 1
       955: 1
       957: 1
       981: 1
      1022: 1
      1027: 1
      1036: 1
      1037: 1
      1039: 1
      1077: 1
      1119: 1
      1126: 1
      1127: 1
      1136: 1
      1159: 1
      1238: 1
      1321: 1

1322:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: 2q^2+3q+1
        11: q^2+2q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^2+2q+1
        19: q^3+3q^2+3q+1
        20: 2q+1
        21: q^3+3q^2+3q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: q^2+2q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: 2q^2+3q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: q^2+2q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: 2q+1
        58: 2q^2+3q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: 2q+1
        72: q^3+3q^2+3q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: 2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^2+2q+1
        84: q+1
        85: q^3+3q^2+3q+1
        86: q+1
        87: 1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: 2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       112: q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q^2+2q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 2q^2+3q+1
       126: q+1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: 2q^2+3q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q^2+2q+1
       164: q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       170: q^2+2q+1
       171: q^2+2q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^3+3q^2+3q+1
       178: q+1
       179: 1
       180: q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q+1
       184: q+1
       185: q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q+1
       189: 1
       190: q+1
       191: q+1
       192: 2q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       216: q+1
       218: q+1
       220: 1
       221: q^2+2q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: 1
       244: q^2+2q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 2q^2+3q+1
       250: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q^2+2q+1
       283: q+1
       284: q+1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q^2+2q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q^2+2q+1
       304: q^2+2q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: 2q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: q+1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: 2q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       383: q+1
       385: q+1
       387: 1
       388: q^2+2q+1
       389: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       431: q+1
       432: q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       455: q^2+2q+1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       495: q+1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       516: 1
       517: 1
       518: q+1
       524: 1
       525: 1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: q+1
       560: 1
       562: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: q+1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: q+1
       646: q+1
       647: q+1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       689: 1
       697: 1
       698: 1
       700: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: q+1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       734: q+1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       755: 1
       756: 1
       763: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: q+1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: q+1
       861: 1
       869: 1
       870: 1
       877: 1
       900: 1
       906: 1
       914: 1
       915: 1
       922: 1
       923: 1
       924: 1
       925: 1
       931: 1
       932: 1
       946: 1
       954: 1
       955: 1
       957: 1
       960: 1
       979: 1
      1014: 1
      1015: 1
      1022: 1
      1025: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1078: 1
      1120: 1
      1128: 1
      1129: 1
      1136: 1
      1159: 1
      1217: 1
      1236: 1
      1322: 1

1323:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 2q^2+3q+1
         6: 3q^2+3q+1
         7: q^2+2q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 2q+1
        12: 2q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: 3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: 3q^2+3q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q^2+2q+1
        25: 3q^2+3q+1
        26: q+1
        27: 3q^2+3q+1
        28: 2q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: 2q+1
        33: 3q^2+3q+1
        34: q^2+2q+1
        35: 3q^2+3q+1
        36: 3q^2+3q+1
        37: 3q^2+3q+1
        38: 2q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q^2+3q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: 1
        55: q+1
        56: q+1
        57: 3q^2+3q+1
        58: q+1
        59: q+1
        60: q+1
        61: q^2+2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q^2+3q+1
        66: q+1
        67: 2q^2+3q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 3q^2+3q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: 3q^2+3q+1
        77: q+1
        78: 3q^2+3q+1
        79: 2q+1
        80: 2q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: 2q+1
        84: 2q^2+3q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: 2q^2+3q+1
        91: 2q^2+3q+1
        92: 2q+1
        93: 2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q+1
       103: q^2+2q+1
       104: q+1
       105: 1
       106: q+1
       107: q^2+2q+1
       108: 1
       109: q+1
       110: 1
       111: q+1
       112: q+1
       113: q^2+2q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: 2q^2+3q+1
       125: q+1
       126: q+1
       128: q^2+2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 1
       139: q+1
       140: q+1
       141: 3q^2+3q+1
       142: q+1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: q+1
       151: 2q^2+3q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: 1
       160: q+1
       161: 1
       162: 2q^2+3q+1
       165: q+1
       166: q+1
       167: 2q+1
       169: 2q+1
       170: q^2+2q+1
       172: q^2+2q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q^2+3q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q+1
       181: 2q^2+3q+1
       183: 2q^2+3q+1
       184: 2q+1
       185: 2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       214: q^2+2q+1
       215: q+1
       216: q+1
       218: 1
       220: 2q+1
       221: q+1
       222: q+1
       224: 1
       225: 2q+1
       227: 2q+1
       228: q+1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: 1
       233: q+1
       234: 1
       235: q+1
       236: q+1
       237: q^2+2q+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: 2q^2+3q+1
       249: q+1
       250: q+1
       252: q^2+2q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       258: 1
       259: 1
       260: q+1
       261: q^2+2q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: q+1
       267: q+1
       272: 1
       273: 2q+1
       276: q+1
       277: 1
       278: q^2+2q+1
       282: q+1
       283: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: 1
       293: q+1
       294: 1
       295: 2q^2+3q+1
       298: q+1
       299: q+1
       300: 2q+1
       302: 2q+1
       303: q^2+2q+1
       305: q^2+2q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: 1
       312: 1
       315: q+1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: q+1
       341: 1
       345: 1
       346: q+1
       347: q+1
       349: 1
       351: 2q+1
       355: 1
       356: q+1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: q+1
       374: 1
       375: q+1
       376: q+1
       377: 1
       378: 1
       379: 1
       381: q^2+2q+1
       382: q+1
       383: q+1
       385: 1
       387: 2q+1
       388: q+1
       389: q+1
       391: 1
       392: 2q+1
       394: 2q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: q+1
       426: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: 1
       436: q+1
       437: q^2+2q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: q+1
       443: q+1
       448: 1
       449: 2q+1
       452: q+1
       453: 1
       454: q^2+2q+1
       458: q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: q+1
       506: 1
       510: 1
       516: q+1
       517: 1
       518: 1
       519: 1
       522: q+1
       523: 1
       524: 1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q+1
       535: 1
       536: 1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: q+1
       548: 1
       552: 1
       553: q+1
       554: q+1
       556: 1
       558: 2q+1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: q+1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: q+1
       628: 1
       633: 1
       635: q+1
       641: q+1
       645: 1
       646: q+1
       648: q+1
       650: 1
       658: 1
       659: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       704: 1
       705: 1
       710: 1
       712: q+1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: q+1
       745: 1
       749: 1
       756: 1
       757: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: q+1
       853: 1
       862: 1
       870: 1
       871: 1
       876: 1
       893: 1
       907: 1
       915: 1
       916: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       939: 1
       946: 1
       948: 1
       961: 1
       977: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1060: 1
      1079: 1
      1121: 1
      1129: 1
      1130: 1
      1135: 1
      1152: 1
      1218: 1
      1234: 1
      1323: 1

1324:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       599: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       742: 1
       757: 1
       758: 1
       761: 1
       774: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       843: 1
       863: 1
       871: 1
       872: 1
       875: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       962: 1
      1016: 1
      1017: 1
      1020: 1
      1033: 1
      1080: 1
      1122: 1
      1130: 1
      1131: 1
      1134: 1
      1219: 1
      1324: 1

1325:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 2q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+3q+1
         9: 3q^2+3q+1
        10: 2q+1
        11: 3q^2+3q+1
        12: 2q^2+3q+1
        13: 3q^2+3q+1
        14: 2q^2+3q+1
        15: 3q^2+3q+1
        16: 3q^2+3q+1
        17: 2q^2+3q+1
        18: 3q^2+3q+1
        19: 3q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: 2q^2+3q+1
        24: q^2+2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 3q^2+3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 2q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q^2+3q+1
        36: 3q^2+3q+1
        37: 2q+1
        38: 3q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q^2+3q+1
        43: 3q^2+3q+1
        44: q+1
        45: 3q^2+3q+1
        46: q^2+2q+1
        47: 3q^2+3q+1
        48: 2q^2+3q+1
        49: 3q^2+3q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 1
        54: q^2+2q+1
        55: q+1
        56: q^2+2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q^2+3q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q^2+3q+1
        75: q^2+2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 3q^2+3q+1
        80: 2q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: 2q^2+3q+1
        88: q+1
        89: q+1
        91: q+1
        92: 3q^2+3q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q^2+3q+1
       100: 3q^2+3q+1
       101: q+1
       102: 3q^2+3q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q^2+2q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q^2+3q+1
       134: 2q^2+3q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 1
       138: q^2+2q+1
       139: q+1
       140: q^2+2q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: 2q^2+3q+1
       153: 2q+1
       154: 2q^2+3q+1
       155: 2q^2+3q+1
       156: q+1
       157: q^2+2q+1
       158: 1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: 2q^2+3q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: 2q^2+3q+1
       180: q+1
       181: q+1
       183: q+1
       184: 3q^2+3q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: q+1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 2q+1
       214: q+1
       215: q+1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q^2+2q+1
       236: 2q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: 1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 1
       248: 2q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q^2+3q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       277: 1
       278: q+1
       281: q+1
       282: 1
       283: q+1
       285: q+1
       286: q^2+2q+1
       288: 2q^2+3q+1
       289: q+1
       290: q^2+2q+1
       291: 1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       310: q+1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 1
       346: q+1
       348: q+1
       349: 1
       350: 1
       356: q^2+2q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 2q+1
       374: 1
       375: q+1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: 2q+1
       381: q+1
       382: q+1
       384: q+1
       385: 1
       386: q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       419: q+1
       420: 1
       425: 1
       426: q+1
       429: q+1
       430: 1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: 1
       448: 1
       449: q+1
       452: q+1
       453: 1
       454: q+1
       457: q+1
       458: 1
       459: q+1
       461: q+1
       462: q^2+2q+1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: q+1
       493: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       507: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 1
       549: 1
       550: q+1
       551: 2q+1
       552: 1
       553: q+1
       555: q+1
       556: 1
       557: 1
       564: q+1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: q+1
       599: 1
       604: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       626: 1
       627: q+1
       628: 1
       633: 1
       634: q+1
       635: 1
       640: 1
       641: q+1
       644: q+1
       645: 1
       652: 1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       686: 1
       687: 1
       693: 1
       705: 1
       707: 1
       708: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: q+1
       732: 1
       738: 1
       740: 1
       741: q+1
       742: 1
       746: 1
       747: 1
       757: 1
       759: 1
       760: 1
       774: 1
       783: 1
       792: 1
       799: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: q+1
       843: 1
       848: 1
       864: 1
       871: 1
       873: 1
       874: 1
       888: 1
       909: 1
       916: 1
       918: 1
       919: 1
       924: 1
       925: 1
       926: 1
       928: 1
       929: 1
       930: 1
       934: 1
       943: 1
       944: 1
       950: 1
       963: 1
       997: 1
      1016: 1
      1018: 1
      1019: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1081: 1
      1123: 1
      1130: 1
      1132: 1
      1133: 1
      1147: 1
      1220: 1
      1254: 1
      1325: 1

1326:    0: q^3+2q^2+2q+1
         1: q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^3+q^2+2q+1
         9: 2q+1
        10: q^2+q+1
        11: q^3+q^2+2q+1
        12: q^3+q^2+2q+1
        13: q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: 2q+1
        19: q^3+2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^3+q^2+2q+1
        24: q^3+q^2+2q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: 2q+1
        29: q^2+q+1
        30: 2q+1
        31: q^2+q+1
        32: q^3+q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^3+q^2+2q+1
        36: 2q+1
        37: q^2+q+1
        38: q^3+q^2+2q+1
        39: q^3+q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+2q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: q^3+q^2+2q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q^2+1
        68: 2q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^3+q^2+2q+1
        75: q^3+q^2+2q+1
        76: q+1
        77: q+1
        78: q^2+q+1
        79: 2q+1
        80: q^2+q+1
        81: 2q+1
        82: q^2+q+1
        83: q^3+q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: q^2+1
       128: q^2+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: q^3+q^2+2q+1
       141: 1
       142: q+1
       143: q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q^2+1
       152: 2q+1
       153: q^2+q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: q^2+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q^2+q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: 1
       251: q^2+1
       252: q^2+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: 1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       298: q+1
       299: q+1
       300: q+1
       302: q+1
       303: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: q^2+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: 1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: q+1
       453: q+1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: q+1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       687: 1
       693: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       758: 1
       759: 1
       760: 1
       761: 1
       792: 1
       799: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       944: 1
       950: 1
       964: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1051: 1
      1058: 1
      1082: 1
      1124: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1221: 1
      1326: 1

1327:    0: q^3+4q^2+3q+1
         1: q^2+2q+1
         2: q^3+4q^2+3q+1
         3: 3q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 3q^2+3q+1
         9: 2q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: 2q^2+3q+1
        13: q^2+2q+1
        14: q^3+4q^2+3q+1
        15: 3q^2+3q+1
        16: q^2+2q+1
        17: q^3+4q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+4q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 3q^2+3q+1
        24: 2q^2+3q+1
        25: 2q+1
        26: q+1
        27: 3q^2+3q+1
        28: 2q+1
        29: 3q^2+3q+1
        30: 2q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 3q^2+3q+1
        36: 2q+1
        37: 3q^2+3q+1
        38: 3q^2+3q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+3q+1
        43: 2q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+4q^2+3q+1
        49: 2q^2+3q+1
        50: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q^2+3q+1
        57: q+1
        58: q+1
        59: q+1
        60: 3q^2+3q+1
        61: 2q^2+3q+1
        62: 2q+1
        63: q+1
        64: q^2+2q+1
        65: 2q+1
        66: q+1
        67: q^2+2q+1
        68: 2q+1
        69: 2q^2+3q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 3q^2+3q+1
        75: 2q^2+3q+1
        76: 2q+1
        77: q+1
        78: 3q^2+3q+1
        79: 2q+1
        80: 3q^2+3q+1
        81: 2q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q^2+3q+1
        88: 2q+1
        89: 2q+1
        91: 2q^2+3q+1
        92: 2q+1
        93: 2q^2+3q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+3q+1
       100: 2q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: 2q+1
       105: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q^2+2q+1
       112: q+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: 2q^2+3q+1
       119: 1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: q+1
       133: q^2+2q+1
       134: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q^2+3q+1
       141: q+1
       142: q+1
       143: q+1
       144: 3q^2+3q+1
       145: 2q^2+3q+1
       146: 2q+1
       147: q+1
       148: q^2+2q+1
       149: 2q+1
       150: q+1
       151: q^2+2q+1
       152: 2q+1
       153: 2q^2+3q+1
       154: q^2+2q+1
       155: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       165: 2q^2+3q+1
       166: 2q+1
       167: 2q+1
       169: q^2+2q+1
       170: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q^2+3q+1
       180: 2q+1
       181: 2q+1
       183: 2q^2+3q+1
       184: 2q+1
       185: 2q^2+3q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       191: q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q^2+2q+1
       199: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q^2+2q+1
       220: 1
       221: q+1
       222: 1
       223: q+1
       224: 1
       225: q+1
       227: q+1
       229: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q^2+2q+1
       236: q+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: 2q^2+3q+1
       243: 1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 2q+1
       254: q+1
       255: q+1
       256: q+1
       257: q^2+2q+1
       259: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       272: 2q+1
       273: 1
       276: q^2+2q+1
       277: q+1
       278: q+1
       281: q+1
       282: q+1
       283: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       298: 2q^2+3q+1
       299: 2q+1
       300: 2q+1
       302: q^2+2q+1
       303: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       312: 1
       314: q+1
       316: 1
       317: q+1
       321: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: q+1
       329: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: q+1
       355: 1
       358: q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q^2+2q+1
       366: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q^2+2q+1
       387: 1
       388: q+1
       389: 1
       390: q+1
       391: 1
       392: q+1
       394: q+1
       397: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       411: 1
       412: 1
       418: q+1
       419: q+1
       425: q+1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       435: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       448: 2q+1
       449: 1
       452: q^2+2q+1
       453: q+1
       454: q+1
       457: q+1
       458: q+1
       459: 2q+1
       461: 1
       462: q+1
       463: q+1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       519: 1
       521: q+1
       523: 1
       524: q+1
       528: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: q+1
       536: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: q+1
       562: 1
       566: 1
       568: q+1
       570: 1
       571: q+1
       581: 1
       589: 1
       597: 1
       598: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       626: 1
       627: 1
       633: q+1
       634: q+1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       654: 1
       662: 1
       664: 1
       669: 1
       671: 1
       673: 1
       674: 1
       681: 1
       684: 1
       688: 1
       691: 1
       692: 1
       693: 1
       694: 1
       708: 1
       710: 1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       727: 1
       728: q+1
       729: 1
       730: 1
       733: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       754: 1
       760: 1
       762: 1
       782: 1
       791: 1
       799: 1
       800: 1
       806: 1
       810: 1
       812: q+1
       814: 1
       815: q+1
       825: 1
       833: 1
       841: 1
       842: 1
       848: 1
       849: 1
       852: 1
       853: 1
       866: 1
       874: 1
       876: 1
       892: 1
       895: 1
       911: 1
       919: 1
       921: 1
       926: 1
       928: 1
       930: 1
       931: 1
       938: 1
       941: 1
       945: 1
       948: 1
       949: 1
       950: 1
       951: 1
       965: 1
      1005: 1
      1019: 1
      1021: 1
      1041: 1
      1050: 1
      1058: 1
      1059: 1
      1065: 1
      1083: 1
      1125: 1
      1133: 1
      1135: 1
      1151: 1
      1154: 1
      1222: 1
      1262: 1
      1327: 1

1328:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: 1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q^2+q+1
        25: q+1
        26: 1
        27: q^2+q+1
        28: 1
        29: 1
        30: q+1
        31: q^2+q+1
        32: 1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: 1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: q^2+q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q^2+q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q^2+q+1
        76: q+1
        77: 1
        78: q^2+q+1
        79: 1
        80: 1
        81: q+1
        82: q^2+q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q^2+q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: 1
       145: q^2+q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q^2+q+1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       267: q+1
       272: 1
       273: 1
       276: 1
       277: 1
       278: q+1
       282: q+1
       283: 1
       285: 1
       286: 1
       287: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       411: 1
       413: 1
       418: 1
       420: q+1
       426: 1
       430: 1
       431: 1
       433: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       443: q+1
       448: 1
       449: 1
       452: 1
       453: 1
       454: q+1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       581: 1
       589: 1
       599: 1
       605: 1
       609: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       626: 1
       628: 1
       633: 1
       635: q+1
       641: 1
       645: 1
       646: 1
       648: 1
       655: 1
       663: 1
       664: 1
       670: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       709: 1
       710: 1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       761: 1
       762: 1
       782: 1
       801: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       825: 1
       833: 1
       843: 1
       849: 1
       853: 1
       867: 1
       875: 1
       876: 1
       893: 1
       912: 1
       920: 1
       921: 1
       927: 1
       929: 1
       930: 1
       931: 1
       939: 1
       946: 1
       948: 1
       966: 1
      1020: 1
      1021: 1
      1041: 1
      1060: 1
      1084: 1
      1126: 1
      1134: 1
      1135: 1
      1152: 1
      1223: 1
      1328: 1

1329:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 3q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 2q^2+3q+1
        11: 2q+1
        12: 2q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: 3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 3q^2+3q+1
        23: 2q+1
        24: 2q^2+3q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q+1
        33: q^2+2q+1
        34: 3q^2+3q+1
        35: 3q^2+3q+1
        36: 3q^2+3q+1
        37: 2q^2+3q+1
        38: 2q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q^2+3q+1
        52: q^2+2q+1
        53: 2q+1
        54: 2q+1
        55: 2q^2+3q+1
        56: 2q+1
        57: 2q+1
        58: 2q+1
        59: 2q^2+3q+1
        60: 2q+1
        61: q^2+3q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: 2q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 3q^2+3q+1
        74: 2q+1
        75: 2q^2+3q+1
        76: 2q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q+1
        80: 2q+1
        81: 2q^2+3q+1
        82: q^2+3q+1
        83: 2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+3q+1
        87: 2q+1
        88: q^2+2q+1
        89: q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: q^2+2q+1
       102: 2q+1
       103: q^2+2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: 2q+1
       111: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q^2+3q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: 2q+1
       125: 2q+1
       126: q^2+3q+1
       128: q^2+3q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q^2+2q+1
       137: 2q+1
       138: 2q+1
       139: 2q^2+3q+1
       140: 2q+1
       141: 2q+1
       142: 2q+1
       143: 2q^2+3q+1
       144: 2q+1
       145: q^2+3q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: 2q+1
       150: q^2+3q+1
       151: q^2+3q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       157: q^2+2q+1
       158: q+1
       159: 2q+1
       160: q^2+2q+1
       161: q+1
       162: q+1
       163: q+1
       164: q^2+2q+1
       165: q+1
       166: q+1
       167: 1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+3q+1
       179: 2q+1
       180: q^2+2q+1
       181: q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: 2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q+1
       193: q+1
       194: 2q+1
       195: q+1
       196: 2q+1
       197: q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       208: q+1
       209: 1
       210: 2q+1
       211: q+1
       212: q+1
       215: 2q+1
       216: q+1
       218: q^2+3q+1
       220: q+1
       221: q+1
       222: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+3q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 2q+1
       246: 2q+1
       247: q+1
       248: 2q+1
       249: 2q+1
       250: q^2+3q+1
       252: q^2+3q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: 2q+1
       257: q+1
       261: q+1
       262: 1
       263: q+1
       264: q+1
       265: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: q^2+2q+1
       291: q+1
       292: 2q+1
       293: q^2+2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q^2+2q+1
       298: q+1
       299: q+1
       300: 1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       316: q+1
       317: 1
       318: q+1
       323: q+1
       324: 2q+1
       325: q+1
       326: 2q+1
       327: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       339: q+1
       341: q+1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: q+1
       355: 1
       360: q+1
       361: 2q+1
       362: q+1
       363: 2q+1
       364: q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       375: q+1
       376: 1
       377: 2q+1
       378: q+1
       379: q+1
       382: 2q+1
       383: q+1
       385: q^2+3q+1
       387: q+1
       388: q+1
       389: 2q+1
       391: q+1
       392: 1
       393: q+1
       394: q+1
       399: 1
       400: q+1
       401: 1
       402: q+1
       403: 1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       421: q+1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       471: 1
       472: 1
       480: q+1
       481: 1
       482: q+1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       497: q+1
       504: 1
       506: 1
       511: 1
       512: 1
       514: 1
       523: q+1
       524: 1
       525: q+1
       530: q+1
       531: 2q+1
       532: q+1
       533: 2q+1
       534: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       546: q+1
       548: q+1
       553: q+1
       554: 1
       556: q+1
       558: 1
       559: 1
       560: q+1
       562: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       614: 1
       615: q+1
       616: 1
       617: q+1
       618: 1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       629: 1
       630: 1
       631: q+1
       632: 1
       633: 1
       636: q+1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       673: 1
       674: 1
       675: 1
       691: 1
       698: 1
       700: 1
       710: 1
       711: 1
       719: q+1
       720: 1
       721: q+1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       736: q+1
       743: 1
       745: 1
       750: 1
       751: 1
       753: 1
       762: 1
       763: 1
       771: 1
       773: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       802: 1
       805: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       868: 1
       876: 1
       877: 1
       902: 1
       913: 1
       921: 1
       922: 1
       930: 1
       931: 1
       932: 1
       948: 1
       955: 1
       957: 1
       967: 1
       984: 1
       986: 1
      1021: 1
      1022: 1
      1030: 1
      1032: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1061: 1
      1064: 1
      1085: 1
      1127: 1
      1135: 1
      1136: 1
      1161: 1
      1224: 1
      1241: 1
      1243: 1
      1329: 1

1330:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       300: q+1
       301: q+1
       302: 1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       397: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       485: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       575: 1
       583: 1
       585: 1
       586: 1
       612: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       649: 1
       657: 1
       658: 1
       665: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: 1
       720: 1
       721: 1
       724: 1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       776: 1
       819: 1
       827: 1
       829: 1
       830: 1
       861: 1
       878: 1
       879: 1
       886: 1
       899: 1
       906: 1
       914: 1
       915: 1
       922: 1
       933: 1
       934: 1
       935: 1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
      1035: 1
      1086: 1
      1120: 1
      1137: 1
      1138: 1
      1145: 1
      1158: 1
      1330: 1

1331:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: 1
        24: q^2+1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q^2+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: 1
        61: q^2+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q+1
        73: q+1
        74: 1
        75: q^2+1
        76: q^2+q+1
        77: q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: q^2+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       124: q^2+q+1
       125: q+1
       126: q+1
       127: 1
       128: q^2+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q^2+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q^2+q+1
       142: q+1
       143: q+1
       144: 1
       145: q^2+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: q+1
       158: q+1
       159: 1
       162: q+1
       165: 1
       167: q+1
       169: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: q+1
       209: q+1
       210: 1
       213: 1
       214: q^2+1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       225: q+1
       227: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q^2+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: q^2+q+1
       249: q+1
       250: q+1
       251: 1
       252: q^2+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       259: 1
       261: q+1
       262: 1
       266: 1
       273: q+1
       276: 1
       288: 1
       290: q+1
       291: q+1
       292: 1
       295: q+1
       298: 1
       300: q+1
       302: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: q+1
       332: 1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       347: q+1
       348: 1
       351: q+1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       376: q+1
       377: 1
       380: 1
       381: q^2+1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       394: q+1
       397: 1
       399: 1
       412: 1
       435: 1
       437: q+1
       438: 1
       442: 1
       449: q+1
       452: 1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: q+1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: q+1
       539: 1
       543: 1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       554: q+1
       555: 1
       558: q+1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       650: 1
       658: 1
       659: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       688: 1
       690: 1
       704: 1
       705: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: 1
       810: 1
       862: 1
       879: 1
       880: 1
       885: 1
       890: 1
       907: 1
       915: 1
       916: 1
       921: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       945: 1
       947: 1
      1087: 1
      1121: 1
      1138: 1
      1139: 1
      1144: 1
      1149: 1
      1331: 1

1332:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        92: q+1
        94: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       134: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       159: 1
       160: q+1
       161: 1
       173: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       184: q+1
       186: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       258: 1
       259: 1
       260: q+1
       264: 1
       265: 1
       286: q+1
       288: 1
       289: q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       306: q+1
       308: q+1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       348: 1
       349: q+1
       350: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: q+1
       440: 1
       441: 1
       462: q+1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       507: 1
       508: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       564: 1
       610: 1
       611: 1
       617: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       808: 1
       863: 1
       880: 1
       881: 1
       884: 1
       888: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: 1
       940: 1
       943: 1
       944: 1
       950: 1
      1088: 1
      1122: 1
      1139: 1
      1140: 1
      1143: 1
      1147: 1
      1332: 1

1333:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        92: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       159: 1
       176: 1
       177: 1
       178: 1
       179: 1
       184: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       259: 1
       288: 1
       290: 1
       292: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       435: 1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       652: 1
       659: 1
       661: 1
       662: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       705: 1
       707: 1
       708: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       864: 1
       880: 1
       882: 1
       883: 1
       909: 1
       916: 1
       918: 1
       919: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
      1089: 1
      1123: 1
      1139: 1
      1141: 1
      1142: 1
      1333: 1

1334:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       490: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       611: 1
       617: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: 1
       693: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: 1
       729: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       865: 1
       881: 1
       882: 1
       883: 1
       884: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       944: 1
       950: 1
      1090: 1
      1124: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1334: 1

1335:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       312: 1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: 1
       521: 1
       523: 1
       524: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       654: 1
       662: 1
       664: 1
       669: 1
       679: 1
       681: 1
       683: 1
       684: 1
       688: 1
       690: 1
       708: 1
       710: 1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       810: 1
       866: 1
       883: 1
       885: 1
       890: 1
       911: 1
       919: 1
       921: 1
       926: 1
       936: 1
       938: 1
       940: 1
       941: 1
       945: 1
       947: 1
      1091: 1
      1125: 1
      1142: 1
      1144: 1
      1149: 1
      1335: 1

1336:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q+1
        31: q^2+q+1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q^2+q+1
        76: q+1
        77: q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q+1
        82: q^2+q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       413: 1
       418: 1
       431: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       571: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       628: 1
       633: 1
       646: 1
       655: 1
       663: 1
       664: 1
       670: 1
       674: 1
       680: 1
       682: 1
       683: 1
       684: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       709: 1
       710: 1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       754: 1
       811: 1
       815: 1
       867: 1
       884: 1
       885: 1
       891: 1
       895: 1
       912: 1
       920: 1
       921: 1
       927: 1
       931: 1
       937: 1
       939: 1
       940: 1
       941: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
      1092: 1
      1126: 1
      1143: 1
      1144: 1
      1150: 1
      1154: 1
      1336: 1

1337:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 1
       407: 1
       408: 1
       414: 1
       415: 1
       416: 1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       511: 1
       512: 1
       513: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       577: 1
       585: 1
       586: 1
       614: 1
       622: 1
       623: 1
       629: 1
       630: 1
       631: 1
       656: 1
       664: 1
       665: 1
       683: 1
       684: 1
       685: 1
       690: 1
       698: 1
       699: 1
       710: 1
       711: 1
       719: 1
       720: 1
       721: 1
       726: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       750: 1
       751: 1
       752: 1
       778: 1
       821: 1
       829: 1
       830: 1
       868: 1
       885: 1
       886: 1
       901: 1
       913: 1
       921: 1
       922: 1
       940: 1
       941: 1
       942: 1
       947: 1
       955: 1
       956: 1
      1037: 1
      1093: 1
      1127: 1
      1144: 1
      1145: 1
      1160: 1
      1337: 1

1338:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       238: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       572: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       657: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       703: 1
       712: 1
       713: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       775: 1
       807: 1
       808: 1
       816: 1
       818: 1
       826: 1
       827: 1
       828: 1
       832: 1
       850: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       898: 1
       914: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
      1014: 1
      1034: 1
      1094: 1
      1128: 1
      1137: 1
      1146: 1
      1147: 1
      1155: 1
      1157: 1
      1338: 1

1339:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       302: 1
       303: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: q+1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       676: 1
       677: 1
       678: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       807: 1
       808: 1
       809: 1
       815: 1
       826: 1
       870: 1
       879: 1
       887: 1
       888: 1
       889: 1
       895: 1
       915: 1
       923: 1
       924: 1
       925: 1
       931: 1
       933: 1
       934: 1
       935: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
      1015: 1
      1095: 1
      1129: 1
      1138: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1339: 1

1340:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: 2q^2+4q+1
         3: q^3+4q^2+4q+1
         4: q^3+4q^2+4q+1
         5: 2q^2+4q+1
         6: 2q^2+4q+1
         7: 3q+1
         8: 2q^2+4q+1
         9: q^3+4q^2+4q+1
        10: 2q^2+4q+1
        11: 2q^2+4q+1
        12: q^3+4q^2+4q+1
        13: q^3+4q^2+4q+1
        14: 2q^2+4q+1
        15: q^3+4q^2+4q+1
        16: 2q^2+4q+1
        17: q^2+4q+1
        18: 2q^2+4q+1
        19: 2q^2+4q+1
        20: 2q^2+4q+1
        21: 3q+1
        22: 3q+1
        23: 2q+1
        24: q^2+2q+1
        25: 2q^2+4q+1
        26: 3q+1
        27: 2q^2+4q+1
        28: 2q^2+4q+1
        29: q^2+4q+1
        30: q^3+4q^2+4q+1
        31: 2q^2+4q+1
        32: 2q^2+4q+1
        33: 2q^2+4q+1
        34: 3q+1
        35: 2q^2+4q+1
        36: q^3+4q^2+4q+1
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: q^3+4q^2+4q+1
        40: q^2+4q+1
        41: 3q+1
        42: q^2+4q+1
        43: 2q^2+4q+1
        44: 2q+1
        45: 2q^2+4q+1
        46: q^2+2q+1
        47: 2q^2+4q+1
        48: q^2+4q+1
        49: 2q^2+4q+1
        50: 2q+1
        51: q^2+2q+1
        52: 3q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 2q^2+4q+1
        58: 3q+1
        59: 3q+1
        60: 2q+1
        61: q^2+2q+1
        62: q^2+4q+1
        63: 3q+1
        64: q^2+4q+1
        65: 2q^2+4q+1
        66: 3q+1
        67: 2q^2+4q+1
        68: 2q^2+4q+1
        69: q^2+4q+1
        70: 2q^2+4q+1
        71: 2q^2+4q+1
        72: 3q+1
        73: 3q+1
        74: 2q+1
        75: q^2+2q+1
        76: 2q^2+4q+1
        77: 3q+1
        78: 2q^2+4q+1
        79: 2q^2+4q+1
        80: q^2+4q+1
        81: q^3+4q^2+4q+1
        82: 2q^2+4q+1
        83: 2q^2+4q+1
        84: q^2+4q+1
        85: 3q+1
        86: 3q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        91: 2q+1
        92: 2q^2+4q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+4q+1
        98: 3q+1
        99: q^2+4q+1
       100: 2q^2+4q+1
       101: 2q+1
       102: 2q^2+4q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 2q+1
       113: q^2+2q+1
       114: 3q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q^2+4q+1
       120: 3q+1
       121: 3q+1
       122: 2q+1
       123: q+1
       124: 2q^2+4q+1
       125: 3q+1
       126: 3q+1
       127: 2q+1
       128: q^2+2q+1
       129: q^2+4q+1
       130: 3q+1
       131: q^2+4q+1
       132: 2q^2+4q+1
       133: 2q+1
       134: 2q+1
       135: q^2+2q+1
       136: 3q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 2q^2+4q+1
       142: 3q+1
       143: 3q+1
       144: 2q+1
       145: q^2+2q+1
       146: q^2+4q+1
       147: 3q+1
       148: q^2+4q+1
       149: 2q^2+4q+1
       150: 3q+1
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: q^2+4q+1
       154: 2q^2+4q+1
       155: 2q+1
       156: q+1
       157: 3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+4q+1
       177: 3q+1
       178: 3q+1
       179: 2q+1
       180: q+1
       181: 2q+1
       183: 2q+1
       184: 2q^2+4q+1
       185: 2q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: q+1
       208: 3q+1
       209: q+1
       210: q+1
       211: q+1
       212: 1
       213: 2q+1
       214: q^2+2q+1
       215: 3q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: q^2+4q+1
       221: 3q+1
       222: 3q+1
       223: 2q+1
       224: q+1
       225: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: 2q+1
       237: q^2+2q+1
       238: 3q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: q^2+4q+1
       244: 3q+1
       245: 3q+1
       246: 2q+1
       247: q+1
       248: 2q^2+4q+1
       249: 3q+1
       250: 3q+1
       251: 2q+1
       252: q^2+2q+1
       253: q^2+4q+1
       254: 3q+1
       255: q^2+4q+1
       256: 2q^2+4q+1
       257: 2q+1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: 2q+1
       276: q+1
       277: 1
       278: q+1
       282: 1
       283: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: 2q+1
       289: q+1
       290: 3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: 2q+1
       298: q+1
       299: 1
       300: 2q+1
       302: 2q+1
       303: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       345: q+1
       346: 3q+1
       347: q+1
       348: q+1
       349: q+1
       350: 1
       351: 2q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 2q+1
       374: q+1
       375: 3q+1
       376: q+1
       377: q+1
       378: q+1
       379: 1
       380: 2q+1
       381: q^2+2q+1
       382: 3q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: q^2+4q+1
       388: 3q+1
       389: 3q+1
       390: 2q+1
       391: q+1
       392: 2q+1
       394: 2q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       449: 2q+1
       452: q+1
       453: 1
       454: q+1
       458: 1
       459: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: q+1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: 2q+1
       552: q+1
       553: 3q+1
       554: q+1
       555: q+1
       556: q+1
       557: 1
       558: 2q+1
       561: q+1
       562: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       599: 1
       605: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: q+1
       628: 1
       633: 1
       635: 1
       641: q+1
       645: 1
       646: q+1
       648: q+1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       754: 1
       757: 1
       774: 1
       801: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       843: 1
       849: q+1
       853: 1
       871: 1
       880: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       897: 1
       916: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       959: 1
      1016: 1
      1033: 1
      1060: 1
      1096: 1
      1130: 1
      1139: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1156: 1
      1340: 1

1341:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       582: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       660: 1
       668: 1
       669: 1
       670: 1
       678: 1
       679: 1
       680: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       695: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       732: 1
       733: 1
       734: 1
       735: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       754: 1
       758: 1
       809: 1
       810: 1
       811: 1
       826: 1
       872: 1
       881: 1
       889: 1
       890: 1
       891: 1
       917: 1
       925: 1
       926: 1
       927: 1
       935: 1
       936: 1
       937: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       952: 1
      1017: 1
      1097: 1
      1131: 1
      1140: 1
      1148: 1
      1149: 1
      1150: 1
      1341: 1

1342:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: q+1
       169: 1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       302: 1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       463: q+1
       468: 1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: 1
       521: 1
       522: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       568: 1
       569: 1
       582: 1
       590: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       661: 1
       668: 1
       671: 1
       672: 1
       678: 1
       681: 1
       682: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       695: 1
       707: 1
       714: 1
       717: 1
       718: 1
       723: 1
       724: 1
       725: 1
       727: 1
       728: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       754: 1
       759: 1
       792: 1
       800: 1
       801: 1
       806: 1
       809: 1
       812: 1
       813: 1
       826: 1
       834: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       873: 1
       882: 1
       889: 1
       892: 1
       893: 1
       918: 1
       925: 1
       928: 1
       929: 1
       935: 1
       938: 1
       939: 1
       944: 1
       945: 1
       946: 1
       948: 1
       949: 1
       952: 1
      1006: 1
      1018: 1
      1051: 1
      1059: 1
      1060: 1
      1065: 1
      1098: 1
      1132: 1
      1141: 1
      1148: 1
      1151: 1
      1152: 1
      1263: 1
      1342: 1

1343:    0: q^3+q^2+2q+1
         1: q^2+q+1
         2: 2q+1
         3: q^3+q^2+2q+1
         4: q^3+q^2+2q+1
         5: q^3+q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: q^3+q^2+2q+1
        12: q^3+q^2+2q+1
        13: q^2+q+1
        14: 2q+1
        15: q^3+q^2+2q+1
        16: q^2+q+1
        17: 2q+1
        18: q^3+q^2+2q+1
        19: q^3+q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: q+1
        26: q+1
        27: 2q+1
        28: q^2+q+1
        29: 2q+1
        30: q^2+q+1
        31: 2q+1
        32: q^3+q^2+2q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q^2+q+1
        37: 2q+1
        38: q^3+q^2+2q+1
        39: q^3+q^2+2q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q^2+q+1
        44: q+1
        45: q^3+q^2+2q+1
        46: q^2+1
        47: q^2+q+1
        48: 2q+1
        49: q^3+q^2+2q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: q+1
        63: q+1
        64: 2q+1
        65: q+1
        66: q+1
        67: 2q+1
        68: q^2+q+1
        69: 2q+1
        70: q^3+q^2+2q+1
        71: q+1
        72: q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: q+1
        77: q+1
        78: 2q+1
        79: q^2+q+1
        80: 2q+1
        81: q^2+q+1
        82: 2q+1
        83: q^3+q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: 2q+1
        88: 1
        89: 1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q^2+1
        95: 1
        96: q^2+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q^2+q+1
       101: q+1
       102: q^3+q^2+2q+1
       103: q^2+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: q+1
       130: q+1
       131: 2q+1
       132: q^2+q+1
       133: q+1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: q+1
       146: q+1
       147: q+1
       148: 2q+1
       149: q+1
       150: q+1
       151: 2q+1
       152: q^2+q+1
       153: 2q+1
       154: q^3+q^2+2q+1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: q^2+1
       174: 1
       175: q^2+1
       176: q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 1
       181: 1
       183: q+1
       184: q^2+q+1
       185: q+1
       186: q^2+1
       187: 1
       188: q^2+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: 1
       227: q+1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: q+1
       238: q+1
       239: 1
       240: q+1
       241: 1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: q+1
       253: q+1
       254: q+1
       255: 2q+1
       256: q^2+q+1
       257: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: q^2+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: q^2+1
       307: 1
       308: q^2+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: 1
       354: q+1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       366: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: q+1
       375: q+1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: q+1
       382: q+1
       383: 1
       384: q+1
       385: 1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: 1
       392: 1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       412: 1
       418: 1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       449: 1
       452: q+1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q^2+1
       463: 1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       544: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: q+1
       553: q+1
       554: 1
       555: q+1
       556: 1
       557: 1
       558: 1
       561: q+1
       562: 1
       566: 1
       568: 1
       570: 1
       589: 1
       597: 1
       598: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       627: 1
       633: 1
       634: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       662: 1
       669: 1
       671: 1
       673: 1
       679: 1
       681: 1
       683: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       708: 1
       715: 1
       717: 1
       719: 1
       724: 1
       726: 1
       727: 1
       728: 1
       729: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       754: 1
       760: 1
       799: 1
       800: 1
       806: 1
       810: 1
       812: 1
       814: 1
       833: 1
       841: 1
       842: 1
       848: 1
       849: 1
       852: 1
       853: 1
       874: 1
       883: 1
       890: 1
       892: 1
       894: 1
       919: 1
       926: 1
       928: 1
       930: 1
       936: 1
       938: 1
       940: 1
       945: 1
       947: 1
       948: 1
       949: 1
       950: 1
       959: 1
      1013: 1
      1019: 1
      1058: 1
      1059: 1
      1065: 1
      1099: 1
      1133: 1
      1142: 1
      1149: 1
      1151: 1
      1153: 1
      1270: 1
      1343: 1

1344:    0: q^4+2q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^4+2q^2+q+1
         4: q^4+2q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^4+2q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^4+2q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^4+2q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q^2+q+1
        76: q+1
        77: q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: 1
       214: q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: 1
       227: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: 1
       354: 1
       355: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: 1
       377: 1
       378: q+1
       379: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       411: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: q+1
       553: q+1
       554: 1
       555: 1
       556: q+1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       589: 1
       599: 1
       605: 1
       609: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       663: 1
       670: 1
       672: 1
       673: 1
       680: 1
       682: 1
       683: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       709: 1
       716: 1
       718: 1
       719: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       754: 1
       761: 1
       801: 1
       811: 1
       813: 1
       814: 1
       833: 1
       843: 1
       849: 1
       853: 1
       875: 1
       884: 1
       891: 1
       893: 1
       894: 1
       920: 1
       927: 1
       929: 1
       930: 1
       937: 1
       939: 1
       940: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       959: 1
      1020: 1
      1060: 1
      1100: 1
      1134: 1
      1143: 1
      1150: 1
      1152: 1
      1153: 1
      1344: 1

1345:    0: q^2+q+1
         1: 1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: 1
         7: 1
         8: q^2+q+1
         9: 1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: 1
        14: q^2+q+1
        15: q^2+q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: q^2+q+1
        25: 1
        26: 1
        27: q^2+q+1
        28: 1
        29: q+1
        30: 1
        31: q^2+q+1
        32: q+1
        33: 1
        34: 1
        35: q^2+q+1
        36: 1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: q+1
        61: q^2+q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q^2+q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: q^2+q+1
        76: 1
        77: 1
        78: q^2+q+1
        79: 1
        80: q+1
        81: 1
        82: q^2+q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: q+1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: q+1
       128: q^2+q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: q+1
       145: q^2+q+1
       146: 1
       147: 1
       148: q+1
       149: 1
       150: 1
       151: q^2+q+1
       152: 1
       153: q+1
       154: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: q+1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: 1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: 1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 1
       251: q+1
       252: q^2+q+1
       253: 1
       254: 1
       255: q+1
       256: 1
       257: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: q+1
       355: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: 1
       389: 1
       390: q+1
       391: 1
       392: 1
       394: q+1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       418: 1
       426: 1
       430: 1
       431: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: q+1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       471: 1
       480: 1
       481: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       523: 1
       524: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: q+1
       562: 1
       570: 1
       571: 1
       581: 1
       589: 1
       605: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       633: 1
       641: 1
       645: 1
       646: 1
       648: 1
       664: 1
       673: 1
       674: 1
       683: 1
       684: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       710: 1
       719: 1
       720: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       754: 1
       762: 1
       782: 1
       814: 1
       815: 1
       825: 1
       833: 1
       849: 1
       853: 1
       876: 1
       885: 1
       894: 1
       895: 1
       905: 1
       921: 1
       930: 1
       931: 1
       940: 1
       941: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       959: 1
      1021: 1
      1041: 1
      1101: 1
      1135: 1
      1144: 1
      1153: 1
      1154: 1
      1164: 1
      1345: 1

1346:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: q+1
       196: 1
       197: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       244: q+1
       245: 1
       246: 1
       247: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: q+1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       362: q+1
       363: 1
       364: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       438: 1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       489: 1
       490: 1
       491: 1
       498: q+1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: 1
       524: 1
       525: 1
       532: q+1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       554: 1
       555: 1
       556: 1
       557: 1
       559: 1
       560: 1
       561: 1
       562: 1
       571: 1
       572: 1
       579: 1
       586: 1
       587: 1
       588: 1
       606: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       665: 1
       674: 1
       675: 1
       684: 1
       685: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       711: 1
       720: 1
       721: 1
       728: 1
       729: 1
       730: 1
       737: q+1
       738: 1
       739: 1
       744: 1
       745: 1
       746: 1
       747: 1
       751: 1
       752: 1
       753: 1
       754: 1
       763: 1
       780: 1
       815: 1
       816: 1
       823: 1
       830: 1
       831: 1
       832: 1
       850: 1
       877: 1
       886: 1
       895: 1
       896: 1
       903: 1
       922: 1
       931: 1
       932: 1
       941: 1
       942: 1
       949: 1
       950: 1
       951: 1
       956: 1
       957: 1
       958: 1
      1022: 1
      1039: 1
      1102: 1
      1136: 1
      1145: 1
      1154: 1
      1155: 1
      1162: 1
      1346: 1

1347:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q^2+1
        23: 1
        24: q^2+1
        25: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: q^2+1
        32: 1
        33: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: q^2+1
        56: 1
        57: q^2+1
        60: 1
        61: q^2+1
        62: 1
        64: 1
        65: q^2+1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: q^2+1
       118: 1
       119: 1
       122: 1
       123: 1
       124: q^2+1
       127: 1
       128: q^2+1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q^2+1
       140: 1
       141: q^2+1
       144: 1
       145: q^2+1
       146: 1
       148: 1
       149: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: q^2+1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: q^2+1
       242: 1
       243: 1
       246: 1
       247: 1
       248: q^2+1
       251: 1
       252: q^2+1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: q^2+1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       702: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       887: 1
       897: 1
       905: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       977: 1
      1023: 1
      1033: 1
      1041: 1
      1060: 1
      1103: 1
      1146: 1
      1156: 1
      1164: 1
      1234: 1
      1347: 1

1348:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^3+2q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^3+2q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^3+2q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^3+2q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: 1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: 1
        51: q+1
        52: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^3+2q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q^2+2q+1
        93: 1
        94: q^2+2q+1
        95: 1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: 1
       102: q^2+2q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: q+1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+2q+1
       133: 1
       134: 1
       135: q+1
       136: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 1
       156: q+1
       157: q+1
       159: 1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q^2+2q+1
       174: 1
       175: q^2+2q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q^2+2q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q^2+2q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: q+1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q+1
       215: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: 1
       258: 1
       259: 1
       260: q+1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q^2+2q+1
       287: 1
       288: 1
       289: q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       348: 1
       349: q+1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q+1
       382: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+2q+1
       463: 1
       474: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       517: 1
       526: 1
       527: 1
       533: 1
       535: 1
       536: 1
       537: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: 1
       573: 1
       574: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       617: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       713: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       765: 1
       774: 1
       775: 1
       781: 1
       794: 1
       801: 1
       802: 1
       805: 1
       808: 1
       817: 1
       818: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       888: 1
       897: 1
       898: 1
       904: 1
       924: 1
       934: 1
       943: 1
       944: 1
       950: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       978: 1
      1008: 1
      1024: 1
      1033: 1
      1034: 1
      1040: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1104: 1
      1147: 1
      1156: 1
      1157: 1
      1163: 1
      1235: 1
      1265: 1
      1348: 1

1349:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 1
        21: q^2+2q+1
        22: 1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: 1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q^2+2q+1
        59: 1
        60: 1
        61: 1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: 1
        72: q^2+2q+1
        73: 1
        74: 1
        75: 1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q^2+2q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q^2+2q+1
       126: 1
       127: 1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q^2+2q+1
       143: 1
       144: 1
       145: 1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 1
       149: q^2+2q+1
       150: q^2+2q+1
       151: 1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q^2+2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q^2+2q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q^2+2q+1
       250: 1
       251: 1
       252: 1
       253: q^2+2q+1
       254: q^2+2q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q^2+2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       431: q+1
       432: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       455: q+1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       493: 1
       494: 1
       495: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: q+1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: q+1
       646: q+1
       647: q+1
       668: 1
       678: 1
       687: 1
       688: 1
       689: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       714: 1
       723: 1
       724: 1
       725: 1
       728: 1
       732: 1
       733: 1
       734: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       809: 1
       818: 1
       819: 1
       820: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: q+1
       889: 1
       898: 1
       899: 1
       900: 1
       903: 1
       925: 1
       935: 1
       944: 1
       945: 1
       946: 1
       949: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       979: 1
      1025: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1105: 1
      1148: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1236: 1
      1349: 1

1350:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       312: 1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       476: 1
       485: 1
       487: 1
       494: 1
       496: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: 1
       528: 1
       530: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       669: 1
       679: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       715: 1
       724: 1
       726: 1
       733: 1
       735: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       829: 1
       830: 1
       890: 1
       899: 1
       901: 1
       926: 1
       936: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       980: 1
      1026: 1
      1035: 1
      1037: 1
      1106: 1
      1149: 1
      1158: 1
      1160: 1
      1237: 1
      1350: 1

1351:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       401: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       477: 1
       486: 1
       487: 1
       489: 1
       495: 1
       496: 1
       498: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       613: 1
       614: 1
       616: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       670: 1
       680: 1
       689: 1
       690: 1
       692: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       716: 1
       725: 1
       726: 1
       728: 1
       734: 1
       735: 1
       737: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       768: 1
       777: 1
       778: 1
       780: 1
       811: 1
       820: 1
       821: 1
       823: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: 1
       891: 1
       900: 1
       901: 1
       903: 1
       927: 1
       937: 1
       946: 1
       947: 1
       949: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       981: 1
      1027: 1
      1036: 1
      1037: 1
      1039: 1
      1107: 1
      1150: 1
      1159: 1
      1160: 1
      1162: 1
      1238: 1
      1351: 1

1352:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 2q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: 2q+1
         9: 3q^2+3q+1
        10: 2q^2+3q+1
        11: 3q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 2q^2+3q+1
        15: 3q^2+3q+1
        16: 3q^2+3q+1
        17: 2q^2+3q+1
        18: 2q^2+3q+1
        19: 3q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: 3q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+3q+1
        31: 2q^2+3q+1
        32: 3q^2+3q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: 3q^2+3q+1
        37: 2q^2+3q+1
        38: 3q^2+3q+1
        39: 3q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: 3q^2+3q+1
        48: 2q^2+3q+1
        49: 2q^2+3q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: q^2+2q+1
        63: 2q^2+3q+1
        64: 2q+1
        65: q^2+2q+1
        66: 2q^2+3q+1
        67: 2q+1
        68: 3q^2+3q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: q^2+2q+1
        77: 2q^2+3q+1
        78: 2q+1
        79: 3q^2+3q+1
        80: 2q^2+3q+1
        81: 3q^2+3q+1
        82: 2q^2+3q+1
        83: 3q^2+3q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q+1
        90: q^2+2q+1
        91: q+1
        92: 2q^2+3q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q^2+3q+1
       101: q^2+2q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: q+1
       114: q+1
       115: 1
       116: 2q+1
       117: q+1
       118: q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: q+1
       129: q^2+2q+1
       130: 2q^2+3q+1
       131: 2q+1
       132: 2q^2+3q+1
       133: q^2+2q+1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q+1
       145: q+1
       146: q^2+2q+1
       147: 2q^2+3q+1
       148: 2q+1
       149: q^2+2q+1
       150: 2q^2+3q+1
       151: 2q+1
       152: 3q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q^2+2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: q+1
       182: q^2+2q+1
       183: q+1
       184: 2q^2+3q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       191: 1
       194: 1
       195: 1
       199: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       206: q+1
       208: q+1
       209: 1
       210: 2q+1
       211: q+1
       212: q+1
       213: q+1
       215: q+1
       216: 1
       217: 2q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q+1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: q+1
       238: q+1
       239: 1
       240: 2q+1
       241: q+1
       242: q+1
       243: q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: q+1
       248: q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q^2+2q+1
       254: 2q^2+3q+1
       255: 2q+1
       256: 2q^2+3q+1
       257: q^2+2q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q^2+2q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       314: 1
       321: 1
       324: 1
       325: 1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       344: q+1
       346: q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       358: 1
       361: 1
       362: 1
       366: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       373: q+1
       375: q+1
       376: 1
       377: 2q+1
       378: q+1
       379: q+1
       380: q+1
       382: q+1
       383: 1
       384: 2q+1
       385: q+1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: q+1
       393: q^2+2q+1
       394: q+1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       478: 1
       485: 1
       488: 1
       489: 1
       494: 1
       497: 1
       498: 1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       509: 1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       521: 1
       528: 1
       531: 1
       532: 1
       536: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       544: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       551: q+1
       553: q+1
       554: 1
       555: 2q+1
       556: q+1
       557: q+1
       558: 1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       568: 1
       575: 1
       578: 1
       579: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       591: 1
       596: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       629: 1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       671: 1
       681: 1
       688: 1
       691: 1
       692: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       717: 1
       724: 1
       727: 1
       728: 1
       733: 1
       736: 1
       737: 1
       741: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       748: 1
       750: 1
       751: 1
       752: q+1
       753: 1
       754: 1
       769: 1
       776: 1
       779: 1
       780: 1
       793: 1
       798: 1
       800: 1
       802: 1
       804: 1
       805: 1
       806: 1
       812: 1
       819: 1
       822: 1
       823: 1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       835: 1
       840: 1
       842: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       892: 1
       899: 1
       902: 1
       903: 1
       928: 1
       938: 1
       945: 1
       948: 1
       949: 1
       953: 1
       955: 1
       956: 1
       957: 1
       958: 1
       982: 1
      1007: 1
      1012: 1
      1028: 1
      1035: 1
      1038: 1
      1039: 1
      1052: 1
      1057: 1
      1059: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1108: 1
      1151: 1
      1158: 1
      1161: 1
      1162: 1
      1239: 1
      1264: 1
      1269: 1
      1352: 1

1353:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: 1
        55: q+1
        57: q+1
        58: q+1
        59: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       106: q+1
       107: 1
       109: 1
       113: q+1
       114: q+1
       115: 1
       117: q+1
       119: q+1
       120: q+1
       121: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       139: q+1
       141: q+1
       142: q+1
       143: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       160: q+1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       192: 1
       194: 1
       200: q+1
       201: 1
       203: 1
       207: q+1
       208: q+1
       209: 1
       211: q+1
       214: q+1
       215: q+1
       216: 1
       218: q+1
       220: q+1
       221: q+1
       222: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       233: 1
       237: q+1
       238: q+1
       239: 1
       241: q+1
       243: q+1
       244: q+1
       245: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       260: q+1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       315: 1
       322: 1
       324: 1
       330: q+1
       331: 1
       333: 1
       338: q+1
       339: 1
       341: 1
       345: q+1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: q+1
       368: 1
       370: 1
       374: q+1
       375: q+1
       376: 1
       378: q+1
       381: q+1
       382: q+1
       383: 1
       385: q+1
       387: q+1
       388: q+1
       389: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       479: 1
       486: 1
       488: 1
       495: 1
       497: 1
       503: q+1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       537: q+1
       538: 1
       540: 1
       545: q+1
       546: 1
       548: 1
       552: q+1
       553: q+1
       554: 1
       556: q+1
       558: 1
       559: 1
       560: 1
       562: 1
       569: 1
       576: 1
       578: 1
       584: 1
       585: 1
       587: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       628: 1
       629: 1
       630: 1
       632: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       672: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       718: 1
       725: 1
       727: 1
       734: 1
       736: 1
       742: q+1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       770: 1
       777: 1
       779: 1
       794: 1
       801: 1
       802: 1
       805: 1
       813: 1
       820: 1
       822: 1
       828: 1
       829: 1
       831: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       893: 1
       900: 1
       902: 1
       929: 1
       939: 1
       946: 1
       948: 1
       954: 1
       955: 1
       957: 1
       983: 1
      1008: 1
      1029: 1
      1036: 1
      1038: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1109: 1
      1152: 1
      1159: 1
      1161: 1
      1240: 1
      1265: 1
      1353: 1

1354:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: 2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q^2+2q+1
        37: 2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: 2q+1
        60: q+1
        61: q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: 2q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: q+1
       150: 2q+1
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: 1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: 2q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 2q+1
       251: q+1
       252: q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: 2q+1
       257: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: 1
       351: 1
       352: 1
       353: q+1
       354: q+1
       355: 1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: 1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: 2q+1
       390: q+1
       391: q+1
       392: 1
       393: q+1
       394: q+1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       496: 1
       497: 1
       498: 1
       499: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: 1
       558: 1
       559: 1
       560: q+1
       561: q+1
       562: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: q+1
       632: 1
       633: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       673: 1
       683: 1
       690: 1
       691: 1
       692: 1
       693: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       719: 1
       726: 1
       727: 1
       728: 1
       729: 1
       735: 1
       736: 1
       737: 1
       738: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       750: 1
       751: 1
       752: q+1
       753: 1
       754: 1
       771: 1
       778: 1
       779: 1
       780: 1
       781: 1
       802: 1
       805: 1
       814: 1
       821: 1
       822: 1
       823: 1
       824: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       894: 1
       901: 1
       902: 1
       903: 1
       904: 1
       930: 1
       940: 1
       947: 1
       948: 1
       949: 1
       950: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       984: 1
      1030: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1061: 1
      1064: 1
      1110: 1
      1153: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1241: 1
      1354: 1

1355:    0: 2q^2+2q+1
         1: q^2+q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: q^2+2q+1
         6: q^2+q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q^2+2q+1
        25: q^2+q+1
        26: q+1
        27: q^2+2q+1
        28: q+1
        29: q^2+2q+1
        30: q^2+q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: q^2+q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+q+1
        37: 2q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q+1
        48: q^2+2q+1
        49: 2q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q^2+2q+1
        62: q+1
        63: q+1
        64: 2q+1
        65: q^2+q+1
        66: q+1
        67: q^2+2q+1
        68: q+1
        69: q^2+2q+1
        70: 2q+1
        72: q+1
        73: q+1
        74: q+1
        75: q^2+2q+1
        76: q^2+q+1
        77: q+1
        78: q^2+2q+1
        79: q+1
        80: q^2+2q+1
        81: q^2+q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: q+1
        90: 1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: q+1
       118: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+2q+1
       129: q+1
       130: q+1
       131: 2q+1
       132: q+1
       133: 2q+1
       137: q+1
       138: 1
       139: q+1
       140: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q+1
       148: 2q+1
       149: q^2+q+1
       150: q+1
       151: q^2+2q+1
       152: q+1
       153: q^2+2q+1
       154: 2q+1
       158: q+1
       159: 1
       160: q+1
       161: q+1
       163: 1
       164: 1
       165: q+1
       166: 2q+1
       167: q+1
       168: 1
       169: 2q+1
       170: q+1
       171: 1
       172: q+1
       173: q+1
       174: 2q+1
       175: 2q+1
       177: q+1
       178: q+1
       179: q+1
       180: 2q+1
       181: q+1
       182: 1
       183: 2q+1
       184: q+1
       185: 2q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       195: 1
       196: 1
       197: 1
       202: 1
       203: q+1
       204: 1
       205: 1
       209: q+1
       210: 1
       211: q+1
       212: q+1
       216: q+1
       217: 1
       218: q+1
       219: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: 1
       227: 2q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       239: q+1
       240: 1
       241: q+1
       242: q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: 2q+1
       256: q+1
       257: 2q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: 1
       275: 1
       276: q+1
       277: 2q+1
       279: 1
       280: 1
       282: q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: 2q+1
       291: q+1
       292: 1
       293: q+1
       294: q+1
       296: 1
       297: 1
       298: q+1
       299: 2q+1
       300: q+1
       301: 1
       302: 2q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: 2q+1
       308: 2q+1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: q+1
       334: 1
       335: 1
       340: 1
       341: q+1
       342: 1
       343: 1
       347: q+1
       348: 1
       349: q+1
       350: q+1
       352: 1
       353: 1
       354: q+1
       355: 2q+1
       362: 1
       363: 1
       364: 1
       369: 1
       370: q+1
       371: 1
       372: 1
       376: q+1
       377: 1
       378: q+1
       379: q+1
       383: q+1
       384: 1
       385: q+1
       386: q+1
       388: q+1
       389: q+1
       390: q+1
       391: 2q+1
       392: q+1
       393: 1
       394: 2q+1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       422: 1
       424: 1
       427: 1
       428: 1
       430: q+1
       431: q+1
       432: 1
       433: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       450: 1
       451: 1
       452: q+1
       453: 2q+1
       455: 1
       456: 1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: 2q+1
       481: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: q+1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       540: q+1
       541: 1
       542: 1
       547: 1
       548: q+1
       549: 1
       550: 1
       554: q+1
       555: 1
       556: q+1
       557: q+1
       559: 1
       560: 1
       561: q+1
       562: 2q+1
       571: 1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       595: 1
       601: 1
       603: 1
       606: 1
       607: 1
       609: q+1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       637: 1
       639: 1
       642: 1
       643: 1
       645: q+1
       646: q+1
       647: 1
       648: q+1
       674: 1
       684: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       702: 1
       720: 1
       728: 1
       729: 1
       730: 1
       737: 1
       738: 1
       739: 1
       744: 1
       745: q+1
       746: 1
       747: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       772: 1
       780: 1
       781: 1
       782: 1
       797: 1
       803: 1
       805: 1
       815: 1
       823: 1
       824: 1
       825: 1
       830: 1
       831: 1
       832: 1
       833: 1
       839: 1
       845: 1
       847: 1
       850: 1
       851: 1
       853: q+1
       895: 1
       903: 1
       904: 1
       905: 1
       931: 1
       941: 1
       949: 1
       950: 1
       951: 1
       956: 1
       957: 1
       958: 1
       959: 1
       985: 1
      1011: 1
      1031: 1
      1039: 1
      1040: 1
      1041: 1
      1056: 1
      1062: 1
      1064: 1
      1111: 1
      1154: 1
      1162: 1
      1163: 1
      1164: 1
      1242: 1
      1268: 1
      1355: 1

1356:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        22: q^2+1
        23: 1
        24: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: q^2+1
        32: 1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: q^2+1
        56: 1
        59: q^2+1
        60: 1
        61: q^2+1
        63: 1
        64: 1
        66: q^2+1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        73: q^2+1
        74: 1
        75: q^2+1
        77: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: q^2+1
       118: 1
       121: 1
       122: 1
       123: 1
       126: q^2+1
       127: 1
       128: q^2+1
       130: 1
       131: 1
       132: 1
       133: 1
       138: 1
       139: q^2+1
       140: 1
       143: q^2+1
       144: 1
       145: q^2+1
       147: 1
       148: 1
       150: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: q^2+1
       219: 1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: q^2+1
       242: 1
       245: 1
       246: 1
       247: 1
       250: q^2+1
       251: 1
       252: q^2+1
       254: 1
       255: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       363: 1
       364: 1
       371: 1
       372: 1
       377: 1
       378: 1
       379: 1
       384: 1
       385: q^2+1
       386: 1
       389: 1
       390: 1
       391: 1
       393: 1
       394: 1
       402: 1
       403: 1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       424: 1
       428: 1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       456: 1
       458: 1
       460: 1
       461: 1
       462: 1
       463: 1
       482: 1
       490: 1
       491: 1
       499: 1
       500: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       525: 1
       533: 1
       534: 1
       541: 1
       542: 1
       549: 1
       550: 1
       555: 1
       556: 1
       557: 1
       560: 1
       561: 1
       562: 1
       572: 1
       580: 1
       581: 1
       588: 1
       589: 1
       603: 1
       607: 1
       609: 1
       617: 1
       618: 1
       625: 1
       626: 1
       631: 1
       632: 1
       633: 1
       639: 1
       643: 1
       645: 1
       647: 1
       648: 1
       675: 1
       685: 1
       693: 1
       694: 1
       701: 1
       702: 1
       721: 1
       729: 1
       730: 1
       738: 1
       739: 1
       746: 1
       747: 1
       752: 1
       753: 1
       754: 1
       773: 1
       781: 1
       782: 1
       805: 1
       816: 1
       824: 1
       825: 1
       832: 1
       833: 1
       847: 1
       851: 1
       853: 1
       896: 1
       904: 1
       905: 1
       932: 1
       942: 1
       950: 1
       951: 1
       958: 1
       959: 1
       986: 1
      1032: 1
      1040: 1
      1041: 1
      1064: 1
      1112: 1
      1155: 1
      1163: 1
      1164: 1
      1243: 1
      1356: 1

1357:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       309: 1
       310: q+1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       385: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       639: 1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: 1
       663: 1
       666: 1
       667: 1
       675: 1
       697: 1
       718: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       854: 1
       855: 1
       860: 1
       863: 1
       869: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       986: 1
      1008: 1
      1029: 1
      1066: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1357: 1

1358:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q^2+3q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: 2q^2+3q+1
        12: q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q^2+3q+1
        29: 2q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: q^2+2q+1
        50: 2q^2+3q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: 2q+1
        54: 2q^2+3q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: 2q^2+3q+1
        85: q^3+3q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q+1
       104: q^2+2q+1
       105: 2q^2+3q+1
       106: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q^2+2q+1
       111: q+1
       112: 2q+1
       113: q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 2q^2+3q+1
       156: q^2+2q+1
       157: 2q^2+3q+1
       158: 2q+1
       159: 2q^2+3q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^3+3q^2+3q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q^2+2q+1
       191: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       208: q+1
       210: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: q+1
       232: q+1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       258: q^2+2q+1
       259: 2q^2+3q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q^2+2q+1
       265: q+1
       266: 2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: 2q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: q+1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: q+1
       357: q+1
       358: q+1
       359: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: q+1
       396: q^2+2q+1
       397: 2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: 1
       404: q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: q+1
       416: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       450: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       482: 1
       492: 1
       493: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       516: 1
       517: q+1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: q+1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       563: 1
       564: q+1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: q+1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       610: q+1
       611: q+1
       612: q+1
       613: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       662: 1
       676: 1
       677: 1
       685: 1
       696: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       773: 1
       783: 1
       784: 1
       790: 1
       791: 1
       793: 1
       800: 1
       802: 1
       804: 1
       807: 1
       808: q+1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: q+1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       840: 1
       850: 1
       854: 1
       856: 1
       859: 1
       864: 1
       878: 1
       906: 1
       918: 1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       970: 1
       972: 1
       973: 1
       987: 1
       988: 1
       996: 1
      1007: 1
      1014: 1
      1015: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1067: 1
      1165: 1
      1167: 1
      1170: 1
      1175: 1
      1189: 1
      1217: 1
      1229: 1
      1358: 1

1359:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        60: q+1
        61: q+1
        62: q+1
        64: q+1
        65: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       118: q+1
       119: q+1
       122: q+1
       123: q+1
       124: 1
       127: 1
       128: 1
       129: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       205: 1
       206: q+1
       207: q+1
       212: q+1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: q+1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       277: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       328: q+1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       411: 1
       412: q+1
       413: q+1
       418: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: q+1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       704: 1
       707: 1
       756: 1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       855: 1
       856: 1
       857: 1
       858: 1
       887: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1015: 1
      1018: 1
      1068: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1359: 1

1360:    0: 2q^2+2q+1
         1: q^2+q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: q^2+2q+1
         5: 2q^2+2q+1
         6: q+1
         7: q^2+q+1
         8: 2q^2+2q+1
         9: q^2+q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: 2q^2+2q+1
        24: 2q+1
        25: q+1
        27: q^2+2q+1
        28: q^2+q+1
        29: q^2+2q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q+1
        37: q+1
        38: q^2+2q+1
        39: 2q+1
        40: q+1
        41: q^2+q+1
        42: 2q^2+2q+1
        43: q^2+q+1
        44: q^2+2q+1
        45: 2q^2+2q+1
        46: 2q+1
        47: q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q^2+q+1
        55: q+1
        56: 2q+1
        57: q+1
        60: q^2+2q+1
        61: 2q+1
        62: q+1
        64: q^2+2q+1
        65: q+1
        67: 2q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: q+1
        74: q^2+2q+1
        75: 2q+1
        76: 1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: q^2+q+1
        87: 2q^2+2q+1
        88: 2q+1
        89: q+1
        91: q^2+2q+1
        92: q^2+q+1
        93: q^2+2q+1
        94: q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: q+1
        99: q^2+2q+1
       100: q+1
       101: q+1
       102: q^2+2q+1
       103: 2q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+1
       112: q+1
       113: 1
       118: 2q+1
       119: q+1
       122: q^2+2q+1
       123: q+1
       124: q+1
       127: 2q+1
       128: 2q+1
       129: q+1
       131: 2q+1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 2q+1
       141: 1
       144: q+1
       145: q+1
       146: 1
       148: q+1
       149: 1
       151: q+1
       152: q+1
       153: q+1
       154: 2q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q^2+q+1
       160: q+1
       161: 2q+1
       162: q+1
       165: q^2+2q+1
       166: 2q+1
       167: q+1
       169: q^2+2q+1
       170: q+1
       172: 2q+1
       173: q+1
       174: 2q+1
       175: 2q+1
       176: q+1
       177: q+1
       178: q+1
       179: q^2+2q+1
       180: 2q+1
       181: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: 2q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: 1
       205: 2q+1
       206: q+1
       207: 1
       212: q+1
       213: q+1
       214: 1
       219: 2q+1
       220: q+1
       223: 2q+1
       224: q+1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: 2q+1
       236: 1
       237: 1
       242: q+1
       243: 1
       246: q+1
       248: 1
       251: q+1
       252: q+1
       253: 1
       255: q+1
       256: q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: 2q+1
       266: q+1
       267: 1
       272: 2q+1
       273: q+1
       276: q^2+2q+1
       277: q+1
       278: q+1
       281: 2q+1
       282: 2q+1
       283: q+1
       285: 2q+1
       286: q+1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 2q+1
       295: 1
       298: q+1
       299: q+1
       300: 1
       302: q+1
       303: 1
       305: q+1
       306: q+1
       307: q+1
       308: 2q+1
       310: 1
       311: 1
       312: q+1
       313: 1
       314: q+1
       315: 1
       316: q+1
       317: 1
       319: 1
       327: 1
       328: 1
       335: q+1
       336: 1
       343: 2q+1
       344: q+1
       345: 1
       350: q+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       372: q+1
       373: 1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: q+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       404: 1
       411: 2q+1
       412: q+1
       413: 1
       418: q+1
       419: q+1
       420: 1
       425: 2q+1
       426: q+1
       429: 2q+1
       430: q+1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: 2q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: q+1
       454: 1
       457: q+1
       458: q+1
       459: 1
       461: q+1
       462: q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: q+1
       470: 1
       471: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: q+1
       551: 1
       558: 1
       561: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       568: q+1
       569: 1
       570: q+1
       571: 1
       573: 1
       581: 1
       582: 1
       589: q+1
       590: 1
       597: 2q+1
       598: q+1
       599: 1
       604: q+1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       626: q+1
       627: 1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: q+1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       686: 1
       694: 1
       695: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       731: 1
       739: 1
       748: 1
       757: 1
       758: 1
       759: 1
       760: q+1
       761: 1
       762: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: q+1
       800: 1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: q+1
       842: 1
       849: 1
       852: 1
       857: 1
       858: 1
       897: 1
       905: 1
       909: 1
       911: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1042: 1
      1050: 1
      1059: 1
      1069: 1
      1168: 1
      1169: 1
      1208: 1
      1216: 1
      1220: 1
      1222: 1
      1360: 1

1361:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+3q+1
        29: 2q+1
        30: q^2+3q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: 1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: q+1
        68: q^2+3q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        94: q^2+3q+1
        95: 2q+1
        96: q^2+3q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: q^2+3q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q+1
       146: 1
       147: q+1
       149: 1
       150: q+1
       151: q+1
       152: 2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 1
       163: q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: 2q+1
       172: q+1
       173: q^2+3q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       244: 1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: q+1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: q^2+3q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: 2q+1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: q+1
       300: 1
       301: q+1
       303: 1
       304: q+1
       305: q+1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q+1
       380: 1
       381: 1
       382: 1
       384: q+1
       385: q+1
       386: q+1
       388: 1
       392: 1
       393: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: 2q+1
       411: 1
       412: 1
       413: 1
       414: 1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: q+1
       447: q+1
       448: q+1
       450: 1
       454: 1
       455: 1
       456: q+1
       457: q+1
       458: q+1
       459: 1
       460: q+1
       462: q+1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       482: 1
       484: 1
       490: 1
       491: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       549: q+1
       559: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: 1
       613: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: q+1
       634: 1
       635: 1
       636: 1
       638: q+1
       639: q+1
       640: q+1
       642: 1
       646: 1
       647: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       675: 1
       685: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       775: 1
       781: 1
       782: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       840: q+1
       850: 1
       858: 1
       859: 1
       860: 1
       865: 1
       896: 1
       898: 1
       918: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       986: 1
       996: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1070: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1207: 1
      1209: 1
      1229: 1
      1361: 1

1362:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        81: 1
        82: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: 1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: q+1
       137: q+1
       139: 1
       141: q+1
       142: q+1
       143: q+1
       145: 1
       149: 1
       150: 1
       151: 1
       155: 1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       186: 1
       187: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: q+1
       233: 1
       237: 1
       238: q+1
       239: q+1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: q+1
       291: q+1
       293: 1
       295: q+1
       296: q+1
       297: q+1
       299: 1
       303: 1
       304: 1
       305: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       359: 1
       361: 1
       367: 1
       368: q+1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       436: 1
       437: q+1
       439: 1
       443: 1
       444: q+1
       445: q+1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       495: 1
       497: 1
       504: 1
       511: 1
       512: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       592: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       606: 1
       607: 1
       613: 1
       615: 1
       621: 1
       622: q+1
       624: 1
       635: 1
       636: 1
       637: 1
       639: 1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       669: 1
       682: 1
       698: 1
       718: 1
       734: 1
       736: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       773: 1
       776: 1
       778: 1
       786: 1
       788: 1
       795: 1
       802: 1
       803: 1
       813: 1
       820: 1
       822: 1
       836: 1
       837: 1
       839: 1
       854: 1
       861: 1
       862: 1
       868: 1
       939: 1
       960: 1
       961: 1
       967: 1
       968: 1
       969: 1
       970: 1
       975: 1
       976: 1
       980: 1
       993: 1
      1009: 1
      1029: 1
      1045: 1
      1047: 1
      1071: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1250: 1
      1362: 1

1363:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        75: q+1
        76: q+1
        78: q+1
        81: q+1
        82: q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       103: q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: q+1
       136: q+1
       137: q+1
       139: q+1
       141: q+1
       145: q+1
       149: q+1
       151: 1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       180: q+1
       181: q+1
       183: q+1
       186: q+1
       187: q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       230: q+1
       231: q+1
       233: q+1
       237: q+1
       248: 1
       252: 1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: q+1
       293: q+1
       295: q+1
       299: q+1
       303: q+1
       305: 1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       315: 1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: q+1
       361: 1
       381: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       433: 1
       436: q+1
       437: q+1
       439: q+1
       443: q+1
       454: 1
       458: 1
       465: q+1
       466: 1
       467: q+1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       569: 1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: q+1
       615: 1
       635: 1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       682: 1
       689: 1
       756: q+1
       757: 1
       758: q+1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       813: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       872: 1
       961: 1
       962: 1
       966: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       993: 1
      1000: 1
      1072: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1183: 1
      1363: 1

1364:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: q+1
       105: 2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: q+1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: 1
       266: 2q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       396: q+1
       397: 2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       688: 1
       704: 1
       707: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: 1
       769: 1
       770: 1
       771: 1
       772: 1
       776: 1
       778: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       856: 1
       862: 1
       864: 1
       866: 1
       879: 1
       882: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       980: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       999: 1
      1015: 1
      1018: 1
      1073: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1190: 1
      1193: 1
      1364: 1

1365:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        79: q+1
        81: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       138: q+1
       139: q+1
       140: q+1
       152: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       184: q+1
       186: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       234: q+1
       235: q+1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       292: q+1
       293: q+1
       294: q+1
       306: q+1
       308: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: q+1
       357: q+1
       363: q+1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       440: q+1
       441: q+1
       462: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: q+1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       610: q+1
       611: q+1
       617: q+1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       808: q+1
       857: 1
       863: 1
       864: 1
       865: 1
       888: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1074: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1199: 1
      1365: 1

1366:    0: q^3+4q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+4q^2+4q+1
         3: 2q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: 3q^2+4q+1
         7: 3q^2+4q+1
         8: 2q^2+4q+1
         9: q^2+4q+1
        10: 2q^2+4q+1
        11: 2q^2+4q+1
        12: 2q^2+4q+1
        13: 3q^2+4q+1
        14: q^3+4q^2+4q+1
        15: 2q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+4q+1
        19: q^3+4q^2+4q+1
        20: 2q+1
        21: 3q^2+4q+1
        22: q^2+4q+1
        23: 2q^2+4q+1
        24: 2q^2+4q+1
        25: q^2+4q+1
        26: 3q+1
        27: 2q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+4q+1
        30: q^2+4q+1
        31: 2q^2+4q+1
        32: 2q^2+4q+1
        33: 3q^2+4q+1
        34: 3q^2+4q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 3q^2+4q+1
        41: 3q^2+4q+1
        42: 2q^2+4q+1
        43: q^2+4q+1
        44: 2q^2+4q+1
        45: 2q^2+4q+1
        46: 2q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+4q^2+4q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: q^2+4q+1
        54: q^2+4q+1
        55: q^2+4q+1
        56: 2q^2+4q+1
        57: 2q+1
        58: 3q+1
        59: 3q+1
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: q^2+4q+1
        63: 3q+1
        64: q^2+2q+1
        65: q^2+4q+1
        66: 3q+1
        67: q+1
        68: q^2+4q+1
        69: 2q^2+4q+1
        70: q+1
        71: q+1
        72: 3q^2+4q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: 3q^2+4q+1
        86: q^2+4q+1
        87: 2q^2+4q+1
        88: 2q^2+4q+1
        89: q^2+4q+1
        90: 3q+1
        91: 2q^2+4q+1
        92: q^2+4q+1
        93: 2q^2+4q+1
        94: q^2+4q+1
        95: 2q^2+4q+1
        96: 2q^2+4q+1
        97: 3q^2+4q+1
        98: 3q^2+4q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: q^2+4q+1
       109: q^2+4q+1
       110: q^2+4q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: 3q+1
       116: 3q+1
       117: 3q+1
       118: 2q^2+4q+1
       119: q+1
       120: 3q+1
       121: q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 1
       125: 3q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+4q+1
       130: 3q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       149: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: q^2+4q+1
       159: q^2+4q+1
       160: q^2+4q+1
       161: 2q^2+4q+1
       162: 2q+1
       163: 3q+1
       164: 3q+1
       165: 2q^2+4q+1
       166: 2q^2+4q+1
       167: q^2+4q+1
       168: 3q+1
       169: q^2+2q+1
       170: q^2+4q+1
       171: 3q+1
       172: q+1
       173: q^2+4q+1
       174: 2q^2+4q+1
       175: q+1
       176: q+1
       177: 3q^2+4q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: 1
       195: q^2+4q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: 3q+1
       203: 3q+1
       204: 3q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q^2+2q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 3q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       242: 2q+1
       248: 1
       251: q+1
       252: q+1
       253: 2q+1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: q^2+4q+1
       263: q^2+4q+1
       264: q^2+4q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: 3q+1
       270: 3q+1
       271: 3q+1
       272: 2q^2+4q+1
       273: q+1
       274: 3q+1
       275: q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 1
       279: 3q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+4q+1
       284: 3q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       303: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: 3q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       365: q+1
       380: 1
       381: 1
       386: q+1
       392: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: 1
       401: q^2+4q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: 3q+1
       409: 3q+1
       410: 3q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q^2+2q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 3q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       448: 2q+1
       454: 1
       457: q+1
       458: q+1
       459: 2q+1
       462: q+1
       463: q+1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: q+1
       521: 1
       522: 1
       524: q+1
       543: 1
       565: 2q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: 3q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       634: 1
       635: 1
       640: q+1
       646: q+1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       674: 1
       678: 1
       681: 1
       682: 1
       684: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       707: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       766: q+1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: q+1
       812: 1
       813: 1
       815: q+1
       834: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       882: 1
       889: 1
       895: 1
       964: 1
       965: 1
       966: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       985: 1
       989: 1
       992: 1
       993: 1
       995: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1018: 1
      1075: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1193: 1
      1200: 1
      1206: 1
      1366: 1

1367:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       105: q+1
       107: q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 1
       120: 2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: q+1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       199: q+1
       201: q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: q+1
       261: q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: 1
       266: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: 1
       274: 2q+1
       275: q+1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       318: 1
       321: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       366: q+1
       368: q+1
       369: q+1
       370: 1
       371: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       397: q+1
       399: 1
       400: 1
       401: q+1
       402: 1
       403: 1
       405: q+1
       407: q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       414: 1
       415: q+1
       416: q+1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       450: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       469: 1
       471: 1
       472: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       521: 1
       524: 1
       525: 1
       528: q+1
       531: 1
       532: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       566: 1
       568: 1
       570: 1
       571: 1
       572: 1
       575: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       612: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       620: q+1
       622: q+1
       623: q+1
       624: 1
       625: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       654: 1
       656: 1
       662: 1
       664: 1
       665: 1
       669: 1
       681: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       711: 1
       717: 1
       733: 1
       736: 1
       737: 1
       760: 1
       762: 1
       763: 1
       767: 1
       769: 1
       771: 1
       772: 1
       773: 1
       776: 1
       778: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       812: 1
       815: 1
       816: 1
       819: q+1
       822: 1
       823: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: 1
       859: 1
       866: 1
       868: 1
       886: 1
       899: 1
       938: 1
       965: 1
       967: 1
       973: 1
       975: 1
       976: 1
       980: 1
       992: 1
       995: 1
       996: 1
       999: 1
      1007: 1
      1009: 1
      1010: 1
      1022: 1
      1028: 1
      1044: 1
      1047: 1
      1048: 1
      1076: 1
      1170: 1
      1177: 1
      1179: 1
      1197: 1
      1210: 1
      1249: 1
      1367: 1

1368:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        81: 2q+1
        82: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       103: 2q+1
       106: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: q+1
       136: q+1
       137: 2q+1
       139: 2q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       145: 2q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: q+1
       160: 2q+1
       161: q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q+1
       168: q+1
       169: 1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       186: 2q+1
       187: 2q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       230: q+1
       231: q+1
       233: 2q+1
       237: q+1
       238: q+1
       239: 2q+1
       241: 2q+1
       248: 1
       249: 2q+1
       250: q+1
       252: q+1
       260: q+1
       261: q+1
       262: q+1
       263: 2q+1
       264: q+1
       265: q+1
       267: q+1
       268: q+1
       269: 2q+1
       270: q+1
       271: 2q+1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 2q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: 2q+1
       293: 2q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       299: 2q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       313: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       359: q+1
       361: 1
       367: q+1
       368: q+1
       370: 2q+1
       381: 1
       382: 1
       383: q+1
       385: q+1
       398: q+1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       406: q+1
       407: q+1
       408: q+1
       409: 2q+1
       410: q+1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: q+1
       424: q+1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       436: q+1
       437: q+1
       439: 2q+1
       443: q+1
       444: q+1
       445: 2q+1
       447: 2q+1
       454: 1
       455: 2q+1
       456: q+1
       458: q+1
       470: 1
       471: 1
       472: q+1
       477: 1
       479: 1
       480: 1
       481: 1
       482: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: q+1
       531: 1
       545: 1
       546: 1
       548: q+1
       567: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: q+1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       613: q+1
       615: 1
       621: q+1
       622: q+1
       624: 2q+1
       635: 1
       636: 1
       637: q+1
       639: q+1
       655: 1
       656: 1
       663: 1
       664: 1
       665: 1
       670: 1
       674: 1
       675: 1
       682: 1
       689: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       761: 1
       762: 1
       763: q+1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       813: 1
       820: q+1
       822: 1
       836: 1
       837: 1
       839: q+1
       860: 1
       867: 1
       868: 1
       877: 1
       900: 1
       939: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       981: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1029: 1
      1045: 1
      1047: 1
      1077: 1
      1171: 1
      1178: 1
      1179: 1
      1188: 1
      1211: 1
      1250: 1
      1368: 1

1369:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        81: q+1
        82: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       149: q+1
       150: q+1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       186: q+1
       187: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: q+1
       297: 1
       299: 1
       303: q+1
       304: q+1
       305: 1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       359: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       529: 1
       545: 1
       546: 1
       548: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       613: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       637: 1
       639: 1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       689: 1
       697: 1
       698: 1
       700: 1
       734: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       820: 1
       836: 1
       837: 1
       839: 1
       861: 1
       869: 1
       870: 1
       877: 1
       900: 1
       960: 1
       968: 1
       969: 1
       976: 1
       977: 1
       978: 1
       979: 1
       985: 1
       986: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1045: 1
      1078: 1
      1172: 1
      1180: 1
      1181: 1
      1188: 1
      1211: 1
      1369: 1

1370:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q^2+1
        24: 1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        40: q^2+q+1
        41: q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: q^2+1
        61: 1
        62: q^2+q+1
        63: q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        78: q+1
        81: q+1
        82: q+1
        84: q^2+q+1
        85: q+1
        86: q+1
        87: q^2+1
        88: 1
        89: q^2+q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q^2+q+1
       120: q+1
       121: q+1
       122: q^2+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       135: 1
       136: q+1
       137: q+1
       139: 1
       141: q+1
       145: 1
       149: q+1
       151: q+1
       155: q^2+1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q^2+1
       166: 1
       167: q^2+q+1
       168: q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       183: q+1
       186: q+1
       187: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       214: 1
       215: q+1
       216: q+1
       218: 1
       220: q+1
       221: q+1
       222: q+1
       224: 1
       225: q+1
       227: q+1
       230: 1
       231: q+1
       233: 1
       237: 1
       248: q+1
       252: 1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q^2+q+1
       274: q+1
       275: q+1
       276: q^2+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       289: 1
       290: q+1
       291: q+1
       293: 1
       295: q+1
       299: 1
       303: q+1
       305: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: q+1
       341: 1
       345: 1
       346: q+1
       347: q+1
       349: 1
       351: q+1
       355: 1
       359: 1
       361: 1
       381: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: 1
       420: 1
       421: q+1
       422: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       433: q+1
       436: 1
       437: q+1
       439: 1
       443: 1
       454: q+1
       458: 1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: q+1
       506: 1
       510: 1
       522: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: q+1
       595: 1
       599: 1
       600: q+1
       601: q+1
       603: 1
       605: q+1
       609: 1
       613: 1
       615: 1
       635: 1
       650: 1
       658: 1
       659: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       756: 1
       757: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: q+1
       797: 1
       801: 1
       813: 1
       862: 1
       870: 1
       871: 1
       876: 1
       893: 1
       961: 1
       969: 1
       970: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1079: 1
      1173: 1
      1181: 1
      1182: 1
      1187: 1
      1204: 1
      1370: 1

1371:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        81: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: 1
       136: 1
       139: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       186: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       289: 1
       290: 1
       293: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       436: 1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       757: 1
       758: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       863: 1
       871: 1
       872: 1
       875: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
      1080: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1371: 1

1372:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        79: q+1
        81: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       139: 1
       140: 1
       152: q+1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       184: q+1
       186: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       228: 1
       229: q+1
       230: 1
       234: 1
       235: 1
       256: q+1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       288: q+1
       289: 1
       290: q+1
       292: q+1
       293: 1
       294: 1
       306: q+1
       308: q+1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       348: q+1
       349: 1
       350: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       434: 1
       435: q+1
       436: 1
       440: 1
       441: 1
       462: q+1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       507: 1
       508: 1
       517: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       610: 1
       611: 1
       617: 1
       652: 1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       686: 1
       687: 1
       693: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       808: 1
       864: 1
       871: 1
       873: 1
       874: 1
       888: 1
       963: 1
       970: 1
       972: 1
       973: 1
       978: 1
       979: 1
       980: 1
       982: 1
       983: 1
       984: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1081: 1
      1175: 1
      1182: 1
      1184: 1
      1185: 1
      1199: 1
      1372: 1

1373:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 1
       363: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: 1
       617: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       687: 1
       693: 1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       998: 1
      1004: 1
      1082: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1373: 1

1374:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q+1
        62: q+1
        63: q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       199: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       358: 1
       361: 1
       362: 1
       363: 1
       364: 1
       380: 1
       386: 1
       392: 1
       397: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       403: 1
       405: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       521: 1
       524: 1
       566: 1
       568: 1
       570: 1
       571: 1
       575: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       617: 1
       618: 1
       634: 1
       640: 1
       646: 1
       654: 1
       662: 1
       664: 1
       669: 1
       671: 1
       673: 1
       674: 1
       681: 1
       684: 1
       688: 1
       691: 1
       692: 1
       693: 1
       694: 1
       760: 1
       762: 1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       806: 1
       812: 1
       815: 1
       866: 1
       874: 1
       876: 1
       892: 1
       895: 1
       965: 1
       973: 1
       975: 1
       980: 1
       982: 1
       984: 1
       985: 1
       992: 1
       995: 1
       999: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1083: 1
      1177: 1
      1185: 1
      1187: 1
      1203: 1
      1206: 1
      1374: 1

1375:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       313: 1
       315: 1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       567: 1
       569: 1
       570: 1
       571: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: 1
       615: 1
       635: 1
       655: 1
       663: 1
       664: 1
       670: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       761: 1
       762: 1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       813: 1
       867: 1
       875: 1
       876: 1
       893: 1
       966: 1
       974: 1
       975: 1
       981: 1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1084: 1
      1178: 1
      1186: 1
      1187: 1
      1204: 1
      1375: 1

1376:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       361: 1
       368: 1
       370: 1
       382: 1
       383: 1
       385: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       497: 1
       504: 1
       506: 1
       511: 1
       512: 1
       514: 1
       531: 1
       546: 1
       548: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       615: 1
       622: 1
       624: 1
       636: 1
       637: 1
       639: 1
       656: 1
       664: 1
       665: 1
       673: 1
       674: 1
       675: 1
       691: 1
       698: 1
       700: 1
       736: 1
       762: 1
       763: 1
       771: 1
       772: 1
       773: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       788: 1
       795: 1
       797: 1
       802: 1
       803: 1
       805: 1
       822: 1
       837: 1
       839: 1
       868: 1
       876: 1
       877: 1
       902: 1
       967: 1
       975: 1
       976: 1
       984: 1
       985: 1
       986: 1
      1002: 1
      1009: 1
      1011: 1
      1047: 1
      1085: 1
      1179: 1
      1187: 1
      1188: 1
      1213: 1
      1376: 1

1377:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^2+2q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^2+2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q+1
        21: q^3+3q^2+3q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: q^2+2q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: 2q^2+3q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q^2+3q+1
        63: 2q^2+3q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^3+3q^2+3q+1
        73: q+1
        74: q+1
        75: 1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q^3+3q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 2q^2+3q+1
        90: 2q^2+3q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q+1
       104: q+1
       105: 2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: 2q+1
       113: q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: q+1
       120: 2q^2+3q+1
       121: q+1
       122: q+1
       124: 1
       125: q^2+2q+1
       126: 1
       127: 1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: 1
       146: q^2+2q+1
       147: q^2+2q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q^2+3q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: 1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q+1
       176: q+1
       177: q^3+3q^2+3q+1
       178: q+1
       179: q+1
       180: 1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: q+1
       191: 2q+1
       192: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       208: q+1
       209: q+1
       210: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q^2+2q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       244: q^2+2q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: 1
       266: 2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: q+1
       274: 2q^2+3q+1
       275: q+1
       276: q+1
       278: 1
       279: q^2+2q+1
       280: 1
       281: 1
       282: 1
       283: q^2+2q+1
       284: q^2+2q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q^2+2q+1
       297: q+1
       298: q+1
       299: 1
       300: q^2+2q+1
       301: q^2+2q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: 2q+1
       322: q+1
       325: q+1
       326: 1
       327: 1
       329: q+1
       331: q+1
       332: q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       392: q+1
       393: q+1
       395: 1
       396: q+1
       397: 2q+1
       398: q+1
       401: q+1
       402: 1
       403: 1
       404: q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: q+1
       415: q+1
       416: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q^2+2q+1
       428: 1
       429: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       450: q^2+2q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       481: 1
       482: 1
       485: q+1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       527: 1
       528: q+1
       529: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: q+1
       563: 1
       564: 1
       565: q+1
       571: 1
       572: 1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       579: q+1
       580: 1
       581: 1
       583: q+1
       585: q+1
       586: q+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: q+1
       646: q+1
       647: q+1
       649: 1
       657: 1
       658: 1
       665: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       711: 1
       714: 1
       732: 1
       733: 1
       734: 1
       737: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: q+1
       772: 1
       773: 1
       776: q+1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       818: 1
       819: q+1
       820: 1
       823: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: q+1
       861: 1
       878: 1
       879: 1
       886: 1
       899: 1
       906: 1
       935: 1
       960: 1
       968: 1
       969: 1
       976: 1
       987: 1
       988: 1
       989: 1
       995: 1
       996: 1
       999: 1
      1007: 1
      1009: 1
      1010: 1
      1014: 1
      1015: 1
      1022: 1
      1025: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1086: 1
      1172: 1
      1189: 1
      1190: 1
      1197: 1
      1210: 1
      1217: 1
      1246: 1
      1377: 1

1378:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 2q^2+3q+1
         5: 3q^2+3q+1
         6: 3q^2+3q+1
         7: q^2+2q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 2q^2+3q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: 3q^2+3q+1
        19: 2q^2+3q+1
        20: 3q^2+3q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q+1
        25: 3q^2+3q+1
        26: q+1
        27: 3q^2+3q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+3q+1
        38: q^2+2q+1
        39: 2q+1
        40: 3q^2+3q+1
        41: q^2+2q+1
        42: 3q^2+3q+1
        43: 3q^2+3q+1
        44: 3q^2+3q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: q+1
        57: 3q^2+3q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q+1
        62: 2q^2+3q+1
        63: q+1
        64: 2q^2+3q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q^2+3q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q+1
        76: 2q^2+3q+1
        78: 2q^2+3q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 3q^2+3q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: 3q^2+3q+1
        90: q+1
        91: 3q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: 1
       107: q^2+2q+1
       108: q+1
       109: 1
       110: 1
       111: q+1
       112: q^2+2q+1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: 2q^2+3q+1
       120: q+1
       121: q+1
       122: q^2+2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: q+1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 1
       140: 1
       141: 2q^2+3q+1
       144: q+1
       145: q+1
       146: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: q+1
       162: 3q^2+3q+1
       163: q+1
       164: q+1
       165: q^2+2q+1
       166: q+1
       167: 2q^2+3q+1
       168: q+1
       169: 2q^2+3q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q^2+3q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q+1
       181: 2q^2+3q+1
       183: 2q^2+3q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       189: q+1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q^2+2q+1
       208: q+1
       209: q+1
       210: 1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       225: 2q+1
       227: 2q+1
       228: 1
       229: q+1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q+1
       242: 1
       243: q^2+2q+1
       246: q+1
       248: 2q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: 1
       261: q^2+2q+1
       262: q+1
       263: 1
       264: 1
       265: q+1
       266: q^2+2q+1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: q+1
       273: 2q^2+3q+1
       274: q+1
       275: q+1
       276: q^2+2q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 1
       282: q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       287: 2q+1
       288: q+1
       289: q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q+1
       293: 1
       294: 1
       295: 2q^2+3q+1
       298: q+1
       299: q+1
       300: q^2+2q+1
       302: q^2+2q+1
       303: 2q+1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: 1
       312: q+1
       315: 1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       329: 1
       331: q+1
       332: 1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       347: q+1
       348: 1
       351: 2q+1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: q+1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       392: q+1
       394: q+1
       395: q+1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: q+1
       404: q+1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: q^2+2q+1
       414: q+1
       415: q+1
       416: 1
       419: 1
       420: q+1
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: 2q+1
       427: q+1
       428: q+1
       429: 1
       431: 2q+1
       433: 2q+1
       434: 1
       435: q+1
       436: 1
       437: q^2+2q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: q+1
       448: 1
       449: q^2+2q+1
       452: q+1
       454: 2q+1
       457: 1
       458: q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: q+1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: q+1
       561: 1
       563: q+1
       564: 1
       565: 1
       566: q+1
       569: 1
       570: 1
       571: 1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q+1
       583: 1
       585: q+1
       586: 1
       590: 1
       591: 1
       592: 1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: q+1
       601: q+1
       602: 1
       605: 2q+1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: q+1
       634: 1
       635: q+1
       640: 1
       641: q+1
       644: 1
       646: q+1
       648: q+1
       650: 1
       658: 1
       659: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       688: 1
       690: 1
       704: 1
       705: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       762: 1
       764: q+1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       776: 1
       778: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: q+1
       796: 1
       800: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: q+1
       852: 1
       862: 1
       879: 1
       880: 1
       885: 1
       890: 1
       907: 1
       933: 1
       961: 1
       969: 1
       970: 1
       975: 1
       980: 1
       987: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       999: 1
      1001: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1042: 1
      1050: 1
      1059: 1
      1087: 1
      1173: 1
      1190: 1
      1191: 1
      1196: 1
      1201: 1
      1218: 1
      1244: 1
      1378: 1

1379:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 2q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+3q+1
         9: 3q^2+3q+1
        10: 2q+1
        11: 2q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 2q^2+3q+1
        15: 3q^2+3q+1
        16: 3q^2+3q+1
        17: 2q^2+3q+1
        18: 3q^2+3q+1
        19: 3q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: 2q^2+3q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q^2+3q+1
        29: 2q+1
        30: 3q^2+3q+1
        31: 2q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q^2+3q+1
        36: 3q^2+3q+1
        37: q+1
        38: q^2+2q+1
        39: 3q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q^2+3q+1
        43: 3q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: 2q^2+3q+1
        49: 3q^2+3q+1
        50: q^2+2q+1
        51: 2q^2+3q+1
        52: q^2+2q+1
        53: 1
        54: q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q^2+3q+1
        69: 2q+1
        70: 2q^2+3q+1
        71: 2q^2+3q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: 2q^2+3q+1
        76: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: 3q^2+3q+1
        82: q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+3q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: 3q^2+3q+1
        95: 2q+1
        96: 2q^2+3q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q^2+3q+1
       100: 3q^2+3q+1
       101: q+1
       102: q^2+2q+1
       103: 3q^2+3q+1
       104: q^2+2q+1
       105: q+1
       106: q^2+2q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q^2+2q+1
       112: q+1
       113: 2q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q^2+3q+1
       134: q+1
       135: 2q^2+3q+1
       136: q^2+2q+1
       137: 1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: 2q^2+3q+1
       157: q^2+2q+1
       158: 1
       159: q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q+1
       175: 2q^2+3q+1
       176: 2q^2+3q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: 2q^2+3q+1
       181: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: 3q^2+3q+1
       187: q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: q+1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 2q+1
       208: q+1
       210: 1
       211: q+1
       212: q+1
       213: 1
       214: 2q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       247: q+1
       248: q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q^2+2q+1
       258: q^2+2q+1
       259: q+1
       260: q^2+2q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q^2+2q+1
       266: q+1
       267: 2q+1
       268: q+1
       269: 1
       270: 1
       271: q+1
       272: q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: q+1
       277: 2q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q^2+3q+1
       288: q+1
       289: 2q^2+3q+1
       290: q^2+2q+1
       291: 1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: q+1
       298: 1
       299: q+1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: q+1
       329: 1
       330: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 2q+1
       346: q+1
       348: 1
       349: q+1
       350: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       372: 1
       373: 1
       374: q+1
       379: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       391: q+1
       395: q^2+2q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: q+1
       405: 1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: q+1
       413: 2q+1
       414: q+1
       416: 1
       417: q+1
       418: q+1
       419: 1
       420: 2q+1
       421: q+1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 2q+1
       427: q+1
       428: q+1
       429: 1
       430: 2q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: q+1
       448: 1
       449: q+1
       452: 1
       453: q+1
       454: q+1
       457: 1
       458: q+1
       459: q+1
       461: q+1
       462: q^2+2q+1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: q+1
       484: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       507: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: q+1
       557: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: q+1
       583: 1
       584: q+1
       588: 1
       589: q+1
       590: 1
       591: 1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 2q+1
       600: q+1
       602: 1
       603: q+1
       604: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: q+1
       633: 1
       634: 1
       635: q+1
       640: 1
       641: q+1
       644: 1
       645: q+1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       709: 1
       722: 1
       731: 1
       740: 1
       747: 1
       757: 1
       758: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: q+1
       775: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: 1
       794: q+1
       798: 1
       799: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: q+1
       848: 1
       863: 1
       880: 1
       881: 1
       884: 1
       888: 1
       908: 1
       943: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: 1
       988: 1
       989: 1
       990: 1
       991: 1
       993: 1
       994: 1
       997: 1
       998: 1
      1004: 1
      1016: 1
      1017: 1
      1020: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1088: 1
      1174: 1
      1191: 1
      1192: 1
      1195: 1
      1199: 1
      1219: 1
      1254: 1
      1379: 1

1380:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       543: 1
       550: 1
       551: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       652: 1
       659: 1
       661: 1
       662: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       705: 1
       707: 1
       708: 1
       731: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       834: 1
       841: 1
       842: 1
       864: 1
       880: 1
       882: 1
       883: 1
       909: 1
       963: 1
       970: 1
       972: 1
       973: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
      1016: 1
      1018: 1
      1019: 1
      1042: 1
      1089: 1
      1175: 1
      1191: 1
      1193: 1
      1194: 1
      1220: 1
      1380: 1

1381:    0: q^3+2q^2+2q+1
         1: q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^3+q^2+2q+1
         9: 2q+1
        10: q^2+q+1
        11: q^3+q^2+2q+1
        12: q^3+q^2+2q+1
        13: q^2+2q+1
        14: q^3+2q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^3+q^2+2q+1
        24: q^3+q^2+2q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: 2q+1
        29: q^2+q+1
        30: 2q+1
        31: q^2+q+1
        32: q^3+q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^3+q^2+2q+1
        43: 2q+1
        44: q^2+q+1
        45: q^3+q^2+2q+1
        46: q^3+q^2+2q+1
        47: q^2+2q+1
        48: q^3+2q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: q^3+q^2+2q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q^2+1
        65: q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^3+q^2+2q+1
        88: q^3+q^2+2q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: 2q+1
        93: q^2+q+1
        94: 2q+1
        95: q^2+q+1
        96: q^3+q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+q+1
       119: 1
       120: q+1
       121: 1
       122: q^2+1
       123: q^2+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 1
       144: q+1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: 2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: q^3+q^2+2q+1
       162: 1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: q^2+q+1
       167: q+1
       168: q+1
       169: q^2+1
       170: q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: q^2+q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: q^2+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q^2+q+1
       273: 1
       274: q+1
       275: 1
       276: q^2+1
       277: q^2+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       298: q+1
       299: q+1
       300: q+1
       302: 1
       303: q+1
       305: q+1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: q^2+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: 1
       453: 1
       454: 1
       457: q+1
       458: q+1
       459: q+1
       461: 1
       462: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       490: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: 1
       645: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: 1
       693: 1
       706: 1
       707: 1
       708: 1
       709: 1
       740: 1
       747: 1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: 1
       781: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       865: 1
       881: 1
       882: 1
       883: 1
       884: 1
       910: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       998: 1
      1004: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1051: 1
      1058: 1
      1090: 1
      1176: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1221: 1
      1381: 1

1382:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: 1
        25: q+1
        26: 1
        27: q^2+q+1
        28: q+1
        29: q^2+q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q^2+q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: q^2+q+1
        61: 1
        62: q+1
        63: 1
        64: q^2+q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: 1
        89: q+1
        90: 1
        91: q^2+q+1
        92: q+1
        93: q^2+q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: 1
       121: 1
       122: q^2+q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       148: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q^2+q+1
       166: 1
       167: q+1
       168: 1
       169: q^2+q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: q+1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       229: q+1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       242: 1
       243: q+1
       246: q+1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: q+1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q^2+q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: q+1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: q+1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       373: q+1
       380: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: q+1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       435: q+1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       448: 1
       449: q+1
       452: q+1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: q+1
       521: 1
       523: 1
       524: 1
       534: 1
       550: 1
       551: 1
       558: 1
       561: 1
       566: q+1
       568: 1
       570: 1
       571: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       612: q+1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       627: q+1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       654: 1
       662: 1
       664: 1
       669: 1
       679: 1
       681: 1
       683: 1
       684: 1
       688: 1
       690: 1
       708: 1
       710: 1
       739: 1
       748: 1
       760: 1
       762: 1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       810: q+1
       812: 1
       814: 1
       815: 1
       825: 1
       841: 1
       842: 1
       849: 1
       852: 1
       866: 1
       883: 1
       885: 1
       890: 1
       911: 1
       965: 1
       973: 1
       975: 1
       980: 1
       990: 1
       992: 1
       994: 1
       995: 1
       999: 1
      1001: 1
      1019: 1
      1021: 1
      1050: 1
      1059: 1
      1091: 1
      1177: 1
      1194: 1
      1196: 1
      1201: 1
      1222: 1
      1382: 1

1383:    0: q^3+4q^2+3q+1
         1: q^2+2q+1
         2: q^3+4q^2+3q+1
         3: 3q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 3q^2+3q+1
         9: 2q+1
        10: 3q^2+3q+1
        11: 2q^2+3q+1
        12: 3q^2+3q+1
        13: q^2+2q+1
        14: q^3+4q^2+3q+1
        15: 2q^2+3q+1
        16: q^2+2q+1
        17: q^3+4q^2+3q+1
        18: 3q^2+3q+1
        19: q^3+4q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 3q^2+3q+1
        25: 2q+1
        26: q+1
        27: 3q^2+3q+1
        28: 2q+1
        29: 2q^2+3q+1
        30: 2q+1
        31: 3q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+3q+1
        36: 2q+1
        37: 2q^2+3q+1
        38: 2q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 3q^2+3q+1
        43: 2q+1
        44: 3q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: q^2+2q+1
        48: q^3+4q^2+3q+1
        49: 2q^2+3q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q^2+3q+1
        57: q+1
        58: q+1
        59: q+1
        60: 2q^2+3q+1
        61: 3q^2+3q+1
        62: 2q+1
        63: q+1
        64: q^2+2q+1
        65: 2q+1
        66: q+1
        67: q^2+2q+1
        68: 2q+1
        69: 2q^2+3q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q^2+3q+1
        76: 2q+1
        78: 2q^2+3q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q^2+3q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q^2+3q+1
        88: 3q^2+3q+1
        89: 2q+1
        90: q+1
        91: 3q^2+3q+1
        92: 2q+1
        93: 2q^2+3q+1
        94: 2q+1
        95: 3q^2+3q+1
        96: 2q^2+3q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+3q+1
       100: 2q+1
       101: 2q^2+3q+1
       102: 2q+1
       103: 2q^2+3q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q^2+2q+1
       113: q+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: 2q^2+3q+1
       119: q+1
       120: q+1
       121: 1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+2q+1
       129: 2q+1
       130: q+1
       131: q+1
       132: q+1
       133: q^2+2q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       144: 2q+1
       145: 2q^2+3q+1
       146: 2q+1
       148: q+1
       149: 2q+1
       151: q^2+2q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q^2+3q+1
       162: q+1
       163: q+1
       164: q+1
       165: 2q^2+3q+1
       166: 3q^2+3q+1
       167: 2q+1
       168: q+1
       169: q^2+2q+1
       170: 2q+1
       171: q+1
       172: q^2+2q+1
       173: 2q+1
       174: 2q^2+3q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q^2+3q+1
       181: 2q+1
       183: 2q^2+3q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q^2+3q+1
       188: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q^2+2q+1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q^2+2q+1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: q+1
       225: q+1
       227: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       237: q+1
       242: 2q+1
       243: q+1
       246: q+1
       247: q+1
       248: 1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       255: 1
       256: q+1
       257: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q^2+2q+1
       267: q+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: 2q^2+3q+1
       273: q+1
       274: q+1
       275: 1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q^2+2q+1
       283: 2q+1
       284: q+1
       285: q+1
       286: q+1
       287: q^2+2q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       298: 2q+1
       299: 2q^2+3q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       305: q^2+2q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       313: q+1
       315: 1
       316: 1
       317: q+1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: q+1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       372: 1
       374: q+1
       379: q+1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       398: q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q^2+2q+1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q^2+2q+1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: q+1
       431: q+1
       433: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       443: q+1
       448: 2q+1
       449: q+1
       452: q+1
       453: q+1
       454: 1
       457: q+1
       458: q^2+2q+1
       459: 2q+1
       461: 1
       462: q+1
       463: q+1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: q+1
       522: 1
       523: 1
       524: q+1
       534: 1
       542: 1
       550: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: q+1
       569: 1
       570: 1
       571: q+1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: q+1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       626: 1
       628: q+1
       633: q+1
       635: 1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       655: 1
       663: 1
       664: 1
       670: 1
       674: 1
       680: 1
       682: 1
       683: 1
       684: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       709: 1
       710: 1
       730: 1
       739: 1
       747: 1
       749: 1
       754: 1
       761: 1
       762: 1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: q+1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       801: 1
       806: 1
       811: q+1
       813: 1
       814: 1
       815: q+1
       825: 1
       833: 1
       841: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       867: 1
       884: 1
       885: 1
       891: 1
       895: 1
       912: 1
       951: 1
       966: 1
       974: 1
       975: 1
       981: 1
       985: 1
       991: 1
       993: 1
       994: 1
       995: 1
      1000: 1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1020: 1
      1021: 1
      1041: 1
      1050: 1
      1058: 1
      1060: 1
      1065: 1
      1092: 1
      1178: 1
      1195: 1
      1196: 1
      1202: 1
      1206: 1
      1223: 1
      1262: 1
      1383: 1

1384:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 2q^2+3q+1
         5: 3q^2+3q+1
         6: q^2+2q+1
         7: 3q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: 3q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 3q^2+3q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q+1
        40: q^2+2q+1
        41: 3q^2+3q+1
        42: 3q^2+3q+1
        43: 3q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q^2+3q+1
        52: q^2+2q+1
        53: 2q+1
        54: 2q^2+3q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: 2q+1
        59: 2q^2+3q+1
        60: q^2+3q+1
        61: 2q+1
        62: 2q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+3q+1
        74: q^2+2q+1
        75: 2q+1
        76: q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 2q+1
        89: 2q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^2+3q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 2q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       114: 2q+1
       115: 2q+1
       116: q^2+3q+1
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: q^2+3q+1
       122: q^2+3q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q^2+2q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       157: q^2+2q+1
       158: 2q+1
       159: 2q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: 2q+1
       167: 2q+1
       168: q^2+3q+1
       169: q^2+3q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+3q+1
       179: q^2+2q+1
       180: 2q+1
       181: q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: q+1
       193: 2q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       208: 2q+1
       209: q+1
       210: q^2+3q+1
       215: q+1
       216: 1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       225: 1
       226: q+1
       227: q+1
       231: q+1
       232: q+1
       233: 1
       234: q+1
       235: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: 2q+1
       265: 2q+1
       268: 2q+1
       269: 2q+1
       270: q^2+3q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: q^2+3q+1
       276: q^2+3q+1
       278: q+1
       279: q+1
       280: 2q+1
       281: q+1
       282: 2q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: 2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q^2+2q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: 1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       316: q+1
       317: 1
       318: q+1
       323: 2q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       331: q+1
       332: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       360: q+1
       361: 1
       362: 1
       363: q+1
       364: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       375: q+1
       377: q+1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 2q+1
       400: q+1
       401: q+1
       402: 2q+1
       403: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: 2q+1
       411: 2q+1
       414: 2q+1
       415: q+1
       416: q^2+3q+1
       421: q+1
       422: 1
       423: q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: q+1
       428: 2q+1
       429: q+1
       431: 1
       432: q+1
       433: q+1
       437: q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: q+1
       457: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       471: 1
       472: 1
       480: q+1
       481: 1
       482: q+1
       487: q+1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       504: 1
       505: 1
       511: 1
       512: 1
       513: 1
       523: 1
       524: 1
       525: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       570: q+1
       571: 1
       572: q+1
       577: 2q+1
       578: q+1
       579: q+1
       580: 2q+1
       581: q+1
       585: q+1
       586: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       600: q+1
       601: 1
       602: q+1
       605: 1
       606: 1
       607: q+1
       608: 1
       614: q+1
       615: 1
       616: 1
       617: q+1
       618: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       629: q+1
       631: q+1
       636: 1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       683: 1
       684: 1
       685: 1
       690: 1
       698: 1
       699: 1
       710: 1
       711: 1
       719: 1
       721: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       750: 1
       752: 1
       762: 1
       763: 1
       771: q+1
       772: 1
       773: q+1
       778: q+1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       795: 1
       796: 1
       802: 1
       803: 1
       804: 1
       814: 1
       815: 1
       816: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       868: 1
       885: 1
       886: 1
       901: 1
       913: 1
       940: 1
       942: 1
       967: 1
       975: 1
       976: 1
       994: 1
       995: 1
       996: 1
      1001: 1
      1009: 1
      1010: 1
      1021: 1
      1022: 1
      1030: 1
      1032: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1061: 1
      1063: 1
      1093: 1
      1179: 1
      1196: 1
      1197: 1
      1212: 1
      1224: 1
      1251: 1
      1253: 1
      1384: 1

1385:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       264: q+1
       265: 1
       266: q+1
       267: q+1
       268: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: 1
       396: q+1
       402: 1
       403: 1
       404: q+1
       405: q+1
       406: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       525: 1
       527: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       657: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       703: 1
       732: 1
       755: 1
       764: 1
       765: 1
       773: 1
       774: 1
       775: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       816: 1
       818: 1
       834: 1
       835: 1
       836: 1
       840: 1
       850: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       898: 1
       968: 1
       977: 1
       978: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1014: 1
      1043: 1
      1094: 1
      1180: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1209: 1
      1385: 1

1386:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: q+1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       676: 1
       677: 1
       678: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       815: 1
       834: 1
       870: 1
       879: 1
       887: 1
       888: 1
       889: 1
       895: 1
       969: 1
       977: 1
       978: 1
       979: 1
       985: 1
       987: 1
       988: 1
       989: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: 1
      1095: 1
      1181: 1
      1190: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1386: 1

1387:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: 2q^2+4q+1
         3: q^3+4q^2+4q+1
         4: 2q^2+4q+1
         5: q^3+4q^2+4q+1
         6: 2q^2+4q+1
         7: 3q+1
         8: 2q^2+4q+1
         9: q^3+4q^2+4q+1
        10: 2q^2+4q+1
        11: q^3+4q^2+4q+1
        12: 2q^2+4q+1
        13: 2q^2+4q+1
        14: q^2+4q+1
        15: 2q^2+4q+1
        16: q^3+4q^2+4q+1
        17: 2q^2+4q+1
        18: q^3+4q^2+4q+1
        19: 2q^2+4q+1
        20: 2q^2+4q+1
        21: 3q+1
        22: 3q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q^2+4q+1
        26: 3q+1
        27: 2q^2+4q+1
        28: q^3+4q^2+4q+1
        29: 2q^2+4q+1
        30: 2q^2+4q+1
        31: q^2+4q+1
        32: 2q^2+4q+1
        33: q^2+4q+1
        34: 3q+1
        35: q^2+4q+1
        36: 2q^2+4q+1
        37: 2q+1
        38: q^2+2q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: 3q+1
        42: 2q^2+4q+1
        43: q^3+4q^2+4q+1
        44: 2q^2+4q+1
        45: q^3+4q^2+4q+1
        46: 2q^2+4q+1
        47: 2q^2+4q+1
        48: q^2+4q+1
        49: 2q^2+4q+1
        50: q^2+2q+1
        51: 2q+1
        52: 3q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 2q^2+4q+1
        58: 3q+1
        59: 3q+1
        60: q^2+2q+1
        61: 2q+1
        62: 2q^2+4q+1
        63: 3q+1
        64: 2q^2+4q+1
        65: q^2+4q+1
        66: 3q+1
        67: q^2+4q+1
        68: 2q^2+4q+1
        69: q^2+4q+1
        70: 2q^2+4q+1
        71: q^2+4q+1
        72: 3q+1
        73: 3q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+4q+1
        82: 2q+1
        83: q^2+2q+1
        84: 2q^2+4q+1
        85: 3q+1
        86: 3q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q^2+4q+1
        90: 3q+1
        91: 2q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+4q+1
        94: 2q^2+4q+1
        95: q^2+4q+1
        96: 2q^2+4q+1
        97: q^2+4q+1
        98: 3q+1
        99: q^2+4q+1
       100: 2q^2+4q+1
       101: 2q+1
       102: q^2+2q+1
       103: 2q^2+4q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q^2+2q+1
       113: 2q+1
       114: 3q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 2q^2+4q+1
       120: 3q+1
       121: 3q+1
       122: q^2+2q+1
       123: 2q+1
       124: q^2+4q+1
       125: 3q+1
       126: 3q+1
       127: q+1
       128: 2q+1
       129: q^2+4q+1
       130: 3q+1
       131: q^2+4q+1
       132: 2q^2+4q+1
       133: 2q+1
       134: q+1
       135: 2q+1
       136: 3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: 2q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: 2q+1
       157: 3q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 2q^2+4q+1
       163: 3q+1
       164: 3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q^2+4q+1
       168: 3q+1
       169: 2q^2+4q+1
       170: q^2+4q+1
       171: 3q+1
       172: q^2+4q+1
       173: 2q^2+4q+1
       174: q^2+4q+1
       175: 2q^2+4q+1
       176: q^2+4q+1
       177: 3q+1
       178: 3q+1
       179: q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       186: 2q^2+4q+1
       187: 2q+1
       188: q^2+2q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q^2+2q+1
       207: 2q+1
       208: 3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: 2q+1
       215: 3q+1
       216: q+1
       217: q+1
       218: q+1
       219: 1
       220: q^2+4q+1
       221: 3q+1
       222: 3q+1
       223: q+1
       224: 2q+1
       225: 2q+1
       227: 2q+1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       248: 2q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: q+1
       266: q^2+2q+1
       267: 2q+1
       268: 3q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 2q^2+4q+1
       274: 3q+1
       275: 3q+1
       276: q^2+2q+1
       277: 2q+1
       278: q^2+4q+1
       279: 3q+1
       280: 3q+1
       281: q+1
       282: 2q+1
       283: q^2+4q+1
       284: 3q+1
       285: q^2+4q+1
       286: 2q^2+4q+1
       287: 2q+1
       288: q+1
       289: 2q+1
       290: 3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: 2q+1
       298: 1
       299: q+1
       300: q+1
       302: q+1
       303: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: q+1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 2q+1
       346: 3q+1
       347: q+1
       348: q+1
       349: q+1
       350: 1
       351: 2q+1
       354: 1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       392: q+1
       394: q+1
       395: q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: q^2+2q+1
       413: 2q+1
       414: 3q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: 2q+1
       421: 3q+1
       422: q+1
       423: q+1
       424: q+1
       425: 1
       426: q^2+4q+1
       427: 3q+1
       428: 3q+1
       429: q+1
       430: 2q+1
       431: 2q+1
       433: 2q+1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: q+1
       452: 1
       454: 2q+1
       457: 1
       458: q+1
       459: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       543: 1
       550: 1
       551: 1
       558: q+1
       561: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: q+1
       590: 1
       591: q+1
       592: q+1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 2q+1
       600: 3q+1
       601: q+1
       602: q+1
       603: q+1
       604: 1
       605: 2q+1
       608: 1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: q+1
       640: 1
       641: q+1
       644: 1
       646: q+1
       648: q+1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: 1
       731: 1
       748: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: q+1
       794: q+1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: q+1
       806: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       834: 1
       841: 1
       842: 1
       849: q+1
       852: 1
       871: 1
       880: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       897: 1
       970: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1013: 1
      1016: 1
      1042: 1
      1059: 1
      1096: 1
      1182: 1
      1191: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1208: 1
      1387: 1

1388:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q+1
        41: q+1
        42: q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: q+1
       148: 1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: q+1
       302: 1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       463: q+1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: 1
       519: 1
       520: 1
       535: 1
       543: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       660: 1
       668: 1
       669: 1
       670: 1
       678: 1
       679: 1
       680: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       695: 1
       706: 1
       740: 1
       748: 1
       749: 1
       754: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       784: 1
       785: 1
       786: 1
       787: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       806: 1
       809: 1
       810: 1
       811: 1
       826: 1
       834: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       872: 1
       881: 1
       889: 1
       890: 1
       891: 1
       952: 1
       971: 1
       979: 1
       980: 1
       981: 1
       989: 1
       990: 1
       991: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1006: 1
      1017: 1
      1051: 1
      1059: 1
      1060: 1
      1065: 1
      1097: 1
      1183: 1
      1192: 1
      1200: 1
      1201: 1
      1202: 1
      1263: 1
      1388: 1

1389:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       468: 1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: 1
       521: 1
       522: 1
       543: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       661: 1
       668: 1
       671: 1
       672: 1
       678: 1
       681: 1
       682: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       695: 1
       707: 1
       759: 1
       766: 1
       769: 1
       770: 1
       775: 1
       776: 1
       777: 1
       779: 1
       780: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       806: 1
       809: 1
       812: 1
       813: 1
       834: 1
       873: 1
       882: 1
       889: 1
       892: 1
       893: 1
       972: 1
       979: 1
       982: 1
       983: 1
       989: 1
       992: 1
       993: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1006: 1
      1018: 1
      1098: 1
      1184: 1
      1193: 1
      1200: 1
      1203: 1
      1204: 1
      1389: 1

1390:    0: q^4+2q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^4+2q^2+q+1
         4: q+1
         5: q^4+2q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^4+2q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^4+2q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: 1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^4+2q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: 1
        62: q+1
        63: q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: 1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: 1
       167: q+1
       168: q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       373: 1
       380: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       405: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       421: q+1
       422: 1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       519: 1
       521: 1
       523: 1
       550: 1
       551: 1
       558: 1
       561: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       600: q+1
       601: 1
       602: q+1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       627: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       662: 1
       669: 1
       671: 1
       673: 1
       679: 1
       681: 1
       683: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       708: 1
       748: 1
       760: 1
       767: 1
       769: 1
       771: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       806: 1
       810: 1
       812: 1
       814: 1
       841: 1
       842: 1
       849: 1
       852: 1
       874: 1
       883: 1
       890: 1
       892: 1
       894: 1
       973: 1
       980: 1
       982: 1
       984: 1
       990: 1
       992: 1
       994: 1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1013: 1
      1019: 1
      1059: 1
      1099: 1
      1185: 1
      1194: 1
      1201: 1
      1203: 1
      1205: 1
      1390: 1

1391:    0: q^3+q^2+2q+1
         1: q^2+q+1
         2: 2q+1
         3: q^3+q^2+2q+1
         4: q^3+q^2+2q+1
         5: q^3+q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q^2+q+1
        10: 2q+1
        11: q^3+q^2+2q+1
        12: q^3+q^2+2q+1
        13: q^2+q+1
        14: 2q+1
        15: q^3+q^2+2q+1
        16: q^2+q+1
        17: 2q+1
        18: q^3+q^2+2q+1
        19: q^3+q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: q+1
        26: q+1
        27: 2q+1
        28: q^2+q+1
        29: 2q+1
        30: q^2+q+1
        31: 2q+1
        32: q^3+q^2+2q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q^2+q+1
        37: q+1
        38: q^2+1
        39: q^3+q^2+2q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q^2+q+1
        44: 2q+1
        45: q^3+q^2+2q+1
        46: q^3+q^2+2q+1
        47: q^2+q+1
        48: 2q+1
        49: q^3+q^2+2q+1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 2q+1
        65: q+1
        66: q+1
        67: 2q+1
        68: q^2+q+1
        69: 2q+1
        70: q^3+q^2+2q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 2q+1
        76: 1
        78: q+1
        79: q^2+1
        80: 1
        81: q^2+q+1
        82: q+1
        83: q^2+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: q+1
        90: q+1
        91: 2q+1
        92: q^2+q+1
        93: 2q+1
        94: q^2+q+1
        95: 2q+1
        96: q^3+q^2+2q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q^2+q+1
       101: q+1
       102: q^2+1
       103: q^3+q^2+2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       113: q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: q+1
       130: q+1
       131: 2q+1
       132: q^2+q+1
       133: q+1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: q^2+1
       153: 1
       154: q^2+1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: q+1
       168: q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: 2q+1
       173: q^2+q+1
       174: 2q+1
       175: q^3+q^2+2q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 2q+1
       181: 1
       183: q+1
       184: q^2+1
       185: 1
       186: q^2+q+1
       187: q+1
       188: q^2+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       207: q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: q+1
       214: q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: 1
       227: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: q^2+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       267: q+1
       268: q+1
       269: 1
       270: 1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: 2q+1
       283: q+1
       284: q+1
       285: 2q+1
       286: q^2+q+1
       287: q+1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: q^2+1
       307: 1
       308: q^2+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: 1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       372: 1
       374: 1
       379: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       413: q+1
       414: q+1
       415: 1
       416: 1
       417: q+1
       418: q+1
       420: q+1
       421: q+1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: 2q+1
       431: 1
       433: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: q+1
       459: 1
       461: 1
       462: q^2+1
       463: 1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: 1
       522: 1
       523: 1
       542: 1
       550: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       599: q+1
       600: q+1
       601: 1
       602: 1
       603: q+1
       604: 1
       605: 1
       608: 1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       626: 1
       628: 1
       633: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       663: 1
       670: 1
       672: 1
       673: 1
       680: 1
       682: 1
       683: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       709: 1
       747: 1
       749: 1
       754: 1
       761: 1
       768: 1
       770: 1
       771: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       801: 1
       806: 1
       811: 1
       813: 1
       814: 1
       833: 1
       841: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       875: 1
       884: 1
       891: 1
       893: 1
       894: 1
       959: 1
       974: 1
       981: 1
       983: 1
       984: 1
       991: 1
       993: 1
       994: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1013: 1
      1020: 1
      1058: 1
      1060: 1
      1065: 1
      1100: 1
      1186: 1
      1195: 1
      1202: 1
      1204: 1
      1205: 1
      1270: 1
      1391: 1

1392:    0: q^2+q+1
         1: 1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: 1
         7: 1
         8: q^2+q+1
         9: 1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q^2+q+1
        24: q+1
        25: 1
        26: 1
        27: q^2+q+1
        28: 1
        29: q^2+q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: q^2+q+1
        43: 1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: q^2+q+1
        61: q+1
        62: 1
        63: 1
        64: q^2+q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q^2+q+1
        88: q+1
        89: 1
        90: 1
        91: q^2+q+1
        92: 1
        93: q^2+q+1
        94: 1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q^2+q+1
       123: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: q^2+q+1
       166: q+1
       167: 1
       168: 1
       169: q^2+q+1
       170: 1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: q+1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: q+1
       225: 1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: 1
       274: 1
       275: 1
       276: q^2+q+1
       277: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: q+1
       283: 1
       284: 1
       285: q+1
       286: 1
       287: q+1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: q+1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: q+1
       431: 1
       433: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       471: 1
       480: 1
       481: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       523: 1
       524: 1
       534: 1
       550: 1
       558: 1
       561: 1
       570: 1
       571: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: q+1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       664: 1
       673: 1
       674: 1
       683: 1
       684: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       710: 1
       739: 1
       762: 1
       771: 1
       772: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       806: 1
       814: 1
       815: 1
       825: 1
       841: 1
       849: 1
       852: 1
       876: 1
       885: 1
       894: 1
       895: 1
       905: 1
       975: 1
       984: 1
       985: 1
       994: 1
       995: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1013: 1
      1021: 1
      1050: 1
      1101: 1
      1187: 1
      1196: 1
      1205: 1
      1206: 1
      1216: 1
      1392: 1

1393:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: q+1
       196: 1
       197: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: q+1
       326: 1
       327: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       401: q+1
       402: 1
       403: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       422: 1
       423: 1
       424: 1
       425: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       438: 1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       489: q+1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: 1
       524: 1
       525: 1
       532: 1
       547: 1
       548: 1
       549: 1
       559: 1
       571: 1
       572: 1
       579: q+1
       580: 1
       581: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       603: 1
       604: 1
       606: 1
       607: 1
       608: 1
       609: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       665: 1
       674: 1
       675: 1
       684: 1
       685: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       711: 1
       737: 1
       763: 1
       772: 1
       773: 1
       780: q+1
       781: 1
       782: 1
       789: 1
       790: 1
       791: 1
       796: 1
       797: 1
       798: 1
       799: 1
       803: 1
       804: 1
       805: 1
       806: 1
       815: 1
       816: 1
       823: 1
       838: 1
       839: 1
       840: 1
       850: 1
       877: 1
       886: 1
       895: 1
       896: 1
       903: 1
       976: 1
       985: 1
       986: 1
       995: 1
       996: 1
      1003: 1
      1004: 1
      1005: 1
      1010: 1
      1011: 1
      1012: 1
      1022: 1
      1048: 1
      1102: 1
      1188: 1
      1197: 1
      1206: 1
      1207: 1
      1214: 1
      1393: 1

1394:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: 1
        20: q^2+1
        23: q^2+1
        24: 1
        25: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: q^2+1
        51: 1
        56: 1
        57: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        64: q^2+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       111: 1
       112: q^2+1
       113: 1
       118: 1
       119: q^2+1
       122: q^2+1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q^2+1
       156: 1
       161: 1
       162: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       169: q^2+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: q^2+1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: q^2+1
       267: 1
       272: 1
       273: q^2+1
       276: q^2+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       403: 1
       404: 1
       411: 1
       412: q^2+1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       618: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       702: 1
       712: 1
       731: 1
       739: 1
       748: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       887: 1
       897: 1
       905: 1
       933: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1023: 1
      1042: 1
      1050: 1
      1059: 1
      1103: 1
      1198: 1
      1208: 1
      1216: 1
      1244: 1
      1394: 1

1395:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q+1
         3: q^3+2q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^3+2q^2+2q+1
        10: q+1
        11: q^3+2q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q^3+2q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: 1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^3+2q^2+2q+1
        44: q+1
        45: q^3+2q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: q+1
        51: 1
        52: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q^2+2q+1
        80: 1
        81: q^2+2q+1
        82: 1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^3+2q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: 1
       102: q^2+2q+1
       103: q^2+2q+1
       104: 1
       105: q+1
       106: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+2q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q^2+2q+1
       153: 1
       154: q^2+2q+1
       155: q+1
       156: 1
       157: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q^2+2q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q^2+2q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: q+1
       200: 1
       204: 1
       205: 1
       206: q+1
       207: 1
       208: q+1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+2q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: 1
       288: q+1
       289: 1
       290: q+1
       292: q+1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       348: q+1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+2q+1
       463: 1
       474: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       517: 1
       526: 1
       527: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       564: 1
       573: 1
       574: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       617: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       713: 1
       731: 1
       732: 1
       738: 1
       741: 1
       748: 1
       750: 1
       752: 1
       765: 1
       774: 1
       775: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: 1
       817: 1
       818: 1
       824: 1
       827: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       888: 1
       897: 1
       898: 1
       904: 1
       934: 1
       953: 1
       978: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1024: 1
      1042: 1
      1043: 1
      1049: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1104: 1
      1199: 1
      1208: 1
      1209: 1
      1215: 1
      1245: 1
      1264: 1
      1395: 1

1396:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 1
        21: q^2+2q+1
        22: 1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: 1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q^2+2q+1
        59: 1
        60: 1
        61: 1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: 1
        72: q^2+2q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q^2+2q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q^2+2q+1
       126: 1
       127: 1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q^2+2q+1
       164: 1
       165: 1
       166: 1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 1
       170: q^2+2q+1
       171: q^2+2q+1
       172: 1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q+1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q^2+2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q^2+2q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q^2+2q+1
       280: 1
       281: 1
       282: 1
       283: q^2+2q+1
       284: q^2+2q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       392: q+1
       393: q+1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q^2+2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       493: 1
       494: 1
       495: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: q+1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: q+1
       646: q+1
       647: q+1
       668: 1
       678: 1
       687: 1
       688: 1
       689: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       714: 1
       732: 1
       733: 1
       734: 1
       737: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       784: 1
       785: 1
       786: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: 1
       818: 1
       819: 1
       820: 1
       823: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: q+1
       889: 1
       898: 1
       899: 1
       900: 1
       903: 1
       935: 1
       979: 1
       989: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1025: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1105: 1
      1200: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1246: 1
      1396: 1

1397:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       105: q+1
       107: 1
       108: 1
       112: q+1
       114: q+1
       115: 1
       116: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       191: 1
       193: 1
       199: q+1
       201: 1
       202: 1
       206: q+1
       208: q+1
       209: 1
       210: q+1
       213: q+1
       215: q+1
       216: 1
       217: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: 1
       266: q+1
       268: q+1
       269: 1
       270: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 1
       321: 1
       323: 1
       329: q+1
       331: 1
       332: 1
       337: q+1
       339: 1
       340: 1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: q+1
       407: 1
       408: 1
       412: q+1
       414: q+1
       415: 1
       416: q+1
       419: q+1
       421: q+1
       422: 1
       423: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       476: 1
       485: 1
       487: 1
       494: 1
       496: 1
       502: q+1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: 1
       528: 1
       530: 1
       536: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: q+1
       585: 1
       586: 1
       591: q+1
       593: 1
       594: 1
       598: q+1
       600: q+1
       601: 1
       602: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       669: 1
       679: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       715: 1
       733: 1
       735: 1
       741: 1
       748: 1
       750: 1
       752: 1
       767: 1
       776: 1
       778: 1
       785: 1
       787: 1
       793: q+1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       810: 1
       819: 1
       821: 1
       827: 1
       835: 1
       837: 1
       838: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       890: 1
       899: 1
       901: 1
       936: 1
       953: 1
       980: 1
       990: 1
       999: 1
      1001: 1
      1007: 1
      1009: 1
      1010: 1
      1026: 1
      1044: 1
      1046: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1106: 1
      1201: 1
      1210: 1
      1212: 1
      1247: 1
      1264: 1
      1397: 1

1398:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 2q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: 2q+1
         9: 3q^2+3q+1
        10: 2q^2+3q+1
        11: 3q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+3q+1
        17: 2q^2+3q+1
        18: 3q^2+3q+1
        19: 3q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: q^2+2q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: 3q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+3q+1
        31: 2q^2+3q+1
        32: 3q^2+3q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: 3q^2+3q+1
        44: 2q^2+3q+1
        45: 3q^2+3q+1
        46: 3q^2+3q+1
        47: 3q^2+3q+1
        48: 2q^2+3q+1
        49: 2q^2+3q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q+1
        57: q+1
        58: q^2+2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q^2+2q+1
        63: 2q^2+3q+1
        64: 2q+1
        65: q^2+2q+1
        66: 2q^2+3q+1
        67: 2q+1
        68: 3q^2+3q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: q+1
        77: q^2+2q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: q^2+2q+1
        90: 2q^2+3q+1
        91: 2q+1
        92: 3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q^2+3q+1
        95: 2q^2+3q+1
        96: 3q^2+3q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: 2q^2+3q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+3q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: 2q+1
       118: q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: q+1
       123: 2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q^2+2q+1
       130: 2q^2+3q+1
       131: 2q+1
       132: 2q^2+3q+1
       133: q^2+2q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q^2+2q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q^2+2q+1
       168: 2q^2+3q+1
       169: 2q+1
       170: q^2+2q+1
       171: 2q^2+3q+1
       172: 2q+1
       173: 3q^2+3q+1
       174: 2q^2+3q+1
       175: 2q^2+3q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: q+1
       182: q^2+2q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: 2q^2+3q+1
       187: q^2+2q+1
       188: q^2+2q+1
       192: 1
       193: 1
       195: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: 2q+1
       212: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q^2+2q+1
       227: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: 2q+1
       272: q+1
       273: q+1
       274: q^2+2q+1
       275: 2q+1
       276: q+1
       277: 2q+1
       278: q+1
       279: q^2+2q+1
       280: 2q+1
       281: q+1
       282: 2q+1
       283: q^2+2q+1
       284: 2q^2+3q+1
       285: 2q+1
       286: 2q^2+3q+1
       287: q^2+2q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q^2+2q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       313: 1
       322: 1
       323: 1
       325: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       398: 1
       399: 1
       401: 1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: 2q+1
       418: q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: q^2+2q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: q+1
       432: q^2+2q+1
       433: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       477: 1
       486: 1
       487: 1
       489: 1
       495: 1
       496: 1
       498: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       541: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: 2q+1
       604: q+1
       605: 1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       613: 1
       614: 1
       616: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       670: 1
       680: 1
       689: 1
       690: 1
       692: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       716: 1
       734: 1
       735: 1
       737: 1
       742: 1
       746: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       768: 1
       777: 1
       778: 1
       780: 1
       786: 1
       787: 1
       789: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       801: 1
       802: 1
       803: 1
       804: 1
       805: q+1
       806: 1
       811: 1
       820: 1
       821: 1
       823: 1
       828: 1
       832: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       891: 1
       900: 1
       901: 1
       903: 1
       937: 1
       954: 1
       958: 1
       981: 1
       991: 1
      1000: 1
      1001: 1
      1003: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1027: 1
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1057: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1107: 1
      1202: 1
      1211: 1
      1212: 1
      1214: 1
      1248: 1
      1265: 1
      1269: 1
      1398: 1

1399:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       314: 1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       358: 1
       361: 1
       362: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       478: 1
       485: 1
       488: 1
       489: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       521: 1
       528: 1
       531: 1
       532: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       568: 1
       575: 1
       578: 1
       579: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       671: 1
       681: 1
       688: 1
       691: 1
       692: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       717: 1
       733: 1
       736: 1
       737: 1
       769: 1
       776: 1
       779: 1
       780: 1
       785: 1
       788: 1
       789: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       812: 1
       819: 1
       822: 1
       823: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: 1
       892: 1
       899: 1
       902: 1
       903: 1
       938: 1
       982: 1
       992: 1
       999: 1
      1002: 1
      1003: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1028: 1
      1044: 1
      1047: 1
      1048: 1
      1108: 1
      1203: 1
      1210: 1
      1213: 1
      1214: 1
      1249: 1
      1399: 1

1400:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       315: 1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       479: 1
       486: 1
       488: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       569: 1
       576: 1
       578: 1
       584: 1
       585: 1
       587: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       637: 1
       639: 1
       672: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       770: 1
       777: 1
       779: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       837: 1
       839: 1
       893: 1
       900: 1
       902: 1
       939: 1
       983: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1029: 1
      1045: 1
      1047: 1
      1109: 1
      1204: 1
      1211: 1
      1213: 1
      1250: 1
      1400: 1

1401:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q^2+2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: q^2+2q+1
        44: 2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: 2q+1
        60: q+1
        61: q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: 2q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: 2q+1
       165: q+1
       166: q+1
       167: q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: 1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: 2q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: 2q+1
       281: q+1
       282: q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: 1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: q+1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: 1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: 2q+1
       429: q+1
       430: q+1
       431: 1
       432: q+1
       433: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: q+1
       457: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       496: 1
       497: 1
       498: 1
       499: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: 1
       605: 1
       606: 1
       607: q+1
       608: 1
       609: q+1
       614: 1
       615: 1
       616: 1
       617: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       631: 1
       636: 1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       673: 1
       683: 1
       690: 1
       691: 1
       692: 1
       693: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       719: 1
       735: 1
       736: 1
       737: 1
       738: 1
       750: 1
       752: 1
       771: 1
       778: 1
       779: 1
       780: 1
       781: 1
       787: 1
       788: 1
       789: 1
       790: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       802: 1
       803: 1
       804: 1
       805: q+1
       806: 1
       814: 1
       821: 1
       822: 1
       823: 1
       824: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       894: 1
       901: 1
       902: 1
       903: 1
       904: 1
       940: 1
       984: 1
       994: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1030: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1061: 1
      1063: 1
      1110: 1
      1205: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1251: 1
      1401: 1

1402:    0: 2q^2+2q+1
         1: q^2+q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: q^2+q+1
        26: q+1
        27: q^2+2q+1
        28: q^2+q+1
        29: 2q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+q+1
        41: q+1
        42: q^2+2q+1
        43: q^2+q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: q+1
        48: q^2+2q+1
        49: 2q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q+1
        62: q^2+q+1
        63: q+1
        64: q^2+2q+1
        65: q+1
        66: q+1
        67: 2q+1
        68: q+1
        69: q^2+2q+1
        70: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: q+1
        77: 1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        85: q+1
        86: q+1
        87: q^2+2q+1
        88: q+1
        89: q^2+q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+q+1
        93: 2q^2+2q+1
        94: q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       115: q+1
       116: q+1
       117: 1
       118: q+1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: q+1
       130: q+1
       131: 2q+1
       132: q+1
       133: 2q+1
       137: q+1
       138: q+1
       139: 1
       140: q+1
       142: 1
       143: 1
       144: 2q+1
       145: q+1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: 2q+1
       152: q+1
       153: 2q+1
       154: 2q+1
       158: q+1
       159: q+1
       160: 1
       161: q+1
       163: q+1
       164: q+1
       165: q^2+2q+1
       166: q+1
       167: q^2+q+1
       168: q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: 2q+1
       173: q+1
       174: q^2+2q+1
       175: 2q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: q+1
       181: q+1
       182: 1
       183: 2q+1
       184: q+1
       185: 2q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       195: 1
       196: 1
       197: 1
       202: q+1
       203: 1
       204: 1
       205: 1
       209: q+1
       210: q+1
       211: 1
       212: q+1
       216: q+1
       217: q+1
       218: 1
       219: q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: 1
       227: 2q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: q+1
       249: 1
       250: 1
       251: 2q+1
       252: q+1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: 2q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       269: q+1
       270: q+1
       271: 1
       272: q+1
       274: q+1
       275: q+1
       276: q^2+2q+1
       277: q+1
       279: q+1
       280: q+1
       281: 2q+1
       282: q+1
       283: q+1
       284: q+1
       285: 2q+1
       286: q+1
       287: 2q+1
       291: q+1
       292: q+1
       293: 1
       294: q+1
       296: 1
       297: 1
       298: 2q+1
       299: q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: 2q+1
       306: q+1
       307: 2q+1
       308: 2q+1
       317: 1
       325: 1
       326: 1
       327: 1
       332: q+1
       333: 1
       334: 1
       335: 1
       340: q+1
       341: 1
       342: 1
       343: 1
       347: q+1
       348: q+1
       349: 1
       350: q+1
       352: 1
       353: 1
       354: 2q+1
       355: q+1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       388: 1
       389: 1
       390: q+1
       392: q+1
       393: 1
       394: q+1
       401: 1
       402: 1
       403: 1
       408: q+1
       409: 1
       410: 1
       411: 1
       415: q+1
       416: q+1
       417: 1
       418: q+1
       422: q+1
       423: q+1
       424: 1
       425: q+1
       427: q+1
       428: q+1
       429: 2q+1
       430: q+1
       431: q+1
       432: 1
       433: 2q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       450: 1
       451: 1
       452: q+1
       455: 1
       456: 1
       457: 2q+1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: 2q+1
       481: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: q+1
       506: 1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       559: 1
       560: 1
       561: q+1
       571: 1
       579: 1
       580: 1
       581: 1
       586: q+1
       587: 1
       588: 1
       589: 1
       594: q+1
       595: 1
       596: 1
       597: 1
       601: q+1
       602: q+1
       603: 1
       604: q+1
       606: 1
       607: 1
       608: 2q+1
       609: q+1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       642: 1
       643: 1
       644: q+1
       646: q+1
       647: 1
       648: q+1
       674: 1
       684: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       702: 1
       720: 1
       737: 1
       738: 1
       739: 1
       744: 1
       751: 1
       752: 1
       772: 1
       780: 1
       781: 1
       782: 1
       789: 1
       790: 1
       791: 1
       796: q+1
       797: 1
       798: 1
       799: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       815: 1
       823: 1
       824: 1
       825: 1
       830: 1
       838: 1
       839: 1
       840: 1
       841: 1
       845: 1
       846: 1
       850: 1
       851: 1
       852: q+1
       895: 1
       903: 1
       904: 1
       905: 1
       941: 1
       956: 1
       985: 1
       995: 1
      1003: 1
      1004: 1
      1005: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1031: 1
      1048: 1
      1049: 1
      1050: 1
      1055: 1
      1062: 1
      1063: 1
      1111: 1
      1206: 1
      1214: 1
      1215: 1
      1216: 1
      1252: 1
      1267: 1
      1402: 1

1403:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: 1
        22: q^2+1
        23: q^2+1
        24: 1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        54: q^2+1
        55: 1
        56: 1
        59: q^2+1
        60: q^2+1
        61: 1
        63: q^2+1
        64: q^2+1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: q^2+1
        87: q^2+1
        88: 1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: 1
       111: 1
       116: q^2+1
       117: 1
       118: 1
       121: q^2+1
       122: q^2+1
       123: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: q^2+1
       160: 1
       161: 1
       164: q^2+1
       165: q^2+1
       166: 1
       168: q^2+1
       169: q^2+1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: q^2+1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: q^2+1
       271: 1
       272: 1
       275: q^2+1
       276: q^2+1
       277: 1
       280: 1
       281: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       363: 1
       364: 1
       371: 1
       372: 1
       377: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       393: 1
       394: 1
       402: 1
       403: 1
       410: 1
       411: 1
       416: q^2+1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       456: 1
       457: 1
       458: 1
       460: 1
       461: 1
       462: 1
       463: 1
       482: 1
       490: 1
       491: 1
       499: 1
       500: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       525: 1
       533: 1
       534: 1
       549: 1
       550: 1
       555: 1
       560: 1
       561: 1
       572: 1
       580: 1
       581: 1
       588: 1
       589: 1
       596: 1
       597: 1
       602: 1
       603: 1
       604: 1
       607: 1
       608: 1
       609: 1
       617: 1
       618: 1
       625: 1
       626: 1
       631: 1
       638: 1
       639: 1
       640: 1
       643: 1
       644: 1
       647: 1
       648: 1
       675: 1
       685: 1
       693: 1
       694: 1
       701: 1
       702: 1
       721: 1
       738: 1
       739: 1
       752: 1
       773: 1
       781: 1
       782: 1
       790: 1
       791: 1
       798: 1
       799: 1
       804: 1
       805: 1
       806: 1
       816: 1
       824: 1
       825: 1
       840: 1
       841: 1
       846: 1
       851: 1
       852: 1
       896: 1
       904: 1
       905: 1
       942: 1
       986: 1
       996: 1
      1004: 1
      1005: 1
      1012: 1
      1013: 1
      1032: 1
      1049: 1
      1050: 1
      1063: 1
      1112: 1
      1207: 1
      1215: 1
      1216: 1
      1253: 1
      1403: 1

1404:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q^2+2q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       338: 1
       346: 1
       351: 1
       352: 1
       353: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       482: 1
       511: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       545: 1
       553: 1
       558: 1
       559: 1
       560: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       592: 1
       600: 1
       605: 1
       606: 1
       607: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       656: 1
       657: 1
       659: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       721: 1
       750: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       773: 1
       802: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       836: 1
       844: 1
       849: 1
       850: 1
       851: 1
       854: 1
       906: 1
       907: 1
       913: 1
       914: 1
       916: 1
       960: 1
       961: 1
       967: 1
       968: 1
       970: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1032: 1
      1061: 1
      1113: 1
      1165: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1227: 1
      1404: 1

1405:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        60: 1
        61: q+1
        62: 1
        64: 1
        65: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q+1
       118: 1
       119: 1
       122: 1
       123: 1
       124: q+1
       128: q+1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       214: q+1
       220: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: 1
       246: 1
       247: 1
       248: q+1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       272: 1
       273: 1
       276: 1
       277: 1
       278: q+1
       282: q+1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 1
       345: 1
       351: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       381: q+1
       387: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: q+1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: 1
       452: 1
       453: 1
       454: q+1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       510: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       552: 1
       558: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: q+1
       641: 1
       645: 1
       646: 1
       648: 1
       650: 1
       651: 1
       655: 1
       666: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       749: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       855: 1
       907: 1
       908: 1
       912: 1
       923: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1060: 1
      1114: 1
      1166: 1
      1218: 1
      1219: 1
      1223: 1
      1234: 1
      1405: 1

1406:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        60: q+1
        61: 1
        62: q+1
        64: q+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       118: 1
       119: q+1
       122: q+1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       148: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: q+1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       242: 1
       243: q+1
       246: q+1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       336: 1
       343: 1
       344: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: q+1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       449: q+1
       452: q+1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       492: 1
       500: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       590: 1
       597: 1
       598: 1
       605: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: q+1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       650: 1
       652: 1
       654: 1
       676: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       783: 1
       791: 1
       800: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       856: 1
       907: 1
       909: 1
       911: 1
       933: 1
       961: 1
       963: 1
       965: 1
       987: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1042: 1
      1050: 1
      1059: 1
      1115: 1
      1167: 1
      1218: 1
      1220: 1
      1222: 1
      1244: 1
      1406: 1

1407:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       483: 1
       492: 1
       501: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       651: 1
       652: 1
       653: 1
       686: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       722: 1
       731: 1
       740: 1
       747: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       774: 1
       783: 1
       792: 1
       799: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       857: 1
       908: 1
       909: 1
       910: 1
       943: 1
       962: 1
       963: 1
       964: 1
       997: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1116: 1
      1168: 1
      1219: 1
      1220: 1
      1221: 1
      1254: 1
      1407: 1

1408:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q+1
        48: q^2+2q+1
        49: 2q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: 1
        60: 2q+1
        61: 2q+1
        62: q+1
        64: q+1
        65: q+1
        67: q+1
        68: q+1
        69: 2q+1
        70: q+1
        71: 1
        72: q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 1
       113: 1
       118: 2q+1
       119: 1
       122: q+1
       123: q+1
       124: 1
       127: q+1
       128: q+1
       129: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: 2q+1
       141: 1
       144: 2q+1
       145: 2q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q+1
       153: 2q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: 2q+1
       162: 1
       165: 2q+1
       166: 2q+1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q+1
       174: 2q+1
       175: q+1
       176: 1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       183: 2q+1
       184: q+1
       185: 2q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: 1
       205: 1
       206: 1
       207: 1
       212: q+1
       213: 1
       214: 1
       219: q+1
       220: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: 1
       242: 2q+1
       243: 1
       246: q+1
       247: q+1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: 1
       272: 2q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: q+1
       282: q+1
       283: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: 2q+1
       295: 1
       298: 2q+1
       299: 2q+1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q+1
       307: 2q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: 1
       372: 1
       373: 1
       374: 1
       379: q+1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: 1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: q+1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 2q+1
       449: 1
       452: q+1
       453: q+1
       454: 1
       457: q+1
       458: q+1
       459: q+1
       461: 1
       462: q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       491: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: q+1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       694: 1
       695: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       730: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       782: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       858: 1
       910: 1
       911: 1
       912: 1
       951: 1
       952: 1
       964: 1
       965: 1
       966: 1
      1005: 1
      1006: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1041: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1117: 1
      1169: 1
      1221: 1
      1222: 1
      1223: 1
      1262: 1
      1263: 1
      1408: 1

1409:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: q+1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: 1
       244: 1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 1
       314: 1
       316: 1
       317: 1
       318: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: q+1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: q+1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       469: 1
       471: 1
       472: 1
       476: 1
       478: 1
       480: 1
       482: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       519: 1
       521: 1
       523: 1
       524: 1
       525: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       544: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       568: 1
       570: 1
       571: 1
       572: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: q+1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       654: 1
       656: 1
       662: 1
       685: 1
       696: 1
       708: 1
       710: 1
       711: 1
       715: 1
       717: 1
       719: 1
       721: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       760: 1
       762: 1
       763: 1
       767: 1
       769: 1
       771: 1
       773: 1
       790: 1
       791: 1
       793: 1
       800: 1
       802: 1
       804: 1
       810: 1
       812: 1
       814: 1
       815: 1
       816: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       835: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       859: 1
       911: 1
       913: 1
       919: 1
       942: 1
       953: 1
       965: 1
       967: 1
       973: 1
       996: 1
      1007: 1
      1019: 1
      1021: 1
      1022: 1
      1026: 1
      1028: 1
      1030: 1
      1032: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1118: 1
      1170: 1
      1222: 1
      1224: 1
      1230: 1
      1253: 1
      1264: 1
      1409: 1

1410:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: 2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 2q+1
        95: q+1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: q+1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       470: 1
       471: 1
       472: 1
       477: 1
       479: 1
       480: 1
       482: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       520: 1
       522: 1
       523: 1
       524: 1
       525: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       537: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       655: 1
       656: 1
       663: 1
       675: 1
       697: 1
       709: 1
       710: 1
       711: 1
       716: 1
       718: 1
       719: 1
       721: 1
       729: 1
       730: 1
       742: 1
       749: 1
       750: 1
       753: 1
       761: 1
       762: 1
       763: 1
       768: 1
       770: 1
       771: 1
       773: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       860: 1
       912: 1
       913: 1
       920: 1
       932: 1
       954: 1
       966: 1
       967: 1
       974: 1
       986: 1
      1008: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1119: 1
      1171: 1
      1223: 1
      1224: 1
      1231: 1
      1243: 1
      1265: 1
      1410: 1

1411:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: 1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: 1
        75: 1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: 1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q^2+2q+1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: 1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q^2+2q+1
       297: q+1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: q+1
       353: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       381: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       392: q+1
       393: q+1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       485: 1
       495: 1
       504: 1
       511: 1
       512: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       545: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       559: q+1
       560: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       592: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       606: q+1
       607: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       646: q+1
       647: q+1
       648: 1
       649: 1
       657: 1
       658: 1
       665: 1
       698: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: 1
       720: 1
       721: 1
       724: 1
       734: 1
       743: 1
       750: 1
       751: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: 1
       772: 1
       773: 1
       776: 1
       786: 1
       795: 1
       802: 1
       803: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       850: q+1
       851: 1
       861: 1
       906: 1
       914: 1
       915: 1
       922: 1
       955: 1
       960: 1
       968: 1
       969: 1
       976: 1
      1009: 1
      1014: 1
      1015: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1032: 1
      1035: 1
      1045: 1
      1054: 1
      1061: 1
      1062: 1
      1120: 1
      1172: 1
      1217: 1
      1225: 1
      1226: 1
      1233: 1
      1266: 1
      1411: 1

1412:    0: q^2+3q+1
         1: q^2+3q+1
         2: q^2+3q+1
         3: q^2+3q+1
         4: q^2+3q+1
         5: q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q+1
        12: q+1
        13: q^2+3q+1
        14: q^2+3q+1
        15: q^2+3q+1
        16: q^2+3q+1
        17: q^2+3q+1
        18: q^2+3q+1
        19: q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: q+1
        27: q^2+3q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: 1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q+1
        39: q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q+1
        46: q+1
        47: q^2+3q+1
        48: q^2+3q+1
        49: q^2+3q+1
        50: q+1
        51: q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q+1
        55: q+1
        56: 1
        57: q^2+3q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q+1
        76: q^2+3q+1
        77: q+1
        78: q^2+3q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: 1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: q+1
        88: q+1
        89: q^2+3q+1
        90: q+1
        91: q^2+3q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: 1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: q+1
       107: q^2+3q+1
       108: q+1
       109: q+1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q+1
       139: q+1
       140: 1
       141: q^2+3q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q+1
       160: q+1
       161: 1
       162: q^2+3q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q+1
       181: q^2+3q+1
       182: q+1
       183: q^2+3q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: 1
       189: 1
       190: 1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: q+1
       231: q^2+3q+1
       232: q+1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q+1
       260: q+1
       261: q^2+3q+1
       262: q+1
       263: q+1
       264: 1
       265: 1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: q+1
       293: q+1
       294: 1
       295: q^2+3q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: q+1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       356: 1
       357: 1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: q+1
       437: q^2+3q+1
       438: q+1
       439: q+1
       440: 1
       441: 1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       495: 1
       497: 1
       504: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       545: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       569: q+1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       592: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       610: 1
       611: 1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       648: 1
       650: 1
       658: 1
       659: 1
       664: 1
       669: 1
       682: 1
       704: 1
       705: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       734: 1
       736: 1
       743: 1
       756: 1
       757: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       776: 1
       778: 1
       786: 1
       788: 1
       795: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       813: q+1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       862: 1
       907: 1
       915: 1
       916: 1
       921: 1
       926: 1
       939: 1
       961: 1
       969: 1
       970: 1
       975: 1
       980: 1
       993: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1045: 1
      1047: 1
      1054: 1
      1121: 1
      1173: 1
      1218: 1
      1226: 1
      1227: 1
      1232: 1
      1237: 1
      1250: 1
      1412: 1

1413:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q^2+2q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q^2+2q+1
        31: 1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: 1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: 1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 1
        54: q+1
        55: q^2+2q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: 1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q^2+2q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: 1
       102: q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       503: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       742: 1
       757: 1
       758: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: 1
       775: 1
       781: 1
       794: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       863: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: 1
      1016: 1
      1017: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1040: 1
      1053: 1
      1122: 1
      1174: 1
      1219: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1413: 1

1414:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q^2+2q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: 1
        38: q^2+2q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: 1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: 1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q^2+2q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q^2+2q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: 1
       102: q^2+2q+1
       103: q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: 1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: 1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q^2+2q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: 1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       492: 1
       493: 1
       499: 1
       502: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       564: q+1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       652: 1
       659: 1
       661: 1
       662: 1
       677: 1
       705: 1
       707: 1
       708: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       731: 1
       732: 1
       738: 1
       741: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       783: 1
       784: 1
       790: 1
       793: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       864: 1
       909: 1
       916: 1
       918: 1
       919: 1
       934: 1
       963: 1
       970: 1
       972: 1
       973: 1
       988: 1
      1016: 1
      1018: 1
      1019: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1042: 1
      1043: 1
      1049: 1
      1052: 1
      1123: 1
      1175: 1
      1220: 1
      1227: 1
      1229: 1
      1230: 1
      1245: 1
      1414: 1

1415:    0: q^3+3q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^3+3q^2+4q+1
         3: q^2+4q+1
         4: q^3+3q^2+4q+1
         5: q^3+3q^2+4q+1
         6: 2q^2+3q+1
         7: q^3+3q^2+4q+1
         8: q^2+4q+1
         9: q^2+4q+1
        10: 2q+1
        11: q^2+4q+1
        12: q^2+4q+1
        13: q^3+3q^2+4q+1
        14: q^3+3q^2+4q+1
        15: q^2+4q+1
        16: q^3+3q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+4q+1
        19: q^3+3q^2+4q+1
        20: 2q+1
        21: 2q^2+3q+1
        22: q^2+4q+1
        23: q^2+4q+1
        24: q^2+4q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+4q+1
        29: 2q+1
        30: q^2+4q+1
        31: 2q+1
        32: q^2+4q+1
        33: 2q^2+3q+1
        34: q^3+3q^2+4q+1
        35: q^2+4q+1
        36: q^2+4q+1
        37: 2q+1
        38: q^2+4q+1
        39: q^2+4q+1
        40: 2q^2+3q+1
        41: q^3+3q^2+4q+1
        42: q^2+4q+1
        43: q^2+4q+1
        44: 2q+1
        45: q^2+4q+1
        46: q^2+4q+1
        47: q^3+3q^2+4q+1
        48: q^3+3q^2+4q+1
        49: q^2+4q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: q+1
        54: q^2+4q+1
        55: q^2+4q+1
        56: q^2+4q+1
        57: 1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: q+1
        68: q^2+4q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: 2q^2+3q+1
        73: q^2+4q+1
        74: q^2+4q+1
        75: q^2+4q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: q^2+4q+1
        80: 2q+1
        81: q^2+4q+1
        82: 2q+1
        83: q^2+4q+1
        84: 2q+1
        85: 2q^2+3q+1
        86: q^2+4q+1
        87: q^2+4q+1
        88: q^2+4q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+4q+1
        93: 2q+1
        94: q^2+4q+1
        95: 2q+1
        96: q^2+4q+1
        97: 2q^2+3q+1
        98: q^3+3q^2+4q+1
        99: q^2+4q+1
       100: q^2+4q+1
       101: 2q+1
       102: q^2+4q+1
       103: q^2+4q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 1
       108: q+1
       109: q+1
       110: q^2+4q+1
       111: 2q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 1
       132: 2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q+1
       138: q^2+4q+1
       139: q^2+4q+1
       140: q^2+4q+1
       141: 1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: 2q+1
       151: q+1
       152: q^2+4q+1
       153: 2q+1
       154: 2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: q+1
       159: q^2+4q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: 1
       163: q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: 2q+1
       172: q+1
       173: q^2+4q+1
       174: 2q+1
       175: 2q+1
       176: 2q+1
       177: 2q^2+3q+1
       178: q^2+4q+1
       179: q^2+4q+1
       180: q^2+4q+1
       181: q+1
       182: 2q+1
       183: 2q+1
       184: q^2+4q+1
       185: 2q+1
       186: q^2+4q+1
       187: 2q+1
       188: q^2+4q+1
       190: 2q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 2q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 1
       232: q+1
       233: q+1
       234: q^2+4q+1
       235: 2q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: 2q+1
       255: 1
       256: 2q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 1
       262: q+1
       263: q+1
       264: q^2+4q+1
       265: 2q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: 2q+1
       285: 1
       286: 2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: q+1
       292: q^2+4q+1
       293: q^2+4q+1
       294: q^2+4q+1
       295: 1
       296: q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q+1
       301: 2q+1
       302: q+1
       303: q+1
       304: 2q+1
       305: q+1
       306: q^2+4q+1
       307: 2q+1
       308: 2q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: 2q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 2q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: 2q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: 2q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: 2q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: 2q+1
       411: 1
       412: 1
       413: 1
       414: 1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 1
       438: q+1
       439: q+1
       440: q^2+4q+1
       441: 2q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: 2q+1
       461: 1
       462: 2q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       490: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       535: 1
       536: 1
       537: 1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       582: 1
       583: 1
       584: 1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: 2q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: 2q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: 2q+1
       626: 1
       627: 1
       628: 1
       629: 1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       687: 1
       693: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: 1
       729: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: 1
       781: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       826: 1
       827: 1
       828: 1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       865: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       944: 1
       950: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       998: 1
      1004: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1034: 1
      1040: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1124: 1
      1176: 1
      1221: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1255: 1
      1261: 1
      1415: 1

1416:    0: q^3+4q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+4q^2+4q+1
         3: 2q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: 3q^2+4q+1
         7: 3q^2+4q+1
         8: 2q^2+4q+1
         9: q^2+4q+1
        10: 2q^2+4q+1
        11: 2q^2+4q+1
        12: 2q+1
        13: 3q^2+4q+1
        14: q^3+4q^2+4q+1
        15: 2q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+4q+1
        19: q^3+4q^2+4q+1
        20: 3q+1
        21: 3q^2+4q+1
        22: q^2+4q+1
        23: 2q^2+4q+1
        24: 2q+1
        25: q^2+4q+1
        26: 2q+1
        27: 2q^2+4q+1
        28: q^2+4q+1
        29: 2q^2+4q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 3q^2+4q+1
        34: 3q^2+4q+1
        35: 2q^2+4q+1
        36: q^2+4q+1
        37: 2q^2+4q+1
        38: 2q^2+4q+1
        39: 2q+1
        40: 3q^2+4q+1
        41: 3q^2+4q+1
        42: 2q^2+4q+1
        43: q^2+4q+1
        44: 2q^2+4q+1
        45: 2q^2+4q+1
        46: 2q+1
        47: 3q^2+4q+1
        48: q^3+4q^2+4q+1
        49: 2q^2+4q+1
        50: 3q+1
        52: 3q+1
        53: q^2+4q+1
        54: q^2+4q+1
        55: 2q+1
        56: 2q+1
        57: 3q+1
        58: 2q+1
        59: 2q+1
        60: 2q^2+4q+1
        61: 2q+1
        62: q^2+4q+1
        63: 2q+1
        64: q^2+2q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 3q+1
        72: 3q^2+4q+1
        73: q^2+4q+1
        74: 2q^2+4q+1
        75: 2q+1
        76: q^2+4q+1
        77: 2q+1
        78: 2q^2+4q+1
        79: q^2+4q+1
        80: 2q^2+4q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 3q+1
        85: 3q^2+4q+1
        86: q^2+4q+1
        87: 2q^2+4q+1
        88: 2q+1
        89: q^2+4q+1
        90: 2q+1
        91: 2q^2+4q+1
        92: q^2+4q+1
        93: 2q^2+4q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 3q^2+4q+1
        98: 3q^2+4q+1
        99: 2q^2+4q+1
       100: q^2+4q+1
       101: 2q^2+4q+1
       102: 2q^2+4q+1
       103: 2q+1
       105: 3q+1
       107: 3q+1
       108: q^2+4q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 3q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q^2+2q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 3q+1
       136: 3q+1
       137: q^2+4q+1
       138: q^2+4q+1
       139: 2q+1
       140: 2q+1
       141: 3q+1
       142: 2q+1
       143: 2q+1
       144: 2q^2+4q+1
       145: 2q+1
       146: q^2+4q+1
       147: 2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 3q+1
       157: 3q+1
       158: q^2+4q+1
       159: q^2+4q+1
       160: 2q+1
       161: 2q+1
       162: 3q+1
       163: 2q+1
       164: 2q+1
       165: 2q^2+4q+1
       166: 2q+1
       167: q^2+4q+1
       168: 2q+1
       169: q^2+2q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 3q+1
       177: 3q^2+4q+1
       178: q^2+4q+1
       179: 2q^2+4q+1
       180: 2q+1
       181: q^2+4q+1
       182: 2q+1
       183: 2q^2+4q+1
       184: q^2+4q+1
       185: 2q^2+4q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       191: 3q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       199: q+1
       201: q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       208: 1
       209: q+1
       210: q+1
       213: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       229: 3q+1
       231: 3q+1
       232: q^2+4q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 3q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q^2+2q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: 3q+1
       261: 3q+1
       262: q^2+4q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 3q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q^2+2q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 3q+1
       290: 3q+1
       291: q^2+4q+1
       292: q^2+4q+1
       293: 2q+1
       294: 2q+1
       295: 3q+1
       296: 2q+1
       297: 2q+1
       298: 2q^2+4q+1
       299: 2q+1
       300: q^2+4q+1
       301: 2q+1
       302: q^2+2q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       312: q+1
       314: q+1
       316: 1
       317: q+1
       321: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: 3q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       366: q+1
       368: q+1
       369: 2q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       375: 1
       376: q+1
       377: q+1
       380: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       394: 1
       397: 3q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       405: q+1
       407: q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: 1
       415: q+1
       416: q+1
       419: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: q+1
       433: 1
       435: 3q+1
       437: 3q+1
       438: q^2+4q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 3q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q^2+2q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: q+1
       521: q+1
       523: 1
       524: q+1
       528: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: q+1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       566: q+1
       568: q+1
       570: 1
       571: q+1
       575: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       612: 3q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       620: q+1
       622: q+1
       623: 2q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       629: 1
       630: q+1
       631: q+1
       634: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       648: 1
       654: 1
       662: 1
       664: 1
       669: 1
       681: 1
       684: 1
       688: 1
       708: 1
       710: 1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       733: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       760: 1
       762: 1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       810: q+1
       812: q+1
       814: 1
       815: q+1
       819: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: q+1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       852: 1
       866: 1
       911: 1
       919: 1
       921: 1
       926: 1
       938: 1
       941: 1
       945: 1
       965: 1
       973: 1
       975: 1
       980: 1
       992: 1
       995: 1
       999: 1
      1019: 1
      1021: 1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1044: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1125: 1
      1177: 1
      1222: 1
      1230: 1
      1232: 1
      1237: 1
      1249: 1
      1252: 1
      1256: 1
      1416: 1

1417:    0: q^3+4q^2+4q+1
         1: 3q^2+4q+1
         2: q^3+4q^2+4q+1
         3: 2q^2+4q+1
         4: q^3+4q^2+4q+1
         5: q^3+4q^2+4q+1
         6: 3q^2+4q+1
         7: 3q^2+4q+1
         8: 2q^2+4q+1
         9: q^2+4q+1
        10: 2q^2+4q+1
        11: 2q+1
        12: 2q^2+4q+1
        13: 3q^2+4q+1
        14: q^3+4q^2+4q+1
        15: 2q^2+4q+1
        16: 3q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+4q+1
        19: q^3+4q^2+4q+1
        20: 3q+1
        21: 3q^2+4q+1
        22: q^2+4q+1
        23: 2q+1
        24: 2q^2+4q+1
        25: q^2+4q+1
        26: 2q+1
        27: 2q^2+4q+1
        28: 2q+1
        29: 2q+1
        30: q^2+4q+1
        31: 2q^2+4q+1
        32: 2q+1
        33: 3q^2+4q+1
        34: 3q^2+4q+1
        35: 2q^2+4q+1
        36: q^2+4q+1
        37: 2q^2+4q+1
        38: 2q+1
        39: 2q^2+4q+1
        40: 3q^2+4q+1
        41: 3q^2+4q+1
        42: 2q^2+4q+1
        43: q^2+4q+1
        44: 2q^2+4q+1
        45: 2q+1
        46: 2q^2+4q+1
        47: 3q^2+4q+1
        48: q^3+4q^2+4q+1
        49: 2q^2+4q+1
        51: 3q+1
        52: 3q+1
        53: q^2+4q+1
        54: 2q+1
        55: q^2+4q+1
        56: 2q+1
        57: 3q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q^2+4q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: q^2+4q+1
        66: 2q+1
        67: q^2+2q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 3q+1
        72: 3q^2+4q+1
        73: q^2+4q+1
        74: 2q+1
        75: 2q^2+4q+1
        76: q^2+4q+1
        77: 2q+1
        78: 2q^2+4q+1
        79: 2q+1
        80: 2q+1
        81: q^2+4q+1
        82: 2q^2+4q+1
        83: 2q+1
        84: 3q+1
        85: 3q^2+4q+1
        86: q^2+4q+1
        87: 2q+1
        88: 2q^2+4q+1
        89: q^2+4q+1
        90: 2q+1
        91: 2q^2+4q+1
        92: 2q+1
        93: 2q+1
        94: q^2+4q+1
        95: 2q^2+4q+1
        96: 2q+1
        97: 3q^2+4q+1
        98: 3q^2+4q+1
        99: 2q^2+4q+1
       100: q^2+4q+1
       101: 2q^2+4q+1
       102: 2q+1
       103: 2q^2+4q+1
       106: 3q+1
       107: 3q+1
       108: 2q+1
       109: q^2+4q+1
       110: 2q+1
       111: q+1
       113: 3q+1
       114: q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: 2q+1
       126: q+1
       128: q^2+2q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 3q+1
       136: 3q+1
       137: q^2+4q+1
       138: 2q+1
       139: q^2+4q+1
       140: 2q+1
       141: 3q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q^2+4q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: q^2+4q+1
       150: 2q+1
       151: q^2+2q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       156: 3q+1
       157: 3q+1
       158: q^2+4q+1
       159: 2q+1
       160: q^2+4q+1
       161: 2q+1
       162: 3q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q^2+4q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: q^2+4q+1
       171: 2q+1
       172: q^2+2q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 3q+1
       177: 3q^2+4q+1
       178: q^2+4q+1
       179: 2q+1
       180: 2q^2+4q+1
       181: q^2+4q+1
       182: 2q+1
       183: 2q^2+4q+1
       184: 2q+1
       185: 2q+1
       186: q^2+4q+1
       187: 2q^2+4q+1
       188: 2q+1
       192: 3q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: q+1
       215: 1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       230: 3q+1
       231: 3q+1
       232: 2q+1
       233: q^2+4q+1
       234: 2q+1
       235: q+1
       237: 3q+1
       238: q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: 2q+1
       250: q+1
       252: q^2+2q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       260: 3q+1
       261: 3q+1
       262: 2q+1
       263: q^2+4q+1
       264: 2q+1
       265: q+1
       267: 3q+1
       268: q+1
       269: 2q+1
       270: q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       282: q^2+2q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 3q+1
       290: 3q+1
       291: q^2+4q+1
       292: 2q+1
       293: q^2+4q+1
       294: 2q+1
       295: 3q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q^2+4q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: q^2+4q+1
       304: 2q+1
       305: q^2+2q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       313: q+1
       315: q+1
       316: 1
       317: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 3q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       367: q+1
       368: q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       381: q+1
       382: 1
       383: q+1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: q+1
       394: 1
       398: 3q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       406: q+1
       407: q+1
       408: q+1
       409: 2q+1
       410: q+1
       411: 1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: q+1
       421: 1
       422: q+1
       424: q+1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       433: 1
       436: 3q+1
       437: 3q+1
       438: 2q+1
       439: q^2+4q+1
       440: 2q+1
       441: q+1
       443: 3q+1
       444: q+1
       445: 2q+1
       446: q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       458: q^2+2q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       520: q+1
       522: q+1
       523: 1
       524: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       567: q+1
       569: q+1
       570: 1
       571: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: q+1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: 3q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       621: q+1
       622: q+1
       623: q+1
       624: 2q+1
       625: q+1
       626: 1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: q+1
       636: 1
       637: q+1
       639: q+1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       648: 1
       655: 1
       663: 1
       664: 1
       670: 1
       674: 1
       682: 1
       689: 1
       709: 1
       710: 1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       761: 1
       762: 1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       811: q+1
       813: q+1
       814: 1
       815: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: q+1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       853: 1
       867: 1
       912: 1
       920: 1
       921: 1
       927: 1
       931: 1
       939: 1
       946: 1
       966: 1
       974: 1
       975: 1
       981: 1
       985: 1
       993: 1
      1000: 1
      1020: 1
      1021: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1126: 1
      1178: 1
      1223: 1
      1231: 1
      1232: 1
      1238: 1
      1242: 1
      1250: 1
      1257: 1
      1417: 1

1418:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: 1
       497: 1
       504: 1
       511: 1
       512: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       559: 1
       560: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       606: 1
       607: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       698: 1
       710: 1
       711: 1
       719: 1
       720: 1
       721: 1
       726: 1
       736: 1
       743: 1
       750: 1
       751: 1
       762: 1
       763: 1
       771: 1
       772: 1
       773: 1
       778: 1
       788: 1
       795: 1
       802: 1
       803: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       850: 1
       851: 1
       868: 1
       913: 1
       921: 1
       922: 1
       955: 1
       967: 1
       975: 1
       976: 1
      1009: 1
      1021: 1
      1022: 1
      1030: 1
      1031: 1
      1032: 1
      1037: 1
      1047: 1
      1054: 1
      1061: 1
      1062: 1
      1127: 1
      1179: 1
      1224: 1
      1232: 1
      1233: 1
      1266: 1
      1418: 1

1419:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: 1
        51: q+1
        52: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q^2+2q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: q+1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: q+1
       136: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q^2+2q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: q+1
       290: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: q+1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       385: q+1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       545: q+1
       552: 1
       553: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: q+1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       657: 1
       666: 1
       667: 1
       675: 1
       697: 1
       703: 1
       712: 1
       713: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       742: 1
       749: 1
       750: 1
       753: 1
       755: 1
       764: 1
       765: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: 1
       816: 1
       817: 1
       818: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: q+1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       869: 1
       914: 1
       923: 1
       924: 1
       932: 1
       954: 1
       968: 1
       977: 1
       978: 1
       986: 1
      1008: 1
      1014: 1
      1023: 1
      1024: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1128: 1
      1180: 1
      1225: 1
      1234: 1
      1235: 1
      1243: 1
      1265: 1
      1419: 1

1420:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: 2q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: q^2+3q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: 2q+1
        39: q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: 2q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        50: q+1
        51: 2q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: 1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: q^2+3q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 2q+1
        76: q^2+3q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: q^2+3q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: 2q+1
       103: q^2+3q+1
       104: q+1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: q+1
       113: 2q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: 1
       144: q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: q^2+3q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: q+1
       162: 2q+1
       163: q+1
       164: 1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: q^2+3q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 2q+1
       181: q^2+3q+1
       182: q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: 2q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: 2q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: q+1
       267: 2q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: 1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: 2q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: q+1
       295: 2q+1
       296: q+1
       297: 1
       298: q+1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: q^2+3q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: q+1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: q+1
       443: 2q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: 1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       616: 1
       617: 1
       618: 1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       648: 1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       689: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       734: 1
       742: 1
       743: 1
       745: 1
       749: 1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: 1
       807: 1
       808: 1
       809: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       853: 1
       870: 1
       915: 1
       923: 1
       924: 1
       925: 1
       931: 1
       946: 1
       969: 1
       977: 1
       978: 1
       979: 1
       985: 1
      1000: 1
      1015: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1129: 1
      1181: 1
      1226: 1
      1234: 1
      1235: 1
      1236: 1
      1242: 1
      1257: 1
      1420: 1

1421:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: q+1
        51: q+1
        52: q^2+3q+1
        53: q+1
        54: q+1
        55: q+1
        56: 1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 1
        62: 2q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: 2q+1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: 1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: 2q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: 2q+1
       120: 2q+1
       121: 2q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       134: q+1
       135: q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: 1
       146: 2q+1
       147: 2q+1
       148: 2q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: 2q+1
       186: q^2+2q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: 1
       208: 2q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       214: 1
       215: q+1
       218: 1
       220: q+1
       221: q+1
       222: q+1
       224: 1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: 2q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: 2q+1
       244: 2q+1
       245: 2q+1
       246: q+1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: 2q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       288: q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: q+1
       299: 1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: q+1
       349: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       374: 1
       375: 2q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       381: 1
       382: q+1
       385: 1
       387: q+1
       388: q+1
       389: q+1
       391: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: 2q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: q+1
       556: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: q+1
       603: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: 1
       629: 2q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       635: 1
       636: q+1
       639: 1
       641: q+1
       642: q+1
       643: q+1
       645: 1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       742: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: q+1
       847: 1
       871: 1
       916: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       970: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
      1016: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1053: 1
      1130: 1
      1182: 1
      1227: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1421: 1

1422:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       221: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       253: 1
       254: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       388: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       565: 1
       566: 1
       567: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       660: 1
       668: 1
       669: 1
       670: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       809: 1
       810: 1
       811: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       872: 1
       917: 1
       925: 1
       926: 1
       927: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1017: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1131: 1
      1183: 1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1422: 1

1423:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: 1
        28: 2q+1
        29: q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: 1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: 2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: 1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: q+1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       468: 1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       518: 1
       521: 1
       522: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: 1
       544: 1
       545: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: q+1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       661: 1
       668: 1
       671: 1
       672: 1
       687: 1
       707: 1
       714: 1
       717: 1
       718: 1
       723: 1
       724: 1
       725: 1
       727: 1
       728: 1
       732: 1
       740: 1
       741: 1
       742: 1
       746: 1
       759: 1
       766: 1
       769: 1
       770: 1
       775: 1
       776: 1
       777: 1
       779: 1
       780: 1
       784: 1
       792: 1
       793: 1
       794: 1
       798: 1
       809: 1
       812: 1
       813: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       834: 1
       835: 1
       836: 1
       840: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       873: 1
       918: 1
       925: 1
       928: 1
       929: 1
       944: 1
       972: 1
       979: 1
       982: 1
       983: 1
       998: 1
      1018: 1
      1025: 1
      1028: 1
      1029: 1
      1034: 1
      1035: 1
      1036: 1
      1038: 1
      1039: 1
      1043: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1132: 1
      1184: 1
      1229: 1
      1236: 1
      1239: 1
      1240: 1
      1255: 1
      1423: 1

1424:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: 1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       114: 1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: 1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: 1
       244: 1
       245: q+1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       349: 1
       350: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       499: 1
       502: 1
       507: 1
       508: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       544: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       556: 1
       557: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       662: 1
       669: 1
       671: 1
       673: 1
       693: 1
       708: 1
       715: 1
       717: 1
       719: 1
       724: 1
       726: 1
       727: 1
       728: 1
       729: 1
       738: 1
       741: 1
       746: 1
       747: 1
       760: 1
       767: 1
       769: 1
       771: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       790: 1
       793: 1
       798: 1
       799: 1
       810: 1
       812: 1
       814: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       835: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       847: 1
       848: 1
       874: 1
       919: 1
       926: 1
       928: 1
       930: 1
       950: 1
       973: 1
       980: 1
       982: 1
       984: 1
      1004: 1
      1019: 1
      1026: 1
      1028: 1
      1030: 1
      1035: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1049: 1
      1052: 1
      1057: 1
      1058: 1
      1133: 1
      1185: 1
      1230: 1
      1237: 1
      1239: 1
      1241: 1
      1261: 1
      1424: 1

1425:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       663: 1
       670: 1
       672: 1
       673: 1
       709: 1
       716: 1
       718: 1
       719: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       742: 1
       761: 1
       768: 1
       770: 1
       771: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       811: 1
       813: 1
       814: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       875: 1
       920: 1
       927: 1
       929: 1
       930: 1
       974: 1
       981: 1
       983: 1
       984: 1
      1020: 1
      1027: 1
      1029: 1
      1030: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1053: 1
      1134: 1
      1186: 1
      1231: 1
      1238: 1
      1240: 1
      1241: 1
      1425: 1

1426:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+1
        12: q+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q^2+1
        24: q+1
        25: q+1
        26: 1
        27: q^2+q+1
        28: 1
        29: q^2+1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: q^2+1
        39: q+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q^2+1
        46: q+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: q^2+1
        61: q+1
        62: 1
        63: 1
        64: q^2+1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q^2+1
        75: q+1
        76: q+1
        77: 1
        78: q^2+q+1
        79: 1
        80: q^2+1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q^2+1
        88: q+1
        89: q+1
        90: 1
        91: q^2+q+1
        92: 1
        93: q^2+1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: q^2+q+1
       102: q^2+1
       103: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: q^2+1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: q^2+1
       145: q+1
       146: 1
       147: 1
       148: q^2+1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q^2+1
       166: q+1
       167: 1
       168: 1
       169: q^2+1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q^2+1
       180: q+1
       181: q+1
       182: 1
       183: q^2+q+1
       184: 1
       185: q^2+1
       186: q+1
       187: q+1
       188: 1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: q^2+1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: q^2+1
       277: 1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: q^2+1
       299: q+1
       300: 1
       301: 1
       302: q^2+1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: q^2+1
       453: 1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: 1
       480: 1
       481: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       497: 1
       504: 1
       506: 1
       523: 1
       524: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: 1
       548: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       570: 1
       571: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       648: 1
       664: 1
       673: 1
       674: 1
       691: 1
       710: 1
       719: 1
       720: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       736: 1
       743: 1
       745: 1
       762: 1
       771: 1
       772: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       788: 1
       795: 1
       797: 1
       814: 1
       815: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       837: 1
       839: 1
       844: 1
       845: 1
       847: 1
       849: 1
       853: 1
       876: 1
       921: 1
       930: 1
       931: 1
       948: 1
       975: 1
       984: 1
       985: 1
      1002: 1
      1021: 1
      1030: 1
      1031: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1047: 1
      1054: 1
      1056: 1
      1135: 1
      1187: 1
      1232: 1
      1241: 1
      1242: 1
      1259: 1
      1426: 1

1427:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       115: q+1
       116: 1
       117: q+1
       118: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: q+1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: 1
       139: q+1
       140: 1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       158: q+1
       159: 1
       160: q+1
       161: 1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: q+1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: q+1
       218: q+1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: q+1
       234: 1
       235: 1
       239: q+1
       240: 1
       241: q+1
       242: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: q+1
       250: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       263: q+1
       264: 1
       265: 1
       269: q+1
       270: 1
       271: q+1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: q+1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       292: 1
       293: q+1
       294: 1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       341: q+1
       347: 1
       349: 1
       352: 1
       353: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: q+1
       371: 1
       372: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: q+1
       385: q+1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: q+1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: 1
       422: q+1
       424: q+1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       438: 1
       439: q+1
       440: 1
       441: 1
       445: q+1
       446: 1
       447: q+1
       448: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: q+1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       489: 1
       490: 1
       491: 1
       506: 1
       512: 1
       514: 1
       524: 1
       525: 1
       532: 1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       548: q+1
       554: 1
       556: 1
       559: 1
       560: 1
       562: 1
       571: 1
       572: 1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       595: q+1
       601: 1
       603: 1
       606: 1
       607: 1
       609: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: q+1
       625: 1
       626: 1
       630: 1
       631: 1
       632: 1
       633: 1
       637: q+1
       639: q+1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       665: 1
       674: 1
       675: 1
       700: 1
       711: 1
       720: 1
       721: 1
       728: 1
       729: 1
       730: 1
       745: 1
       751: 1
       753: 1
       763: 1
       772: 1
       773: 1
       780: 1
       781: 1
       782: 1
       797: 1
       803: 1
       805: 1
       815: 1
       816: 1
       823: 1
       824: 1
       825: 1
       830: 1
       831: 1
       832: 1
       833: 1
       839: q+1
       845: 1
       847: 1
       850: 1
       851: 1
       853: 1
       877: 1
       922: 1
       931: 1
       932: 1
       957: 1
       976: 1
       985: 1
       986: 1
      1011: 1
      1022: 1
      1031: 1
      1032: 1
      1039: 1
      1040: 1
      1041: 1
      1056: 1
      1062: 1
      1064: 1
      1136: 1
      1188: 1
      1233: 1
      1242: 1
      1243: 1
      1268: 1
      1427: 1

1428:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: q+1
        51: 1
        52: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: q+1
       200: 1
       204: 1
       205: 1
       206: q+1
       208: q+1
       210: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: 1
       290: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       329: q+1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       377: q+1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       416: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       492: 1
       493: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: 1
       533: 1
       534: 1
       536: q+1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: 1
       580: 1
       581: 1
       583: q+1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       631: q+1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       657: 1
       676: 1
       677: 1
       685: 1
       696: 1
       703: 1
       712: 1
       713: 1
       721: 1
       731: 1
       732: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       764: 1
       765: 1
       773: 1
       783: 1
       784: 1
       790: 1
       791: 1
       793: 1
       800: 1
       802: 1
       804: 1
       807: 1
       808: 1
       816: 1
       817: 1
       818: 1
       824: 1
       825: 1
       827: q+1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       878: 1
       914: 1
       933: 1
       934: 1
       942: 1
       953: 1
       968: 1
       987: 1
       988: 1
       996: 1
      1007: 1
      1014: 1
      1023: 1
      1024: 1
      1032: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1137: 1
      1189: 1
      1225: 1
      1244: 1
      1245: 1
      1253: 1
      1264: 1
      1428: 1

1429:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: 2q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: q^2+3q+1
        26: q+1
        27: 2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: 2q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: 2q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        50: 2q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        57: 2q+1
        58: q+1
        59: 1
        60: 2q+1
        61: q+1
        62: q^2+3q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: q^2+3q+1
        77: q+1
        78: 2q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: q+1
        87: 2q+1
        88: q+1
        89: q^2+3q+1
        90: q+1
        91: 2q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+3q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: 2q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: q+1
       141: 2q+1
       142: q+1
       143: 1
       144: 2q+1
       145: q+1
       146: q^2+3q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: q+1
       162: 2q+1
       163: q+1
       164: 1
       165: 2q+1
       166: q+1
       167: q^2+3q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: q+1
       179: 2q+1
       180: q+1
       181: q^2+3q+1
       182: q+1
       183: 2q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: 2q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: q+1
       295: 2q+1
       296: q+1
       297: 1
       298: 2q+1
       299: q+1
       300: q^2+3q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: 2q+1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       485: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       616: 1
       617: 1
       618: 1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       648: 1
       658: 1
       676: 1
       677: 1
       678: 1
       684: 1
       688: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       724: 1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       776: 1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       807: 1
       808: 1
       809: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       852: 1
       879: 1
       915: 1
       933: 1
       934: 1
       935: 1
       941: 1
       945: 1
       969: 1
       987: 1
       988: 1
       989: 1
       995: 1
       999: 1
      1015: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1035: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1138: 1
      1190: 1
      1226: 1
      1244: 1
      1245: 1
      1246: 1
      1252: 1
      1256: 1
      1429: 1

1430:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: 2q+1
        32: q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: q+1
        51: q+1
        52: q^2+3q+1
        53: q+1
        54: q+1
        55: q+1
        56: 1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: 2q+1
        83: q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: 2q+1
        96: q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: 1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: 2q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       124: 2q+1
       125: 2q+1
       126: 2q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       134: q+1
       135: q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: 2q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: 2q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: q+1
       210: 1
       213: 1
       214: q+1
       215: 2q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: 2q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: 2q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       278: 2q+1
       279: 2q+1
       280: 2q+1
       281: 1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       288: q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       348: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       377: 1
       380: 1
       381: q+1
       382: 2q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: q+1
       416: 1
       419: 1
       420: q+1
       421: 2q+1
       422: q+1
       423: 1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: 2q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: q+1
       602: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: q+1
       631: 1
       634: 1
       635: q+1
       636: 2q+1
       637: q+1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       659: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: q+1
       846: 1
       880: 1
       916: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       970: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
      1016: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: 1
      1139: 1
      1191: 1
      1227: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1430: 1

1431:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: 1
        28: 2q+1
        29: q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: 1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: 2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: 1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       507: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       565: 1
       566: 1
       567: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       660: 1
       678: 1
       679: 1
       680: 1
       687: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       732: 1
       733: 1
       734: 1
       735: 1
       737: 1
       740: 1
       741: 1
       742: 1
       746: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: 1
       784: 1
       785: 1
       786: 1
       787: 1
       789: 1
       792: 1
       793: 1
       794: 1
       798: 1
       809: 1
       810: 1
       811: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       832: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       881: 1
       917: 1
       935: 1
       936: 1
       937: 1
       944: 1
       971: 1
       989: 1
       990: 1
       991: 1
       998: 1
      1017: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1048: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1140: 1
      1192: 1
      1228: 1
      1246: 1
      1247: 1
      1248: 1
      1255: 1
      1431: 1

1432:    0: q+1
         1: q+1
         2: q+1
         3: 1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       468: 1
       475: 1
       478: 1
       479: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       518: 1
       521: 1
       522: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       661: 1
       678: 1
       681: 1
       682: 1
       707: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       759: 1
       766: 1
       769: 1
       770: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       809: 1
       812: 1
       813: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       882: 1
       918: 1
       935: 1
       938: 1
       939: 1
       972: 1
       989: 1
       992: 1
       993: 1
      1018: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1141: 1
      1193: 1
      1229: 1
      1246: 1
      1249: 1
      1250: 1
      1432: 1

1433:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       469: 1
       476: 1
       478: 1
       480: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       662: 1
       679: 1
       681: 1
       683: 1
       708: 1
       715: 1
       717: 1
       719: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       760: 1
       767: 1
       769: 1
       771: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: 1
       810: 1
       812: 1
       814: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       883: 1
       919: 1
       936: 1
       938: 1
       940: 1
       973: 1
       990: 1
       992: 1
       994: 1
      1019: 1
      1026: 1
      1028: 1
      1030: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: 1
      1142: 1
      1194: 1
      1230: 1
      1247: 1
      1249: 1
      1251: 1
      1433: 1

1434:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: 2q+1
        31: q+1
        32: q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q+1
        57: 1
        58: 1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: q+1
        67: q+1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: 2q+1
        95: q+1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: q+1
       127: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: 1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: q+1
       281: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: 1
       334: 1
       335: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: q+1
       457: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       470: 1
       477: 1
       479: 1
       480: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: 1
       507: 1
       508: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: 1
       588: 1
       589: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       663: 1
       680: 1
       682: 1
       683: 1
       693: 1
       709: 1
       716: 1
       718: 1
       719: 1
       729: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       742: 1
       746: 1
       747: 1
       761: 1
       768: 1
       770: 1
       771: 1
       781: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       794: 1
       798: 1
       799: 1
       811: 1
       813: 1
       814: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       828: 1
       832: 1
       833: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       884: 1
       920: 1
       937: 1
       939: 1
       940: 1
       950: 1
       974: 1
       991: 1
       993: 1
       994: 1
      1004: 1
      1020: 1
      1027: 1
      1029: 1
      1030: 1
      1040: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1053: 1
      1057: 1
      1058: 1
      1143: 1
      1195: 1
      1231: 1
      1248: 1
      1250: 1
      1251: 1
      1261: 1
      1434: 1

1435:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q+1
        12: q^2+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q^2+1
        25: q+1
        26: 1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: 1
        31: q^2+1
        32: 1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: q+1
        39: q^2+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q+1
        46: q^2+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        61: q^2+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q^2+1
        76: q+1
        77: 1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: 1
        82: q^2+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+1
        89: q+1
        90: 1
        91: q^2+q+1
        92: q+1
        93: q+1
        94: 1
        95: q^2+1
        96: 1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: q^2+q+1
       102: q+1
       103: q^2+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: q^2+1
       146: q+1
       147: 1
       148: q+1
       149: 1
       150: 1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: q^2+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: q^2+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q^2+1
       181: q+1
       182: 1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: 1
       187: q^2+1
       188: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: q^2+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: q^2+1
       300: q+1
       301: 1
       302: q+1
       303: 1
       304: 1
       305: q^2+1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: q^2+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: 1
       480: 1
       481: 1
       487: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       523: 1
       524: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       570: 1
       571: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       648: 1
       664: 1
       683: 1
       684: 1
       690: 1
       710: 1
       719: 1
       720: 1
       726: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       762: 1
       771: 1
       772: 1
       778: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       795: 1
       796: 1
       814: 1
       815: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       845: 1
       846: 1
       849: 1
       852: 1
       885: 1
       921: 1
       940: 1
       941: 1
       947: 1
       975: 1
       994: 1
       995: 1
      1001: 1
      1021: 1
      1030: 1
      1031: 1
      1037: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1054: 1
      1055: 1
      1144: 1
      1196: 1
      1232: 1
      1251: 1
      1252: 1
      1258: 1
      1435: 1

1436:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       108: q+1
       109: 1
       110: 1
       111: 1
       115: q+1
       116: q+1
       117: 1
       118: 1
       120: q+1
       121: q+1
       122: q+1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q+1
       138: q+1
       139: 1
       140: 1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: q+1
       159: q+1
       160: 1
       161: 1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: q+1
       203: 1
       204: 1
       205: 1
       209: q+1
       210: q+1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       232: q+1
       233: 1
       234: 1
       235: 1
       239: q+1
       240: q+1
       241: 1
       242: 1
       244: q+1
       245: q+1
       246: q+1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: q+1
       263: 1
       264: 1
       265: 1
       269: q+1
       270: q+1
       271: 1
       272: 1
       274: q+1
       275: q+1
       276: q+1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: q+1
       292: q+1
       293: 1
       294: 1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       352: 1
       353: 1
       354: 1
       362: 1
       363: 1
       364: 1
       369: q+1
       370: 1
       371: 1
       372: 1
       376: q+1
       377: q+1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: q+1
       409: 1
       410: 1
       411: 1
       415: q+1
       416: q+1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       438: q+1
       439: 1
       440: 1
       441: 1
       445: q+1
       446: q+1
       447: 1
       448: 1
       450: q+1
       451: q+1
       452: q+1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       498: 1
       499: 1
       500: 1
       505: 1
       512: 1
       513: 1
       524: 1
       525: 1
       532: 1
       533: 1
       534: 1
       539: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       559: 1
       560: 1
       561: 1
       571: 1
       572: 1
       579: 1
       580: 1
       581: 1
       586: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       606: 1
       607: 1
       608: 1
       616: 1
       617: 1
       618: 1
       623: q+1
       624: 1
       625: 1
       626: 1
       630: q+1
       631: q+1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       665: 1
       684: 1
       685: 1
       699: 1
       711: 1
       720: 1
       721: 1
       737: 1
       738: 1
       739: 1
       744: 1
       751: 1
       752: 1
       763: 1
       772: 1
       773: 1
       789: 1
       790: 1
       791: 1
       796: 1
       803: 1
       804: 1
       815: 1
       816: 1
       823: 1
       824: 1
       825: 1
       830: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       845: 1
       846: 1
       850: 1
       851: 1
       852: 1
       886: 1
       922: 1
       941: 1
       942: 1
       956: 1
       976: 1
       995: 1
       996: 1
      1010: 1
      1022: 1
      1031: 1
      1032: 1
      1048: 1
      1049: 1
      1050: 1
      1055: 1
      1062: 1
      1063: 1
      1145: 1
      1197: 1
      1233: 1
      1252: 1
      1253: 1
      1267: 1
      1436: 1

1437:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        56: 2q+1
        57: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        64: q+1
        65: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       118: 2q+1
       119: q+1
       122: q+1
       123: q+1
       124: q+1
       127: q+1
       128: q+1
       129: 2q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       140: 2q+1
       141: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       148: q+1
       149: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       161: 2q+1
       162: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       169: q+1
       170: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: q+1
       197: q+1
       198: 2q+1
       205: 1
       206: q+1
       207: q+1
       212: q+1
       213: q+1
       214: q+1
       219: q+1
       220: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       242: 2q+1
       243: q+1
       246: q+1
       247: q+1
       248: q+1
       251: q+1
       252: q+1
       253: 2q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       272: 2q+1
       273: q+1
       276: q+1
       277: q+1
       278: q+1
       281: q+1
       282: q+1
       283: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       294: 2q+1
       295: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       319: 1
       327: 1
       328: q+1
       335: 1
       336: q+1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       364: q+1
       365: 2q+1
       372: 1
       373: q+1
       374: q+1
       379: q+1
       380: q+1
       381: q+1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       395: q+1
       403: q+1
       404: 2q+1
       411: 1
       412: q+1
       413: q+1
       418: q+1
       419: q+1
       420: q+1
       425: q+1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       448: 2q+1
       449: q+1
       452: q+1
       453: q+1
       454: q+1
       457: q+1
       458: q+1
       459: 2q+1
       461: 1
       462: q+1
       463: q+1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: q+1
       526: 1
       534: 1
       535: q+1
       542: 1
       543: q+1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: q+1
       573: 1
       581: 1
       582: q+1
       589: 1
       590: q+1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: q+1
       618: q+1
       619: 2q+1
       626: 1
       627: q+1
       628: q+1
       633: q+1
       634: q+1
       635: q+1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: q+1
       817: 1
       825: 1
       826: q+1
       833: 1
       834: q+1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       887: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1146: 1
      1198: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1437: 1

1438:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: 1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q^2+2q+1
        29: 1
        30: q^2+2q+1
        31: 1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: 1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: 1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q^2+2q+1
        69: 1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q^2+2q+1
        80: 1
        81: q^2+2q+1
        82: 1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q^2+2q+1
        93: 1
        94: q^2+2q+1
        95: 1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: 1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q^2+2q+1
       134: q+1
       135: q+1
       136: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q^2+2q+1
       153: 1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q^2+2q+1
       174: 1
       175: q^2+2q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q^2+2q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q^2+2q+1
       189: q+1
       190: q+1
       196: q+1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+2q+1
       258: q+1
       259: q+1
       260: q+1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q^2+2q+1
       288: q+1
       289: q+1
       290: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       310: q+1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: q+1
       357: q+1
       363: q+1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       395: q+1
       396: q+1
       402: q+1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+2q+1
       474: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: q+1
       526: 1
       527: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       564: q+1
       573: 1
       574: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       610: q+1
       611: q+1
       617: q+1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       713: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       765: 1
       774: 1
       775: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       808: q+1
       817: 1
       818: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       888: 1
       924: 1
       934: 1
       943: 1
       944: 1
       950: 1
       978: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1024: 1
      1033: 1
      1034: 1
      1040: 1
      1042: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1147: 1
      1199: 1
      1235: 1
      1245: 1
      1254: 1
      1255: 1
      1261: 1
      1438: 1

1439:    0: q^3+3q^2+4q+1
         1: q^3+3q^2+4q+1
         2: q^3+3q^2+4q+1
         3: q^2+4q+1
         4: q^3+3q^2+4q+1
         5: q^3+3q^2+4q+1
         6: q^3+3q^2+4q+1
         7: 2q^2+3q+1
         8: 2q+1
         9: q^2+4q+1
        10: q^2+4q+1
        11: q^2+4q+1
        12: q^2+4q+1
        13: q^3+3q^2+4q+1
        14: q^3+3q^2+4q+1
        15: q^2+4q+1
        16: q^3+3q^2+4q+1
        17: q^3+3q^2+4q+1
        18: q^2+4q+1
        19: q^3+3q^2+4q+1
        20: 2q+1
        21: 2q^2+3q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: q^2+4q+1
        26: 2q+1
        27: 2q+1
        28: q^2+4q+1
        29: q^2+4q+1
        30: q^2+4q+1
        31: q^2+4q+1
        32: q^2+4q+1
        33: q^3+3q^2+4q+1
        34: 2q^2+3q+1
        35: 2q+1
        36: q^2+4q+1
        37: q^2+4q+1
        38: q^2+4q+1
        39: q^2+4q+1
        40: q^3+3q^2+4q+1
        41: 2q^2+3q+1
        42: 2q+1
        43: q^2+4q+1
        44: q^2+4q+1
        45: q^2+4q+1
        46: q^2+4q+1
        47: q^3+3q^2+4q+1
        48: q^3+3q^2+4q+1
        49: q^2+4q+1
        50: 2q+1
        51: 2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: 2q+1
        58: 2q+1
        59: 1
        60: 2q+1
        61: 2q+1
        62: q^2+4q+1
        63: 2q+1
        64: q+1
        65: q^2+4q+1
        66: 2q+1
        67: q+1
        68: q^2+4q+1
        69: q^2+4q+1
        70: 2q+1
        71: 2q+1
        72: 2q^2+3q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        76: q^2+4q+1
        77: 2q+1
        78: 2q+1
        79: q^2+4q+1
        80: q^2+4q+1
        81: q^2+4q+1
        82: q^2+4q+1
        83: q^2+4q+1
        84: 2q+1
        85: 2q^2+3q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        89: q^2+4q+1
        90: 2q+1
        91: 2q+1
        92: q^2+4q+1
        93: q^2+4q+1
        94: q^2+4q+1
        95: q^2+4q+1
        96: q^2+4q+1
        97: q^3+3q^2+4q+1
        98: 2q^2+3q+1
        99: 2q+1
       100: q^2+4q+1
       101: q^2+4q+1
       102: q^2+4q+1
       103: q^2+4q+1
       104: 2q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: 2q+1
       113: 2q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 2q+1
       119: q+1
       120: 2q+1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: 2q+1
       126: 1
       127: q+1
       128: q+1
       129: q^2+4q+1
       130: 2q+1
       131: 1
       132: 2q+1
       133: 2q+1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 2q+1
       141: 2q+1
       142: 2q+1
       143: 1
       144: 2q+1
       145: 2q+1
       146: q^2+4q+1
       147: 2q+1
       148: q+1
       149: q^2+4q+1
       150: 2q+1
       151: q+1
       152: q^2+4q+1
       153: q^2+4q+1
       154: 2q+1
       155: 2q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 1
       165: 2q+1
       166: 2q+1
       167: q^2+4q+1
       168: 2q+1
       169: q+1
       170: q^2+4q+1
       171: 2q+1
       172: q+1
       173: q^2+4q+1
       174: q^2+4q+1
       175: 2q+1
       176: 2q+1
       177: 2q^2+3q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: q^2+4q+1
       182: 2q+1
       183: 2q+1
       184: q^2+4q+1
       185: q^2+4q+1
       186: q^2+4q+1
       187: q^2+4q+1
       188: q^2+4q+1
       190: q+1
       191: q+1
       192: q+1
       195: q+1
       198: 2q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: 2q+1
       227: 1
       228: 2q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       236: 2q+1
       237: 2q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: 2q+1
       250: 1
       251: q+1
       252: q+1
       253: q^2+4q+1
       254: 2q+1
       255: 1
       256: 2q+1
       257: 2q+1
       258: 2q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       266: 2q+1
       267: 2q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: 1
       281: q+1
       282: q+1
       283: q^2+4q+1
       284: 2q+1
       285: 1
       286: 2q+1
       287: 2q+1
       288: 2q+1
       289: 2q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 1
       298: 2q+1
       299: 2q+1
       300: q^2+4q+1
       301: 2q+1
       302: q+1
       303: q^2+4q+1
       304: 2q+1
       305: q+1
       306: q^2+4q+1
       307: q^2+4q+1
       308: 2q+1
       311: q+1
       320: 1
       321: 1
       322: 1
       325: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       362: q+1
       365: 2q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: 2q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       401: q+1
       404: 2q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: 2q+1
       433: 1
       434: 2q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       442: 2q+1
       443: 2q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: 1
       457: q+1
       458: q+1
       459: q^2+4q+1
       460: 2q+1
       461: 1
       462: 2q+1
       463: 2q+1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       493: 1
       494: 1
       495: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: q+1
       527: 1
       528: 1
       529: 1
       532: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: q+1
       574: 1
       575: 1
       576: 1
       579: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       616: q+1
       619: 2q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: 2q+1
       648: 1
       668: 1
       678: 1
       687: 1
       688: 1
       689: 1
       692: 1
       695: 1
       714: 1
       723: 1
       724: 1
       725: 1
       728: 1
       732: 1
       733: 1
       734: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       754: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       784: 1
       785: 1
       786: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       806: 1
       809: q+1
       818: 1
       819: 1
       820: 1
       823: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       889: 1
       925: 1
       935: 1
       944: 1
       945: 1
       946: 1
       949: 1
       952: 1
       979: 1
       989: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1006: 1
      1025: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1059: 1
      1060: 1
      1065: 1
      1148: 1
      1200: 1
      1236: 1
      1246: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1263: 1
      1439: 1

1440:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        57: q+1
        58: 1
        59: 1
        60: q+1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        76: q+1
        77: 1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       105: q+1
       107: q+1
       108: q+1
       112: q+1
       114: 1
       115: 1
       116: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       136: q+1
       137: q+1
       138: q+1
       141: q+1
       142: 1
       143: 1
       144: q+1
       146: q+1
       147: 1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       162: q+1
       163: 1
       164: 1
       165: q+1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: q+1
       193: q+1
       199: 1
       201: 1
       202: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       229: q+1
       231: q+1
       232: q+1
       236: q+1
       238: 1
       239: 1
       240: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: q+1
       261: q+1
       262: q+1
       266: q+1
       268: 1
       269: 1
       270: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       295: q+1
       296: 1
       297: 1
       298: q+1
       300: q+1
       301: 1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: q+1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: q+1
       360: q+1
       366: 1
       368: 1
       369: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       397: q+1
       399: q+1
       405: 1
       407: 1
       408: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       435: q+1
       437: q+1
       438: q+1
       442: q+1
       444: 1
       445: 1
       446: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       476: 1
       485: 1
       487: 1
       494: 1
       496: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: q+1
       528: 1
       530: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       566: q+1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       591: 1
       593: 1
       594: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       612: q+1
       614: q+1
       620: 1
       622: 1
       623: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       648: 1
       669: 1
       679: 1
       688: 1
       690: 1
       715: 1
       724: 1
       726: 1
       733: 1
       735: 1
       741: 1
       743: 1
       744: 1
       748: 1
       767: 1
       776: 1
       778: 1
       785: 1
       787: 1
       793: 1
       795: 1
       796: 1
       800: 1
       810: q+1
       819: 1
       821: 1
       827: 1
       829: 1
       830: 1
       835: 1
       837: 1
       838: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       852: 1
       890: 1
       926: 1
       936: 1
       945: 1
       947: 1
       980: 1
       990: 1
       999: 1
      1001: 1
      1026: 1
      1035: 1
      1037: 1
      1044: 1
      1046: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1149: 1
      1201: 1
      1237: 1
      1247: 1
      1256: 1
      1258: 1
      1440: 1

1441:    0: q^3+2q^2+2q+1
         1: q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+q+1
         9: 2q+1
        10: q^3+q^2+2q+1
        11: 2q+1
        12: q^3+q^2+2q+1
        13: q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q^2+q+1
        25: 2q+1
        26: q+1
        27: q^2+q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: q^3+q^2+2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+q+1
        36: 2q+1
        37: q^3+q^2+2q+1
        38: 2q+1
        39: q^3+q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+q+1
        43: 2q+1
        44: q^3+q^2+2q+1
        45: 2q+1
        46: q^3+q^2+2q+1
        47: q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+q^2+2q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q^2+q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q^2+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q^2+q+1
        76: 2q+1
        77: q+1
        78: q^2+q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: q^3+q^2+2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q^2+q+1
        89: 2q+1
        90: q+1
        91: q^2+q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: q^3+q^2+2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+q+1
       100: 2q+1
       101: q^3+q^2+2q+1
       102: 2q+1
       103: q^3+q^2+2q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: q^2+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       145: q^2+q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q^2+1
       152: 2q+1
       153: 2q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: q^2+q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q^2+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q^2+q+1
       181: 2q+1
       182: q+1
       183: q^2+q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: q^3+q^2+2q+1
       188: 2q+1
       192: q+1
       193: q+1
       195: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: q^2+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: q^2+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 1
       298: q+1
       299: q^2+q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q^2+1
       306: 2q+1
       307: 2q+1
       308: q+1
       313: q+1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       359: q+1
       360: q+1
       362: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       398: q+1
       399: q+1
       401: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: q^2+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       477: 1
       486: 1
       487: 1
       489: 1
       495: 1
       496: 1
       498: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       510: 1
       515: 1
       520: q+1
       529: 1
       530: 1
       532: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: q+1
       576: 1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       613: q+1
       614: q+1
       616: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       670: 1
       680: 1
       689: 1
       690: 1
       692: 1
       716: 1
       725: 1
       726: 1
       728: 1
       734: 1
       735: 1
       737: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       749: 1
       754: 1
       768: 1
       777: 1
       778: 1
       780: 1
       786: 1
       787: 1
       789: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       801: 1
       806: 1
       811: q+1
       820: 1
       821: 1
       823: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       891: 1
       927: 1
       937: 1
       946: 1
       947: 1
       949: 1
       981: 1
       991: 1
      1000: 1
      1001: 1
      1003: 1
      1027: 1
      1036: 1
      1037: 1
      1039: 1
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1060: 1
      1065: 1
      1150: 1
      1202: 1
      1238: 1
      1248: 1
      1257: 1
      1258: 1
      1260: 1
      1441: 1

1442:    0: q^3+2q^2+2q+1
         1: q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+q+1
         9: 2q+1
        10: q^3+q^2+2q+1
        11: q^3+q^2+2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q^2+q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q^2+q+1
        28: 2q+1
        29: q^3+q^2+2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+q+1
        36: 2q+1
        37: q^3+q^2+2q+1
        38: q^3+q^2+2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+q+1
        43: 2q+1
        44: q^3+q^2+2q+1
        45: q^3+q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+q^2+2q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q^2+q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q^2+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q^2+q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: q^2+q+1
        79: 2q+1
        80: q^3+q^2+2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q^2+q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: q^2+q+1
        92: 2q+1
        93: q^3+q^2+2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+q+1
       100: 2q+1
       101: q^3+q^2+2q+1
       102: q^3+q^2+2q+1
       103: 2q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: q^2+1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: q^2+q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: q^2+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q^2+q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: q^2+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q^2+q+1
       180: q+1
       181: 2q+1
       182: q+1
       183: q^2+q+1
       184: 2q+1
       185: q^3+q^2+2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       191: q+1
       194: q+1
       195: q+1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       229: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       236: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: q^2+1
       247: 1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       266: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: q^2+1
       277: 1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 1
       298: q^2+q+1
       299: q+1
       300: 2q+1
       301: q+1
       302: q^2+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       314: q+1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       358: q+1
       361: q+1
       362: q+1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       397: q+1
       400: q+1
       401: q+1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       435: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       442: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: q^2+1
       453: 1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       478: 1
       485: 1
       488: 1
       489: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       515: 1
       521: q+1
       528: 1
       531: 1
       532: 1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       568: q+1
       575: 1
       578: 1
       579: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: q+1
       615: q+1
       616: q+1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       671: 1
       681: 1
       688: 1
       691: 1
       692: 1
       717: 1
       724: 1
       727: 1
       728: 1
       733: 1
       736: 1
       737: 1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       754: 1
       769: 1
       776: 1
       779: 1
       780: 1
       785: 1
       788: 1
       789: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       806: 1
       812: q+1
       819: 1
       822: 1
       823: 1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       892: 1
       928: 1
       938: 1
       945: 1
       948: 1
       949: 1
       982: 1
       992: 1
       999: 1
      1002: 1
      1003: 1
      1028: 1
      1035: 1
      1038: 1
      1039: 1
      1044: 1
      1047: 1
      1048: 1
      1052: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1059: 1
      1065: 1
      1151: 1
      1203: 1
      1239: 1
      1249: 1
      1256: 1
      1259: 1
      1260: 1
      1442: 1

1443:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: q+1
        55: q+1
        57: q+1
        58: 1
        59: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        88: q+1
        89: q+1
        90: 1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       106: q+1
       107: q+1
       109: q+1
       113: q+1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: q+1
       136: q+1
       137: q+1
       139: q+1
       141: q+1
       142: 1
       143: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       158: q+1
       160: q+1
       162: q+1
       163: 1
       164: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: q+1
       182: 1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       192: q+1
       194: q+1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: q+1
       231: q+1
       233: q+1
       237: q+1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       260: q+1
       261: q+1
       263: q+1
       267: q+1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: q+1
       290: q+1
       291: q+1
       293: q+1
       295: q+1
       296: 1
       297: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       315: q+1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: q+1
       361: q+1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       398: q+1
       400: q+1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       436: q+1
       437: q+1
       439: q+1
       443: q+1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       479: 1
       486: 1
       488: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: q+1
       529: 1
       531: 1
       537: 1
       538: 1
       540: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       569: q+1
       576: 1
       578: 1
       584: 1
       585: 1
       587: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: q+1
       615: q+1
       621: 1
       622: 1
       624: 1
       628: 1
       629: 1
       630: 1
       632: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       648: 1
       672: 1
       682: 1
       689: 1
       691: 1
       718: 1
       725: 1
       727: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       770: 1
       777: 1
       779: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       813: q+1
       820: 1
       822: 1
       828: 1
       829: 1
       831: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       853: 1
       893: 1
       929: 1
       939: 1
       946: 1
       948: 1
       983: 1
       993: 1
      1000: 1
      1002: 1
      1029: 1
      1036: 1
      1038: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1152: 1
      1204: 1
      1240: 1
      1250: 1
      1257: 1
      1259: 1
      1443: 1

1444:    0: 2q^3+6q^2+4q+1
         1: 3q^2+3q+1
         2: q^3+5q^2+4q+1
         3: 2q^3+6q^2+4q+1
         4: 2q^3+6q^2+4q+1
         5: 2q^3+6q^2+4q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: q^3+5q^2+4q+1
         9: 3q^2+3q+1
        10: 3q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 3q^2+3q+1
        14: q^3+5q^2+4q+1
        15: 2q^3+6q^2+4q+1
        16: 3q^2+3q+1
        17: q^3+5q^2+4q+1
        18: 2q^3+6q^2+4q+1
        19: 2q^3+6q^2+4q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q+1
        26: 2q+1
        27: 3q^2+4q+1
        28: 2q^2+3q+1
        29: 2q^2+4q+1
        30: 2q^2+3q+1
        31: 2q^2+4q+1
        32: 2q^2+4q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: q^3+5q^2+4q+1
        36: 3q^2+3q+1
        37: 3q^2+4q+1
        38: q^3+4q^2+4q+1
        39: q^3+4q^2+4q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: q^3+5q^2+4q+1
        43: 3q^2+3q+1
        44: 3q^2+4q+1
        45: q^3+4q^2+4q+1
        46: q^3+4q^2+4q+1
        47: 3q^2+3q+1
        48: q^3+5q^2+4q+1
        49: 2q^3+6q^2+4q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: 2q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: 2q+1
        63: 2q+1
        64: 2q^2+4q+1
        65: 2q+1
        66: 2q+1
        67: 2q^2+4q+1
        68: q^2+3q+1
        69: q^2+4q+1
        70: 2q^2+4q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 2q+1
        77: 2q+1
        78: 3q^2+4q+1
        79: 2q^2+3q+1
        80: 2q^2+4q+1
        81: 2q^2+3q+1
        82: 2q^2+4q+1
        83: 2q^2+4q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q+1
        90: 2q+1
        91: 3q^2+4q+1
        92: 2q^2+3q+1
        93: 2q^2+4q+1
        94: 2q^2+3q+1
        95: 2q^2+4q+1
        96: 2q^2+4q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: q^3+5q^2+4q+1
       100: 3q^2+3q+1
       101: 3q^2+4q+1
       102: q^3+4q^2+4q+1
       103: q^3+4q^2+4q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: 2q+1
       119: 2q+1
       120: q+1
       121: 2q+1
       122: q^2+3q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: 2q+1
       127: 2q+1
       128: q^2+3q+1
       129: 2q+1
       130: 2q+1
       131: q^2+4q+1
       132: q^2+3q+1
       133: 2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 2q+1
       141: 2q+1
       142: q+1
       143: 2q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: 2q+1
       147: 2q+1
       148: 2q^2+4q+1
       149: 2q+1
       150: 2q+1
       151: 2q^2+4q+1
       152: q^2+3q+1
       153: q^2+4q+1
       154: 2q^2+4q+1
       157: q^2+2q+1
       158: q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: 2q+1
       162: 2q+1
       163: q+1
       164: 2q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 2q+1
       168: 2q+1
       169: 2q^2+4q+1
       170: 2q+1
       171: 2q+1
       172: 2q^2+4q+1
       173: q^2+3q+1
       174: q^2+4q+1
       175: 2q^2+4q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: 2q+1
       182: 2q+1
       183: 3q^2+4q+1
       184: 2q^2+3q+1
       185: 2q^2+4q+1
       186: 2q^2+3q+1
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       227: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 2q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: 2q+1
       243: 2q+1
       244: q+1
       245: 2q+1
       246: q^2+3q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q^2+3q+1
       253: 2q+1
       254: 2q+1
       255: q^2+4q+1
       256: q^2+3q+1
       257: 2q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: 2q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: 2q+1
       273: 2q+1
       274: q+1
       275: 2q+1
       276: q^2+3q+1
       277: 2q+1
       278: 2q+1
       279: q+1
       280: 2q+1
       281: 2q+1
       282: q^2+3q+1
       283: 2q+1
       284: 2q+1
       285: q^2+4q+1
       286: q^2+3q+1
       287: 2q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: 2q+1
       295: 2q+1
       296: q+1
       297: 2q+1
       298: q^2+3q+1
       299: q^2+3q+1
       300: 2q+1
       301: 2q+1
       302: 2q^2+4q+1
       303: 2q+1
       304: 2q+1
       305: 2q^2+4q+1
       306: q^2+3q+1
       307: q^2+4q+1
       308: 2q^2+4q+1
       316: q+1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: 1
       351: q+1
       354: q+1
       355: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 2q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       387: 2q+1
       388: q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q+1
       394: 2q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 2q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: 2q+1
       427: q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q+1
       433: 2q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: 2q+1
       444: q+1
       445: 1
       446: q+1
       447: q+1
       448: 2q+1
       449: 2q+1
       450: q+1
       451: 2q+1
       452: q^2+3q+1
       453: 2q+1
       454: 2q+1
       455: q+1
       456: 2q+1
       457: 2q+1
       458: q^2+3q+1
       459: 2q+1
       460: 2q+1
       461: q^2+4q+1
       462: q^2+3q+1
       463: 2q+1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       496: 1
       497: 1
       498: 1
       499: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       523: q+1
       530: 1
       531: 1
       532: 1
       533: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: 1
       558: q+1
       561: q+1
       562: q+1
       570: q+1
       577: 1
       578: 1
       579: 1
       580: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: 1
       605: q+1
       608: q+1
       609: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 2q+1
       629: q+1
       630: 1
       631: q+1
       632: q+1
       633: q+1
       636: q+1
       637: 1
       638: q+1
       639: q+1
       640: q+1
       641: 2q+1
       642: q+1
       643: 2q+1
       644: 2q+1
       645: 2q+1
       646: q+1
       648: 2q+1
       673: 1
       683: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       719: 1
       726: 1
       727: 1
       728: 1
       729: 1
       735: 1
       736: 1
       737: 1
       738: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       754: 1
       771: 1
       778: 1
       779: 1
       780: 1
       781: 1
       787: 1
       788: 1
       789: 1
       790: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       806: 1
       814: q+1
       821: 1
       822: 1
       823: 1
       824: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: 1
       849: q+1
       852: q+1
       853: q+1
       894: 1
       930: 1
       940: 1
       947: 1
       948: 1
       949: 1
       950: 1
       959: 1
       984: 1
       994: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1013: 1
      1030: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1065: 1
      1153: 1
      1205: 1
      1241: 1
      1251: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1270: 1
      1444: 1

1445:    0: q^2+2q+1
         1: q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 2q+1
         9: q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q+1
        14: q^2+2q+1
        15: 2q+1
        16: q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: 1
        27: 2q+1
        28: q+1
        29: 2q+1
        30: q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: q+1
        35: 2q+1
        36: q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q+1
        41: q+1
        42: 2q+1
        43: q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q+1
        48: q^2+2q+1
        49: 2q+1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        58: 1
        59: 1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q+1
        68: q+1
        69: 2q+1
        70: q+1
        72: q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        77: 1
        78: 2q+1
        79: q+1
        80: 2q+1
        81: q+1
        82: 2q+1
        83: 2q+1
        85: q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        90: 1
        91: 2q+1
        92: q+1
        93: 2q+1
        94: q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       115: 1
       116: 1
       117: 1
       118: 2q+1
       120: 1
       121: 1
       122: q+1
       123: q+1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: q+1
       130: 1
       131: 1
       132: q+1
       133: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 2q+1
       142: 1
       143: 1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: q+1
       153: 2q+1
       154: q+1
       158: q+1
       159: q+1
       160: q+1
       161: 2q+1
       163: 1
       164: 1
       165: 2q+1
       166: 2q+1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: q+1
       174: 2q+1
       175: q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       182: 1
       183: 2q+1
       184: q+1
       185: 2q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       195: q+1
       196: q+1
       197: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       216: 1
       217: 1
       218: 1
       219: q+1
       221: 1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       239: 1
       240: 1
       241: 1
       242: 2q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: q+1
       254: 1
       255: 1
       256: q+1
       257: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       269: 1
       270: 1
       271: 1
       272: 2q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       279: 1
       280: 1
       281: q+1
       282: q+1
       283: q+1
       284: 1
       285: 1
       286: q+1
       287: q+1
       291: q+1
       292: q+1
       293: q+1
       294: 2q+1
       296: 1
       297: 1
       298: 2q+1
       299: 2q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: 2q+1
       308: q+1
       317: q+1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       354: 1
       355: 1
       362: q+1
       363: q+1
       364: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       383: 1
       384: 1
       385: 1
       386: q+1
       388: 1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       401: q+1
       402: q+1
       403: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       422: 1
       423: 1
       424: 1
       425: q+1
       427: 1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       445: 1
       446: 1
       447: 1
       448: 2q+1
       450: 1
       451: 1
       452: q+1
       453: q+1
       455: 1
       456: 1
       457: q+1
       458: q+1
       459: q+1
       460: 1
       461: 1
       462: q+1
       463: q+1
       481: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       524: q+1
       532: 1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       556: 1
       557: 1
       561: 1
       562: 1
       571: q+1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       603: 1
       604: 1
       608: 1
       609: 1
       616: q+1
       617: q+1
       618: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       637: 1
       638: 1
       639: 1
       640: q+1
       642: 1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       674: 1
       684: 1
       692: 1
       693: 1
       694: 1
       720: 1
       728: 1
       729: 1
       730: 1
       737: 1
       738: 1
       739: 1
       744: 1
       745: 1
       746: 1
       747: 1
       754: 1
       772: 1
       780: 1
       781: 1
       782: 1
       789: 1
       790: 1
       791: 1
       796: 1
       797: 1
       798: 1
       799: 1
       806: 1
       815: q+1
       823: 1
       824: 1
       825: 1
       830: 1
       831: 1
       832: 1
       833: 1
       838: 1
       839: 1
       840: 1
       841: 1
       845: 1
       846: 1
       847: 1
       848: 1
       852: 1
       853: 1
       895: 1
       931: 1
       941: 1
       949: 1
       950: 1
       951: 1
       985: 1
       995: 1
      1003: 1
      1004: 1
      1005: 1
      1031: 1
      1039: 1
      1040: 1
      1041: 1
      1048: 1
      1049: 1
      1050: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1065: 1
      1154: 1
      1206: 1
      1242: 1
      1252: 1
      1260: 1
      1261: 1
      1262: 1
      1445: 1

1446:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        63: 2q+1
        64: q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       110: 2q+1
       111: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       121: q+1
       122: q+1
       123: q+1
       126: q+1
       127: q+1
       128: q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       147: 2q+1
       148: q+1
       150: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       168: 2q+1
       169: q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       196: q+1
       197: q+1
       204: 2q+1
       205: 1
       210: q+1
       211: q+1
       212: q+1
       217: q+1
       218: q+1
       219: q+1
       222: 1
       223: 1
       224: 1
       226: q+1
       227: 1
       234: 2q+1
       235: q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       245: q+1
       246: q+1
       247: q+1
       250: q+1
       251: q+1
       252: q+1
       254: 2q+1
       255: 1
       256: q+1
       257: q+1
       264: 2q+1
       265: q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       275: q+1
       276: q+1
       277: q+1
       280: q+1
       281: q+1
       282: q+1
       284: 2q+1
       285: 1
       286: q+1
       287: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       301: 2q+1
       302: q+1
       304: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       318: q+1
       326: 1
       327: 1
       334: q+1
       335: 1
       342: q+1
       343: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       363: q+1
       364: q+1
       371: 2q+1
       372: 1
       377: q+1
       378: q+1
       379: q+1
       384: q+1
       385: q+1
       386: q+1
       389: 1
       390: 1
       391: 1
       393: q+1
       394: 1
       402: q+1
       403: q+1
       410: 2q+1
       411: 1
       416: q+1
       417: q+1
       418: q+1
       423: q+1
       424: q+1
       425: q+1
       428: 1
       429: 1
       430: 1
       432: q+1
       433: 1
       440: 2q+1
       441: q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       451: q+1
       452: q+1
       453: q+1
       456: q+1
       457: q+1
       458: q+1
       460: 2q+1
       461: 1
       462: q+1
       463: q+1
       482: 1
       490: 1
       491: 1
       499: 1
       500: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       525: q+1
       533: 1
       534: 1
       541: q+1
       542: 1
       549: q+1
       550: 1
       555: 1
       556: 1
       557: 1
       560: 1
       561: 1
       562: 1
       572: q+1
       580: 1
       581: 1
       588: q+1
       589: 1
       596: q+1
       597: 1
       602: 1
       603: 1
       604: 1
       607: 1
       608: 1
       609: 1
       617: q+1
       618: q+1
       625: 2q+1
       626: 1
       631: q+1
       632: q+1
       633: q+1
       638: q+1
       639: q+1
       640: q+1
       643: 1
       644: 1
       645: 1
       647: q+1
       648: 1
       675: 1
       685: 1
       693: 1
       694: 1
       701: 1
       721: 1
       729: 1
       730: 1
       738: 1
       739: 1
       746: 1
       747: 1
       752: 1
       753: 1
       754: 1
       773: 1
       781: 1
       782: 1
       790: 1
       791: 1
       798: 1
       799: 1
       804: 1
       805: 1
       806: 1
       816: q+1
       824: 1
       825: 1
       832: q+1
       833: 1
       840: q+1
       841: 1
       846: 1
       847: 1
       848: 1
       851: 1
       852: 1
       853: 1
       896: 1
       932: 1
       942: 1
       950: 1
       951: 1
       958: 1
       986: 1
       996: 1
      1004: 1
      1005: 1
      1012: 1
      1032: 1
      1040: 1
      1041: 1
      1049: 1
      1050: 1
      1057: 1
      1058: 1
      1063: 1
      1064: 1
      1065: 1
      1155: 1
      1207: 1
      1243: 1
      1253: 1
      1261: 1
      1262: 1
      1269: 1
      1446: 1

1447:    0: q^2+1
         1: q^2+1
         2: 1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: 1
         8: 1
         9: q^2+1
        10: 1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: 1
        15: q^2+1
        16: q^2+1
        17: 1
        18: q^2+1
        19: q^2+1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: q^2+1
        29: 1
        30: q^2+1
        31: 1
        32: q^2+1
        33: 1
        35: 1
        36: q^2+1
        37: 1
        38: q^2+1
        39: q^2+1
        40: 1
        42: 1
        43: q^2+1
        44: 1
        45: q^2+1
        46: q^2+1
        47: q^2+1
        48: 1
        49: q^2+1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: q^2+1
        69: 1
        70: q^2+1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: q^2+1
        80: 1
        81: q^2+1
        82: 1
        83: q^2+1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: q^2+1
        93: 1
        94: q^2+1
        95: 1
        96: q^2+1
        97: 1
        99: 1
       100: q^2+1
       101: 1
       102: q^2+1
       103: q^2+1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: q^2+1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q^2+1
       153: 1
       154: q^2+1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q^2+1
       174: 1
       175: q^2+1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: q^2+1
       185: 1
       186: q^2+1
       187: 1
       188: q^2+1
       189: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q^2+1
       257: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: q^2+1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q^2+1
       307: 1
       308: q^2+1
       319: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q^2+1
       463: 1
       483: 1
       492: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       686: 1
       695: 1
       702: 1
       722: 1
       731: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       774: 1
       783: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       897: 1
       943: 1
       952: 1
       959: 1
       997: 1
      1006: 1
      1013: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1156: 1
      1208: 1
      1254: 1
      1263: 1
      1270: 1
      1447: 1

1448:    0: q^2+2q+1
         1: q^2+2q+1
         2: q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q+1
         8: 1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q+1
        35: 1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q+1
        49: q^2+2q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q^2+2q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: 1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: 1
       110: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q^2+2q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       190: 1
       198: 1
       199: 1
       200: 1
       204: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       264: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       320: 1
       328: 1
       329: 1
       330: 1
       334: 1
       336: 1
       337: 1
       338: 1
       342: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: 1
       365: 1
       366: 1
       367: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: 1
       404: 1
       405: 1
       406: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       440: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       484: 1
       493: 1
       501: 1
       502: 1
       503: 1
       507: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       527: 1
       535: 1
       536: 1
       537: 1
       541: 1
       543: 1
       544: 1
       545: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       574: 1
       582: 1
       583: 1
       584: 1
       588: 1
       590: 1
       591: 1
       592: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: 1
       619: 1
       620: 1
       621: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       687: 1
       695: 1
       696: 1
       697: 1
       701: 1
       723: 1
       732: 1
       740: 1
       741: 1
       742: 1
       746: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       775: 1
       784: 1
       792: 1
       793: 1
       794: 1
       798: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       818: 1
       826: 1
       827: 1
       828: 1
       832: 1
       834: 1
       835: 1
       836: 1
       840: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       898: 1
       944: 1
       952: 1
       953: 1
       954: 1
       958: 1
       998: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1034: 1
      1043: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1157: 1
      1209: 1
      1255: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1448: 1

1449:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       191: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       321: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       358: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       397: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: q+1
       432: q+1
       433: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       485: 1
       494: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       528: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       575: 1
       583: 1
       585: 1
       586: 1
       591: 1
       593: 1
       594: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       612: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       647: q+1
       648: 1
       688: 1
       696: 1
       698: 1
       699: 1
       724: 1
       733: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       776: 1
       785: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       819: 1
       827: 1
       829: 1
       830: 1
       835: 1
       837: 1
       838: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       899: 1
       945: 1
       953: 1
       955: 1
       956: 1
       999: 1
      1007: 1
      1009: 1
      1010: 1
      1035: 1
      1044: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1158: 1
      1210: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1449: 1

1450:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: q+1
        59: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: q+1
       121: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: q+1
       143: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: q+1
       164: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       192: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       243: 1
       244: q+1
       245: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: q+1
       275: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: q+1
       297: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       322: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       359: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       381: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       398: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       449: 1
       450: q+1
       451: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       486: 1
       495: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       529: 1
       537: 1
       538: 1
       540: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: q+1
       560: 1
       562: 1
       576: 1
       584: 1
       585: 1
       587: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       613: 1
       621: 1
       622: 1
       624: 1
       628: 1
       629: 1
       630: 1
       632: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       689: 1
       697: 1
       698: 1
       700: 1
       725: 1
       734: 1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       777: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       820: 1
       828: 1
       829: 1
       831: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: q+1
       851: 1
       853: 1
       900: 1
       946: 1
       954: 1
       955: 1
       957: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1036: 1
      1045: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1159: 1
      1211: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1450: 1

1451:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       108: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       193: 1
       201: 1
       202: 1
       208: 1
       209: 1
       210: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       231: 1
       232: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       323: 1
       331: 1
       332: 1
       339: 1
       340: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       360: 1
       368: 1
       369: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: 1
       407: 1
       408: 1
       414: 1
       415: 1
       416: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       437: 1
       438: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       487: 1
       496: 1
       504: 1
       505: 1
       511: 1
       512: 1
       513: 1
       530: 1
       538: 1
       539: 1
       546: 1
       547: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       577: 1
       585: 1
       586: 1
       593: 1
       594: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       614: 1
       622: 1
       623: 1
       629: 1
       630: 1
       631: 1
       636: 1
       637: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       690: 1
       698: 1
       699: 1
       726: 1
       735: 1
       743: 1
       744: 1
       750: 1
       751: 1
       752: 1
       778: 1
       787: 1
       795: 1
       796: 1
       802: 1
       803: 1
       804: 1
       821: 1
       829: 1
       830: 1
       837: 1
       838: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       901: 1
       947: 1
       955: 1
       956: 1
      1001: 1
      1009: 1
      1010: 1
      1037: 1
      1046: 1
      1054: 1
      1055: 1
      1061: 1
      1062: 1
      1063: 1
      1160: 1
      1212: 1
      1258: 1
      1266: 1
      1267: 1
      1451: 1

1452:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       109: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       194: 1
       201: 1
       203: 1
       208: 1
       209: 1
       211: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       231: 1
       233: 1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       263: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       324: 1
       331: 1
       333: 1
       339: 1
       341: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       361: 1
       368: 1
       370: 1
       375: 1
       376: 1
       378: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       400: 1
       407: 1
       409: 1
       414: 1
       415: 1
       417: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       439: 1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       488: 1
       497: 1
       504: 1
       506: 1
       511: 1
       512: 1
       514: 1
       531: 1
       538: 1
       540: 1
       546: 1
       548: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       578: 1
       585: 1
       587: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       615: 1
       622: 1
       624: 1
       629: 1
       630: 1
       632: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       691: 1
       698: 1
       700: 1
       727: 1
       736: 1
       743: 1
       745: 1
       750: 1
       751: 1
       753: 1
       779: 1
       788: 1
       795: 1
       797: 1
       802: 1
       803: 1
       805: 1
       822: 1
       829: 1
       831: 1
       837: 1
       839: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       902: 1
       948: 1
       955: 1
       957: 1
      1002: 1
      1009: 1
      1011: 1
      1038: 1
      1047: 1
      1054: 1
      1056: 1
      1061: 1
      1062: 1
      1064: 1
      1161: 1
      1213: 1
      1259: 1
      1266: 1
      1268: 1
      1452: 1

1453:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        53: 1
        54: 1
        55: 1
        56: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       108: 1
       109: 1
       110: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       137: 1
       138: 1
       139: 1
       140: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       158: 1
       159: 1
       160: 1
       161: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       195: 1
       202: 1
       203: 1
       204: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       232: 1
       233: 1
       234: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       262: 1
       263: 1
       264: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       291: 1
       292: 1
       293: 1
       294: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       325: 1
       332: 1
       333: 1
       334: 1
       340: 1
       341: 1
       342: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       362: 1
       369: 1
       370: 1
       371: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       401: 1
       408: 1
       409: 1
       410: 1
       415: 1
       416: 1
       417: 1
       418: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       438: 1
       439: 1
       440: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       489: 1
       498: 1
       505: 1
       506: 1
       507: 1
       512: 1
       513: 1
       514: 1
       515: 1
       532: 1
       539: 1
       540: 1
       541: 1
       547: 1
       548: 1
       549: 1
       554: 1
       555: 1
       556: 1
       557: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       579: 1
       586: 1
       587: 1
       588: 1
       594: 1
       595: 1
       596: 1
       601: 1
       602: 1
       603: 1
       604: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       616: 1
       623: 1
       624: 1
       625: 1
       630: 1
       631: 1
       632: 1
       633: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       692: 1
       699: 1
       700: 1
       701: 1
       728: 1
       737: 1
       744: 1
       745: 1
       746: 1
       751: 1
       752: 1
       753: 1
       754: 1
       780: 1
       789: 1
       796: 1
       797: 1
       798: 1
       803: 1
       804: 1
       805: 1
       806: 1
       823: 1
       830: 1
       831: 1
       832: 1
       838: 1
       839: 1
       840: 1
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       903: 1
       949: 1
       956: 1
       957: 1
       958: 1
      1003: 1
      1010: 1
      1011: 1
      1012: 1
      1039: 1
      1048: 1
      1055: 1
      1056: 1
      1057: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1162: 1
      1214: 1
      1260: 1
      1267: 1
      1268: 1
      1269: 1
      1453: 1

1454:    0: q^2+1
         1: q^2+1
         2: 1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         7: 1
         8: 1
         9: q^2+1
        10: 1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: 1
        15: q^2+1
        16: q^2+1
        17: 1
        18: q^2+1
        19: q^2+1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: q^2+1
        29: 1
        30: q^2+1
        31: 1
        32: q^2+1
        34: 1
        35: 1
        36: q^2+1
        37: 1
        38: q^2+1
        39: q^2+1
        41: 1
        42: 1
        43: q^2+1
        44: 1
        45: q^2+1
        46: q^2+1
        47: q^2+1
        48: 1
        49: q^2+1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: q^2+1
        69: 1
        70: q^2+1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: q^2+1
        80: 1
        81: q^2+1
        82: 1
        83: q^2+1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: q^2+1
        93: 1
        94: q^2+1
        95: 1
        96: q^2+1
        98: 1
        99: 1
       100: q^2+1
       101: 1
       102: q^2+1
       103: q^2+1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: q^2+1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: q^2+1
       153: 1
       154: q^2+1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: q^2+1
       174: 1
       175: q^2+1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: q^2+1
       185: 1
       186: q^2+1
       187: 1
       188: q^2+1
       196: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: q^2+1
       257: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       281: 1
       282: 1
       284: 1
       285: 1
       286: q^2+1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: q^2+1
       307: 1
       308: q^2+1
       326: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       363: 1
       371: 1
       372: 1
       377: 1
       378: 1
       379: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       391: 1
       393: 1
       394: 1
       402: 1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       456: 1
       457: 1
       458: 1
       460: 1
       461: 1
       462: q^2+1
       463: 1
       490: 1
       499: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       533: 1
       541: 1
       542: 1
       549: 1
       550: 1
       555: 1
       556: 1
       557: 1
       560: 1
       561: 1
       562: 1
       580: 1
       588: 1
       589: 1
       596: 1
       597: 1
       602: 1
       603: 1
       604: 1
       607: 1
       608: 1
       609: 1
       617: 1
       625: 1
       626: 1
       631: 1
       632: 1
       633: 1
       638: 1
       639: 1
       640: 1
       643: 1
       644: 1
       645: 1
       647: 1
       648: 1
       693: 1
       701: 1
       702: 1
       729: 1
       738: 1
       746: 1
       747: 1
       752: 1
       753: 1
       754: 1
       781: 1
       790: 1
       798: 1
       799: 1
       804: 1
       805: 1
       806: 1
       824: 1
       832: 1
       833: 1
       840: 1
       841: 1
       846: 1
       847: 1
       848: 1
       851: 1
       852: 1
       853: 1
       904: 1
       950: 1
       958: 1
       959: 1
      1004: 1
      1012: 1
      1013: 1
      1040: 1
      1049: 1
      1057: 1
      1058: 1
      1063: 1
      1064: 1
      1065: 1
      1163: 1
      1215: 1
      1261: 1
      1269: 1
      1270: 1
      1454: 1

1455:    0: 1
         2: 1
         3: 1
         4: 1
         5: 1
         8: 1
        10: 1
        11: 1
        12: 1
        14: 1
        15: 1
        17: 1
        18: 1
        19: 1
        23: 1
        24: 1
        27: 1
        29: 1
        31: 1
        32: 1
        35: 1
        37: 1
        38: 1
        39: 1
        42: 1
        44: 1
        45: 1
        46: 1
        48: 1
        49: 1
        56: 1
        60: 1
        61: 1
        64: 1
        67: 1
        69: 1
        70: 1
        74: 1
        75: 1
        78: 1
        80: 1
        82: 1
        83: 1
        87: 1
        88: 1
        91: 1
        93: 1
        95: 1
        96: 1
        99: 1
       101: 1
       102: 1
       103: 1
       111: 1
       118: 1
       122: 1
       123: 1
       127: 1
       128: 1
       131: 1
       133: 1
       140: 1
       144: 1
       145: 1
       148: 1
       151: 1
       153: 1
       154: 1
       161: 1
       165: 1
       166: 1
       169: 1
       172: 1
       174: 1
       175: 1
       179: 1
       180: 1
       183: 1
       185: 1
       187: 1
       188: 1
       197: 1
       205: 1
       212: 1
       219: 1
       223: 1
       224: 1
       227: 1
       235: 1
       242: 1
       246: 1
       247: 1
       251: 1
       252: 1
       255: 1
       257: 1
       265: 1
       272: 1
       276: 1
       277: 1
       281: 1
       282: 1
       285: 1
       287: 1
       294: 1
       298: 1
       299: 1
       302: 1
       305: 1
       307: 1
       308: 1
       327: 1
       335: 1
       343: 1
       350: 1
       354: 1
       355: 1
       364: 1
       372: 1
       379: 1
       386: 1
       390: 1
       391: 1
       394: 1
       403: 1
       411: 1
       418: 1
       425: 1
       429: 1
       430: 1
       433: 1
       441: 1
       448: 1
       452: 1
       453: 1
       457: 1
       458: 1
       461: 1
       463: 1
       491: 1
       500: 1
       508: 1
       515: 1
       534: 1
       542: 1
       550: 1
       557: 1
       561: 1
       562: 1
       581: 1
       589: 1
       597: 1
       604: 1
       608: 1
       609: 1
       618: 1
       626: 1
       633: 1
       640: 1
       644: 1
       645: 1
       648: 1
       694: 1
       702: 1
       730: 1
       739: 1
       747: 1
       754: 1
       782: 1
       791: 1
       799: 1
       806: 1
       825: 1
       833: 1
       841: 1
       848: 1
       852: 1
       853: 1
       905: 1
       951: 1
       959: 1
      1005: 1
      1013: 1
      1041: 1
      1050: 1
      1058: 1
      1065: 1
      1164: 1
      1216: 1
      1262: 1
      1270: 1
      1455: 1

1456:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^3+2q^2+2q+1
        53: q^2+q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+q+1
       108: q+1
       109: q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: q+1
       113: q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q^2+2q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q^2+q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       210: q+1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: q+1
       262: q+1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: q+1
       310: q^2+2q+1
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: q+1
       382: q+1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: q+1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: 1
       478: 1
       479: q+1
       480: q+1
       482: q+1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: q+1
       565: 1
       566: q+1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       649: q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: q+1
       657: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: q+1
       719: 1
       721: 1
       731: 1
       732: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       836: 1
       844: 1
       849: 1
       850: 1
       851: 1
       854: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       942: 1
       953: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1032: 1
      1061: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1074: 1
      1094: 1
      1103: 1
      1104: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1227: 1
      1271: 1
      1272: 1
      1273: 1
      1301: 1
      1311: 1
      1357: 1
      1404: 1
      1456: 1

1457:    0: 4q^4+14q^3+16q^2+7q+1
         1: q^4+9q^3+15q^2+7q+1
         2: 4q^4+14q^3+16q^2+7q+1
         3: q^4+9q^3+15q^2+7q+1
         4: q^4+9q^3+14q^2+7q+1
         5: q^4+9q^3+14q^2+7q+1
         6: q^4+9q^3+15q^2+7q+1
         7: q^4+9q^3+15q^2+7q+1
         8: q^4+9q^3+15q^2+7q+1
         9: 5q^3+14q^2+7q+1
        10: q^4+9q^3+15q^2+7q+1
        11: 3q^3+11q^2+7q+1
        12: 3q^3+11q^2+7q+1
        13: 5q^3+13q^2+7q+1
        14: q^4+9q^3+14q^2+7q+1
        15: 3q^3+11q^2+7q+1
        16: 5q^3+13q^2+7q+1
        17: q^4+9q^3+14q^2+7q+1
        18: 3q^3+11q^2+7q+1
        19: 7q^3+13q^2+7q+1
        20: 2q^3+9q^2+6q+1
        21: q^4+9q^3+15q^2+7q+1
        22: 5q^3+14q^2+7q+1
        23: 3q^3+11q^2+7q+1
        24: 3q^3+11q^2+7q+1
        25: 5q^3+14q^2+7q+1
        26: 2q^3+9q^2+6q+1
        27: q^4+9q^3+15q^2+7q+1
        28: q^3+10q^2+7q+1
        29: 3q^3+11q^2+7q+1
        30: q^3+10q^2+7q+1
        31: 3q^3+11q^2+7q+1
        32: q^3+9q^2+7q+1
        33: 5q^3+13q^2+7q+1
        34: 5q^3+13q^2+7q+1
        35: 3q^3+11q^2+7q+1
        36: q^3+10q^2+7q+1
        37: 3q^3+11q^2+7q+1
        38: 4q^2+5q+1
        39: 2q^3+9q^2+7q+1
        40: 5q^3+13q^2+7q+1
        41: 5q^3+13q^2+7q+1
        42: 3q^3+11q^2+7q+1
        43: q^3+10q^2+7q+1
        44: 3q^3+11q^2+7q+1
        45: 2q^3+9q^2+7q+1
        46: 4q^2+5q+1
        47: 4q^3+12q^2+7q+1
        48: 7q^3+13q^2+7q+1
        49: q^3+9q^2+7q+1
        50: 4q^2+4q+1
        51: 4q^2+4q+1
        52: 2q^3+9q^2+6q+1
        53: 5q^3+14q^2+7q+1
        54: q^3+10q^2+7q+1
        55: q^3+10q^2+7q+1
        56: q^3+9q^2+7q+1
        57: 2q^3+9q^2+6q+1
        58: 2q^3+9q^2+6q+1
        59: 2q^3+9q^2+6q+1
        60: 3q^3+11q^2+7q+1
        61: 3q^3+11q^2+7q+1
        62: q^3+10q^2+7q+1
        63: 6q^2+6q+1
        64: q^3+5q^2+6q+1
        65: q^3+10q^2+7q+1
        66: 6q^2+6q+1
        67: q^3+5q^2+6q+1
        68: 8q^2+7q+1
        69: q^3+9q^2+7q+1
        70: 5q^2+7q+1
        71: 6q^2+6q+1
        72: 5q^3+13q^2+7q+1
        73: q^3+10q^2+7q+1
        74: 4q^2+5q+1
        75: 2q^3+9q^2+7q+1
        76: q^3+10q^2+7q+1
        77: 4q^2+4q+1
        78: 3q^3+11q^2+7q+1
        79: 3q^2+5q+1
        80: 4q^2+5q+1
        81: q^3+8q^2+7q+1
        82: 2q^3+9q^2+7q+1
        83: 3q^2+5q+1
        84: 6q^2+6q+1
        85: 5q^3+13q^2+7q+1
        86: q^3+10q^2+7q+1
        87: 2q^3+9q^2+7q+1
        88: 4q^2+5q+1
        89: q^3+10q^2+7q+1
        90: 4q^2+4q+1
        91: 3q^3+11q^2+7q+1
        92: q^3+8q^2+7q+1
        93: 2q^3+9q^2+7q+1
        94: 3q^2+5q+1
        95: 4q^2+5q+1
        96: 3q^2+5q+1
        97: 4q^3+12q^2+7q+1
        98: 4q^3+12q^2+7q+1
        99: q^3+9q^2+7q+1
       100: 8q^2+7q+1
       101: q^3+9q^2+7q+1
       102: 3q^2+5q+1
       103: 3q^2+5q+1
       104: 2q^2+3q+1
       105: 4q^2+4q+1
       106: 4q^2+4q+1
       107: 2q^3+9q^2+6q+1
       108: q^3+10q^2+7q+1
       109: q^3+10q^2+7q+1
       110: 8q^2+7q+1
       111: 5q^2+7q+1
       112: 4q^2+4q+1
       113: 4q^2+4q+1
       114: q^3+5q^2+5q+1
       115: 2q^3+9q^2+6q+1
       116: 6q^2+6q+1
       117: 6q^2+6q+1
       118: q^3+9q^2+7q+1
       119: 2q^2+5q+1
       120: 6q^2+6q+1
       121: 2q^2+5q+1
       122: q^3+5q^2+6q+1
       123: q^2+3q+1
       124: 2q^2+5q+1
       125: 6q^2+6q+1
       126: 2q^2+5q+1
       127: q^2+3q+1
       128: q^3+5q^2+6q+1
       129: 8q^2+7q+1
       130: 5q^2+6q+1
       131: 2q^2+6q+1
       132: 5q^2+7q+1
       133: 5q^2+7q+1
       134: q^2+3q+1
       135: 3q^2+4q+1
       136: 6q^2+6q+1
       137: q^3+10q^2+7q+1
       138: 3q^2+5q+1
       139: q^3+8q^2+7q+1
       140: 3q^2+5q+1
       141: 6q^2+6q+1
       142: 4q^2+4q+1
       143: 4q^2+4q+1
       144: 4q^2+5q+1
       145: 2q^3+9q^2+7q+1
       146: 3q^2+5q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: q^3+8q^2+7q+1
       150: 3q^2+4q+1
       151: q^3+5q^2+6q+1
       152: 2q^2+5q+1
       153: 3q^2+5q+1
       154: q^2+5q+1
       155: 3q^2+4q+1
       156: q^2+3q+1
       157: 6q^2+6q+1
       158: q^3+10q^2+7q+1
       159: q^3+8q^2+7q+1
       160: 3q^2+5q+1
       161: 3q^2+5q+1
       162: 6q^2+6q+1
       163: 4q^2+4q+1
       164: 4q^2+4q+1
       165: 2q^3+9q^2+7q+1
       166: 4q^2+5q+1
       167: q^3+8q^2+7q+1
       168: 3q^2+4q+1
       169: q^3+5q^2+6q+1
       170: 3q^2+5q+1
       171: q^2+3q+1
       172: q^2+3q+1
       173: 2q^2+5q+1
       174: 3q^2+5q+1
       175: q^2+5q+1
       176: 5q^2+6q+1
       177: 4q^3+12q^2+7q+1
       178: 8q^2+7q+1
       179: 3q^2+5q+1
       180: 3q^2+5q+1
       181: 8q^2+7q+1
       182: 2q^2+3q+1
       183: q^3+9q^2+7q+1
       184: 2q^2+5q+1
       185: 3q^2+5q+1
       186: 2q^2+5q+1
       187: 3q^2+5q+1
       188: q^2+4q+1
       189: q^2+2q+1
       190: 2q^2+3q+1
       191: 4q^2+4q+1
       192: 4q^2+4q+1
       193: 2q^2+5q+1
       194: 2q^2+5q+1
       195: 8q^2+7q+1
       196: 5q^2+7q+1
       197: 5q^2+7q+1
       198: 2q^2+3q+1
       199: 2q^2+3q+1
       200: 2q^2+3q+1
       201: q^3+5q^2+5q+1
       202: 6q^2+6q+1
       203: 6q^2+6q+1
       204: 5q^2+6q+1
       205: 2q^2+6q+1
       206: q^2+3q+1
       207: 2q+1
       208: 4q+1
       209: 2q^2+5q+1
       210: 2q^2+5q+1
       211: 2q+1
       212: q^2+3q+1
       213: 2q+1
       214: q^2+3q+1
       215: 4q+1
       216: 2q^2+5q+1
       217: 2q+1
       218: 2q^2+5q+1
       219: q^2+3q+1
       220: q^2+5q+1
       221: 5q^2+6q+1
       222: q^2+5q+1
       223: 3q+1
       224: 3q+1
       225: 5q^2+7q+1
       226: q^2+2q+1
       227: 2q^2+6q+1
       228: 2q+1
       229: q^2+3q+1
       230: 3q^2+4q+1
       231: 6q^2+6q+1
       232: 3q^2+5q+1
       233: q^3+8q^2+7q+1
       234: 2q^2+5q+1
       235: q^2+5q+1
       236: q^2+3q+1
       237: 3q^2+4q+1
       238: 2q^2+3q+1
       239: 4q^2+4q+1
       240: q^2+3q+1
       241: 3q^2+4q+1
       242: 3q^2+5q+1
       243: 2q+1
       244: q^2+3q+1
       245: 2q+1
       246: q^2+3q+1
       248: 2q^2+5q+1
       249: 3q^2+4q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^3+5q^2+6q+1
       253: 2q^2+5q+1
       254: q^2+3q+1
       255: 3q+1
       256: q^2+5q+1
       257: q^2+5q+1
       258: 2q+1
       259: 3q^2+4q+1
       260: q^2+3q+1
       261: 6q^2+6q+1
       262: q^3+8q^2+7q+1
       263: 3q^2+5q+1
       264: 2q^2+5q+1
       265: q^2+5q+1
       266: 3q^2+4q+1
       267: q^2+3q+1
       268: 2q^2+3q+1
       269: 4q^2+4q+1
       270: 3q^2+4q+1
       271: q^2+3q+1
       272: 3q^2+5q+1
       273: 2q^2+5q+1
       274: 3q^2+4q+1
       275: q^2+3q+1
       276: q^3+5q^2+6q+1
       277: q^2+3q+1
       278: 2q+1
       279: q^2+3q+1
       280: 2q+1
       282: q^2+3q+1
       283: 2q^2+5q+1
       284: q^2+3q+1
       285: 3q+1
       286: q^2+5q+1
       287: q^2+5q+1
       288: q^2+3q+1
       289: q^2+3q+1
       290: 5q^2+6q+1
       291: 8q^2+7q+1
       292: 2q^2+5q+1
       293: 2q^2+5q+1
       294: q^2+4q+1
       295: 5q^2+6q+1
       296: 2q^2+3q+1
       297: 2q^2+3q+1
       298: 3q^2+5q+1
       299: 3q^2+5q+1
       300: 2q^2+5q+1
       301: 2q+1
       302: q^2+3q+1
       303: 2q^2+5q+1
       304: 2q+1
       305: q^2+3q+1
       306: 4q+1
       307: q^2+4q+1
       308: 4q+1
       309: q^2+2q+1
       310: q^2+2q+1
       311: 2q^2+3q+1
       312: q^2+3q+1
       313: 2q+1
       314: 2q+1
       315: q^2+3q+1
       316: q^2+5q+1
       317: 5q^2+7q+1
       318: q^2+2q+1
       319: q+1
       320: q^2+2q+1
       321: 2q^2+3q+1
       322: 2q^2+3q+1
       323: 4q+1
       324: 4q+1
       325: 5q^2+6q+1
       326: q^2+5q+1
       327: 2q^2+6q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: 4q+1
       332: 2q^2+5q+1
       333: 2q+1
       334: 2q+1
       335: 3q+1
       336: q+1
       337: q+1
       338: 2q+1
       339: 4q+1
       340: 2q+1
       341: 2q^2+5q+1
       342: 2q+1
       343: 3q+1
       344: 2q+1
       345: 2q+1
       346: 4q+1
       347: q^2+5q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: q^2+5q+1
       352: q^2+2q+1
       353: q+1
       354: 3q+1
       355: 3q+1
       356: q+1
       357: 2q+1
       358: q^2+3q+1
       359: 3q^2+4q+1
       360: 2q+1
       361: 2q^2+5q+1
       362: 2q^2+5q+1
       363: q^2+5q+1
       364: q^2+5q+1
       365: 2q+1
       366: q+1
       367: q^2+2q+1
       368: 2q^2+3q+1
       369: q^2+3q+1
       370: 3q^2+4q+1
       371: q^2+3q+1
       372: 3q+1
       373: q+1
       375: q+1
       376: 2q+1
       377: 2q+1
       380: 2q+1
       381: q^2+3q+1
       382: 2q+1
       383: q^2+3q+1
       384: q+1
       385: q^2+3q+1
       386: q^2+3q+1
       387: 2q+1
       388: q^2+3q+1
       389: 2q+1
       390: 2q+1
       392: q^2+5q+1
       393: q+1
       394: 3q+1
       395: q+1
       396: 2q+1
       397: 3q^2+4q+1
       398: q^2+3q+1
       399: 2q^2+5q+1
       400: 2q+1
       401: 2q^2+5q+1
       402: q^2+5q+1
       403: q^2+5q+1
       404: 2q+1
       405: q^2+2q+1
       406: q+1
       407: 2q^2+3q+1
       408: 3q^2+4q+1
       409: q^2+3q+1
       410: q^2+3q+1
       411: 3q+1
       412: q^2+3q+1
       413: 2q+1
       414: 2q+1
       415: q^2+3q+1
       416: q^2+3q+1
       417: q+1
       418: q^2+3q+1
       420: q+1
       421: q+1
       422: 2q+1
       424: 2q+1
       426: 2q+1
       427: q^2+3q+1
       428: 2q+1
       430: 2q+1
       431: q^2+5q+1
       432: q+1
       433: 3q+1
       434: 2q+1
       435: q^2+3q+1
       436: q^2+3q+1
       437: 5q^2+6q+1
       438: 2q^2+5q+1
       439: 2q^2+5q+1
       440: 4q+1
       441: 4q+1
       442: q^2+3q+1
       443: q^2+3q+1
       444: q^2+2q+1
       445: 2q^2+3q+1
       446: 2q+1
       447: 2q+1
       448: q^2+4q+1
       449: 2q+1
       450: 2q+1
       451: q+1
       452: q^2+3q+1
       454: 2q+1
       455: 2q+1
       456: q+1
       458: q^2+3q+1
       459: 4q+1
       460: 2q+1
       461: 2q+1
       462: 4q+1
       463: 4q+1
       465: q^2+2q+1
       466: q+1
       467: q+1
       468: q+1
       469: 2q+1
       470: 2q+1
       471: q^2+5q+1
       472: q^2+2q+1
       473: q+1
       474: q+1
       475: q^2+2q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 4q+1
       481: q^2+5q+1
       482: q+1
       483: 1
       484: 1
       485: 2q+1
       486: q+1
       487: 4q+1
       489: 2q+1
       490: 2q+1
       491: 3q+1
       492: 1
       493: 1
       494: q+1
       495: 2q+1
       497: 4q+1
       498: 2q+1
       499: 2q+1
       500: 3q+1
       501: q+1
       502: q+1
       503: q+1
       504: 4q+1
       505: 2q+1
       506: 2q+1
       507: q+1
       508: 2q+1
       509: 2q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       521: 2q+1
       522: q^2+3q+1
       523: 2q+1
       524: q^2+5q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q^2+2q+1
       530: q+1
       531: 2q+1
       532: q^2+3q+1
       533: 2q+1
       534: 3q+1
       536: 1
       538: q+1
       539: 2q+1
       543: q+1
       544: 1
       545: q+1
       546: 2q+1
       547: q+1
       548: q^2+3q+1
       549: q+1
       550: 2q+1
       551: q+1
       553: q+1
       554: 2q+1
       555: q+1
       558: 2q+1
       559: q+1
       560: 1
       561: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q^2+3q+1
       567: 2q+1
       569: q+1
       570: 2q+1
       571: q^2+5q+1
       572: q+1
       573: 1
       574: q+1
       575: q^2+2q+1
       576: q+1
       577: 2q+1
       578: q+1
       579: q^2+3q+1
       580: 2q+1
       581: 3q+1
       582: q+1
       583: q+1
       584: 1
       585: 2q+1
       586: q^2+3q+1
       587: q+1
       588: q+1
       589: 2q+1
       592: 1
       593: q+1
       595: 2q+1
       599: q+1
       600: q+1
       601: 2q+1
       603: q+1
       605: 2q+1
       606: q+1
       607: 1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: q^2+3q+1
       613: q^2+3q+1
       614: 2q+1
       615: 2q+1
       616: 4q+1
       617: 4q+1
       618: 4q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q^2+2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: q+1
       629: 1
       630: q+1
       631: q+1
       635: q+1
       636: 1
       637: q+1
       639: q+1
       641: q+1
       642: 2q+1
       643: q+1
       646: 4q+1
       647: q+1
       648: 2q+1
       650: q+1
       651: 1
       652: 1
       653: q+1
       654: 2q+1
       655: 2q+1
       656: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: 4q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: 2q+1
       670: q+1
       674: 2q+1
       675: 1
       676: 1
       677: 1
       678: 1
       681: q+1
       682: 2q+1
       684: 2q+1
       685: 1
       686: 1
       687: 1
       688: q+1
       689: q+1
       692: q+1
       693: q+1
       694: 2q+1
       695: q+1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: q+1
       705: 1
       707: q+1
       708: q+1
       710: 2q+1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       717: 1
       718: q+1
       719: q+1
       720: 2q+1
       721: 1
       724: 1
       726: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       736: 2q+1
       737: q+1
       738: q+1
       739: 2q+1
       741: 1
       743: q+1
       744: q+1
       748: q+1
       750: 1
       751: 1
       752: 1
       756: q+1
       757: 1
       758: q+1
       761: q+1
       762: 2q+1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: 1
       770: 1
       771: q+1
       772: 2q+1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       780: q+1
       781: q+1
       782: 2q+1
       786: 1
       788: q+1
       794: 1
       795: q+1
       797: q+1
       801: q+1
       802: 1
       803: 1
       805: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       813: q+1
       814: q+1
       815: 4q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: 2q+1
       824: q+1
       825: 2q+1
       827: 1
       829: 1
       830: q+1
       836: 1
       837: 1
       839: q+1
       844: 1
       845: q+1
       849: q+1
       850: q+1
       851: 1
       855: 1
       856: 1
       857: 1
       858: q+1
       859: 1
       860: 1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: q+1
       867: q+1
       868: q+1
       870: 1
       872: 1
       877: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: q+1
       907: 1
       909: 1
       911: q+1
       913: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: q+1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: q+1
       941: q+1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       961: 1
       962: 1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: q+1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       985: q+1
       986: 1
       993: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1015: q+1
      1016: 1
      1021: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1029: 1
      1030: 1
      1031: q+1
      1032: 1
      1035: 1
      1037: 1
      1045: 1
      1047: 1
      1054: 1
      1061: 1
      1062: 1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1115: 1
      1118: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1138: 1
      1141: 1
      1145: 1
      1158: 1
      1166: 1
      1171: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1181: 1
      1183: 1
      1188: 1
      1211: 1
      1218: 1
      1224: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1237: 1
      1250: 1
      1266: 1
      1272: 1
      1273: 1
      1276: 1
      1278: 1
      1302: 1
      1309: 1
      1317: 1
      1320: 1
      1363: 1
      1368: 1
      1412: 1
      1418: 1
      1457: 1

1458:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: 1
        16: q^2+q+1
        17: q^2+q+1
        18: 1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+q+1
        41: q^2+q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q^2+q+1
        48: q^2+q+1
        49: 1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: 1
        65: q^2+q+1
        66: q^2+q+1
        67: 1
        68: q^2+q+1
        69: q^2+q+1
        70: 1
        71: 1
        72: q^2+q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q^2+q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q^2+q+1
       105: q^2+q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: 1
       112: q^2+q+1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: 1
       120: q^2+q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q^2+q+1
       126: 1
       127: 1
       128: 1
       129: q^2+q+1
       130: q^2+q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q^2+q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q^2+q+1
       191: q^2+q+1
       192: q^2+q+1
       193: 1
       194: 1
       195: q^2+q+1
       196: 1
       197: 1
       198: q^2+q+1
       199: q^2+q+1
       200: q^2+q+1
       201: q^2+q+1
       202: q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q^2+q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q^2+q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q^2+q+1
       321: q^2+q+1
       322: q^2+q+1
       323: 1
       324: 1
       325: q^2+q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q^2+q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       823: 1
       850: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       906: 1
       918: 1
       935: 1
       938: 1
       939: 1
       960: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1014: 1
      1015: 1
      1022: 1
      1025: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1105: 1
      1141: 1
      1183: 1
      1217: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1293: 1
      1458: 1

1459:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q^2+q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q^2+q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: 1
       246: 1
       248: q+1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: 1
       478: 1
       479: q+1
       480: q+1
       481: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       635: 1
       641: 1
       646: 1
       648: 1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: q+1
       666: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       849: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       909: 1
       911: 1
       933: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1115: 1
      1166: 1
      1218: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1288: 1
      1294: 1
      1459: 1

1460:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: 2q^2+4q+1
         5: 2q^2+4q+1
         6: 2q^2+4q+1
         7: q^3+4q^2+4q+1
         8: q^3+4q^2+4q+1
         9: q^3+4q^2+4q+1
        10: q^3+4q^2+4q+1
        11: 2q^2+4q+1
        12: 2q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+4q+1
        15: 2q^2+4q+1
        16: 2q^2+4q+1
        17: 2q^2+4q+1
        18: 2q^2+4q+1
        19: q^2+4q+1
        20: 2q^2+4q+1
        21: 2q^2+4q+1
        22: q^3+4q^2+4q+1
        23: 2q^2+4q+1
        24: 2q^2+4q+1
        25: 2q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: 2q^2+4q+1
        29: 2q^2+4q+1
        30: 2q^2+4q+1
        31: 2q^2+4q+1
        32: q^2+4q+1
        33: q^2+4q+1
        34: 2q^2+4q+1
        35: 2q^2+4q+1
        36: 2q^2+4q+1
        37: q^2+2q+1
        38: 2q+1
        39: 2q^2+4q+1
        40: q^2+4q+1
        41: 2q^2+4q+1
        42: 2q^2+4q+1
        43: 2q^2+4q+1
        44: q^2+2q+1
        45: 2q^2+4q+1
        46: 2q+1
        47: q^2+4q+1
        48: q^2+4q+1
        49: q^2+4q+1
        50: 2q+1
        51: 2q+1
        52: 2q^2+4q+1
        53: 2q^2+4q+1
        54: 2q^2+4q+1
        55: 2q^2+4q+1
        56: q^2+4q+1
        57: 2q^2+4q+1
        58: 2q^2+4q+1
        59: q^3+4q^2+4q+1
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: q^2+4q+1
        63: 2q^2+4q+1
        64: 2q^2+4q+1
        65: q^2+4q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: q^2+4q+1
        69: q^2+4q+1
        70: q^2+4q+1
        71: q^2+4q+1
        72: q^2+4q+1
        73: 2q^2+4q+1
        74: 2q+1
        75: 2q^2+4q+1
        76: 2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q+1
        80: q+1
        81: 2q^2+4q+1
        82: q^2+2q+1
        83: 2q+1
        84: q^2+4q+1
        85: q^2+4q+1
        86: 2q^2+4q+1
        87: 2q^2+4q+1
        88: 2q+1
        89: 2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+4q+1
        93: q^2+2q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+4q+1
       100: q^2+4q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: 2q+1
       106: 2q+1
       107: 2q^2+4q+1
       108: q^2+4q+1
       109: q^2+4q+1
       110: q^2+4q+1
       111: q^2+4q+1
       112: 2q+1
       113: 2q+1
       114: 2q^2+4q+1
       115: 2q^2+4q+1
       116: 2q^2+4q+1
       117: 2q^2+4q+1
       118: q^2+4q+1
       119: q^2+4q+1
       120: q^2+4q+1
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: 2q+1
       124: q^2+4q+1
       125: q^2+4q+1
       126: 2q^2+4q+1
       127: 2q+1
       128: 2q^2+4q+1
       129: q^2+4q+1
       130: q^2+4q+1
       131: q^2+4q+1
       132: q^2+4q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: q^2+4q+1
       137: 2q+1
       138: 2q+1
       139: 2q^2+4q+1
       140: 2q+1
       141: 2q+1
       142: 2q+1
       143: q^2+2q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       155: 2q+1
       156: q+1
       157: q^2+4q+1
       158: 2q+1
       159: 2q^2+4q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: 2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: q^2+4q+1
       177: q^2+4q+1
       178: q^2+4q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       182: q+1
       183: q+1
       184: 2q+1
       185: 1
       186: 2q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: 2q+1
       193: q^2+4q+1
       194: q^2+4q+1
       195: q^2+4q+1
       196: q^2+4q+1
       197: q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       201: 2q^2+4q+1
       202: q^2+4q+1
       203: q^2+4q+1
       204: q^2+4q+1
       205: q^2+4q+1
       206: 2q+1
       207: q+1
       208: q^2+4q+1
       209: 2q+1
       210: 2q^2+4q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: 2q+1
       215: q^2+4q+1
       216: 2q+1
       217: 2q+1
       218: 2q^2+4q+1
       219: 2q+1
       220: q^2+4q+1
       221: q^2+4q+1
       222: q^2+4q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 1
       237: q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: q^2+2q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 2q+1
       249: 2q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q+1
       257: 1
       258: 1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: 2q+1
       265: 2q+1
       266: q+1
       267: 1
       268: 2q+1
       269: 2q+1
       270: q^2+2q+1
       271: q+1
       272: q+1
       273: 2q+1
       274: 2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: 2q+1
       287: 1
       288: q+1
       289: q+1
       290: q^2+4q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: q^2+4q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: q^2+4q+1
       324: q^2+4q+1
       325: q^2+4q+1
       326: q^2+4q+1
       327: q+1
       328: 1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: q+1
       346: q^2+4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: q+1
       361: 2q+1
       362: q+1
       363: 2q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: q+1
       373: 1
       375: q+1
       377: q+1
       380: 1
       381: q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: 2q+1
       400: q+1
       401: q+1
       402: 2q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       413: 1
       414: 2q+1
       415: 2q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       420: 1
       421: q+1
       424: q+1
       426: q+1
       427: q+1
       428: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       466: q+1
       467: 1
       468: 1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: q^2+4q+1
       481: q+1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: 2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: 2q+1
       498: q+1
       499: 2q+1
       500: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: q+1
       523: q+1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: 2q+1
       532: q+1
       533: q+1
       534: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: q+1
       551: 1
       553: q+1
       555: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       569: 1
       570: q+1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: 2q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: q+1
       592: 1
       599: 1
       600: q+1
       603: q+1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: q+1
       674: 1
       675: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: q+1
       719: q+1
       721: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: 2q+1
       737: q+1
       738: q+1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       770: 1
       771: q+1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       836: 1
       844: 1
       849: 1
       850: 1
       851: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       909: 1
       911: 1
       913: 1
       916: 1
       918: 1
       919: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: q+1
       942: 1
       953: 1
       962: 1
       966: 1
       967: 1
       970: 1
       971: 1
       974: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: q+1
       986: 1
      1008: 1
      1016: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1032: 1
      1061: 1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1093: 1
      1096: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1118: 1
      1123: 1
      1139: 1
      1141: 1
      1142: 1
      1171: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1224: 1
      1227: 1
      1273: 1
      1277: 1
      1278: 1
      1285: 1
      1291: 1
      1300: 1
      1303: 1
      1333: 1
      1371: 1
      1460: 1

1461:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        81: q+1
        82: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       139: q+1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       186: q+1
       187: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       214: q+1
       215: q+1
       216: 1
       218: q+1
       220: q+1
       221: q+1
       222: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       293: q+1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       338: q+1
       339: 1
       341: 1
       345: q+1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       495: 1
       497: 1
       503: q+1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       639: 1
       649: 1
       650: 1
       651: q+1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       939: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1029: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1109: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1182: 1
      1183: 1
      1186: 1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1357: 1
      1371: 1
      1461: 1

1462:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: q^3+5q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: 2q^3+5q^2+4q+1
         5: 3q^3+6q^2+4q+1
         6: q^3+5q^2+4q+1
         7: q^3+5q^2+4q+1
         8: 4q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: q^3+5q^2+4q+1
        11: 3q^3+6q^2+4q+1
        12: 2q^3+5q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: q^3+4q^2+4q+1
        15: 2q^2+3q+1
        16: 3q^3+6q^2+4q+1
        17: q^3+5q^2+4q+1
        18: 2q^3+5q^2+4q+1
        19: 2q^3+5q^2+4q+1
        20: 4q^2+4q+1
        21: q^3+5q^2+4q+1
        22: 4q^2+4q+1
        23: 4q^2+4q+1
        24: 2q^2+3q+1
        25: q^3+5q^2+4q+1
        26: q^3+5q^2+4q+1
        27: 4q^2+4q+1
        28: 3q^3+6q^2+4q+1
        29: q^3+5q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: q^3+4q^2+4q+1
        32: 2q^3+5q^2+4q+1
        33: q^3+4q^2+4q+1
        34: q^3+4q^2+4q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+5q^2+4q+1
        41: q^3+5q^2+4q+1
        42: 3q^2+4q+1
        43: 2q^3+5q^2+4q+1
        44: 2q^2+3q+1
        45: 2q^3+5q^2+4q+1
        46: q^3+3q^2+3q+1
        47: 2q^3+5q^2+4q+1
        48: q^3+4q^2+4q+1
        49: 2q^2+3q+1
        50: 4q^2+4q+1
        51: 2q^2+3q+1
        52: 4q^2+4q+1
        53: 2q^2+3q+1
        54: 4q^2+4q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 4q^2+4q+1
        58: q^3+5q^2+4q+1
        59: 4q^2+4q+1
        60: 4q^2+4q+1
        61: 2q^2+3q+1
        62: q^3+5q^2+4q+1
        63: q^3+5q^2+4q+1
        64: 3q^2+4q+1
        65: q^3+4q^2+4q+1
        66: q^3+4q^2+4q+1
        67: q^2+3q+1
        68: 2q^3+5q^2+4q+1
        69: q^3+4q^2+4q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^3+4q^2+4q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q^2+3q+1
        80: 2q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 3q^2+4q+1
        85: q^3+5q^2+4q+1
        86: 3q^2+4q+1
        87: 3q^2+4q+1
        88: q^2+2q+1
        89: 2q^2+3q+1
        90: 2q^2+3q+1
        91: q^2+3q+1
        92: 2q^3+5q^2+4q+1
        93: 2q^2+3q+1
        94: q^3+3q^2+3q+1
        95: q^2+2q+1
        96: q^3+3q^2+3q+1
        97: q^3+4q^2+4q+1
        98: q^3+4q^2+4q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       104: 2q^2+3q+1
       105: 4q^2+4q+1
       106: 2q^2+3q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: q^2+2q+1
       110: 2q^2+3q+1
       111: 2q+1
       112: 4q^2+4q+1
       113: 2q^2+3q+1
       114: 4q^2+4q+1
       115: 2q^2+3q+1
       116: 4q^2+4q+1
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: 3q^2+4q+1
       120: q^3+5q^2+4q+1
       121: 3q^2+4q+1
       122: 3q^2+4q+1
       123: q^2+2q+1
       124: q^2+3q+1
       125: q^3+4q^2+4q+1
       126: q^2+3q+1
       127: q^2+3q+1
       128: 2q+1
       129: q^3+4q^2+4q+1
       130: q^3+4q^2+4q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: q+1
       138: q^2+3q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       147: 2q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: 2q^2+3q+1
       153: 2q+1
       154: 2q^2+3q+1
       155: 3q^2+4q+1
       156: q^2+2q+1
       157: 3q^2+4q+1
       158: 2q+1
       159: 3q^2+4q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+3q+1
       163: 2q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: q^2+3q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q^3+3q^2+3q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^3+4q^2+4q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q^2+3q+1
       191: 2q^2+3q+1
       192: q^2+2q+1
       193: q^2+2q+1
       194: q+1
       195: q^2+2q+1
       196: 2q+1
       197: q+1
       198: 2q^2+3q+1
       199: 4q^2+4q+1
       200: 2q^2+3q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: q^2+2q+1
       204: 2q^2+3q+1
       205: 2q+1
       206: 3q^2+4q+1
       207: q^2+2q+1
       208: 3q^2+4q+1
       209: 2q+1
       210: 3q^2+4q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q^2+3q+1
       214: 2q+1
       215: q^2+3q+1
       216: q+1
       217: q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: q^2+3q+1
       221: q^3+4q^2+4q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: 1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q+1
       238: 2q+1
       239: q+1
       240: 2q+1
       241: q+1
       242: q+1
       244: 2q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       256: 2q^2+3q+1
       257: 2q+1
       258: q^2+2q+1
       259: 3q^2+4q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q^2+2q+1
       265: q+1
       266: q^2+3q+1
       267: q+1
       268: q^2+3q+1
       269: 2q+1
       270: q^2+3q+1
       271: q+1
       272: q+1
       273: q^2+3q+1
       274: 2q^2+3q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: q+1
       278: q+1
       279: q^2+2q+1
       280: q+1
       281: q+1
       282: 1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+3q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q^2+3q+1
       293: q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 1
       300: 2q+1
       301: 2q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q^2+2q+1
       312: q^2+2q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q^2+3q+1
       321: 2q^2+3q+1
       322: q^2+2q+1
       323: q^2+2q+1
       324: q+1
       325: q^2+2q+1
       326: 2q+1
       327: q+1
       328: q^2+2q+1
       329: 3q^2+4q+1
       330: q^2+2q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q^2+2q+1
       335: q+1
       336: 2q+1
       337: q^2+3q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: 1
       342: 2q+1
       343: 2q+1
       344: q^2+3q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       348: q^2+3q+1
       349: q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 2q+1
       355: 1
       356: 2q+1
       357: 2q+1
       358: q+1
       359: 1
       361: 1
       362: 1
       363: 2q+1
       364: q+1
       365: q+1
       366: 2q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       380: 2q+1
       381: q+1
       382: 2q+1
       383: q+1
       384: 2q+1
       385: q+1
       386: q+1
       388: 2q+1
       392: 2q+1
       393: 2q+1
       395: q+1
       396: q^2+2q+1
       397: 2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: 1
       404: q+1
       405: q^2+3q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: q^2+3q+1
       413: q+1
       414: q^2+3q+1
       415: 2q+1
       416: q^2+3q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q^2+3q+1
       436: q+1
       437: q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       442: 2q+1
       443: 1
       444: 2q+1
       445: q+1
       446: 2q+1
       447: 1
       448: 1
       450: 2q+1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       468: q+1
       469: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q^2+2q+1
       476: q^2+2q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       483: q+1
       484: q^2+2q+1
       485: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: q+1
       491: 1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: 2q+1
       500: q+1
       501: q+1
       502: q^2+3q+1
       503: q+1
       504: q+1
       505: q+1
       506: 1
       507: q+1
       508: q+1
       509: 2q+1
       510: 1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: 1
       515: 1
       516: q+1
       517: 2q+1
       518: 1
       521: 1
       522: 1
       524: 1
       525: q+1
       527: q+1
       528: q+1
       529: 1
       531: 1
       532: 1
       543: q+1
       544: 2q+1
       545: q+1
       546: q+1
       547: q+1
       548: 1
       549: q+1
       559: 2q+1
       563: 1
       564: q+1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q^2+3q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: q+1
       592: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 2q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       634: q+1
       635: 1
       636: q+1
       638: q+1
       639: 1
       640: 1
       642: q+1
       646: q+1
       647: q+1
       649: 1
       650: 1
       652: q+1
       654: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       661: q+1
       662: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 2q+1
       678: 1
       681: 1
       682: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 2q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       703: q+1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: q+1
       733: q+1
       734: 1
       736: 1
       737: 1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: q+1
       776: 2q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       804: q+1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: q+1
       820: 1
       822: 1
       823: 1
       834: 1
       835: q+1
       836: 1
       840: 1
       850: q+1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: q+1
       866: 1
       868: 1
       869: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       877: 1
       878: q+1
       879: 1
       882: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: q+1
       900: 1
       902: 1
       903: 1
       906: 1
       918: 1
       935: 1
       938: 1
       939: 1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       970: 1
       972: 1
       973: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       982: 1
       983: 1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1012: 1
      1014: 1
      1015: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: 1
      1094: 1
      1095: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1141: 1
      1165: 1
      1167: 1
      1170: 1
      1175: 1
      1180: 1
      1182: 1
      1184: 1
      1185: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1209: 1
      1217: 1
      1229: 1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1293: 1
      1305: 1
      1358: 1
      1372: 1
      1385: 1
      1462: 1

1463:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: q+1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       277: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       411: 1
       412: q+1
       413: q+1
       418: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: q+1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: q+1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       707: 1
       756: 1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1015: 1
      1018: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1095: 1
      1098: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1359: 1
      1463: 1

1464:    0: 2q^2+q+1
         1: q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: q^2+q+1
         5: 2q^2+q+1
         6: q+1
         7: q^2+q+1
         8: 2q^2+q+1
         9: q^2+q+1
        10: 2q^2+q+1
        11: 2q^2+q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: 2q^2+q+1
        18: 2q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: 2q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q^2+q+1
        27: 2q^2+q+1
        28: q^2+q+1
        29: 2q^2+q+1
        30: q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q^2+q+1
        42: 2q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: 2q^2+q+1
        46: q+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q^2+q+1
        55: q+1
        56: q^2+q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: 2q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q^2+q+1
        64: 2q^2+q+1
        65: q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: q^2+q+1
        75: q^2+q+1
        76: 1
        78: q^2+1
        79: q+1
        80: q^2+1
        81: q+1
        82: q^2+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q^2+q+1
        87: 2q^2+q+1
        88: q+1
        89: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: 1
       102: q^2+q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q^2+q+1
       112: q+1
       113: 1
       114: q+1
       115: q+1
       116: q^2+q+1
       117: q+1
       118: q^2+q+1
       119: q+1
       120: q+1
       121: q^2+q+1
       122: 2q^2+q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q^2+q+1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q^2+q+1
       141: 1
       144: q^2+1
       145: q^2+1
       146: 1
       148: q^2+1
       149: 1
       151: q^2+1
       152: q+1
       153: q^2+1
       154: q^2+q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       169: q^2+q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q^2+q+1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q^2+q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: q+1
       214: 1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q^2+q+1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: q+1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q^2+q+1
       236: 1
       237: 1
       242: q^2+1
       243: 1
       246: q^2+1
       248: 1
       251: q^2+1
       252: q^2+1
       253: 1
       255: q^2+1
       256: q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       272: q+1
       273: q+1
       276: q^2+q+1
       277: q+1
       278: q+1
       281: q+1
       282: q+1
       283: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: q+1
       313: 1
       314: q+1
       315: 1
       316: q+1
       317: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q^2+q+1
       344: q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       372: q^2+1
       373: 1
       380: 1
       381: 1
       386: q^2+1
       387: 1
       390: q^2+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       404: 1
       411: q+1
       412: q+1
       413: 1
       418: q+1
       419: q+1
       420: 1
       425: q+1
       426: q+1
       429: q+1
       430: q+1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: q+1
       470: 1
       471: 1
       474: 1
       475: 1
       476: q+1
       477: 1
       478: q+1
       479: 1
       480: q+1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: q^2+1
       551: 1
       558: 1
       561: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       568: q+1
       569: 1
       570: q+1
       571: 1
       573: 1
       581: 1
       582: 1
       589: q+1
       590: 1
       597: q+1
       598: q+1
       599: 1
       604: q+1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       659: 1
       660: 1
       661: 1
       662: q+1
       663: 1
       664: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       731: 1
       739: 1
       748: 1
       757: 1
       758: 1
       759: 1
       760: q+1
       761: 1
       762: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: q+1
       800: 1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       880: 1
       882: 1
       883: 1
       885: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       909: 1
       911: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1042: 1
      1050: 1
      1059: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1089: 1
      1091: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1168: 1
      1169: 1
      1208: 1
      1216: 1
      1220: 1
      1222: 1
      1277: 1
      1282: 1
      1283: 1
      1296: 1
      1298: 1
      1360: 1
      1464: 1

1465:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: 2q^2+2q+1
        25: q^2+2q+1
        26: 2q^2+2q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+1
        38: q^2+q+1
        39: q^2+q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: 2q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: 2q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: 2q^2+2q+1
        67: q^2+q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q^2+q+1
        76: 1
        77: q^2+1
        78: q^2+1
        79: q^2+q+1
        80: q^2+1
        81: q^2+q+1
        82: q^2+1
        83: q^2+q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q^2+2q+1
       116: 2q^2+2q+1
       117: 2q^2+2q+1
       118: 2q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q+1
       125: q^2+2q+1
       126: q^2+q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q^2+2q+1
       130: 2q^2+2q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q^2+q+1
       139: q^2+q+1
       140: q^2+q+1
       141: 1
       142: 1
       143: q^2+1
       144: q^2+1
       145: q^2+1
       146: 1
       147: q^2+1
       149: 1
       150: q^2+1
       151: q^2+1
       152: q^2+q+1
       153: q^2+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 2q^2+2q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q^2+q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: q^2+1
       241: q^2+1
       242: q^2+1
       244: 1
       248: 1
       249: 1
       250: q^2+1
       251: q^2+1
       252: q^2+1
       253: 1
       254: q^2+1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: q^2+2q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q^2+q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q^2+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: q^2+1
       385: q^2+1
       386: q^2+1
       388: 1
       392: 1
       393: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: 1
       493: q+1
       494: 1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: q^2+1
       559: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: 1
       613: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       653: q+1
       654: 1
       655: 1
       656: 1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       687: q+1
       688: 1
       689: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       840: 1
       850: 1
       858: 1
       859: 1
       860: 1
       865: q+1
       866: 1
       867: 1
       868: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       882: 1
       886: 1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       918: 1
       935: 1
       938: 1
       939: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       986: 1
       996: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1141: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1207: 1
      1209: 1
      1229: 1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1305: 1
      1361: 1
      1373: 1
      1465: 1

1466:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: q^3+5q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: 3q^3+6q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^3+5q^2+4q+1
         7: q^3+5q^2+4q+1
         8: 4q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: q^3+5q^2+4q+1
        11: 2q^3+5q^2+4q+1
        12: 3q^3+6q^2+4q+1
        13: 3q^3+6q^2+4q+1
        14: q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 2q^3+5q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^2+3q+1
        19: 2q^3+5q^2+4q+1
        20: 4q^2+4q+1
        21: q^3+5q^2+4q+1
        22: 4q^2+4q+1
        23: 2q^2+3q+1
        24: 4q^2+4q+1
        25: q^3+5q^2+4q+1
        26: q^3+5q^2+4q+1
        27: 4q^2+4q+1
        28: 2q^3+5q^2+4q+1
        29: q^3+4q^2+4q+1
        30: 3q^3+6q^2+4q+1
        31: q^3+5q^2+4q+1
        32: 2q^3+5q^2+4q+1
        33: q^3+5q^2+4q+1
        34: q^3+5q^2+4q+1
        35: 3q^2+4q+1
        36: 2q^3+5q^2+4q+1
        37: 2q^2+3q+1
        38: q^3+3q^2+3q+1
        39: 2q^3+5q^2+4q+1
        40: q^3+4q^2+4q+1
        41: q^3+4q^2+4q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^3+5q^2+4q+1
        48: q^3+4q^2+4q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 4q^2+4q+1
        52: 4q^2+4q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 4q^2+4q+1
        56: 2q^2+3q+1
        57: 4q^2+4q+1
        58: q^3+5q^2+4q+1
        59: 4q^2+4q+1
        60: 2q^2+3q+1
        61: 4q^2+4q+1
        62: q^3+4q^2+4q+1
        63: q^3+4q^2+4q+1
        64: q^2+3q+1
        65: q^3+5q^2+4q+1
        66: q^3+5q^2+4q+1
        67: 3q^2+4q+1
        68: 2q^3+5q^2+4q+1
        69: q^3+4q^2+4q+1
        70: 2q^2+3q+1
        71: 3q^2+4q+1
        72: q^3+5q^2+4q+1
        73: 3q^2+4q+1
        74: q^2+2q+1
        75: 3q^2+4q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: q^2+3q+1
        79: q^3+3q^2+3q+1
        80: q^2+2q+1
        81: 2q^3+5q^2+4q+1
        82: 2q^2+3q+1
        83: q^3+3q^2+3q+1
        84: q^2+3q+1
        85: q^3+4q^2+4q+1
        86: q^2+3q+1
        87: 2q+1
        88: q^2+3q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+4q+1
        98: q^3+4q^2+4q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: q^2+2q+1
       103: 2q^2+3q+1
       104: 2q^2+3q+1
       105: 2q^2+3q+1
       106: 4q^2+4q+1
       107: 2q^2+3q+1
       108: q^2+2q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       111: 2q+1
       112: 2q^2+3q+1
       113: 4q^2+4q+1
       114: 4q^2+4q+1
       115: 2q^2+3q+1
       116: 2q^2+3q+1
       117: 4q^2+4q+1
       118: 2q^2+3q+1
       119: q^2+3q+1
       120: q^3+4q^2+4q+1
       121: q^2+3q+1
       122: 2q+1
       123: q^2+3q+1
       124: 3q^2+4q+1
       125: q^3+5q^2+4q+1
       126: 3q^2+4q+1
       127: q^2+2q+1
       128: 3q^2+4q+1
       129: q^3+4q^2+4q+1
       130: q^3+4q^2+4q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q^2+2q+1
       135: 3q^2+4q+1
       136: 3q^2+4q+1
       137: 2q+1
       138: q^2+2q+1
       139: 3q^2+4q+1
       140: q^2+2q+1
       141: q^2+3q+1
       142: 2q^2+3q+1
       143: q^2+3q+1
       144: q+1
       145: q^2+3q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+3q+1
       152: q^3+3q^2+3q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: q+1
       159: 2q+1
       160: q^2+3q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: 2q+1
       171: 2q+1
       173: 2q^2+3q+1
       174: 2q+1
       175: 2q^2+3q+1
       176: q^2+3q+1
       177: q^3+4q^2+4q+1
       178: q^2+3q+1
       179: q+1
       180: q^2+3q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q^2+3q+1
       191: q^2+2q+1
       192: 2q^2+3q+1
       193: q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: 2q+1
       197: q+1
       198: 2q^2+3q+1
       199: 2q^2+3q+1
       200: 4q^2+4q+1
       201: 2q^2+3q+1
       202: q^2+2q+1
       203: 2q^2+3q+1
       204: 2q^2+3q+1
       205: 2q+1
       206: 2q+1
       207: q^2+3q+1
       208: q^2+3q+1
       209: q+1
       210: 2q+1
       211: q^2+3q+1
       212: 2q+1
       213: q^2+2q+1
       214: 3q^2+4q+1
       215: 3q^2+4q+1
       216: 2q+1
       217: q^2+2q+1
       218: 3q^2+4q+1
       219: q^2+2q+1
       220: q^2+3q+1
       221: q^3+4q^2+4q+1
       222: q^2+3q+1
       223: q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 3q^2+4q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q^2+2q+1
       235: q+1
       236: q+1
       237: q^2+3q+1
       238: q^2+3q+1
       239: 2q+1
       240: q+1
       241: q^2+3q+1
       242: q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: 1
       247: q+1
       248: q^2+3q+1
       249: 2q^2+3q+1
       250: q^2+3q+1
       251: q+1
       252: q^2+3q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q+1
       262: 1
       263: q+1
       264: 2q+1
       265: 2q+1
       266: q+1
       267: 2q+1
       268: 2q+1
       269: q+1
       270: q+1
       271: 2q+1
       272: q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 2q+1
       279: 2q+1
       283: 2q+1
       284: 2q+1
       286: 2q^2+3q+1
       287: 2q+1
       288: q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q^2+3q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 1
       299: 2q+1
       300: q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q^2+2q+1
       312: q+1
       313: q+1
       315: q^2+2q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q^2+3q+1
       321: q^2+2q+1
       322: 2q^2+3q+1
       323: q+1
       324: q^2+2q+1
       325: q^2+2q+1
       326: 2q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: q^2+3q+1
       331: q+1
       332: 1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: 3q^2+4q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q^2+2q+1
       343: q+1
       344: q+1
       345: q^2+3q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+3q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       355: 2q+1
       356: q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       365: q+1
       366: q+1
       367: q^2+3q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: 1
       374: q+1
       375: q+1
       377: 1
       378: q+1
       379: 1
       380: q+1
       381: q^2+3q+1
       382: q^2+3q+1
       383: 2q+1
       384: q+1
       385: q^2+3q+1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: 2q+1
       396: 2q+1
       397: 1
       398: q+1
       399: 1
       401: 1
       402: 2q+1
       403: q+1
       404: q+1
       405: q+1
       406: 2q+1
       407: q+1
       408: 1
       409: q+1
       410: q+1
       412: q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: q+1
       417: 2q+1
       418: q+1
       427: 2q+1
       431: 2q+1
       432: 2q+1
       434: q+1
       435: q+1
       436: q^2+3q+1
       437: q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: 2q+1
       444: 2q+1
       445: q+1
       446: 1
       447: 2q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       455: 2q+1
       459: q+1
       460: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       467: q+1
       470: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q^2+2q+1
       476: q+1
       477: q+1
       479: q^2+2q+1
       480: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: 1
       486: q+1
       487: 1
       489: 1
       490: 2q+1
       491: q+1
       492: q+1
       493: q^2+2q+1
       494: q+1
       495: 2q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q^2+3q+1
       504: q+1
       505: 1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 1
       514: 2q+1
       515: 1
       516: 1
       517: q+1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q^2+3q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       563: q+1
       564: 2q+1
       565: 1
       566: 1
       567: 1
       571: 1
       572: q+1
       574: q+1
       575: 1
       576: q+1
       577: 1
       579: 1
       582: q+1
       583: q+1
       584: 2q+1
       585: q+1
       586: 1
       587: q+1
       588: q+1
       606: 2q+1
       610: q+1
       611: q+1
       612: 1
       613: q+1
       614: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 2q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       627: 1
       628: q+1
       629: q+1
       631: 1
       632: q+1
       633: 1
       642: q+1
       646: q+1
       647: q+1
       649: 1
       650: 1
       651: q+1
       655: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       660: q+1
       663: q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: 1
       669: 1
       670: 1
       674: 1
       675: q+1
       676: 1
       677: q+1
       678: q+1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 2q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       703: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       752: 1
       753: q+1
       754: 1
       755: q+1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: q+1
       776: 1
       777: q+1
       778: 1
       780: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       823: 1
       826: 1
       827: 1
       828: q+1
       832: 1
       850: q+1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       867: 1
       868: 1
       869: q+1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       903: 1
       906: 1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q+1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       958: 1
       960: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1014: 1
      1015: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1086: 1
      1087: 1
      1088: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1113: 1
      1114: 1
      1119: 1
      1122: 1
      1128: 1
      1137: 1
      1139: 1
      1140: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1157: 1
      1183: 1
      1217: 1
      1228: 1
      1274: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1304: 1
      1310: 1
      1332: 1
      1338: 1
      1466: 1

1467:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       208: q+1
       209: 1
       210: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       329: q+1
       331: 1
       332: 1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: q+1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       464: 1
       465: 1
       466: q+1
       468: q+1
       469: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       485: 1
       487: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       502: q+1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       631: 1
       649: 1
       650: 1
       652: q+1
       654: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       661: q+1
       662: q+1
       664: 1
       665: 1
       669: 1
       676: 1
       677: q+1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: q+1
       866: 1
       868: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       942: 1
       953: 1
       980: 1
      1026: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1106: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1139: 1
      1141: 1
      1142: 1
      1275: 1
      1286: 1
      1288: 1
      1291: 1
      1311: 1
      1333: 1
      1467: 1

1468:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       144: q+1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: q+1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       372: 1
       373: 1
       374: 1
       379: 1
       380: q+1
       381: q+1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: q+1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: q+1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       758: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       872: 1
       879: 1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
      1015: 1
      1017: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1097: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1276: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1312: 1
      1468: 1

1469:    0: 2q^2+q+1
         1: q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: 2q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q^2+q+1
         8: 2q^2+q+1
         9: q^2+q+1
        10: 2q^2+q+1
        11: q^2+q+1
        12: 2q^2+q+1
        13: q^2+q+1
        14: 2q^2+q+1
        15: 2q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q^2+q+1
        24: 2q^2+q+1
        25: q+1
        26: q^2+q+1
        27: 2q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q^2+q+1
        31: 2q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q^2+q+1
        35: 2q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: 2q^2+q+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+1
        45: q^2+q+1
        46: q^2+q+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        50: 1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q^2+q+1
        61: 2q^2+q+1
        62: q+1
        63: q+1
        64: q^2+q+1
        65: q+1
        66: q^2+q+1
        67: 2q^2+q+1
        68: q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        75: 2q^2+q+1
        76: q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: q^2+q+1
        89: 1
        91: q^2+1
        92: q+1
        93: q^2+1
        94: q+1
        95: q^2+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: 1
       102: q+1
       103: q^2+q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q^2+q+1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q+1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: q^2+q+1
       124: q+1
       125: q+1
       126: q^2+q+1
       127: q+1
       128: 2q^2+q+1
       129: q+1
       130: q+1
       131: q^2+q+1
       132: q+1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       148: q+1
       149: q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q^2+q+1
       162: 1
       165: q^2+1
       166: q^2+1
       167: 1
       169: q^2+1
       170: 1
       172: q^2+1
       173: q+1
       174: q^2+1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q^2+q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q^2+q+1
       206: 1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q^2+q+1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q^2+q+1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       242: q+1
       243: q+1
       246: q+1
       247: q+1
       248: q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       255: q+1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q^2+q+1
       266: 1
       267: 1
       272: q^2+1
       273: 1
       276: q^2+1
       277: q^2+1
       278: 1
       282: q^2+1
       283: 1
       285: q^2+1
       286: q+1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       313: q+1
       314: 1
       315: q+1
       316: q+1
       317: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q^2+q+1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       365: 1
       372: q+1
       373: 1
       374: q+1
       379: q+1
       380: 1
       381: q+1
       386: q+1
       387: q+1
       390: q+1
       391: q+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       411: q^2+1
       412: 1
       413: 1
       418: q^2+1
       420: 1
       426: 1
       430: q^2+1
       431: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: q+1
       471: 1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: 1
       479: q+1
       480: q+1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: q+1
       521: 1
       522: q+1
       523: q+1
       524: 1
       526: 1
       534: 1
       535: 1
       542: q+1
       543: 1
       550: q+1
       551: 1
       552: q+1
       557: q+1
       558: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: q^2+1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: q+1
       664: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q+1
       683: q+1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: q+1
       710: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: q+1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       761: 1
       762: 1
       774: 1
       782: 1
       801: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       875: 1
       876: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       943: 1
       951: 1
       952: 1
       959: 1
       962: 1
       966: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1033: 1
      1041: 1
      1060: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1084: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1116: 1
      1117: 1
      1156: 1
      1164: 1
      1219: 1
      1223: 1
      1277: 1
      1289: 1
      1290: 1
      1295: 1
      1299: 1
      1313: 1
      1469: 1

1470:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: 2q^2+2q+1
        25: q^2+2q+1
        26: 2q^2+2q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+1
        45: q^2+q+1
        46: q^2+q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: 2q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: 2q^2+2q+1
        64: q^2+q+1
        65: q^2+2q+1
        66: 2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: 1
        90: q^2+1
        91: q^2+1
        92: q^2+q+1
        93: q^2+1
        94: q^2+q+1
        95: q^2+1
        96: q^2+q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q^2+2q+1
       116: 2q^2+2q+1
       117: 2q^2+2q+1
       118: 2q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q^2+q+1
       124: q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: 2q^2+2q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: 1
       163: 1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: 1
       168: q^2+1
       169: q^2+1
       170: 1
       171: q^2+1
       173: q^2+q+1
       174: q^2+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 2q^2+2q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q^2+q+1
       211: q^2+q+1
       212: q^2+q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: q^2+2q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q^2+q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: q^2+1
       271: q^2+1
       272: q^2+1
       273: 1
       274: 1
       275: q^2+1
       276: q^2+1
       277: q^2+1
       279: 1
       283: 1
       284: q^2+1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q^2+1
       412: 1
       413: 1
       414: 1
       415: 1
       416: q^2+1
       417: q^2+1
       418: q^2+1
       427: 1
       431: 1
       432: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       489: 1
       490: q+1
       491: 1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: q^2+1
       606: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       653: q+1
       654: 1
       655: 1
       656: 1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       723: 1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       832: 1
       850: 1
       858: 1
       859: 1
       860: 1
       865: q+1
       866: 1
       867: 1
       868: 1
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       932: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       942: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1155: 1
      1157: 1
      1183: 1
      1228: 1
      1278: 1
      1290: 1
      1291: 1
      1292: 1
      1304: 1
      1314: 1
      1334: 1
      1470: 1

1471:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 2q^2+3q+1
        23: 2q+1
        24: 2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: 2q+1
        52: 2q^2+3q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q^2+3q+1
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: q^2+2q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: 2q^2+3q+1
       115: q^2+2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: 2q+1
       123: q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q+1
       135: 2q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 2q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: q^2+2q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: q+1
       208: q^2+3q+1
       209: q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: q+1
       214: 2q+1
       215: q^2+3q+1
       216: q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q+1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: 2q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: 2q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: 2q+1
       339: q+1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       377: 1
       380: 1
       381: q+1
       382: 2q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 2q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       454: q+1
       455: q+1
       456: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 2q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: q+1
       631: 1
       635: 1
       636: q+1
       639: 1
       641: q+1
       642: q+1
       643: q+1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: q+1
       752: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: q+1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       836: 1
       844: q+1
       849: q+1
       850: q+1
       851: q+1
       854: 1
       861: 1
       862: 1
       868: 1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       913: 1
       914: 1
       916: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       942: 1
       953: 1
       960: 1
       961: 1
       967: 1
       968: 1
       970: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1032: 1
      1061: q+1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1086: 1
      1087: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1137: 1
      1139: 1
      1165: 1
      1180: 1
      1182: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1227: 1
      1279: 1
      1286: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1303: 1
      1404: 1
      1471: 1

1472:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: 2q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q^2+2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: q^2+2q+1
        66: q+1
        67: q^2+2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q^2+2q+1
        72: q+1
        73: q+1
        74: 1
        75: q^2+2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       104: q+1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: q+1
       112: q+1
       113: q^2+2q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: q^2+2q+1
       125: q+1
       126: q+1
       127: 1
       128: q^2+2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: 1
       135: q^2+2q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q^2+2q+1
       144: 1
       145: q^2+2q+1
       146: q+1
       148: q+1
       149: q^2+2q+1
       151: q^2+2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: q+1
       162: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       169: 2q+1
       170: 2q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: q+1
       185: q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: q+1
       206: q+1
       207: 2q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: q+1
       213: 1
       214: q^2+2q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: 2q+1
       227: 2q+1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q^2+2q+1
       242: 1
       243: q+1
       246: 1
       247: q+1
       248: q^2+2q+1
       251: 1
       252: q^2+2q+1
       253: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: q+1
       266: q+1
       267: 2q+1
       272: q+1
       273: 2q+1
       276: q+1
       277: 2q+1
       278: 2q+1
       282: 2q+1
       283: 2q+1
       285: 2q+1
       286: 2q+1
       287: 2q+1
       288: 1
       289: 2q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: 2q+1
       298: 1
       299: 2q+1
       300: q+1
       302: q+1
       303: 2q+1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: q+1
       328: q+1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: 2q+1
       354: 1
       355: 2q+1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: q+1
       379: 1
       380: 1
       381: q^2+2q+1
       386: 1
       387: q+1
       390: 1
       391: q+1
       392: q+1
       394: q+1
       395: q+1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: q+1
       404: q+1
       411: q+1
       412: q+1
       413: 2q+1
       418: q+1
       420: 2q+1
       426: 2q+1
       430: 2q+1
       431: 2q+1
       433: 2q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: 2q+1
       448: 1
       449: q+1
       452: 1
       453: q+1
       454: 2q+1
       458: 2q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: 2q+1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       563: q+1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       573: q+1
       581: q+1
       582: q+1
       589: q+1
       599: 2q+1
       605: 2q+1
       609: 2q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: q+1
       633: 1
       635: 2q+1
       641: q+1
       645: q+1
       646: q+1
       648: q+1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: q+1
       774: q+1
       782: q+1
       801: 2q+1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: q+1
       849: q+1
       853: q+1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       908: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       966: 1
       977: q+1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1060: q+1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1146: 1
      1156: 1
      1164: 1
      1166: 1
      1218: 1
      1219: 1
      1223: 1
      1234: 1
      1280: 1
      1287: 1
      1294: 1
      1295: 1
      1299: 1
      1347: 1
      1405: 1
      1472: 1

1473:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: q^2+2q+1
        26: q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q+1
        62: q^2+2q+1
        63: q+1
        64: q^2+2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q^2+2q+1
        85: q+1
        86: q+1
        87: q^2+2q+1
        88: 1
        89: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: q+1
       104: q+1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: q+1
       112: q^2+2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: q+1
       119: q^2+2q+1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: 2q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: q+1
       141: 2q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       148: 2q+1
       149: 2q+1
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q^2+2q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q^2+2q+1
       165: q^2+2q+1
       166: 1
       167: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: q+1
       206: q^2+2q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: 2q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: q+1
       236: 2q+1
       237: q+1
       242: q+1
       243: 2q+1
       246: 2q+1
       248: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q^2+2q+1
       267: 1
       272: 1
       273: q^2+2q+1
       276: q^2+2q+1
       277: 1
       278: q+1
       281: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 2q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: 2q+1
       298: 2q+1
       299: 1
       300: 2q+1
       302: 2q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: 2q+1
       354: 2q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: q+1
       365: q+1
       372: q+1
       373: 2q+1
       380: 2q+1
       381: q+1
       386: q+1
       387: 2q+1
       390: 2q+1
       392: 2q+1
       394: 2q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q^2+2q+1
       413: 1
       418: 1
       419: q+1
       420: 1
       425: 1
       426: q+1
       429: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: 2q+1
       443: 1
       448: 1
       449: 2q+1
       452: 2q+1
       454: q+1
       457: q+1
       458: 1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: 2q+1
       510: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       526: q+1
       534: q+1
       543: q+1
       550: q+1
       551: 2q+1
       558: 2q+1
       561: 2q+1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: q+1
       599: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 2q+1
       634: q+1
       635: 1
       640: 1
       641: q+1
       644: q+1
       646: q+1
       648: q+1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: q+1
       731: q+1
       739: q+1
       748: 2q+1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: q+1
       849: q+1
       852: q+1
       856: 1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       909: 1
       911: 1
       933: q+1
       961: 1
       963: 1
       965: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1042: 1
      1050: 1
      1059: q+1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1115: 1
      1167: 1
      1198: 1
      1208: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1244: 1
      1281: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1394: 1
      1406: 1
      1473: 1

1474:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+2q+1
        50: 2q+1
        51: 2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: q^2+2q+1
       101: 1
       102: q^2+2q+1
       103: q^2+2q+1
       104: 2q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: 2q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: 2q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: 1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 2q+1
       141: q+1
       144: q+1
       145: q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 2q+1
       162: q+1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: 1
       183: 1
       184: q^2+2q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q^2+2q+1
       189: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: 2q+1
       213: 2q+1
       214: 2q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 2q+1
       225: 1
       227: 1
       228: 2q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: 2q+1
       236: q+1
       237: q+1
       242: q+1
       243: q+1
       246: q+1
       247: q+1
       248: q+1
       251: q+1
       252: q+1
       253: q+1
       255: q+1
       256: q^2+2q+1
       257: 1
       258: 2q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: 2q+1
       266: q+1
       267: q+1
       272: q+1
       273: q+1
       276: q+1
       277: q+1
       278: q+1
       281: q+1
       282: q+1
       283: q+1
       285: q+1
       286: q^2+2q+1
       287: 1
       288: 2q+1
       289: 2q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 2q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 2q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       328: 2q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: 2q+1
       336: 2q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: 2q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: 2q+1
       351: 1
       354: 1
       355: 1
       356: 2q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: q+1
       372: q+1
       373: q+1
       374: q+1
       379: q+1
       380: q+1
       381: q+1
       386: q+1
       387: q+1
       390: q+1
       391: q+1
       392: 1
       394: 1
       395: 2q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: q+1
       411: q+1
       412: q+1
       413: q+1
       418: q+1
       419: q+1
       420: q+1
       425: q+1
       426: q+1
       429: q+1
       430: q+1
       431: 1
       433: 1
       434: 2q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: 2q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q^2+2q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 2q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: 2q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: 2q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: 2q+1
       509: 1
       510: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       535: q+1
       542: q+1
       543: q+1
       550: q+1
       551: q+1
       552: q+1
       557: q+1
       558: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: q+1
       582: q+1
       589: q+1
       590: q+1
       597: q+1
       598: q+1
       599: q+1
       604: q+1
       605: 1
       608: 1
       609: 1
       610: 2q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: 2q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       722: q+1
       731: q+1
       740: q+1
       747: q+1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       774: q+1
       783: q+1
       792: q+1
       799: q+1
       800: 1
       801: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       897: 1
       908: 1
       909: 1
       910: 1
       943: q+1
       952: 1
       959: 1
       962: 1
       963: 1
       964: 1
       997: q+1
      1006: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1088: 1
      1089: 1
      1090: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1116: 1
      1156: 1
      1168: 1
      1208: 1
      1219: 1
      1220: 1
      1221: 1
      1254: 1
      1263: 1
      1270: 1
      1282: 1
      1289: 1
      1295: 1
      1296: 1
      1297: 1
      1407: 1
      1447: 1
      1474: 1

1475:    0: 2q^2+2q+1
         1: q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q+1
         7: q+1
         8: 2q^2+2q+1
         9: q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: 1
        21: q+1
        22: q+1
        23: 2q^2+2q+1
        24: 2q^2+2q+1
        25: q+1
        26: q+1
        27: 2q^2+2q+1
        28: q+1
        29: 2q^2+2q+1
        30: q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q+1
        34: q+1
        35: q^2+2q+1
        36: q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: q^2+2q+1
        43: q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q+1
        48: 2q^2+2q+1
        49: 2q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: 2q^2+2q+1
        57: 1
        58: q+1
        59: q+1
        60: 2q^2+2q+1
        61: 2q^2+2q+1
        62: q+1
        63: q+1
        64: q^2+2q+1
        65: q+1
        66: q+1
        67: q^2+2q+1
        68: q+1
        69: 2q^2+2q+1
        70: 2q+1
        71: 1
        72: q+1
        73: q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q+1
        78: q^2+2q+1
        79: q+1
        80: q^2+2q+1
        81: q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 1
        85: q+1
        86: q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q+1
        91: q^2+2q+1
        92: q+1
        93: q^2+2q+1
        94: q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q+1
        98: q+1
        99: 2q+1
       100: q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: 2q^2+2q+1
       119: 1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 1
       125: q+1
       126: q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q+1
       130: q+1
       131: 2q+1
       132: q+1
       133: 2q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q^2+2q+1
       141: 1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q+1
       148: q+1
       149: q+1
       151: q^2+2q+1
       152: q+1
       153: q^2+2q+1
       154: 2q+1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q^2+2q+1
       162: 1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q+1
       169: q^2+2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q^2+2q+1
       175: 2q+1
       176: 1
       177: q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       183: 2q+1
       184: q+1
       185: 2q+1
       186: q+1
       187: 2q+1
       188: 2q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: 2q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 2q+1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q^2+2q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+2q+1
       220: 1
       221: q+1
       222: q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       227: 2q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 2q+1
       236: 1
       237: 1
       242: q^2+2q+1
       243: 1
       246: q+1
       247: q+1
       248: 1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       255: q+1
       256: q+1
       257: 2q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 2q+1
       266: 1
       267: 1
       272: q^2+2q+1
       273: 1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 1
       281: q+1
       282: q+1
       283: q+1
       285: q+1
       286: q+1
       287: 2q+1
       288: 1
       289: 1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: 2q+1
       295: 1
       298: 2q+1
       299: 2q+1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q+1
       307: 2q+1
       308: 2q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       327: 2q+1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 2q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 2q+1
       344: 1
       345: 1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: 2q+1
       351: 1
       354: 2q+1
       355: 2q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: 2q+1
       365: 1
       372: q+1
       373: 1
       374: 1
       379: q+1
       380: 1
       381: 1
       386: q^2+2q+1
       387: 1
       390: q+1
       391: q+1
       392: q+1
       394: q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: 2q+1
       404: 1
       411: q+1
       412: 1
       413: 1
       418: q^2+2q+1
       419: 1
       420: 1
       425: q+1
       426: 1
       429: q+1
       430: q+1
       431: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: 2q+1
       442: 1
       443: 1
       448: 2q+1
       449: 1
       452: q+1
       453: q+1
       454: 1
       457: q+1
       458: q+1
       459: q+1
       461: 1
       462: q+1
       463: 2q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: 2q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: 2q+1
       509: 1
       510: 1
       515: 2q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       534: q+1
       535: 1
       542: q+1
       543: 1
       550: q+1
       551: 1
       552: 1
       557: q+1
       558: 1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       581: q+1
       582: 1
       589: q+1
       590: 1
       597: q+1
       598: 1
       599: 1
       604: q+1
       605: 1
       608: q+1
       609: q+1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: 2q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: q+1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: 2q+1
       695: 1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       730: q+1
       739: q+1
       740: 1
       747: q+1
       748: 1
       749: 1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       782: q+1
       791: q+1
       792: 1
       799: q+1
       800: 1
       801: 1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       905: 1
       910: 1
       911: 1
       912: 1
       951: q+1
       952: 1
       959: 1
       964: 1
       965: 1
       966: 1
      1005: q+1
      1006: 1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1041: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1117: 1
      1164: 1
      1169: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1262: 1
      1263: 1
      1270: 1
      1283: 1
      1290: 1
      1297: 1
      1298: 1
      1299: 1
      1408: 1
      1455: 1
      1475: 1

1476:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q^2+2q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+q+1
        45: q^2+2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: 2q+1
        62: q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: 1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+2q+1
        93: q^2+q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: q+1
       114: q+1
       115: q+1
       116: q^2+2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q+1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: q+1
       151: q+1
       152: 2q+1
       153: q+1
       154: 2q+1
       155: q+1
       157: q+1
       158: 1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: 1
       168: q^2+q+1
       169: q^2+q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       199: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: q+1
       208: q+1
       209: 1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: q+1
       215: q+1
       216: 1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 2q+1
       235: 2q+1
       236: 1
       238: 1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: 1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: q+1
       255: q+1
       256: 2q+1
       257: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       268: 1
       269: 1
       270: q^2+q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q^2+q+1
       276: q^2+q+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: q+1
       314: q+1
       316: q+1
       317: 1
       318: q+1
       321: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: 2q+1
       343: 2q+1
       344: q+1
       346: q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: q+1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 2q+1
       364: q+1
       366: 1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: 1
       375: 1
       377: q+1
       380: 1
       382: 1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 1
       389: q+1
       390: q+1
       392: 1
       393: q+1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: q^2+q+1
       417: 1
       418: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       469: q+1
       471: 1
       472: 1
       476: q+1
       478: q+1
       480: q+1
       481: 1
       482: q+1
       485: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 2q+1
       500: q+1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       519: 1
       521: 1
       523: 1
       524: 1
       525: q+1
       528: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       534: q+1
       536: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q+1
       551: 1
       553: 1
       555: q+1
       558: 1
       559: 1
       560: q+1
       561: q+1
       566: 1
       568: 1
       570: 1
       571: 1
       572: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: q+1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       654: 1
       656: 1
       662: q+1
       664: 1
       665: 1
       669: 1
       671: 1
       673: 1
       674: 1
       675: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: q+1
       688: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 1
       710: 1
       711: 1
       715: 1
       717: 1
       719: 1
       721: q+1
       733: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       739: q+1
       741: 1
       748: 1
       750: 1
       752: q+1
       760: 1
       762: 1
       763: 1
       767: 1
       769: 1
       771: 1
       773: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       790: 1
       791: 1
       793: 1
       798: 1
       799: 1
       800: 1
       802: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: 1
       816: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       835: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       859: 1
       866: 1
       868: 1
       874: 1
       876: 1
       877: 1
       883: 1
       885: 1
       886: 1
       890: 1
       892: 1
       894: 1
       895: 1
       896: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       911: 1
       913: 1
       919: 1
       936: 1
       938: 1
       940: 1
       942: q+1
       953: 1
       965: 1
       967: 1
       973: 1
       980: 1
       982: 1
       984: 1
       986: 1
       996: 1
      1004: 1
      1005: 1
      1007: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1022: 1
      1026: 1
      1028: 1
      1030: 1
      1032: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1076: 1
      1083: 1
      1085: 1
      1091: 1
      1093: 1
      1099: 1
      1101: 1
      1102: 1
      1106: 1
      1108: 1
      1110: 1
      1112: 1
      1118: 1
      1142: 1
      1170: 1
      1185: 1
      1207: 1
      1215: 1
      1216: 1
      1222: 1
      1224: 1
      1230: 1
      1253: 1
      1264: 1
      1284: 1
      1291: 1
      1298: 1
      1300: 1
      1306: 1
      1403: 1
      1409: 1
      1476: 1

1477:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: 2q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: 2q+1
        24: q^2+2q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: 2q+1
        33: q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+q+1
        38: q+1
        39: q^2+2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: q^2+2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: 2q+1
        61: q^2+2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: 1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: q^2+2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: 1
       142: 1
       143: q^2+q+1
       144: 1
       145: q^2+q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: 1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: q+1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: 2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       207: q+1
       208: q+1
       209: 1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: 1
       226: q+1
       227: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q^2+q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q^2+q+1
       251: 1
       252: q^2+q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 2q+1
       265: 2q+1
       267: 1
       268: 1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: 1
       280: q+1
       282: q+1
       283: 1
       284: q+1
       285: q+1
       286: 2q+1
       287: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       313: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 2q+1
       335: 2q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: q^2+q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 2q+1
       403: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       413: 1
       414: 1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       420: 1
       421: 1
       424: q+1
       426: 1
       427: 1
       428: q+1
       430: q+1
       431: 1
       432: q+1
       433: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       470: q+1
       471: 1
       472: 1
       477: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 2q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       525: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       537: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: q+1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       581: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q+1
       592: 1
       599: 1
       600: 1
       603: q+1
       605: 1
       606: 1
       607: q+1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       655: 1
       656: 1
       663: q+1
       664: 1
       665: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: q+1
       680: 1
       682: 1
       683: 1
       684: 1
       685: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 1
       710: 1
       711: 1
       716: 1
       718: 1
       719: 1
       721: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       742: 1
       746: 1
       747: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       761: 1
       762: 1
       763: 1
       768: 1
       770: 1
       771: 1
       773: q+1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       782: q+1
       794: 1
       801: 1
       802: 1
       805: q+1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       860: 1
       867: 1
       868: 1
       875: 1
       876: 1
       877: 1
       884: 1
       885: 1
       886: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       912: 1
       913: 1
       920: 1
       932: 1
       937: 1
       939: 1
       940: 1
       942: 1
       950: 1
       951: 1
       954: 1
       958: 1
       959: 1
       966: 1
       967: 1
       974: 1
       981: 1
       983: 1
       984: 1
       986: q+1
      1008: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1077: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1100: 1
      1101: 1
      1102: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1119: 1
      1143: 1
      1155: 1
      1163: 1
      1164: 1
      1171: 1
      1186: 1
      1223: 1
      1224: 1
      1231: 1
      1243: 1
      1265: 1
      1285: 1
      1292: 1
      1299: 1
      1300: 1
      1307: 1
      1356: 1
      1410: 1
      1477: 1

1478:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^2+q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+q+1
        21: q^3+2q^2+2q+1
        22: q^2+q+1
        23: q+1
        24: q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^2+q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^3+2q^2+2q+1
        59: q^2+q+1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: 1
        75: q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: 1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q^2+q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q^2+2q+1
       126: q+1
       127: 1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q^2+2q+1
       164: q+1
       165: q+1
       166: 1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: 1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q^2+q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: 1
       224: 1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: q+1
       249: q^2+2q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q^2+2q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q^2+2q+1
       297: q+1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q^2+2q+1
       353: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       481: q+1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       657: q+1
       658: q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: 1
       720: 1
       721: 1
       724: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       780: 1
       781: 1
       782: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       850: q+1
       851: 1
       861: q+1
       869: 1
       870: 1
       877: 1
       878: 1
       879: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       906: 1
       914: 1
       915: 1
       922: 1
       933: 1
       934: 1
       935: 1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       960: 1
       968: 1
       969: 1
       976: 1
       977: 1
       978: 1
       979: 1
       985: 1
       986: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1014: 1
      1015: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1032: 1
      1035: 1
      1045: 1
      1054: 1
      1061: 1
      1062: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1120: 1
      1137: 1
      1138: 1
      1145: 1
      1158: 1
      1172: 1
      1180: 1
      1181: 1
      1188: 1
      1211: 1
      1217: 1
      1225: 1
      1226: 1
      1233: 1
      1266: 1
      1293: 1
      1301: 1
      1302: 1
      1309: 1
      1330: 1
      1369: 1
      1411: 1
      1478: 1

1479:    0: q^3+4q^2+4q+1
         1: q^3+4q^2+4q+1
         2: q^3+4q^2+4q+1
         3: q^3+4q^2+4q+1
         4: 2q^2+4q+1
         5: 2q^2+4q+1
         6: q^3+4q^2+4q+1
         7: 2q^2+4q+1
         8: q^3+4q^2+4q+1
         9: q^3+4q^2+4q+1
        10: q^3+4q^2+4q+1
        11: 2q^2+4q+1
        12: 2q^2+4q+1
        13: 2q^2+4q+1
        14: 2q^2+4q+1
        15: 2q^2+4q+1
        16: 2q^2+4q+1
        17: 2q^2+4q+1
        18: 2q^2+4q+1
        19: q^2+4q+1
        20: q^3+4q^2+4q+1
        21: 2q^2+4q+1
        22: 2q^2+4q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+4q^2+4q+1
        26: 2q^2+4q+1
        27: q^3+4q^2+4q+1
        28: 2q^2+4q+1
        29: 2q^2+4q+1
        30: 2q^2+4q+1
        31: 2q^2+4q+1
        32: q^2+4q+1
        33: 2q^2+4q+1
        34: q^2+4q+1
        35: 2q^2+4q+1
        36: 2q^2+4q+1
        37: 2q^2+4q+1
        38: 2q+1
        39: 2q^2+4q+1
        40: 2q^2+4q+1
        41: q^2+4q+1
        42: 2q^2+4q+1
        43: 2q^2+4q+1
        44: 2q^2+4q+1
        45: 2q^2+4q+1
        46: 2q+1
        47: q^2+4q+1
        48: q^2+4q+1
        49: q^2+4q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: 2q^2+4q+1
        53: 2q^2+4q+1
        54: 2q+1
        55: 2q+1
        56: q+1
        57: q^3+4q^2+4q+1
        58: 2q^2+4q+1
        59: 2q^2+4q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+4q+1
        63: q^2+4q+1
        64: 2q^2+4q+1
        65: 2q^2+4q+1
        66: q^2+4q+1
        67: 2q^2+4q+1
        68: q^2+4q+1
        69: q^2+4q+1
        70: q^2+4q+1
        71: 2q^2+4q+1
        72: q^2+4q+1
        73: q^2+4q+1
        74: q+1
        75: q^2+2q+1
        76: 2q^2+4q+1
        77: 2q+1
        78: 2q^2+4q+1
        79: 2q+1
        80: 2q+1
        81: 2q^2+4q+1
        82: 2q^2+4q+1
        83: 2q+1
        84: 2q^2+4q+1
        85: q^2+4q+1
        86: q^2+4q+1
        87: q^2+2q+1
        88: q+1
        89: 2q^2+4q+1
        90: 2q+1
        91: 2q^2+4q+1
        92: 2q^2+4q+1
        93: 2q^2+4q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+4q+1
       100: q^2+4q+1
       101: q^2+4q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: 2q+1
       106: 2q+1
       107: 2q^2+4q+1
       108: 2q+1
       109: 2q+1
       110: q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: 2q^2+4q+1
       115: 2q^2+4q+1
       116: 2q+1
       117: 2q+1
       118: q+1
       119: 2q^2+4q+1
       120: q^2+4q+1
       121: q^2+4q+1
       122: q^2+2q+1
       123: q+1
       124: 2q^2+4q+1
       125: q^2+4q+1
       126: q^2+4q+1
       127: q+1
       128: q^2+2q+1
       129: q^2+4q+1
       130: q^2+4q+1
       131: q^2+4q+1
       132: q^2+4q+1
       133: q^2+4q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+4q+1
       137: q^2+4q+1
       138: q+1
       139: 2q+1
       140: 1
       141: 2q^2+4q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: q^2+2q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q^2+4q+1
       150: 2q+1
       151: 2q^2+4q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+4q+1
       158: q^2+4q+1
       159: 2q+1
       160: q+1
       161: 1
       162: 2q^2+4q+1
       163: 2q+1
       164: 2q+1
       165: q^2+2q+1
       166: q+1
       167: 2q^2+4q+1
       168: 2q+1
       169: 2q^2+4q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: q^2+4q+1
       177: q^2+4q+1
       178: q^2+4q+1
       179: q+1
       180: q+1
       181: q^2+4q+1
       182: q+1
       183: q^2+4q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       201: 2q^2+4q+1
       202: 2q+1
       203: 2q+1
       204: q+1
       205: q+1
       206: q^2+2q+1
       207: q+1
       208: q^2+4q+1
       209: q^2+4q+1
       210: 2q+1
       211: q+1
       212: 1
       213: q+1
       214: q^2+2q+1
       215: q^2+4q+1
       216: q^2+4q+1
       217: q+1
       218: 2q+1
       219: 1
       220: q^2+4q+1
       221: q^2+4q+1
       222: q^2+4q+1
       223: q+1
       224: q+1
       225: q^2+4q+1
       226: q+1
       227: q^2+4q+1
       228: 1
       229: q+1
       230: 2q+1
       231: q^2+4q+1
       232: q+1
       233: 2q+1
       234: 1
       235: 1
       236: q+1
       237: q^2+2q+1
       238: 2q+1
       239: 2q+1
       240: 1
       241: q+1
       242: 1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       248: 2q^2+4q+1
       249: 2q+1
       250: 2q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       258: 1
       259: 2q+1
       260: q+1
       261: q^2+4q+1
       262: 2q+1
       263: q+1
       264: 1
       265: 1
       266: q^2+2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: q+1
       271: 1
       272: 1
       273: 2q^2+4q+1
       274: 2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       279: q+1
       280: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       287: 2q+1
       288: q+1
       289: q+1
       290: q^2+4q+1
       291: q^2+4q+1
       292: q+1
       293: q+1
       294: 1
       295: q^2+4q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: 2q+1
       301: 1
       302: 2q+1
       303: 2q+1
       304: 1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: 2q+1
       315: 2q+1
       316: q+1
       317: q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: 2q+1
       324: 2q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: 2q+1
       330: q+1
       331: q^2+4q+1
       332: 2q+1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 2q+1
       339: q^2+4q+1
       340: q+1
       341: 2q+1
       342: 1
       343: 1
       344: q+1
       345: q+1
       346: q^2+4q+1
       347: q^2+4q+1
       348: q+1
       349: q+1
       350: 1
       351: q^2+4q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: 1
       357: 1
       358: q+1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: 2q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: q+1
       375: q+1
       376: q+1
       377: 1
       380: q+1
       381: q^2+2q+1
       382: 2q+1
       383: 2q+1
       384: 1
       385: q+1
       386: 1
       387: 2q+1
       388: q+1
       389: q+1
       390: q+1
       392: 2q+1
       393: 1
       394: 2q+1
       395: 1
       396: 1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: 2q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q^2+2q+1
       413: q+1
       414: 2q+1
       415: 2q+1
       416: q+1
       417: 1
       418: 1
       420: q+1
       421: q+1
       422: q+1
       424: 1
       426: 2q+1
       427: q+1
       428: q+1
       430: q+1
       431: 2q+1
       432: 1
       433: 2q+1
       434: 1
       435: q+1
       436: q+1
       437: q^2+4q+1
       438: q+1
       439: q+1
       440: 1
       441: 1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 2q+1
       450: 1
       451: 1
       452: q+1
       454: 2q+1
       455: 1
       456: 1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       465: q+1
       466: q+1
       471: q+1
       473: q+1
       474: q+1
       475: q+1
       476: 2q+1
       479: 2q+1
       480: q+1
       481: q+1
       483: 1
       484: 1
       485: 2q+1
       486: q+1
       487: 2q+1
       488: q+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 2q+1
       496: q+1
       497: 2q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: q+1
       504: q^2+4q+1
       505: q+1
       506: q+1
       507: 1
       508: 1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       522: 2q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       536: 1
       538: q+1
       539: 1
       543: 1
       544: 1
       545: q+1
       546: 2q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: q+1
       553: q+1
       554: q+1
       555: 1
       558: 2q+1
       559: 1
       560: 1
       561: q+1
       563: 1
       564: 1
       565: 1
       566: 2q+1
       569: q+1
       570: 1
       571: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: 2q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       592: 1
       593: q+1
       595: 1
       599: q+1
       600: q+1
       601: q+1
       603: 1
       605: 2q+1
       606: 1
       607: 1
       609: q+1
       610: 1
       611: 1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: 1
       643: 1
       646: q+1
       647: 1
       648: q+1
       650: q+1
       658: q+1
       659: q+1
       664: q+1
       666: 1
       667: 1
       668: 1
       669: 2q+1
       672: q+1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       682: 2q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       705: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: q+1
       719: 1
       720: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: q+1
       750: 1
       751: 1
       752: 1
       756: 1
       757: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: q+1
       797: 1
       801: q+1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       813: q+1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: q+1
       850: 1
       851: 1
       862: q+1
       870: 1
       871: 1
       876: 1
       879: 1
       880: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       893: q+1
       894: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       907: 1
       915: 1
       916: 1
       921: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: q+1
       940: 1
       941: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       961: 1
       969: 1
       970: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1045: 1
      1047: 1
      1054: 1
      1061: 1
      1062: 1
      1079: 1
      1087: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1121: 1
      1138: 1
      1139: 1
      1144: 1
      1149: 1
      1158: 1
      1160: 1
      1173: 1
      1181: 1
      1182: 1
      1187: 1
      1204: 1
      1211: 1
      1213: 1
      1218: 1
      1226: 1
      1227: 1
      1232: 1
      1237: 1
      1250: 1
      1266: 1
      1294: 1
      1302: 1
      1303: 1
      1308: 1
      1331: 1
      1350: 1
      1370: 1
      1400: 1
      1412: 1
      1479: 1

1480:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: 2q+1
        24: q^2+3q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: q^3+3q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: q^3+3q^2+3q+1
        37: q+1
        38: q^2+2q+1
        39: q^3+3q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: q^2+3q+1
        52: q^2+3q+1
        53: q+1
        54: 2q+1
        55: q^2+3q+1
        56: 2q+1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: 2q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q^2+3q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^3+3q^2+3q+1
        82: q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q^2+3q+1
        89: q+1
        90: q+1
        91: q+1
        92: 2q^2+3q+1
        93: q+1
        94: 2q^2+3q+1
        95: q+1
        96: 2q^2+3q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 1
       102: q^2+2q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: q^2+3q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: q+1
       116: 2q+1
       117: q^2+3q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: 2q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q+1
       128: q^2+3q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 1
       134: q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: 1
       138: q+1
       139: q^2+3q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 2q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: 1
       159: 2q+1
       160: q^2+3q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: 2q^2+3q+1
       174: q+1
       175: 2q^2+3q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q^2+3q+1
       181: 1
       182: 1
       183: 1
       184: q^2+2q+1
       185: 1
       186: 2q^2+3q+1
       187: 1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       198: 2q+1
       199: 2q+1
       200: q^2+3q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: q^2+3q+1
       208: q^2+3q+1
       209: 1
       210: 2q+1
       211: q^2+3q+1
       212: 2q+1
       213: q+1
       214: q^2+3q+1
       215: q^2+3q+1
       216: 1
       217: q+1
       218: q^2+3q+1
       219: q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       224: q^2+3q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q^2+3q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: 1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: 1
       262: 1
       263: 1
       264: 2q+1
       265: 2q+1
       266: q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: 2q^2+3q+1
       287: 1
       288: q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: 1
       292: q+1
       293: q^2+3q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       310: 2q+1
       311: q+1
       312: q+1
       313: q+1
       315: q+1
       316: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       328: 2q+1
       329: 2q+1
       330: q^2+3q+1
       331: 1
       332: 1
       333: 1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: q^2+3q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q^2+3q+1
       346: q^2+3q+1
       347: 1
       348: q+1
       349: q^2+3q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: 2q+1
       396: 2q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 2q+1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       420: q+1
       421: q+1
       424: q+1
       426: q+1
       427: q+1
       428: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q^2+3q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+2q+1
       463: 1
       466: q+1
       467: q+1
       470: q+1
       474: 2q+1
       475: q+1
       476: q+1
       477: q+1
       479: q+1
       480: q+1
       483: 2q+1
       484: 2q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 2q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: q+1
       502: q+1
       503: q^2+3q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: 2q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: q+1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q+1
       592: q+1
       599: q+1
       600: q+1
       603: q+1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: q+1
       659: q+1
       660: q+1
       663: q+1
       667: 2q+1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       761: 1
       765: q+1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: q+1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       794: q+1
       801: 1
       802: 1
       805: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       863: q+1
       871: 1
       872: 1
       875: 1
       880: 1
       881: 1
       884: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: 1
       940: 1
       943: 1
       944: 1
       950: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: q+1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
      1008: 1
      1016: 1
      1017: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1040: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1080: 1
      1088: 1
      1096: 1
      1097: 1
      1100: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1122: 1
      1139: 1
      1140: 1
      1143: 1
      1147: 1
      1156: 1
      1157: 1
      1163: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1219: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1265: 1
      1295: 1
      1303: 1
      1304: 1
      1307: 1
      1332: 1
      1348: 1
      1371: 1
      1413: 1
      1480: 1

1481:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 2q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^2+3q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: 2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: q^3+3q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q+1
        45: q^3+3q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+3q+1
        51: 2q+1
        52: q^2+3q+1
        53: q+1
        54: q^2+3q+1
        55: 2q+1
        56: 2q+1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: 2q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: 2q+1
        76: q+1
        77: q+1
        78: q+1
        79: 2q^2+3q+1
        80: q+1
        81: 2q^2+3q+1
        82: q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^3+3q^2+3q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 1
       102: 2q^2+3q+1
       103: q^2+2q+1
       104: 2q+1
       105: q^2+3q+1
       106: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: q^2+3q+1
       113: 2q+1
       114: q^2+3q+1
       115: q+1
       116: q^2+3q+1
       117: 2q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q^2+3q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: 1
       138: q^2+3q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: 2q^2+3q+1
       153: q+1
       154: 2q^2+3q+1
       155: q^2+3q+1
       156: q+1
       157: q^2+3q+1
       158: 1
       159: q^2+3q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 2q^2+3q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       198: 2q+1
       199: q^2+3q+1
       200: 2q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: q^2+3q+1
       207: q+1
       208: q^2+3q+1
       209: 1
       210: q^2+3q+1
       211: q+1
       212: q+1
       213: q^2+3q+1
       214: 2q+1
       215: q^2+3q+1
       216: 1
       217: q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: 1
       232: 1
       233: 1
       234: 2q+1
       235: 2q+1
       236: q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+3q+1
       257: 1
       258: q+1
       259: q^2+3q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: 1
       288: q^2+3q+1
       289: q+1
       290: q^2+3q+1
       291: 1
       292: q^2+3q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       310: 2q+1
       311: q+1
       312: q+1
       314: q+1
       315: q+1
       316: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       328: q+1
       329: q^2+3q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: q^2+3q+1
       338: 2q+1
       339: 1
       340: 1
       341: 1
       342: 2q+1
       343: 2q+1
       344: q^2+3q+1
       345: q+1
       346: q^2+3q+1
       347: 1
       348: q^2+3q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 2q+1
       357: 2q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 2q+1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       375: q+1
       377: q+1
       380: q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q^2+3q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+2q+1
       463: 1
       466: q+1
       468: q+1
       469: q+1
       474: 2q+1
       475: q+1
       476: q+1
       478: q+1
       479: q+1
       480: q+1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: 2q+1
       493: 2q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 2q+1
       501: q+1
       502: q^2+3q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: 2q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       536: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q+1
       551: q+1
       553: q+1
       555: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       564: q+1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       652: q+1
       659: q+1
       661: q+1
       662: q+1
       667: q+1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 2q+1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       707: 1
       708: 1
       713: q+1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       731: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       741: q+1
       748: 1
       750: 1
       752: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       864: q+1
       871: 1
       873: 1
       874: 1
       880: 1
       882: 1
       883: 1
       888: q+1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       909: 1
       916: 1
       918: 1
       919: 1
       934: q+1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       953: 1
       963: 1
       970: 1
       972: 1
       973: 1
       978: 1
       979: 1
       980: 1
       982: 1
       983: 1
       984: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1042: 1
      1043: 1
      1049: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1081: 1
      1089: 1
      1096: 1
      1098: 1
      1099: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1123: 1
      1139: 1
      1141: 1
      1142: 1
      1175: 1
      1182: 1
      1184: 1
      1185: 1
      1199: 1
      1208: 1
      1209: 1
      1215: 1
      1220: 1
      1227: 1
      1229: 1
      1230: 1
      1245: 1
      1264: 1
      1296: 1
      1303: 1
      1305: 1
      1306: 1
      1333: 1
      1372: 1
      1395: 1
      1414: 1
      1481: 1

1482:    0: 2q^3+7q^2+5q+1
         1: 2q^3+7q^2+5q+1
         2: q^3+5q^2+5q+1
         3: 2q^3+7q^2+5q+1
         4: 2q^3+7q^2+5q+1
         5: 2q^3+7q^2+5q+1
         6: 3q^2+4q+1
         7: q^3+5q^2+5q+1
         8: 3q^2+5q+1
         9: 2q^3+7q^2+5q+1
        10: q^3+5q^2+5q+1
        11: 2q^3+7q^2+5q+1
        12: 2q^3+7q^2+5q+1
        13: 2q^3+7q^2+5q+1
        14: q^3+5q^2+5q+1
        15: q^3+5q^2+5q+1
        16: 2q^3+7q^2+5q+1
        17: q^3+5q^2+5q+1
        18: q^3+5q^2+5q+1
        19: 2q^3+7q^2+5q+1
        20: 3q+1
        21: 3q^2+4q+1
        22: 3q^2+5q+1
        23: 3q^2+5q+1
        24: 3q^2+5q+1
        25: 3q^2+4q+1
        26: q^3+5q^2+5q+1
        27: 3q^2+5q+1
        28: 2q^3+7q^2+5q+1
        29: q^3+5q^2+5q+1
        30: 2q^3+7q^2+5q+1
        31: q^3+5q^2+5q+1
        32: 2q^3+7q^2+5q+1
        33: 3q^2+4q+1
        34: q^3+5q^2+5q+1
        35: 2q^2+5q+1
        36: q^3+5q^2+5q+1
        37: 2q^2+3q+1
        38: q^3+5q^2+5q+1
        39: q^3+5q^2+5q+1
        40: 3q^2+4q+1
        41: q^3+5q^2+5q+1
        42: 2q^2+5q+1
        43: q^3+5q^2+5q+1
        44: 2q^2+3q+1
        45: q^3+5q^2+5q+1
        46: q^3+5q^2+5q+1
        47: 2q^3+7q^2+5q+1
        48: q^3+5q^2+5q+1
        49: 3q^2+5q+1
        50: 3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+2q+1
        54: 3q^2+5q+1
        55: 3q^2+5q+1
        56: 3q^2+5q+1
        57: 3q+1
        58: 3q^2+4q+1
        59: 3q^2+5q+1
        60: 3q^2+5q+1
        61: 3q^2+5q+1
        62: 3q^2+4q+1
        63: q^3+5q^2+5q+1
        64: 2q^2+5q+1
        65: 3q^2+4q+1
        66: q^3+5q^2+5q+1
        67: 2q^2+5q+1
        68: 2q^3+7q^2+5q+1
        69: q^3+5q^2+5q+1
        70: 3q^2+5q+1
        71: 3q+1
        72: 3q^2+4q+1
        73: 2q^2+5q+1
        74: 2q^2+5q+1
        75: 2q^2+5q+1
        76: q^2+2q+1
        77: 2q^2+3q+1
        78: q^2+3q+1
        79: q^3+5q^2+5q+1
        80: 2q^2+3q+1
        81: q^3+5q^2+5q+1
        82: 2q^2+3q+1
        83: q^3+5q^2+5q+1
        84: 3q+1
        85: 3q^2+4q+1
        86: 2q^2+5q+1
        87: 2q^2+5q+1
        88: 2q^2+5q+1
        89: q^2+2q+1
        90: 2q^2+3q+1
        91: q^2+3q+1
        92: q^3+5q^2+5q+1
        93: 2q^2+3q+1
        94: q^3+5q^2+5q+1
        95: 2q^2+3q+1
        96: q^3+5q^2+5q+1
        97: 3q^2+4q+1
        98: q^3+5q^2+5q+1
        99: q^2+5q+1
       100: 3q^2+5q+1
       101: 2q+1
       102: 3q^2+5q+1
       103: 3q^2+5q+1
       104: 3q+1
       105: 3q+1
       106: 3q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 3q^2+5q+1
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: q^2+2q+1
       116: 3q^2+5q+1
       117: 3q^2+5q+1
       118: 3q^2+5q+1
       119: 3q+1
       120: 3q^2+4q+1
       121: 2q^2+5q+1
       122: 2q^2+5q+1
       123: 2q^2+5q+1
       124: 3q+1
       125: 3q^2+4q+1
       126: 2q^2+5q+1
       127: 2q^2+5q+1
       128: 2q^2+5q+1
       129: 3q^2+4q+1
       130: q^3+5q^2+5q+1
       131: q^2+5q+1
       132: 3q^2+5q+1
       133: 2q+1
       134: 3q+1
       135: 3q+1
       136: 3q+1
       137: q+1
       138: 2q^2+5q+1
       139: 2q^2+5q+1
       140: 2q^2+5q+1
       141: q+1
       142: q^2+2q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: q^2+2q+1
       147: 2q^2+3q+1
       148: 2q+1
       149: q^2+2q+1
       150: 2q^2+3q+1
       151: q^2+3q+1
       152: q^3+5q^2+5q+1
       153: 2q^2+3q+1
       154: 3q^2+5q+1
       155: 3q+1
       156: 3q+1
       157: 3q+1
       158: q+1
       159: 2q^2+5q+1
       160: 2q^2+5q+1
       161: 2q^2+5q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: q^2+2q+1
       168: 2q^2+3q+1
       169: q^2+3q+1
       170: q^2+2q+1
       171: 2q^2+3q+1
       172: 2q+1
       173: q^3+5q^2+5q+1
       174: 2q^2+3q+1
       175: 3q^2+5q+1
       176: 3q+1
       177: 3q^2+4q+1
       178: q^2+5q+1
       179: q^2+5q+1
       180: q^2+5q+1
       181: q+1
       182: 2q+1
       183: 2q+1
       184: 3q^2+5q+1
       185: 2q+1
       186: 3q^2+5q+1
       187: 2q+1
       188: 3q^2+5q+1
       190: 3q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: 3q+1
       198: 3q+1
       199: 3q+1
       200: 3q+1
       201: q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 3q^2+5q+1
       205: 3q+1
       206: 3q+1
       207: 3q+1
       208: 3q+1
       209: q+1
       210: 2q^2+5q+1
       211: 2q^2+5q+1
       212: 2q^2+5q+1
       213: 3q+1
       214: 3q+1
       215: 3q+1
       216: q+1
       217: 2q^2+5q+1
       218: 2q^2+5q+1
       219: 2q^2+5q+1
       220: 3q+1
       221: 3q^2+4q+1
       222: q^2+5q+1
       223: q^2+5q+1
       224: q^2+5q+1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: 3q+1
       229: 3q+1
       230: 3q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q^2+5q+1
       235: 3q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q^2+3q+1
       241: q^2+3q+1
       242: q^2+3q+1
       243: q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q+1
       249: q^2+2q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+2q+1
       254: 2q^2+3q+1
       255: 2q+1
       256: 3q^2+5q+1
       257: 2q+1
       258: 3q+1
       259: 3q+1
       260: 3q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q^2+5q+1
       265: 3q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q^2+3q+1
       271: q^2+3q+1
       272: q^2+3q+1
       273: q+1
       274: q^2+2q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: q^2+3q+1
       278: q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: q^2+2q+1
       284: 2q^2+3q+1
       285: 2q+1
       286: 3q^2+5q+1
       287: 2q+1
       288: 3q+1
       289: 3q+1
       290: 3q+1
       291: q+1
       292: q^2+5q+1
       293: q^2+5q+1
       294: q^2+5q+1
       295: 1
       296: q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q+1
       301: 2q+1
       302: q+1
       303: q+1
       304: 2q+1
       305: q+1
       306: 3q^2+5q+1
       307: 2q+1
       308: 3q^2+5q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       320: 3q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: 3q+1
       328: 3q+1
       329: 3q+1
       330: 3q+1
       331: 1
       332: q+1
       333: q+1
       334: 2q^2+5q+1
       335: 3q+1
       336: 3q+1
       337: 3q+1
       338: 3q+1
       339: 1
       340: q+1
       341: q+1
       342: 2q^2+5q+1
       343: 3q+1
       344: 3q+1
       345: 3q+1
       346: 3q+1
       347: q+1
       348: q^2+5q+1
       349: q^2+5q+1
       350: q^2+5q+1
       351: 1
       352: q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       357: 3q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 3q+1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: q+1
       370: q+1
       371: q^2+3q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q^2+3q+1
       385: q^2+3q+1
       386: q^2+3q+1
       387: q+1
       388: q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q+1
       393: 2q+1
       394: q+1
       396: 3q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: 3q+1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: q+1
       409: q+1
       410: q^2+3q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q^2+3q+1
       417: q^2+3q+1
       418: q^2+3q+1
       419: q+1
       420: q+1
       421: q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: q+1
       427: q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q+1
       432: 2q+1
       433: q+1
       434: 3q+1
       435: 3q+1
       436: 3q+1
       437: 1
       438: q+1
       439: q+1
       440: q^2+5q+1
       441: 3q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: 2q+1
       461: 1
       462: 3q^2+5q+1
       463: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       484: 3q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 3q+1
       493: 3q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 3q+1
       501: 3q+1
       502: 3q+1
       503: 3q+1
       504: 1
       505: q+1
       506: q+1
       507: q^2+5q+1
       508: 3q+1
       509: 1
       510: 1
       511: 1
       512: q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       535: q+1
       536: q+1
       537: q+1
       541: 2q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: q+1
       548: q+1
       549: q^2+3q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: q+1
       587: q+1
       588: q^2+3q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       596: 2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       611: 3q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: 3q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: 2q+1
       626: 1
       627: 1
       628: 1
       629: 1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: 2q+1
       648: 1
       653: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: 3q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: 3q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: 2q+1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: q+1
       729: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       740: q+1
       741: q+1
       742: q+1
       746: 2q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       752: q+1
       753: q+1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       784: q+1
       790: q+1
       792: q+1
       793: q+1
       794: q+1
       798: 2q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       804: q+1
       805: q+1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       826: 1
       827: 1
       828: 1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       865: q+1
       872: 1
       873: 1
       874: 1
       875: 1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       944: q+1
       950: q+1
       952: 1
       953: 1
       954: 1
       958: q+1
       959: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       998: q+1
      1004: q+1
      1006: 1
      1007: 1
      1008: 1
      1012: q+1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1034: 1
      1040: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1082: 1
      1090: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1124: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1157: 1
      1163: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1209: 1
      1215: 1
      1221: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1255: 1
      1261: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1297: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1334: 1
      1373: 1
      1415: 1
      1448: 1
      1454: 1
      1482: 1

1483:    0: 3q^3+8q^2+5q+1
         1: q^3+7q^2+5q+1
         2: 3q^3+8q^2+5q+1
         3: 3q^3+8q^2+5q+1
         4: q^3+6q^2+5q+1
         5: 3q^3+8q^2+5q+1
         6: q^3+7q^2+5q+1
         7: 5q^2+5q+1
         8: 2q^3+6q^2+5q+1
         9: q^3+7q^2+5q+1
        10: 3q^3+8q^2+5q+1
        11: 3q^3+8q^2+5q+1
        12: q^3+6q^2+5q+1
        13: 5q^2+5q+1
        14: q^3+6q^2+5q+1
        15: 4q^2+5q+1
        16: q^3+7q^2+5q+1
        17: 3q^3+8q^2+5q+1
        18: 2q^3+6q^2+5q+1
        19: q^3+6q^2+5q+1
        20: 3q^2+4q+1
        21: 5q^2+5q+1
        22: 3q^2+5q+1
        23: 2q^3+6q^2+5q+1
        24: 2q^2+3q+1
        25: q^3+7q^2+5q+1
        26: 5q^2+5q+1
        27: 2q^3+6q^2+5q+1
        28: q^3+7q^2+5q+1
        29: 3q^3+8q^2+5q+1
        30: 5q^2+5q+1
        31: q^3+6q^2+5q+1
        32: q^3+6q^2+5q+1
        33: 5q^2+5q+1
        34: 4q^2+5q+1
        35: 3q^2+5q+1
        36: 3q^2+5q+1
        37: 4q^2+5q+1
        38: 4q^2+5q+1
        39: 4q^2+5q+1
        40: q^3+7q^2+5q+1
        41: 5q^2+5q+1
        42: q^3+4q^2+5q+1
        43: q^3+5q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 2q^3+6q^2+5q+1
        46: 2q^2+3q+1
        47: 5q^2+5q+1
        48: q^3+6q^2+5q+1
        49: 3q^2+5q+1
        50: 3q^2+4q+1
        52: q^2+4q+1
        53: 3q^2+5q+1
        54: 3q^2+5q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: 3q^2+4q+1
        58: 5q^2+5q+1
        59: 3q^2+5q+1
        60: 2q^3+6q^2+5q+1
        61: 2q^2+3q+1
        62: q^3+7q^2+5q+1
        63: 5q^2+5q+1
        64: q^3+4q^2+5q+1
        65: 5q^2+5q+1
        66: 4q^2+5q+1
        67: 3q^2+5q+1
        68: 5q^2+5q+1
        69: q^3+6q^2+5q+1
        70: 3q^2+5q+1
        71: q^2+4q+1
        72: 4q^2+5q+1
        73: q^2+5q+1
        74: 3q^2+5q+1
        75: q^2+3q+1
        76: 3q^2+5q+1
        77: q^2+3q+1
        78: 3q^2+5q+1
        79: 3q^2+5q+1
        80: 4q^2+5q+1
        81: 3q^2+5q+1
        82: 4q^2+5q+1
        83: 4q^2+5q+1
        84: q^2+4q+1
        85: 5q^2+5q+1
        86: 2q^2+5q+1
        87: q^3+4q^2+5q+1
        88: 2q+1
        89: q^3+5q^2+5q+1
        90: 2q^2+3q+1
        91: q^3+4q^2+5q+1
        92: q^3+5q^2+5q+1
        93: 2q^3+6q^2+5q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: 5q^2+5q+1
        98: 4q^2+5q+1
        99: 2q^2+5q+1
       100: 2q^2+5q+1
       101: 3q^2+5q+1
       102: 3q^2+5q+1
       103: q^2+3q+1
       105: q^2+4q+1
       107: q^2+4q+1
       108: 3q^2+5q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: 2q+1
       112: 3q^2+4q+1
       114: q^2+4q+1
       115: 3q^2+5q+1
       116: 3q^2+5q+1
       117: q^2+3q+1
       118: 2q^2+3q+1
       119: q^2+4q+1
       120: 5q^2+5q+1
       121: 2q^2+5q+1
       122: q^3+4q^2+5q+1
       123: 2q+1
       124: q^2+4q+1
       125: 4q^2+5q+1
       126: q^2+5q+1
       127: 3q^2+5q+1
       128: q^2+3q+1
       129: 5q^2+5q+1
       130: 4q^2+5q+1
       131: 2q^2+5q+1
       132: 2q^2+5q+1
       133: 3q^2+5q+1
       134: q^2+4q+1
       136: 4q+1
       137: q^2+5q+1
       138: q^2+5q+1
       139: 3q+1
       140: q^2+3q+1
       141: q^2+4q+1
       142: q^2+3q+1
       143: 3q+1
       144: 3q^2+5q+1
       145: q^2+3q+1
       146: 3q^2+5q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: 3q^2+5q+1
       150: q^2+3q+1
       151: 3q^2+5q+1
       152: 3q^2+5q+1
       153: 4q^2+5q+1
       154: 3q^2+5q+1
       155: q^2+4q+1
       157: 4q+1
       158: 2q^2+5q+1
       159: 2q^2+5q+1
       160: 2q+1
       161: 2q+1
       162: q^2+4q+1
       163: 2q^2+3q+1
       164: q^2+3q+1
       165: q^3+4q^2+5q+1
       166: 2q+1
       167: q^3+5q^2+5q+1
       168: 2q^2+3q+1
       169: q^3+4q^2+5q+1
       170: 2q^2+3q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+3q+1
       176: 4q+1
       177: 4q^2+5q+1
       178: q^2+5q+1
       179: 2q^2+5q+1
       180: 2q+1
       181: 2q^2+5q+1
       182: 2q+1
       183: 2q^2+5q+1
       184: 2q^2+5q+1
       185: 3q^2+5q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       191: q^2+4q+1
       193: 2q+1
       194: 2q+1
       195: q^2+3q+1
       196: 2q+1
       197: 2q+1
       199: q^2+4q+1
       201: q^2+4q+1
       202: 3q^2+5q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: 2q+1
       206: q^2+4q+1
       208: 4q+1
       209: 2q^2+5q+1
       210: 2q^2+5q+1
       211: 2q+1
       212: 2q+1
       213: q^2+4q+1
       215: 4q+1
       216: q^2+5q+1
       217: q^2+5q+1
       218: 3q+1
       219: q^2+3q+1
       220: 4q+1
       221: 4q^2+5q+1
       222: q^2+5q+1
       223: 2q^2+5q+1
       224: 2q+1
       225: 2q^2+5q+1
       226: 2q+1
       227: 2q^2+5q+1
       229: 4q+1
       231: 4q+1
       232: q^2+5q+1
       233: 3q+1
       234: 3q+1
       235: 2q+1
       236: q^2+4q+1
       238: 2q+1
       239: 3q+1
       240: 3q+1
       241: 2q+1
       242: q^2+3q+1
       243: 2q+1
       244: q^2+3q+1
       245: 2q+1
       246: q^2+3q+1
       248: q^2+4q+1
       249: q^2+3q+1
       250: 3q+1
       251: 3q^2+5q+1
       252: q^2+3q+1
       253: 3q^2+5q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 2q^2+5q+1
       257: 3q^2+5q+1
       259: 4q+1
       261: 4q+1
       262: 2q^2+5q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q^2+4q+1
       268: 2q+1
       269: q^2+3q+1
       270: q^2+3q+1
       271: q+1
       272: 2q+1
       273: q^2+4q+1
       274: 2q^2+3q+1
       275: q^2+3q+1
       276: q^3+4q^2+5q+1
       277: 2q+1
       278: 2q+1
       279: q^2+2q+1
       280: q+1
       281: 2q+1
       282: q+1
       283: 2q^2+3q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+3q+1
       287: q^2+3q+1
       288: 4q+1
       290: 4q+1
       291: q^2+5q+1
       292: q^2+5q+1
       293: 2q+1
       294: 2q+1
       295: 4q+1
       296: 2q+1
       297: 2q+1
       298: 2q^2+5q+1
       299: 2q+1
       300: 2q^2+5q+1
       301: 2q+1
       302: q^2+3q+1
       303: q^2+3q+1
       304: q+1
       305: 2q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       312: 2q+1
       314: 2q+1
       316: q+1
       317: 2q+1
       321: q^2+4q+1
       323: 2q+1
       324: 2q+1
       325: q^2+3q+1
       326: 2q+1
       327: 2q+1
       329: 4q+1
       331: 4q+1
       332: 2q^2+5q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       337: 4q+1
       339: 4q+1
       340: q^2+5q+1
       341: 3q+1
       342: 3q+1
       343: 2q+1
       344: 4q+1
       346: 4q+1
       347: q^2+5q+1
       348: q^2+5q+1
       349: 2q+1
       350: 2q+1
       351: 4q+1
       352: 2q+1
       353: 2q+1
       354: 2q^2+5q+1
       355: 2q+1
       358: 4q+1
       360: q+1
       361: 2q+1
       362: 3q+1
       363: 2q+1
       364: 2q+1
       366: 2q+1
       368: 2q+1
       369: 3q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: 2q+1
       375: q+1
       376: 2q+1
       377: 2q+1
       380: q^2+4q+1
       382: 2q+1
       383: 3q+1
       384: 3q+1
       385: 2q+1
       386: q^2+3q+1
       387: 2q+1
       388: q^2+3q+1
       389: 2q+1
       390: q^2+3q+1
       392: 2q^2+5q+1
       393: 2q+1
       394: q^2+3q+1
       397: 4q+1
       399: 2q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       405: 2q+1
       407: 2q+1
       408: q^2+3q+1
       409: q+1
       410: q+1
       411: 1
       412: q^2+4q+1
       414: 2q+1
       415: q^2+3q+1
       416: q^2+3q+1
       417: q+1
       418: 2q+1
       419: 2q+1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: q+1
       426: 2q+1
       427: q^2+2q+1
       428: q+1
       429: 2q+1
       430: q+1
       431: q^2+3q+1
       432: q+1
       433: 2q+1
       435: 4q+1
       437: 4q+1
       438: q^2+5q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 4q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: q+1
       452: q^2+3q+1
       454: 2q+1
       455: q+1
       456: 1
       457: 2q+1
       458: q+1
       459: q^2+3q+1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: q^2+3q+1
       469: q+1
       471: q+1
       476: 2q+1
       478: 2q+1
       480: q+1
       481: 2q+1
       485: 4q+1
       487: 2q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       494: 4q+1
       496: q+1
       497: 2q+1
       498: 3q+1
       499: 2q+1
       500: 2q+1
       502: 4q+1
       504: 4q+1
       505: q^2+5q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: 4q+1
       511: q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       515: 2q+1
       519: q+1
       521: 2q+1
       523: 1
       524: 2q+1
       528: 2q+1
       530: 1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       536: q+1
       538: q+1
       539: 2q+1
       544: 2q+1
       546: 2q+1
       547: 3q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: 2q+1
       553: q+1
       554: 2q+1
       555: 2q+1
       558: 2q+1
       559: 2q+1
       560: q+1
       561: q^2+3q+1
       566: 2q+1
       568: q+1
       570: 1
       571: q+1
       575: 2q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 2q+1
       585: 2q+1
       586: q^2+3q+1
       587: q+1
       588: q+1
       589: 1
       591: q+1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: 2q+1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: q+1
       605: 2q+1
       606: q+1
       607: 1
       608: 2q+1
       609: q+1
       612: 4q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       620: q+1
       622: q+1
       623: 2q+1
       624: q+1
       625: q+1
       626: 1
       627: 2q+1
       629: 1
       630: q+1
       631: q+1
       634: 2q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       646: q^2+3q+1
       647: q+1
       648: q+1
       654: q+1
       662: q+1
       664: q+1
       669: 2q+1
       671: q+1
       673: 1
       674: q+1
       679: q+1
       681: 2q+1
       683: 1
       684: 2q+1
       688: 4q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       696: q+1
       698: q+1
       699: 2q+1
       700: q+1
       701: q+1
       702: 1
       708: 1
       710: 1
       715: 1
       717: q+1
       719: 1
       720: q+1
       724: q+1
       726: 1
       733: 2q+1
       735: 1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       741: q+1
       743: q+1
       744: 2q+1
       748: 2q+1
       750: 1
       751: q+1
       752: q+1
       760: 1
       762: 1
       767: q+1
       769: 1
       771: 1
       772: 1
       776: 2q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       785: q+1
       788: 1
       789: 1
       790: 1
       791: 1
       793: q+1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: 2q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       810: q+1
       812: q+1
       814: 1
       815: q+1
       819: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: q+1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: 1
       845: 1
       846: 1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       866: q+1
       874: 1
       876: 1
       883: 1
       885: 1
       890: q+1
       892: q+1
       894: 1
       895: q+1
       899: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       911: 1
       919: 1
       921: 1
       926: 1
       936: 1
       938: q+1
       940: 1
       941: q+1
       945: q+1
       947: 1
       953: 1
       955: 1
       956: q+1
       965: 1
       973: 1
       975: 1
       980: q+1
       982: 1
       984: 1
       985: 1
       992: 1
       995: 1
       999: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1044: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: q+1
      1061: 1
      1062: 1
      1063: 1
      1083: 1
      1091: 1
      1099: 1
      1101: 1
      1106: 1
      1108: 1
      1110: 1
      1111: 1
      1125: 1
      1142: 1
      1144: 1
      1149: 1
      1158: 1
      1160: 1
      1177: 1
      1185: 1
      1187: 1
      1203: 1
      1206: 1
      1210: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1222: 1
      1230: 1
      1232: 1
      1237: 1
      1249: 1
      1252: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1298: 1
      1306: 1
      1308: 1
      1335: 1
      1350: 1
      1374: 1
      1399: 1
      1402: 1
      1416: 1
      1449: 1
      1483: 1

1484:    0: 3q^3+8q^2+5q+1
         1: q^3+7q^2+5q+1
         2: 3q^3+8q^2+5q+1
         3: 3q^3+8q^2+5q+1
         4: 3q^3+8q^2+5q+1
         5: q^3+6q^2+5q+1
         6: q^3+7q^2+5q+1
         7: 5q^2+5q+1
         8: 2q^3+6q^2+5q+1
         9: q^3+7q^2+5q+1
        10: 3q^3+8q^2+5q+1
        11: q^3+6q^2+5q+1
        12: 3q^3+8q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 3q^3+8q^2+5q+1
        15: 2q^3+6q^2+5q+1
        16: 5q^2+5q+1
        17: q^3+6q^2+5q+1
        18: 4q^2+5q+1
        19: q^3+6q^2+5q+1
        20: 3q^2+4q+1
        21: 5q^2+5q+1
        22: 3q^2+5q+1
        23: 2q^2+3q+1
        24: 2q^3+6q^2+5q+1
        25: q^3+7q^2+5q+1
        26: 5q^2+5q+1
        27: 2q^3+6q^2+5q+1
        28: 5q^2+5q+1
        29: q^3+6q^2+5q+1
        30: q^3+7q^2+5q+1
        31: 3q^3+8q^2+5q+1
        32: q^3+6q^2+5q+1
        33: q^3+7q^2+5q+1
        34: 5q^2+5q+1
        35: q^3+4q^2+5q+1
        36: q^3+5q^2+5q+1
        37: 2q^3+6q^2+5q+1
        38: 2q^2+3q+1
        39: 2q^3+6q^2+5q+1
        40: 5q^2+5q+1
        41: 4q^2+5q+1
        42: 3q^2+5q+1
        43: 3q^2+5q+1
        44: 4q^2+5q+1
        45: 4q^2+5q+1
        46: 4q^2+5q+1
        47: 5q^2+5q+1
        48: q^3+6q^2+5q+1
        49: 3q^2+5q+1
        51: 3q^2+4q+1
        52: q^2+4q+1
        53: 3q^2+5q+1
        54: q^2+3q+1
        55: 3q^2+5q+1
        56: 2q^2+3q+1
        57: 3q^2+4q+1
        58: 5q^2+5q+1
        59: 3q^2+5q+1
        60: 2q^2+3q+1
        61: 2q^3+6q^2+5q+1
        62: 5q^2+5q+1
        63: 4q^2+5q+1
        64: 3q^2+5q+1
        65: q^3+7q^2+5q+1
        66: 5q^2+5q+1
        67: q^3+4q^2+5q+1
        68: 5q^2+5q+1
        69: q^3+6q^2+5q+1
        70: 3q^2+5q+1
        71: q^2+4q+1
        72: 5q^2+5q+1
        73: 2q^2+5q+1
        74: 2q+1
        75: q^3+4q^2+5q+1
        76: q^3+5q^2+5q+1
        77: 2q^2+3q+1
        78: q^3+4q^2+5q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^3+5q^2+5q+1
        82: 2q^3+6q^2+5q+1
        83: 2q^2+3q+1
        84: q^2+4q+1
        85: 4q^2+5q+1
        86: q^2+5q+1
        87: q^2+3q+1
        88: 3q^2+5q+1
        89: 3q^2+5q+1
        90: q^2+3q+1
        91: 3q^2+5q+1
        92: 3q^2+5q+1
        93: 4q^2+5q+1
        94: 3q^2+5q+1
        95: 4q^2+5q+1
        96: 4q^2+5q+1
        97: 5q^2+5q+1
        98: 4q^2+5q+1
        99: 2q^2+5q+1
       100: 2q^2+5q+1
       101: 3q^2+5q+1
       102: q^2+3q+1
       103: 3q^2+5q+1
       106: q^2+4q+1
       107: q^2+4q+1
       108: q^2+3q+1
       109: 3q^2+5q+1
       110: q^2+3q+1
       111: 2q+1
       113: 3q^2+4q+1
       114: q^2+4q+1
       115: 3q^2+5q+1
       116: q^2+3q+1
       117: 3q^2+5q+1
       118: 2q^2+3q+1
       119: q^2+4q+1
       120: 4q^2+5q+1
       121: q^2+5q+1
       122: q^2+3q+1
       123: 3q^2+5q+1
       124: q^2+4q+1
       125: 5q^2+5q+1
       126: 2q^2+5q+1
       127: 2q+1
       128: q^3+4q^2+5q+1
       129: 5q^2+5q+1
       130: 4q^2+5q+1
       131: 2q^2+5q+1
       132: 2q^2+5q+1
       133: 3q^2+5q+1
       135: q^2+4q+1
       136: 4q+1
       137: 2q^2+5q+1
       138: 2q+1
       139: 2q^2+5q+1
       140: 2q+1
       141: q^2+4q+1
       142: 2q^2+3q+1
       143: q^2+3q+1
       144: 2q+1
       145: q^3+4q^2+5q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: 2q+1
       149: q^3+5q^2+5q+1
       150: 2q^2+3q+1
       151: q^3+4q^2+5q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+3q+1
       156: q^2+4q+1
       157: 4q+1
       158: q^2+5q+1
       159: 3q+1
       160: q^2+5q+1
       161: q^2+3q+1
       162: q^2+4q+1
       163: q^2+3q+1
       164: 3q+1
       165: q^2+3q+1
       166: 3q^2+5q+1
       167: 3q^2+5q+1
       168: q^2+3q+1
       169: 3q^2+5q+1
       170: 3q^2+5q+1
       171: q^2+3q+1
       172: q^2+3q+1
       173: 3q^2+5q+1
       174: 4q^2+5q+1
       175: 3q^2+5q+1
       176: 4q+1
       177: 4q^2+5q+1
       178: q^2+5q+1
       179: 2q+1
       180: 2q^2+5q+1
       181: 2q^2+5q+1
       182: 2q+1
       183: 2q^2+5q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: 2q^2+5q+1
       187: 3q^2+5q+1
       188: q^2+3q+1
       192: q^2+4q+1
       193: 2q+1
       194: 2q+1
       195: q^2+3q+1
       196: 2q+1
       197: 2q+1
       200: q^2+4q+1
       201: q^2+4q+1
       202: q^2+3q+1
       203: 3q^2+5q+1
       204: q^2+3q+1
       205: 2q+1
       207: q^2+4q+1
       208: 4q+1
       209: q^2+5q+1
       210: 3q+1
       211: q^2+5q+1
       212: q^2+3q+1
       214: q^2+4q+1
       215: 4q+1
       216: 2q^2+5q+1
       217: 2q+1
       218: 2q^2+5q+1
       219: 2q+1
       220: 4q+1
       221: 4q^2+5q+1
       222: q^2+5q+1
       223: 2q+1
       224: 2q^2+5q+1
       225: 2q^2+5q+1
       226: 2q+1
       227: 2q^2+5q+1
       230: 4q+1
       231: 4q+1
       232: 2q+1
       233: 2q^2+5q+1
       234: 2q+1
       235: q+1
       237: q^2+4q+1
       238: 2q+1
       239: q^2+3q+1
       240: q+1
       241: q^2+3q+1
       242: 2q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: q^2+4q+1
       249: 2q^2+3q+1
       250: q^2+3q+1
       251: 2q+1
       252: q^3+4q^2+5q+1
       253: 2q^2+3q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       260: 4q+1
       261: 4q+1
       262: 3q+1
       263: q^2+5q+1
       264: 3q+1
       265: 2q+1
       267: q^2+4q+1
       268: 2q+1
       269: 3q+1
       270: 2q+1
       271: 3q+1
       272: q^2+3q+1
       273: q^2+4q+1
       274: q^2+3q+1
       275: 3q+1
       276: q^2+3q+1
       277: 3q^2+5q+1
       278: 2q+1
       279: q^2+3q+1
       280: 2q+1
       282: q^2+3q+1
       283: 3q^2+5q+1
       284: q^2+3q+1
       285: q^2+3q+1
       286: 2q^2+5q+1
       287: 3q^2+5q+1
       289: 4q+1
       290: 4q+1
       291: q^2+5q+1
       292: 2q+1
       293: q^2+5q+1
       294: 2q+1
       295: 4q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q^2+5q+1
       300: q^2+3q+1
       301: q+1
       302: 2q+1
       303: 2q^2+5q+1
       304: 2q+1
       305: q^2+3q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       313: 2q+1
       315: 2q+1
       316: q+1
       317: 2q+1
       322: q^2+4q+1
       323: 2q+1
       324: 2q+1
       325: q^2+3q+1
       326: 2q+1
       327: 2q+1
       330: 4q+1
       331: 4q+1
       332: 3q+1
       333: q^2+5q+1
       334: 3q+1
       335: 2q+1
       338: 4q+1
       339: 4q+1
       340: 2q+1
       341: 2q^2+5q+1
       342: 2q+1
       343: q+1
       345: 4q+1
       346: 4q+1
       347: q^2+5q+1
       348: 2q+1
       349: q^2+5q+1
       350: 2q+1
       351: 4q+1
       352: 2q+1
       353: 2q+1
       354: 2q+1
       355: 2q^2+5q+1
       359: 4q+1
       360: q+1
       361: 2q+1
       362: 2q+1
       363: q+1
       364: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: q^2+3q+1
       371: q+1
       372: 1
       374: 2q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: q+1
       381: q^2+4q+1
       382: 2q+1
       383: q^2+3q+1
       384: q+1
       385: q^2+3q+1
       386: 2q+1
       387: 2q+1
       388: q^2+2q+1
       389: q+1
       390: q+1
       391: 2q+1
       392: q^2+3q+1
       393: q+1
       394: 2q+1
       398: 4q+1
       399: 2q+1
       400: q+1
       401: 3q+1
       402: 2q+1
       403: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 3q+1
       410: 2q+1
       411: q+1
       413: q^2+4q+1
       414: 2q+1
       415: 3q+1
       416: 2q+1
       417: 3q+1
       418: q^2+3q+1
       420: 2q+1
       421: q+1
       422: 2q+1
       424: 2q+1
       426: 2q+1
       427: q^2+3q+1
       428: 2q+1
       430: q^2+3q+1
       431: 2q^2+5q+1
       432: 2q+1
       433: q^2+3q+1
       436: 4q+1
       437: 4q+1
       438: 2q+1
       439: q^2+5q+1
       440: 2q+1
       441: q+1
       443: 4q+1
       444: q+1
       445: 2q+1
       446: q+1
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: q+1
       451: 1
       452: q+1
       453: 2q+1
       454: 2q+1
       455: 2q+1
       456: q+1
       458: q^2+3q+1
       459: q^2+3q+1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: q^2+3q+1
       470: q+1
       471: q+1
       477: 2q+1
       479: 2q+1
       480: q+1
       481: 2q+1
       486: 4q+1
       487: 2q+1
       488: q+1
       489: 3q+1
       490: 2q+1
       491: 2q+1
       495: 4q+1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: q+1
       500: q+1
       503: 4q+1
       504: 4q+1
       505: 2q+1
       506: q^2+5q+1
       507: 2q+1
       508: q+1
       510: 4q+1
       511: q+1
       512: 2q+1
       513: q+1
       514: 2q+1
       515: 2q+1
       520: q+1
       522: 2q+1
       523: 1
       524: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: q^2+3q+1
       549: q+1
       550: 1
       552: 2q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: q+1
       558: 2q+1
       559: q+1
       560: 1
       561: q+1
       562: 2q+1
       567: 2q+1
       569: q+1
       570: 1
       571: 2q+1
       576: 2q+1
       577: q+1
       578: 1
       579: 2q+1
       580: q+1
       581: q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 3q+1
       588: 2q+1
       589: q+1
       592: q+1
       593: q+1
       595: 2q+1
       599: 2q+1
       600: q+1
       601: 2q+1
       603: 2q+1
       605: 2q+1
       606: 2q+1
       607: q+1
       609: q^2+3q+1
       613: 4q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       621: q+1
       622: q+1
       623: q+1
       624: 2q+1
       625: q+1
       626: 1
       628: 2q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: 2q+1
       636: 1
       637: q+1
       639: q+1
       641: q+1
       642: q+1
       643: 1
       645: q+1
       646: q^2+3q+1
       647: q+1
       648: q+1
       655: q+1
       663: q+1
       664: q+1
       670: 2q+1
       672: q+1
       673: 1
       674: 2q+1
       680: q+1
       682: 2q+1
       683: 1
       684: q+1
       689: 4q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       697: q+1
       698: q+1
       699: q+1
       700: 2q+1
       701: q+1
       702: 1
       709: 1
       710: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       725: q+1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       749: 2q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       761: 1
       762: 1
       768: q+1
       770: 1
       771: 1
       772: q+1
       777: 2q+1
       778: q+1
       779: 1
       780: 2q+1
       781: q+1
       782: q+1
       786: q+1
       788: 1
       794: q+1
       795: q+1
       797: 2q+1
       801: 2q+1
       802: 1
       803: q+1
       805: q+1
       811: q+1
       813: q+1
       814: 1
       815: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: q+1
       843: q+1
       844: 1
       845: 1
       847: 1
       849: q+1
       850: q+1
       851: 1
       853: q+1
       867: q+1
       875: 1
       876: 1
       884: 1
       885: 1
       891: q+1
       893: q+1
       894: 1
       895: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       912: 1
       920: 1
       921: 1
       927: 1
       931: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: 1
       974: 1
       975: 1
       981: q+1
       983: 1
       984: 1
       985: q+1
       993: 1
      1000: q+1
      1002: 1
      1008: 1
      1009: 1
      1011: q+1
      1020: 1
      1021: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: q+1
      1061: 1
      1062: 1
      1064: 1
      1084: 1
      1092: 1
      1100: 1
      1101: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1126: 1
      1143: 1
      1144: 1
      1150: 1
      1154: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1178: 1
      1186: 1
      1187: 1
      1204: 1
      1211: 1
      1213: 1
      1223: 1
      1231: 1
      1232: 1
      1238: 1
      1242: 1
      1250: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1299: 1
      1307: 1
      1308: 1
      1336: 1
      1351: 1
      1355: 1
      1375: 1
      1400: 1
      1417: 1
      1450: 1
      1484: 1

1485:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       107: q^2+q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       201: q^2+q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: q+1
       317: q+1
       318: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: q+1
       472: q+1
       480: q+1
       481: q+1
       482: q+1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       570: 1
       571: 1
       572: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       656: q+1
       664: q+1
       665: q+1
       673: 1
       674: 1
       675: 1
       683: 1
       684: 1
       685: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       711: 1
       719: 1
       720: 1
       721: 1
       726: 1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       750: 1
       751: 1
       752: 1
       762: 1
       763: 1
       771: 1
       772: 1
       773: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       788: 1
       795: 1
       797: 1
       802: 1
       803: 1
       805: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       850: 1
       851: 1
       868: q+1
       876: 1
       877: 1
       885: 1
       886: 1
       894: 1
       895: 1
       896: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       913: 1
       921: 1
       922: 1
       940: 1
       941: 1
       942: 1
       947: 1
       955: 1
       956: 1
       967: 1
       975: 1
       976: 1
       984: 1
       985: 1
       986: 1
      1002: 1
      1009: 1
      1011: 1
      1021: 1
      1022: 1
      1030: 1
      1031: 1
      1032: 1
      1037: 1
      1047: 1
      1054: 1
      1061: 1
      1062: 1
      1085: 1
      1093: 1
      1101: 1
      1102: 1
      1110: 1
      1111: 1
      1112: 1
      1127: 1
      1144: 1
      1145: 1
      1160: 1
      1179: 1
      1187: 1
      1188: 1
      1213: 1
      1224: 1
      1232: 1
      1233: 1
      1266: 1
      1300: 1
      1308: 1
      1309: 1
      1337: 1
      1376: 1
      1418: 1
      1485: 1

1486:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: 1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q^2+2q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q^2+2q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: q+1
       479: q+1
       480: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       588: 1
       606: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: 1
       661: q+1
       662: 1
       663: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       832: 1
       850: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       898: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       960: 1
       971: 1
      1014: 1
      1015: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1074: 1
      1094: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1146: 1
      1147: 1
      1155: 1
      1157: 1
      1217: 1
      1228: 1
      1271: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1318: 1
      1338: 1
      1486: 1

1487:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: 1
        24: q^2+1
        25: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: q^2+1
        32: 1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: 1
        55: q^2+1
        56: 1
        57: q^2+1
        60: 1
        61: q^2+1
        62: 1
        64: 1
        65: q^2+1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q^2+1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: q^2+1
       107: q^2+1
       108: 1
       109: q^2+1
       110: 1
       111: 1
       112: 1
       113: q^2+1
       118: 1
       119: 1
       122: 1
       123: 1
       124: q^2+1
       127: 1
       128: q^2+1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q^2+1
       136: q^2+1
       137: q^2+1
       138: 1
       139: q^2+1
       140: 1
       141: q^2+1
       144: 1
       145: q^2+1
       146: 1
       148: 1
       149: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: q^2+1
       193: 1
       194: q^2+1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: q^2+1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q^2+1
       231: q^2+1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       236: 1
       237: q^2+1
       242: 1
       243: 1
       246: 1
       247: 1
       248: q^2+1
       251: 1
       252: q^2+1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q^2+1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q^2+1
       360: 1
       361: q^2+1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: q^2+1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: q^2+1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       887: 1
       897: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1060: 1
      1068: 1
      1069: 1
      1103: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1156: 1
      1164: 1
      1166: 1
      1218: 1
      1219: 1
      1223: 1
      1234: 1
      1272: 1
      1312: 1
      1313: 1
      1347: 1
      1405: 1
      1487: 1

1488:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^2+2q+1
        11: q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+3q+1
        29: 2q+1
        30: q^3+3q^2+3q+1
        31: q^2+2q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: q^3+3q^2+3q+1
        35: q^3+3q^2+3q+1
        36: q^3+3q^2+3q+1
        37: q^2+2q+1
        38: q^2+3q+1
        39: q^3+3q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: q+1
        45: q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q^2+3q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+3q+1
        55: q^3+3q^2+3q+1
        56: q^2+3q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: 2q+1
        61: q^2+2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^2+3q+1
        69: 2q+1
        70: q^2+3q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^3+3q^2+3q+1
        74: q^2+3q+1
        75: q^3+3q^2+3q+1
        76: q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+3q+1
        80: 2q+1
        81: q^3+3q^2+3q+1
        82: q^2+2q+1
        83: q^2+3q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+3q+1
        87: q^2+3q+1
        88: 2q^2+3q+1
        89: 1
        90: q+1
        91: q+1
        92: q^2+3q+1
        93: q+1
        94: 2q^2+3q+1
        95: q+1
        96: q^2+3q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: q+1
       102: q^2+3q+1
       103: 2q^2+3q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+3q+1
       111: q^2+3q+1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: q^2+2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: q^2+3q+1
       133: 1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+3q+1
       139: q^3+3q^2+3q+1
       140: q^2+3q+1
       141: q+1
       142: q+1
       143: q^2+2q+1
       144: 2q+1
       145: q^2+2q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^2+3q+1
       153: 2q+1
       154: q^2+3q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 1
       159: q^2+3q+1
       160: 2q^2+3q+1
       161: q^2+3q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: q+1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: q+1
       172: q+1
       173: q^2+3q+1
       174: q+1
       175: q^2+3q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+3q+1
       179: q^2+3q+1
       180: 2q^2+3q+1
       181: 1
       182: q+1
       183: q+1
       184: q^2+3q+1
       185: q+1
       186: 2q^2+3q+1
       187: q+1
       188: q^2+3q+1
       189: q+1
       190: q+1
       191: 1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q^2+3q+1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 1
       207: q+1
       208: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: 1
       214: q+1
       215: q+1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: 2q+1
       241: q^2+2q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: q^2+3q+1
       257: 1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: 1
       262: 1
       263: 1
       264: q^2+3q+1
       265: q^2+3q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: 1
       280: q+1
       282: q+1
       283: 1
       284: q+1
       285: q+1
       286: q^2+3q+1
       287: 1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 1
       292: q^2+3q+1
       293: 2q^2+3q+1
       294: q^2+3q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: q+1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: q+1
       305: q+1
       306: q^2+3q+1
       307: q+1
       308: q^2+3q+1
       310: q+1
       311: 1
       312: 1
       313: q+1
       314: 1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: 1
       328: 1
       329: 1
       330: q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: 1
       338: q+1
       342: q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q^2+3q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: 1
       374: q+1
       375: q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: 1
       381: q+1
       382: q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: q+1
       388: q+1
       389: 2q+1
       390: q+1
       391: 2q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q^2+3q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       412: 1
       413: 1
       414: 1
       416: q+1
       417: q+1
       418: q+1
       420: 1
       421: 1
       424: q+1
       426: 1
       427: 1
       428: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 1
       438: 1
       439: 1
       440: q^2+3q+1
       441: q^2+3q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: 1
       456: q+1
       458: q+1
       459: 1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: q+1
       471: 1
       472: 1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: 1
       479: q+1
       480: q+1
       482: 1
       483: 1
       484: 1
       490: 2q+1
       491: 1
       492: 1
       493: 1
       499: q+1
       500: 1
       501: 1
       502: 1
       503: q+1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: q+1
       521: 1
       522: q+1
       523: q+1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: 2q+1
       534: 1
       535: 1
       536: 1
       537: q+1
       541: 2q+1
       542: 2q+1
       543: 1
       544: 1
       545: q+1
       549: q+1
       550: q+1
       551: 1
       552: q+1
       553: q+1
       555: q+1
       556: 2q+1
       557: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       581: 1
       582: 1
       583: 1
       584: 1
       588: q+1
       589: q+1
       592: 1
       599: 1
       600: 1
       603: q+1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+3q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: q+1
       626: q+1
       627: 1
       628: 1
       629: 1
       631: q+1
       632: q+1
       633: q+1
       635: 1
       636: 1
       639: q+1
       641: 1
       642: 1
       643: q+1
       645: q+1
       646: 1
       647: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: q+1
       667: 1
       675: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: q+1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       716: q+1
       717: 1
       718: q+1
       719: q+1
       721: 1
       722: 1
       723: 1
       729: 2q+1
       730: 1
       731: 1
       732: 1
       738: q+1
       739: 1
       740: 1
       741: 1
       742: q+1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       781: q+1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: q+1
       825: 1
       826: 1
       827: 1
       828: 1
       832: q+1
       833: q+1
       836: 1
       843: 1
       844: 1
       847: q+1
       849: 1
       850: 1
       851: 1
       853: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       924: 1
       932: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       962: 1
       966: 1
       967: 1
       970: 1
       971: 1
       974: 1
       978: 1
       986: 1
      1008: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: q+1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1069: 1
      1070: 1
      1074: 1
      1104: 1
      1112: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1171: 1
      1174: 1
      1219: 1
      1223: 1
      1224: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1243: 1
      1265: 1
      1273: 1
      1313: 1
      1314: 1
      1318: 1
      1348: 1
      1356: 1
      1410: 1
      1413: 1
      1488: 1

1489:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       104: q+1
       105: q+1
       106: 2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       112: q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: 2q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 2q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: 1
       284: 1
       286: 1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: 2q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: q+1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       383: q+1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: q+1
       459: 1
       460: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: q+1
       497: q+1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       682: q+1
       689: 1
       697: 1
       698: 1
       700: 1
       703: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: q+1
       736: q+1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: 1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       900: 1
       906: 1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       939: q+1
       946: 1
       954: 1
       955: 1
       957: 1
       960: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1014: 1
      1015: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1159: 1
      1183: 1
      1217: 1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1274: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1422: 1
      1489: 1

1490:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       167: q+1
       168: q+1
       169: 1
       176: q+1
       177: q^2+q+1
       178: q+1
       179: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: q+1
       266: q+1
       268: q+1
       269: q+1
       270: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       300: q+1
       301: q+1
       302: 1
       309: q+1
       310: q+1
       311: q+1
       312: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       397: q+1
       399: 1
       405: q+1
       407: q+1
       408: q+1
       412: 1
       414: 1
       415: 1
       416: 1
       435: q+1
       437: q+1
       438: q+1
       442: q+1
       444: q+1
       445: q+1
       446: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       464: q+1
       465: q+1
       466: 1
       468: 1
       469: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       566: 1
       575: q+1
       577: 1
       583: 1
       585: 1
       586: 1
       612: q+1
       614: 1
       620: q+1
       622: q+1
       623: q+1
       627: 1
       629: 1
       630: 1
       631: 1
       649: q+1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       665: 1
       669: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       703: q+1
       704: q+1
       705: 1
       707: 1
       708: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: q+1
       821: 1
       827: 1
       829: 1
       830: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       878: 1
       879: 1
       882: 1
       886: 1
       899: 1
       906: q+1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       980: 1
      1026: 1
      1035: 1
      1037: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1086: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1141: 1
      1145: 1
      1158: 1
      1237: 1
      1275: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1490: 1

1491:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       165: q+1
       166: q+1
       167: q+1
       169: 1
       170: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       272: q+1
       273: 1
       276: 1
       277: 1
       283: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       298: q+1
       299: q+1
       300: q+1
       302: 1
       303: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       412: 1
       413: 1
       418: 1
       431: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       448: q+1
       449: 1
       452: 1
       453: 1
       459: q+1
       462: q+1
       463: q+1
       465: q+1
       466: 1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: 1
       567: 1
       571: q+1
       582: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       627: 1
       628: 1
       633: 1
       646: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: q+1
       758: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       815: q+1
       826: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       872: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       895: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
      1015: q+1
      1017: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1095: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1131: 1
      1138: 1
      1141: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1276: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1339: 1
      1491: 1

1492:    0: 3q^3+8q^2+5q+1
         1: q^3+7q^2+5q+1
         2: 3q^3+8q^2+5q+1
         3: 3q^3+8q^2+5q+1
         4: 3q^3+8q^2+5q+1
         5: q^3+6q^2+5q+1
         6: 5q^2+5q+1
         7: q^3+7q^2+5q+1
         8: 3q^3+8q^2+5q+1
         9: q^3+7q^2+5q+1
        10: 2q^3+6q^2+5q+1
        11: 4q^2+5q+1
        12: 2q^3+6q^2+5q+1
        13: q^3+7q^2+5q+1
        14: 3q^3+8q^2+5q+1
        15: 3q^3+8q^2+5q+1
        16: 5q^2+5q+1
        17: q^3+6q^2+5q+1
        18: q^3+6q^2+5q+1
        19: q^3+6q^2+5q+1
        20: 5q^2+5q+1
        21: 5q^2+5q+1
        22: q^3+7q^2+5q+1
        23: 4q^2+5q+1
        24: 2q^3+6q^2+5q+1
        25: 3q^2+5q+1
        26: 3q^2+4q+1
        27: 2q^3+6q^2+5q+1
        28: 3q^2+5q+1
        29: 3q^2+5q+1
        30: q^3+5q^2+5q+1
        31: q^3+4q^2+5q+1
        32: 3q^2+5q+1
        33: 5q^2+5q+1
        34: q^3+7q^2+5q+1
        35: 3q^3+8q^2+5q+1
        36: q^3+7q^2+5q+1
        37: 2q^3+6q^2+5q+1
        38: 4q^2+5q+1
        39: 2q^3+6q^2+5q+1
        40: 4q^2+5q+1
        41: 5q^2+5q+1
        42: q^3+6q^2+5q+1
        43: 5q^2+5q+1
        44: 2q^2+3q+1
        45: 4q^2+5q+1
        46: 2q^2+3q+1
        47: 5q^2+5q+1
        48: q^3+6q^2+5q+1
        49: q^3+6q^2+5q+1
        50: q^2+3q+1
        51: 2q^2+3q+1
        52: 5q^2+5q+1
        53: 3q^2+5q+1
        54: 3q^2+5q+1
        55: q^3+5q^2+5q+1
        56: 3q^2+5q+1
        57: 3q^2+5q+1
        58: q^2+4q+1
        59: 3q^2+4q+1
        60: 3q^2+5q+1
        61: q^3+4q^2+5q+1
        62: q^2+5q+1
        63: q^2+4q+1
        64: 3q^2+5q+1
        65: 2q^2+5q+1
        66: q^2+4q+1
        67: q^3+4q^2+5q+1
        68: 2q^2+5q+1
        69: 2q^2+5q+1
        70: 3q^2+5q+1
        71: 5q^2+5q+1
        72: 5q^2+5q+1
        73: q^3+7q^2+5q+1
        74: 4q^2+5q+1
        75: 2q^3+6q^2+5q+1
        76: 3q^2+5q+1
        77: 3q^2+4q+1
        78: 2q^3+6q^2+5q+1
        79: 3q^2+5q+1
        80: 3q^2+5q+1
        81: q^3+5q^2+5q+1
        82: q^3+4q^2+5q+1
        83: 3q^2+5q+1
        84: 4q^2+5q+1
        85: 4q^2+5q+1
        86: 5q^2+5q+1
        87: 4q^2+5q+1
        88: 2q^2+3q+1
        89: q^2+3q+1
        91: 2q^2+3q+1
        92: 3q^2+5q+1
        93: q^2+3q+1
        94: 2q^2+3q+1
        95: 2q+1
        96: q^2+3q+1
        97: 4q^2+5q+1
        98: 5q^2+5q+1
        99: q^3+6q^2+5q+1
       100: 5q^2+5q+1
       101: 2q^2+3q+1
       102: 4q^2+5q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: q^2+3q+1
       106: 2q^2+3q+1
       107: 3q^2+5q+1
       108: q^2+5q+1
       109: 2q^2+5q+1
       110: 2q^2+5q+1
       111: 3q^2+5q+1
       112: 3q+1
       113: q^2+3q+1
       114: q^2+4q+1
       115: q^2+4q+1
       116: q^2+4q+1
       117: q^2+4q+1
       118: 2q^2+5q+1
       119: q^2+5q+1
       120: 4q+1
       121: q^2+4q+1
       122: 3q^2+5q+1
       123: 2q+1
       124: 2q^2+5q+1
       125: 4q+1
       126: q^2+4q+1
       127: q^2+3q+1
       128: q^3+4q^2+5q+1
       129: q^2+5q+1
       130: 4q+1
       131: 2q^2+5q+1
       132: 2q^2+5q+1
       133: 2q+1
       134: q^2+3q+1
       135: 2q^2+3q+1
       136: 5q^2+5q+1
       137: 3q^2+5q+1
       138: 3q^2+5q+1
       139: q^3+5q^2+5q+1
       140: 3q^2+5q+1
       141: 3q^2+5q+1
       142: q^2+4q+1
       143: 3q^2+4q+1
       144: 3q^2+5q+1
       145: q^3+4q^2+5q+1
       146: q^2+5q+1
       147: q^2+4q+1
       148: 3q^2+5q+1
       149: 2q^2+5q+1
       150: q^2+4q+1
       151: q^3+4q^2+5q+1
       152: 2q^2+5q+1
       153: 2q^2+5q+1
       154: 3q^2+5q+1
       155: q^2+3q+1
       156: q^2+2q+1
       157: 4q^2+5q+1
       158: q^2+3q+1
       159: 3q^2+5q+1
       160: 2q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       165: q^2+3q+1
       166: 2q+1
       167: 3q+1
       169: q^2+3q+1
       170: 2q+1
       172: 2q+1
       173: q^2+3q+1
       174: 2q+1
       175: q^2+3q+1
       176: 4q^2+5q+1
       177: 4q^2+5q+1
       178: 5q^2+5q+1
       179: 4q^2+5q+1
       180: 2q^2+3q+1
       181: q^2+3q+1
       183: 2q^2+3q+1
       184: 3q^2+5q+1
       185: q^2+3q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: q^2+3q+1
       189: 2q+1
       190: 2q+1
       191: 3q+1
       192: q^2+3q+1
       193: q^2+5q+1
       194: 2q^2+5q+1
       195: q^2+5q+1
       196: 2q^2+5q+1
       197: 2q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: q^2+4q+1
       202: 4q+1
       203: 4q+1
       204: 4q+1
       205: 2q^2+5q+1
       206: 3q+1
       207: q+1
       208: 4q+1
       209: 2q+1
       210: q^2+4q+1
       211: 2q+1
       212: 2q+1
       213: 2q+1
       214: q^2+3q+1
       215: 4q+1
       216: 2q+1
       217: 2q+1
       218: q^2+4q+1
       219: q^2+3q+1
       220: q^2+5q+1
       221: 4q+1
       222: 4q+1
       223: q^2+3q+1
       224: 2q+1
       225: 2q+1
       227: 2q+1
       228: 2q+1
       229: q^2+3q+1
       230: 2q^2+3q+1
       231: 3q^2+5q+1
       232: q^2+5q+1
       233: 2q^2+5q+1
       234: 2q^2+5q+1
       235: 3q^2+5q+1
       236: 3q+1
       237: q^2+3q+1
       238: q^2+4q+1
       239: q^2+4q+1
       240: q^2+4q+1
       241: q^2+4q+1
       242: 2q^2+5q+1
       243: q^2+5q+1
       244: 4q+1
       245: q^2+4q+1
       246: 3q^2+5q+1
       247: 2q+1
       248: 2q^2+5q+1
       249: 4q+1
       250: q^2+4q+1
       251: q^2+3q+1
       252: q^3+4q^2+5q+1
       253: q^2+5q+1
       254: 4q+1
       255: 2q^2+5q+1
       256: 2q^2+5q+1
       257: 2q+1
       258: q+1
       259: q^2+3q+1
       260: q^2+2q+1
       261: q^2+3q+1
       262: 3q+1
       263: 2q+1
       264: q^2+3q+1
       265: q^2+3q+1
       266: 2q+1
       267: q+1
       272: 2q+1
       273: 3q+1
       276: q^2+3q+1
       277: q+1
       278: 2q+1
       282: 2q+1
       283: 2q+1
       285: 2q+1
       286: q^2+3q+1
       287: q+1
       288: q^2+3q+1
       289: q^2+2q+1
       290: 4q^2+5q+1
       291: q^2+3q+1
       292: 3q^2+5q+1
       293: 2q^2+3q+1
       294: q^2+3q+1
       295: q^2+3q+1
       298: q^2+3q+1
       299: 2q+1
       300: 3q+1
       302: q^2+3q+1
       303: 2q+1
       305: 2q+1
       306: q^2+3q+1
       307: 2q+1
       308: q^2+3q+1
       310: 2q+1
       311: 2q+1
       312: 3q+1
       313: q+1
       314: 2q+1
       315: q^2+3q+1
       316: q^2+5q+1
       317: 2q+1
       319: 2q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: 4q+1
       324: 4q+1
       325: 4q+1
       326: 4q+1
       327: 2q+1
       328: 1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: 2q+1
       343: q^2+3q+1
       344: 2q+1
       345: q+1
       346: 4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: 2q+1
       354: q+1
       355: 1
       356: 2q+1
       357: 2q+1
       358: 3q+1
       359: q^2+3q+1
       360: q^2+5q+1
       361: 2q^2+5q+1
       362: q^2+5q+1
       363: 2q^2+5q+1
       364: 2q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: q^2+4q+1
       369: 4q+1
       370: 4q+1
       371: 4q+1
       372: 2q^2+5q+1
       373: 3q+1
       374: q+1
       375: 4q+1
       376: 2q+1
       377: q^2+4q+1
       378: 2q+1
       379: 2q+1
       380: 2q+1
       381: q^2+3q+1
       382: 4q+1
       383: 2q+1
       384: 2q+1
       385: q^2+4q+1
       386: q^2+3q+1
       387: q^2+5q+1
       388: 4q+1
       389: 4q+1
       390: q^2+3q+1
       391: 2q+1
       392: 2q+1
       394: 2q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: q+1
       399: 3q+1
       400: 2q+1
       401: 2q+1
       402: q^2+3q+1
       403: q+1
       404: q+1
       411: 2q+1
       412: 2q+1
       413: 1
       418: q+1
       420: q+1
       426: 2q+1
       430: q+1
       431: q+1
       433: q+1
       434: q+1
       435: q^2+3q+1
       436: q^2+2q+1
       437: q^2+3q+1
       438: 3q+1
       439: 2q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: 2q+1
       443: q+1
       448: 2q+1
       449: 3q+1
       452: q^2+3q+1
       453: q+1
       454: 2q+1
       458: 2q+1
       459: 2q+1
       461: 2q+1
       462: q^2+3q+1
       463: q+1
       466: 2q+1
       467: 1
       468: q+1
       469: 2q+1
       470: q+1
       471: 2q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 4q+1
       481: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: 2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: 1
       492: q+1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: 2q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       515: 1
       517: 2q+1
       518: 2q+1
       519: 3q+1
       520: q+1
       521: 2q+1
       522: q^2+3q+1
       523: q^2+5q+1
       524: 2q+1
       526: 2q+1
       527: q+1
       528: 2q+1
       529: 2q+1
       530: 4q+1
       531: 4q+1
       532: 4q+1
       533: 4q+1
       534: 2q+1
       535: 1
       536: 2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: 2q+1
       550: q^2+3q+1
       551: 2q+1
       552: q+1
       553: 4q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: q+1
       558: 2q+1
       561: q+1
       562: 1
       564: q+1
       565: q+1
       566: 2q+1
       567: 1
       569: q+1
       570: 2q+1
       571: q+1
       573: q+1
       581: q+1
       582: 1
       589: q+1
       599: 1
       605: q+1
       609: 1
       610: q+1
       611: q+1
       612: 2q+1
       613: q+1
       614: 3q+1
       615: 2q+1
       616: 2q+1
       617: q^2+3q+1
       618: q+1
       619: q+1
       626: 2q+1
       627: 2q+1
       628: 1
       633: q+1
       635: q+1
       641: 2q+1
       645: q+1
       646: q+1
       648: q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: q+1
       674: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: q+1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: 2q+1
       706: 1
       707: q+1
       708: 2q+1
       709: q+1
       710: 2q+1
       713: q+1
       714: q+1
       715: 2q+1
       716: q+1
       717: q+1
       718: 2q+1
       719: 4q+1
       720: q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: 2q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: 1
       731: q+1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: 2q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: 1
       741: q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       754: 1
       757: q+1
       758: 1
       761: 1
       762: q+1
       774: 1
       782: 1
       801: 1
       808: q+1
       809: q+1
       810: 2q+1
       811: 1
       813: q+1
       814: 2q+1
       815: q+1
       817: q+1
       825: q+1
       826: 1
       833: q+1
       843: 1
       849: q+1
       853: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       875: 1
       876: 1
       880: 1
       882: 1
       883: 1
       885: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       916: q+1
       917: 1
       918: 1
       919: q+1
       920: q+1
       921: q+1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: q+1
       931: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: q+1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       959: 1
       962: 1
       966: 1
      1016: q+1
      1017: 1
      1020: 1
      1021: q+1
      1033: 1
      1041: 1
      1060: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1084: 1
      1089: 1
      1091: 1
      1096: 1
      1101: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1219: 1
      1223: 1
      1277: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1328: 1
      1333: 1
      1335: 1
      1340: 1
      1345: 1
      1492: 1

1493:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q+1
        19: q^3+3q^2+3q+1
        20: q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q+1
        68: q^2+3q+1
        69: q^2+3q+1
        70: q+1
        71: q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: q^2+3q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: q+1
        85: q^3+3q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q^2+3q+1
       118: q^2+3q+1
       119: 1
       120: q^2+3q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q^2+3q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: q+1
       142: q^2+3q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: q+1
       149: q^2+3q+1
       150: q^2+3q+1
       151: q+1
       152: q^2+3q+1
       153: q^2+3q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^3+3q^2+3q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q^2+3q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q^2+3q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q^2+3q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q^2+3q+1
       240: q^2+3q+1
       241: q^2+3q+1
       242: q^2+3q+1
       243: 1
       244: q^2+3q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q^2+3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       279: 2q+1
       283: 2q+1
       284: 2q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q^2+3q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: 1
       362: q^2+3q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q^2+3q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       401: 2q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       427: 2q+1
       431: q+1
       432: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       455: 2q+1
       459: 2q+1
       460: 2q+1
       462: q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: q+1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q^2+3q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: q+1
       566: 1
       567: 1
       571: q+1
       572: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       579: 2q+1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       606: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       642: 2q+1
       646: q+1
       647: q+1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: q+1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: q+1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       758: 1
       763: q+1
       766: q+1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: q+1
       809: q+1
       810: 1
       811: 1
       815: q+1
       816: q+1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       823: 2q+1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       850: q+1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: 1
       877: 1
       882: 1
       886: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       935: 1
       938: 1
       939: 1
       941: 1
       942: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1017: 1
      1022: q+1
      1025: q+1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: q+1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1102: 1
      1105: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1136: 1
      1141: 1
      1145: 1
      1148: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1183: 1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1278: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1346: 1
      1349: 1
      1422: 1
      1493: 1

1494:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: q^3+5q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: 3q^3+6q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: q^3+5q^2+4q+1
         7: q^3+5q^2+4q+1
         8: q^3+5q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: 4q^2+4q+1
        11: 2q^2+3q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+6q^2+4q+1
        14: q^3+5q^2+4q+1
        15: 3q^3+6q^2+4q+1
        16: 2q^3+5q^2+4q+1
        17: q^3+4q^2+4q+1
        18: 2q^3+5q^2+4q+1
        19: 2q^3+5q^2+4q+1
        20: q^3+5q^2+4q+1
        21: q^3+5q^2+4q+1
        22: q^3+5q^2+4q+1
        23: 2q+1
        24: 2q^2+3q+1
        25: 4q^2+4q+1
        26: 4q^2+4q+1
        27: 4q^2+4q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^3+5q^2+4q+1
        31: 3q^2+4q+1
        32: 2q^2+3q+1
        33: q^3+5q^2+4q+1
        34: q^3+5q^2+4q+1
        35: q^3+5q^2+4q+1
        36: 3q^3+6q^2+4q+1
        37: 4q^2+4q+1
        38: 2q^2+3q+1
        39: 2q^3+5q^2+4q+1
        40: q^3+4q^2+4q+1
        41: q^3+4q^2+4q+1
        42: q^3+4q^2+4q+1
        43: 2q^3+5q^2+4q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: q^3+3q^2+3q+1
        47: 2q^3+5q^2+4q+1
        48: q^3+4q^2+4q+1
        49: 2q^3+5q^2+4q+1
        50: 2q+1
        51: 2q^2+3q+1
        52: q^3+5q^2+4q+1
        53: 2q^2+3q+1
        54: 2q+1
        55: 2q^2+3q+1
        56: 2q+1
        57: 4q^2+4q+1
        58: 4q^2+4q+1
        59: 4q^2+4q+1
        60: 2q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: 3q^2+4q+1
        66: 3q^2+4q+1
        67: 3q^2+4q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+5q^2+4q+1
        72: q^3+5q^2+4q+1
        73: q^3+5q^2+4q+1
        74: 2q+1
        75: 2q^2+3q+1
        76: 4q^2+4q+1
        77: 4q^2+4q+1
        78: 4q^2+4q+1
        79: 2q^2+3q+1
        80: q^2+3q+1
        81: 2q^3+5q^2+4q+1
        82: 3q^2+4q+1
        83: 2q^2+3q+1
        84: q^3+4q^2+4q+1
        85: q^3+4q^2+4q+1
        86: q^3+4q^2+4q+1
        87: 2q+1
        88: q^2+2q+1
        89: 2q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^3+3q^2+3q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^3+4q^2+4q+1
        98: q^3+4q^2+4q+1
        99: q^3+4q^2+4q+1
       100: 2q^3+5q^2+4q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q^3+3q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: 2q^2+3q+1
       107: 2q^2+3q+1
       108: q+1
       109: 2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: q^2+3q+1
       114: 4q^2+4q+1
       115: 2q^2+3q+1
       116: 2q+1
       117: q^2+3q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: 2q+1
       123: q+1
       124: 3q^2+4q+1
       125: 3q^2+4q+1
       126: 3q^2+4q+1
       128: q^2+3q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: 2q+1
       135: 2q^2+3q+1
       136: q^3+5q^2+4q+1
       137: 2q^2+3q+1
       138: 2q+1
       139: 2q^2+3q+1
       140: 2q+1
       141: 4q^2+4q+1
       142: 4q^2+4q+1
       143: 4q^2+4q+1
       144: 2q+1
       145: q^2+3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: 3q^2+4q+1
       150: 3q^2+4q+1
       151: 3q^2+4q+1
       152: 2q^2+3q+1
       153: q^2+3q+1
       154: 2q^2+3q+1
       155: 2q+1
       156: q^2+2q+1
       157: q^3+4q^2+4q+1
       158: q^2+2q+1
       159: 2q+1
       160: q^2+2q+1
       161: q+1
       162: 2q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: q+1
       166: q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^3+4q^2+4q+1
       177: q^3+4q^2+4q+1
       178: q^3+4q^2+4q+1
       179: 2q+1
       180: q^2+2q+1
       181: 2q^2+3q+1
       182: 2q^2+3q+1
       183: 2q^2+3q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: q^3+3q^2+3q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: 2q+1
       193: q+1
       194: 2q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: q^2+3q+1
       201: 2q^2+3q+1
       202: q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: q+1
       208: q^2+3q+1
       209: q+1
       210: 2q+1
       211: q+1
       212: q+1
       214: q^2+3q+1
       215: 3q^2+4q+1
       216: q^2+2q+1
       218: q^2+3q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: 2q+1
       229: 2q+1
       230: 2q^2+3q+1
       231: 2q^2+3q+1
       232: q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q^2+3q+1
       238: 4q^2+4q+1
       239: 2q^2+3q+1
       240: 2q+1
       241: q^2+3q+1
       242: 2q+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: 2q+1
       247: q+1
       248: 3q^2+4q+1
       249: 3q^2+4q+1
       250: 3q^2+4q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 2q^2+3q+1
       257: 2q+1
       258: q+1
       259: 2q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: 1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: 2q^2+3q+1
       269: q^2+2q+1
       270: q+1
       271: q+1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q^2+2q+1
       279: q^2+2q+1
       280: q^2+2q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: 2q+1
       289: q^2+2q+1
       290: q^3+4q^2+4q+1
       291: q^2+2q+1
       292: 2q+1
       293: q^2+2q+1
       294: q+1
       295: 2q^2+3q+1
       296: 2q^2+3q+1
       297: 2q^2+3q+1
       298: q+1
       299: q+1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q+1
       315: 2q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: 2q+1
       323: q+1
       324: 2q+1
       325: q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: q+1
       335: q+1
       338: q^2+3q+1
       339: q^2+2q+1
       341: q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       349: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       355: 1
       356: 2q+1
       357: 2q+1
       358: q+1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: q+1
       363: 2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: 2q+1
       374: q+1
       375: q^2+3q+1
       376: q+1
       377: 2q+1
       378: q+1
       379: q+1
       381: q^2+3q+1
       382: 3q^2+4q+1
       383: q^2+2q+1
       385: q^2+3q+1
       387: q^2+3q+1
       388: q^2+3q+1
       389: q^2+3q+1
       391: q+1
       392: 2q+1
       393: 2q+1
       394: 2q+1
       395: q+1
       396: q+1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q+1
       406: q+1
       407: q^2+2q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: q+1
       421: q^2+2q+1
       424: q+1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: 2q+1
       436: q^2+2q+1
       437: q^2+2q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: 2q^2+3q+1
       445: q^2+2q+1
       446: q+1
       447: q+1
       448: 1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: q+1
       453: 1
       454: q^2+2q+1
       455: q^2+2q+1
       456: q^2+2q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q+1
       479: 2q+1
       480: q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       495: q+1
       497: q+1
       503: q+1
       504: q+1
       506: 1
       510: 1
       511: 2q+1
       512: q+1
       514: 1
       516: q+1
       517: 2q+1
       518: q+1
       519: q+1
       522: 2q+1
       523: q+1
       524: 1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: q+1
       529: 2q+1
       530: q+1
       531: 2q+1
       532: q+1
       533: 2q+1
       534: q+1
       535: q+1
       536: 2q+1
       537: q+1
       538: q+1
       539: 1
       540: 1
       541: q+1
       542: q+1
       545: q^2+3q+1
       546: q^2+2q+1
       548: q+1
       552: q+1
       553: q^2+3q+1
       554: q+1
       556: q+1
       558: 2q+1
       559: 2q+1
       560: 2q+1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       569: q+1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: q+1
       599: 1
       600: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: q+1
       621: q+1
       622: q^2+2q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: q+1
       628: 1
       629: 2q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       635: q+1
       636: q^2+2q+1
       639: q+1
       641: q+1
       642: q+1
       643: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: q+1
       689: 1
       691: 1
       697: 1
       698: q+1
       700: 1
       703: q+1
       704: 1
       705: q+1
       710: 1
       711: 1
       712: q+1
       713: 2q+1
       714: q+1
       715: q+1
       718: 2q+1
       719: q+1
       720: 1
       721: q+1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       734: q+1
       736: q+1
       742: q+1
       743: q+1
       745: 1
       749: 1
       750: 2q+1
       751: q+1
       753: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: q+1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: q+1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       836: q+1
       843: 1
       844: q+1
       847: 1
       849: q+1
       850: q+1
       851: q+1
       853: 1
       854: 1
       861: 1
       862: 1
       868: 1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       906: 1
       907: 1
       913: 1
       914: q+1
       915: 1
       916: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       932: 1
       939: q+1
       946: 1
       948: 1
       954: 1
       955: q+1
       957: 1
       960: 1
       961: 1
       967: 1
       968: 1
       970: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: q+1
      1064: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1109: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1135: 1
      1136: 1
      1152: 1
      1159: 1
      1161: 1
      1165: 1
      1180: 1
      1182: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1227: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1243: 1
      1265: 1
      1279: 1
      1315: 1
      1322: 1
      1323: 1
      1329: 1
      1353: 1
      1404: 1
      1419: 1
      1421: 1
      1494: 1

1495:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: 1
       169: 1
       170: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       272: 1
       273: 1
       276: 1
       277: 1
       278: q+1
       282: q+1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: q+1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: 1
       452: 1
       453: 1
       454: q+1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: q+1
       641: 1
       645: 1
       646: 1
       648: 1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       893: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       939: 1
       946: 1
       948: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1060: 1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1152: 1
      1166: 1
      1218: 1
      1219: 1
      1223: 1
      1234: 1
      1280: 1
      1316: 1
      1323: 1
      1324: 1
      1328: 1
      1405: 1
      1495: 1

1496:    0: 2q^3+6q^2+4q+1
         1: 2q^3+6q^2+4q+1
         2: 2q^3+6q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+6q^2+4q+1
         5: 2q^3+6q^2+4q+1
         6: 2q^3+6q^2+4q+1
         7: q^3+3q^2+3q+1
         8: 4q^2+4q+1
         9: 5q^2+4q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 4q^2+4q+1
        13: 2q^3+6q^2+4q+1
        14: 2q^3+6q^2+4q+1
        15: 5q^2+4q+1
        16: 2q^3+6q^2+4q+1
        17: 2q^3+6q^2+4q+1
        18: 4q^2+4q+1
        19: 2q^3+6q^2+4q+1
        20: 4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: 4q^2+4q+1
        24: 2q^2+3q+1
        25: 5q^2+4q+1
        26: q^2+2q+1
        27: 4q^2+4q+1
        28: 5q^2+4q+1
        29: 5q^2+4q+1
        30: 4q^2+4q+1
        31: 4q^2+4q+1
        32: 4q^2+4q+1
        33: 2q^3+6q^2+4q+1
        34: q^3+3q^2+3q+1
        35: 4q^2+4q+1
        36: 5q^2+4q+1
        37: 5q^2+4q+1
        38: 5q^2+4q+1
        39: 4q^2+4q+1
        40: 2q^3+6q^2+4q+1
        41: q^3+3q^2+3q+1
        42: 3q^2+4q+1
        43: 4q^2+4q+1
        44: 4q^2+4q+1
        45: 4q^2+4q+1
        46: 2q^2+3q+1
        47: 2q^3+6q^2+4q+1
        48: 2q^3+6q^2+4q+1
        49: 4q^2+4q+1
        50: 4q^2+4q+1
        51: 2q^2+3q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: 2q+1
        56: 2q^2+3q+1
        57: 4q^2+4q+1
        58: q^2+2q+1
        59: 2q+1
        60: 4q^2+4q+1
        61: 2q^2+3q+1
        62: 5q^2+4q+1
        63: q^2+2q+1
        64: q^2+3q+1
        65: 4q^2+4q+1
        66: q^2+2q+1
        67: 2q^2+3q+1
        68: 4q^2+4q+1
        69: 4q^2+4q+1
        70: 2q^2+3q+1
        71: 4q^2+4q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: 4q^2+4q+1
        75: 2q^2+3q+1
        76: 5q^2+4q+1
        77: q^2+2q+1
        78: 4q^2+4q+1
        79: 5q^2+4q+1
        80: 5q^2+4q+1
        81: 4q^2+4q+1
        82: 4q^2+4q+1
        83: 4q^2+4q+1
        84: 3q^2+4q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: 3q^2+4q+1
        88: 2q+1
        89: 4q^2+4q+1
        91: 3q^2+4q+1
        92: 4q^2+4q+1
        93: 4q^2+4q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: 2q^3+6q^2+4q+1
        98: q^3+3q^2+3q+1
        99: 3q^2+4q+1
       100: 4q^2+4q+1
       101: 4q^2+4q+1
       102: 4q^2+4q+1
       103: 2q^2+3q+1
       104: 2q^2+3q+1
       105: q^2+3q+1
       106: 2q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: 2q+1
       110: 2q+1
       111: q^2+2q+1
       112: 4q^2+4q+1
       113: 2q^2+3q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: 2q^2+3q+1
       119: q^2+3q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+3q+1
       123: q+1
       124: 2q^2+3q+1
       125: q^2+2q+1
       126: q+1
       127: 2q^2+3q+1
       128: q^2+2q+1
       129: 4q^2+4q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q^2+3q+1
       133: 2q^2+3q+1
       134: 4q^2+4q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: 2q+1
       140: 2q^2+3q+1
       141: 4q^2+4q+1
       142: q^2+2q+1
       143: 2q+1
       144: 4q^2+4q+1
       145: 2q^2+3q+1
       146: 5q^2+4q+1
       147: q^2+2q+1
       148: q^2+3q+1
       149: 4q^2+4q+1
       150: q^2+2q+1
       151: 2q^2+3q+1
       152: 4q^2+4q+1
       153: 4q^2+4q+1
       154: 2q^2+3q+1
       155: 3q^2+4q+1
       156: 2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: 3q^2+4q+1
       165: 3q^2+4q+1
       166: 2q+1
       167: 4q^2+4q+1
       169: q^2+3q+1
       170: 2q^2+3q+1
       172: q^2+2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+2q+1
       176: 3q^2+4q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: 3q^2+4q+1
       180: 2q+1
       181: 4q^2+4q+1
       183: 3q^2+4q+1
       184: 4q^2+4q+1
       185: 4q^2+4q+1
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: 2q^2+3q+1
       189: q^2+2q+1
       190: 2q+1
       191: q^2+3q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q^2+2q+1
       198: 2q^2+3q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: q+1
       206: q^2+3q+1
       207: q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: 2q^2+3q+1
       214: q^2+2q+1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: q^2+2q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: 2q+1
       224: 1
       225: 2q^2+3q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: q^2+3q+1
       230: 2q+1
       231: q^2+3q+1
       232: q^2+3q+1
       233: 2q+1
       234: 2q+1
       235: q^2+2q+1
       236: 4q^2+4q+1
       237: 2q^2+3q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: 2q^2+3q+1
       243: q^2+3q+1
       244: q^2+2q+1
       245: 2q+1
       246: q^2+3q+1
       247: q+1
       248: 2q^2+3q+1
       249: q^2+2q+1
       250: q+1
       251: 2q^2+3q+1
       252: q^2+2q+1
       253: 4q^2+4q+1
       254: q^2+2q+1
       255: 2q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q+1
       259: q^2+3q+1
       260: 2q+1
       261: q^2+3q+1
       262: q^2+3q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 3q^2+4q+1
       267: 2q+1
       272: 2q+1
       273: q^2+3q+1
       276: q^2+3q+1
       277: q+1
       278: q^2+2q+1
       281: q^2+2q+1
       282: q+1
       283: 2q^2+3q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 3q^2+4q+1
       289: 2q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: q^2+3q+1
       293: 2q+1
       294: 2q+1
       295: 3q^2+4q+1
       298: 3q^2+4q+1
       299: 2q+1
       300: 4q^2+4q+1
       302: q^2+3q+1
       303: 2q^2+3q+1
       305: q^2+2q+1
       306: 2q^2+3q+1
       307: 2q^2+3q+1
       308: q^2+2q+1
       309: q^2+2q+1
       310: q+1
       311: 2q+1
       312: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q+1
       335: 1
       336: q^2+2q+1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: 2q+1
       354: 2q+1
       355: 1
       356: q^2+2q+1
       357: 2q+1
       358: q^2+3q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q^2+2q+1
       365: 2q^2+3q+1
       366: 2q+1
       367: q+1
       368: 2q+1
       369: 2q+1
       370: q+1
       371: q+1
       372: q+1
       373: q^2+3q+1
       374: q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: q+1
       379: q+1
       380: 2q^2+3q+1
       381: q^2+2q+1
       382: q+1
       383: q+1
       384: q+1
       385: 1
       386: q^2+2q+1
       387: 2q+1
       388: q^2+2q+1
       389: q+1
       390: 2q+1
       391: 1
       392: 2q^2+3q+1
       394: 2q+1
       395: q+1
       396: 2q+1
       397: q^2+3q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       411: 1
       412: q^2+3q+1
       413: q+1
       418: q+1
       419: q^2+2q+1
       420: q+1
       425: q+1
       426: q+1
       429: q+1
       430: 1
       431: q^2+2q+1
       433: q+1
       434: 2q+1
       435: q^2+3q+1
       436: 2q+1
       437: q^2+3q+1
       438: q^2+3q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 3q^2+4q+1
       443: 2q+1
       448: 2q+1
       449: q^2+3q+1
       452: q^2+3q+1
       453: q+1
       454: q^2+2q+1
       457: q^2+2q+1
       458: q+1
       459: 2q^2+3q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: 1
       468: q+1
       469: 1
       471: 1
       473: q+1
       474: 1
       475: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: q+1
       485: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: 2q+1
       510: 1
       515: 1
       516: q^2+2q+1
       517: q+1
       518: 2q+1
       519: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: q+1
       527: q+1
       528: 2q+1
       529: q+1
       530: q+1
       531: 1
       532: q+1
       533: 1
       534: q+1
       535: q+1
       536: 2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: q+1
       542: 1
       543: q^2+2q+1
       544: q+1
       545: 1
       546: q+1
       547: q+1
       548: 1
       549: 1
       550: q+1
       551: 2q+1
       552: 1
       553: q+1
       554: q+1
       555: q+1
       556: 1
       557: 1
       558: 2q+1
       561: 2q+1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       581: 1
       582: q+1
       589: 1
       590: q+1
       597: 1
       598: q+1
       599: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: q+1
       611: 2q+1
       612: q^2+3q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       626: 1
       627: q^2+3q+1
       628: q+1
       633: q+1
       634: q^2+2q+1
       635: q+1
       640: q+1
       641: q+1
       644: q+1
       645: 1
       646: q^2+2q+1
       648: q+1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       707: q+1
       708: 1
       710: 1
       712: q+1
       713: 1
       714: q+1
       715: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: q+1
       724: 2q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: 1
       730: 1
       731: q+1
       732: 1
       733: q+1
       734: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       740: 1
       741: q+1
       742: 1
       743: q+1
       744: q+1
       745: 1
       746: 1
       747: 1
       748: 2q+1
       749: 1
       754: 1
       756: q+1
       757: 1
       759: q+1
       760: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       825: 1
       826: q+1
       833: 1
       834: q+1
       841: 1
       842: q+1
       843: 1
       848: 1
       849: q+1
       852: q+1
       853: 1
       856: 1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       907: 1
       909: 1
       911: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       943: 1
       944: 1
       945: q+1
       946: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       961: 1
       963: 1
       965: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1015: q+1
      1016: 1
      1018: q+1
      1019: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: q+1
      1060: 1
      1065: 1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1095: 1
      1098: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1129: 1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1138: 1
      1141: 1
      1146: 1
      1147: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1167: 1
      1198: 1
      1218: 1
      1220: 1
      1222: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1281: 1
      1317: 1
      1323: 1
      1325: 1
      1327: 1
      1339: 1
      1342: 1
      1406: 1
      1437: 1
      1496: 1

1497:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       774: 1
       783: 1
       792: 1
       799: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       888: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       934: 1
       943: 1
       944: 1
       950: 1
       962: 1
       963: 1
       964: 1
       997: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1147: 1
      1168: 1
      1219: 1
      1220: 1
      1221: 1
      1254: 1
      1282: 1
      1318: 1
      1324: 1
      1325: 1
      1326: 1
      1407: 1
      1497: 1

1498:    0: 2q^2+2q+1
         1: q^2+2q+1
         2: 2q^2+2q+1
         3: q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: 2q^2+2q+1
        18: 2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: 2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q^2+q+1
        68: 2q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 2q+1
        77: q+1
        78: q^2+2q+1
        79: 2q+1
        80: q^2+2q+1
        81: 2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+2q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       127: q^2+q+1
       128: q^2+q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q^2+2q+1
       141: q+1
       142: q+1
       143: q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q^2+q+1
       152: 2q+1
       153: q^2+2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       169: q+1
       170: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q^2+q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q^2+2q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: q^2+q+1
       252: q^2+q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       272: 2q+1
       273: 1
       276: q+1
       277: q+1
       278: q+1
       281: q+1
       282: q+1
       283: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q^2+q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: q+1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: q+1
       420: q+1
       425: q+1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       448: 2q+1
       449: 1
       452: q+1
       453: q+1
       454: q+1
       457: q+1
       458: q+1
       459: 2q+1
       461: 1
       462: q+1
       463: q+1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: q+1
       566: 1
       567: 1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       581: 1
       582: 1
       589: 1
       590: q+1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       626: 1
       627: 1
       628: 1
       633: q+1
       634: q+1
       635: q+1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       678: 1
       681: 1
       682: 1
       684: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: 1
       759: q+1
       760: 1
       761: 1
       762: 1
       782: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: q+1
       810: 1
       811: 1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       825: 1
       826: 1
       833: 1
       834: q+1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       882: 1
       889: 1
       892: 1
       893: 1
       895: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       935: 1
       938: 1
       939: 1
       941: 1
       944: 1
       945: 1
       946: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       964: 1
       965: 1
       966: 1
      1005: 1
      1006: 1
      1017: 1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1041: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1098: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1141: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1169: 1
      1221: 1
      1222: 1
      1223: 1
      1262: 1
      1263: 1
      1283: 1
      1319: 1
      1326: 1
      1327: 1
      1328: 1
      1342: 1
      1408: 1
      1498: 1

1499:    0: 2q^3+6q^2+4q+1
         1: 2q^3+6q^2+4q+1
         2: 2q^3+6q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+6q^2+4q+1
         5: 2q^3+6q^2+4q+1
         6: q^3+3q^2+3q+1
         7: 2q^3+6q^2+4q+1
         8: 5q^2+4q+1
         9: 5q^2+4q+1
        10: 4q^2+4q+1
        11: 5q^2+4q+1
        12: 4q^2+4q+1
        13: 2q^3+6q^2+4q+1
        14: 2q^3+6q^2+4q+1
        15: 5q^2+4q+1
        16: 2q^3+6q^2+4q+1
        17: 2q^3+6q^2+4q+1
        18: 4q^2+4q+1
        19: 2q^3+6q^2+4q+1
        20: q^2+2q+1
        21: q^3+3q^2+3q+1
        22: 5q^2+4q+1
        23: 5q^2+4q+1
        24: 4q^2+4q+1
        25: q^2+3q+1
        26: 4q^2+4q+1
        27: 4q^2+4q+1
        28: 5q^2+4q+1
        29: 4q^2+4q+1
        30: 4q^2+4q+1
        31: 3q^2+4q+1
        32: 4q^2+4q+1
        33: q^3+3q^2+3q+1
        34: 2q^3+6q^2+4q+1
        35: 5q^2+4q+1
        36: 5q^2+4q+1
        37: 4q^2+4q+1
        38: 5q^2+4q+1
        39: 4q^2+4q+1
        40: q^3+3q^2+3q+1
        41: 2q^3+6q^2+4q+1
        42: 4q^2+4q+1
        43: 4q^2+4q+1
        44: 2q^2+3q+1
        45: 4q^2+4q+1
        46: 2q^2+3q+1
        47: 2q^3+6q^2+4q+1
        48: 2q^3+6q^2+4q+1
        49: 4q^2+4q+1
        50: q^2+2q+1
        52: q^2+2q+1
        53: q^2+3q+1
        54: 5q^2+4q+1
        55: 4q^2+4q+1
        56: 4q^2+4q+1
        57: 2q+1
        58: q^2+3q+1
        59: 4q^2+4q+1
        60: 4q^2+4q+1
        61: 3q^2+4q+1
        62: q^2+3q+1
        63: 4q^2+4q+1
        64: 2q^2+3q+1
        65: q^2+3q+1
        66: 3q^2+4q+1
        67: q^2+3q+1
        68: 4q^2+4q+1
        69: 3q^2+4q+1
        70: 2q^2+3q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: 5q^2+4q+1
        74: 5q^2+4q+1
        75: 4q^2+4q+1
        76: q^2+3q+1
        77: 4q^2+4q+1
        78: 4q^2+4q+1
        79: 5q^2+4q+1
        80: 4q^2+4q+1
        81: 4q^2+4q+1
        82: 3q^2+4q+1
        83: 4q^2+4q+1
        84: q^2+2q+1
        85: q^3+3q^2+3q+1
        86: 4q^2+4q+1
        87: 4q^2+4q+1
        88: 2q^2+3q+1
        89: 2q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: 4q^2+4q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: 2q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: 2q^3+6q^2+4q+1
        99: 4q^2+4q+1
       100: 4q^2+4q+1
       101: 2q^2+3q+1
       102: 4q^2+4q+1
       103: 2q^2+3q+1
       105: q^2+2q+1
       107: 2q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: 4q^2+4q+1
       111: 2q^2+3q+1
       112: 2q+1
       114: 2q+1
       115: q^2+3q+1
       116: 4q^2+4q+1
       117: 3q^2+4q+1
       118: 3q^2+4q+1
       119: q+1
       120: q^2+3q+1
       121: 2q^2+3q+1
       122: 2q^2+3q+1
       123: q^2+2q+1
       124: 2q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q^2+3q+1
       128: q^2+3q+1
       129: q^2+3q+1
       130: 3q^2+4q+1
       131: 2q+1
       132: 2q^2+3q+1
       133: q^2+2q+1
       134: q^2+2q+1
       136: q^2+2q+1
       137: q^2+3q+1
       138: 5q^2+4q+1
       139: 4q^2+4q+1
       140: 4q^2+4q+1
       141: 2q+1
       142: q^2+3q+1
       143: 4q^2+4q+1
       144: 4q^2+4q+1
       145: 3q^2+4q+1
       146: q^2+3q+1
       147: 4q^2+4q+1
       148: 2q^2+3q+1
       149: q^2+3q+1
       150: 3q^2+4q+1
       151: q^2+3q+1
       152: 4q^2+4q+1
       153: 3q^2+4q+1
       154: 2q^2+3q+1
       155: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: 4q^2+4q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: q+1
       163: 2q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: 2q+1
       167: 2q+1
       168: 2q^2+3q+1
       169: q^2+2q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q^2+3q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^3+3q^2+3q+1
       178: 4q^2+4q+1
       179: 4q^2+4q+1
       180: 2q^2+3q+1
       181: 2q+1
       182: 2q^2+3q+1
       183: 2q^2+3q+1
       184: 4q^2+4q+1
       185: 2q^2+3q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: 2q^2+3q+1
       191: 2q+1
       193: q+1
       194: 2q+1
       195: q^2+3q+1
       196: 2q^2+3q+1
       197: q^2+2q+1
       199: 2q+1
       201: 2q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: 3q^2+4q+1
       205: 2q+1
       206: q+1
       208: q+1
       209: q+1
       210: 2q^2+3q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: 2q+1
       215: 2q+1
       216: q+1
       217: q^2+3q+1
       218: q^2+3q+1
       219: q^2+3q+1
       220: q+1
       221: q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: q^2+2q+1
       227: q+1
       229: q^2+2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+3q+1
       234: 4q^2+4q+1
       235: 2q^2+3q+1
       236: 2q+1
       238: 2q+1
       239: q^2+3q+1
       240: 4q^2+4q+1
       241: 3q^2+4q+1
       242: 3q^2+4q+1
       243: q+1
       244: q^2+3q+1
       245: 2q^2+3q+1
       246: 2q^2+3q+1
       247: q^2+2q+1
       248: 2q+1
       249: q^2+3q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: 3q^2+4q+1
       255: 2q+1
       256: 2q^2+3q+1
       257: q^2+2q+1
       259: q^2+2q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q^2+3q+1
       265: q^2+2q+1
       266: q+1
       268: q+1
       269: 2q+1
       270: 2q^2+3q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: 2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: 4q^2+4q+1
       293: 2q^2+3q+1
       294: 2q^2+3q+1
       295: q+1
       296: 2q+1
       297: 2q^2+3q+1
       298: 2q^2+3q+1
       299: 2q+1
       300: 2q+1
       301: 2q^2+3q+1
       302: q^2+2q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q^2+3q+1
       307: 2q+1
       308: q^2+2q+1
       312: q+1
       314: 2q+1
       316: q+1
       317: q+1
       318: q^2+2q+1
       321: 2q+1
       323: q+1
       324: 2q+1
       325: q^2+3q+1
       326: 2q+1
       327: q+1
       329: q+1
       331: 1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q+1
       337: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+3q+1
       343: 2q+1
       344: q+1
       346: q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       358: 2q+1
       360: q+1
       361: 2q+1
       362: q^2+3q+1
       363: 2q^2+3q+1
       364: q^2+2q+1
       366: 2q+1
       368: 2q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: 3q^2+4q+1
       372: 2q+1
       373: q+1
       375: q+1
       376: q+1
       377: 2q^2+3q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: 2q+1
       382: 2q+1
       383: q+1
       384: q^2+3q+1
       385: q^2+3q+1
       386: q^2+3q+1
       387: q+1
       388: q^2+3q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: q+1
       393: q^2+2q+1
       394: q+1
       397: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       405: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: 1
       414: 1
       415: q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: q+1
       421: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       435: q^2+2q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: q+1
       444: q+1
       445: 2q+1
       446: 2q^2+3q+1
       447: 2q+1
       448: 2q+1
       449: 1
       450: 2q+1
       451: q^2+2q+1
       452: q^2+2q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       469: q+1
       471: 1
       472: q+1
       476: q+1
       478: 2q+1
       480: q+1
       481: 1
       482: q+1
       485: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: 1
       494: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       519: q+1
       521: 2q+1
       523: q+1
       524: q+1
       525: q^2+2q+1
       528: 2q+1
       530: q+1
       531: 2q+1
       532: q^2+3q+1
       533: 2q+1
       534: q+1
       536: q+1
       538: 1
       539: q+1
       540: q+1
       541: q^2+2q+1
       542: q+1
       544: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: q^2+3q+1
       550: 2q+1
       551: q+1
       553: q+1
       554: 1
       555: 2q+1
       556: q+1
       557: q+1
       558: 1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       566: 1
       568: q+1
       570: 1
       571: q+1
       572: q+1
       575: q+1
       577: 1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       591: q+1
       596: q+1
       597: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       612: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       620: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: 1
       629: 1
       630: q+1
       631: q^2+2q+1
       632: q+1
       633: q+1
       634: q+1
       636: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       654: 1
       656: 1
       662: q+1
       664: 1
       665: 1
       669: 1
       671: 1
       673: 1
       674: 1
       675: 1
       681: q+1
       684: 1
       685: q+1
       688: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       708: q+1
       710: 1
       711: q+1
       715: q+1
       717: 2q+1
       719: q+1
       720: 1
       721: q+1
       724: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       730: 1
       733: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       741: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       750: 1
       751: 1
       752: q+1
       753: 1
       754: 1
       760: 1
       762: 1
       763: q+1
       767: 1
       769: q+1
       771: 1
       773: 1
       776: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       790: 1
       791: 1
       793: 1
       798: 1
       799: 1
       800: 1
       802: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: q+1
       814: 1
       815: q+1
       816: q+1
       819: q+1
       821: 1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       835: q+1
       840: q+1
       841: 1
       842: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       859: 1
       866: 1
       868: 1
       874: 1
       876: 1
       877: 1
       886: 1
       892: 1
       895: 1
       896: 1
       899: 1
       902: 1
       903: 1
       911: 1
       913: 1
       919: q+1
       921: 1
       922: 1
       926: 1
       928: 1
       930: 1
       931: 1
       932: 1
       938: q+1
       941: 1
       942: q+1
       945: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       953: 1
       955: 1
       956: 1
       957: 1
       958: 1
       965: 1
       967: 1
       973: 1
       980: 1
       982: 1
       984: 1
       986: 1
       996: 1
      1004: 1
      1005: 1
      1007: 1
      1012: 1
      1019: 1
      1021: 1
      1022: q+1
      1026: 1
      1028: q+1
      1030: 1
      1032: 1
      1035: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1049: 1
      1050: 1
      1052: 1
      1057: 1
      1058: 1
      1059: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1076: 1
      1083: 1
      1085: 1
      1102: 1
      1108: 1
      1118: 1
      1125: 1
      1127: 1
      1133: 1
      1135: 1
      1136: 1
      1145: 1
      1151: 1
      1154: 1
      1155: 1
      1158: 1
      1161: 1
      1162: 1
      1170: 1
      1185: 1
      1207: 1
      1222: 1
      1224: 1
      1230: 1
      1237: 1
      1239: 1
      1241: 1
      1243: 1
      1253: 1
      1261: 1
      1262: 1
      1264: 1
      1269: 1
      1284: 1
      1320: 1
      1327: 1
      1329: 1
      1346: 1
      1352: 1
      1409: 1
      1424: 1
      1446: 1
      1499: 1

1500:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: q+1
        24: 2q^2+2q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q+1
        55: 2q^2+2q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: q^2+2q+1
        60: q+1
        61: q^2+2q+1
        62: q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q+1
        75: 2q^2+2q+1
        76: 2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: 2q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q^2+2q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q^2+2q+1
       106: q^2+2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: q^2+2q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 2q+1
       125: 2q+1
       126: q^2+2q+1
       128: q^2+2q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q+1
       139: 2q^2+2q+1
       140: q+1
       141: 2q+1
       142: 2q+1
       143: q^2+2q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q+1
       153: q+1
       154: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q^2+2q+1
       187: q+1
       188: q+1
       192: 2q+1
       193: q+1
       194: 2q+1
       195: q+1
       196: q+1
       197: 1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       214: 2q+1
       215: 2q+1
       216: q+1
       218: q^2+2q+1
       220: q+1
       221: q+1
       222: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       230: q^2+2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: q^2+2q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 2q+1
       249: 2q+1
       250: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       260: q^2+2q+1
       261: q+1
       262: 1
       263: q+1
       264: q+1
       265: q+1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       313: q+1
       315: 2q+1
       316: q+1
       317: 1
       318: 1
       322: 2q+1
       323: q+1
       324: 2q+1
       325: q+1
       326: q+1
       327: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       338: 2q+1
       339: q+1
       341: q+1
       345: q+1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: q+1
       363: q+1
       364: 1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: q+1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       381: 2q+1
       382: 2q+1
       383: q+1
       385: q^2+2q+1
       387: q+1
       388: q+1
       389: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: q+1
       403: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q^2+2q+1
       437: q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       470: q+1
       471: 1
       472: 1
       477: q+1
       479: 2q+1
       480: q+1
       481: 1
       482: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       495: q+1
       497: q+1
       503: q+1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       520: q+1
       522: 2q+1
       523: q+1
       524: 1
       525: 1
       529: 2q+1
       530: q+1
       531: 2q+1
       532: q+1
       533: q+1
       534: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       545: 2q+1
       546: q+1
       548: q+1
       552: q+1
       553: q+1
       554: 1
       556: q+1
       558: 1
       559: 1
       560: 1
       562: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       572: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: q+1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: q+1
       618: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       655: 1
       656: 1
       663: q+1
       664: 1
       665: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: q+1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       709: q+1
       710: 1
       711: 1
       716: q+1
       718: 2q+1
       719: q+1
       720: 1
       721: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       734: q+1
       736: q+1
       742: q+1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       761: 1
       762: 1
       763: 1
       768: 1
       770: q+1
       771: 1
       773: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: q+1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       860: 1
       867: 1
       868: 1
       875: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       912: 1
       913: 1
       920: q+1
       921: 1
       922: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       939: q+1
       946: 1
       948: 1
       954: 1
       955: 1
       957: 1
       966: 1
       967: 1
       974: 1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1029: q+1
      1030: 1
      1032: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1077: 1
      1084: 1
      1085: 1
      1109: 1
      1119: 1
      1126: 1
      1127: 1
      1134: 1
      1135: 1
      1136: 1
      1152: 1
      1159: 1
      1161: 1
      1171: 1
      1186: 1
      1223: 1
      1224: 1
      1231: 1
      1238: 1
      1240: 1
      1241: 1
      1243: 1
      1265: 1
      1285: 1
      1321: 1
      1328: 1
      1329: 1
      1353: 1
      1410: 1
      1425: 1
      1500: 1

1501:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: q+1
       158: q+1
       159: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       167: q+1
       168: q+1
       169: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: q+1
       209: q+1
       210: 1
       213: 1
       214: 1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       259: 1
       261: q+1
       262: 1
       266: 1
       268: q+1
       269: q+1
       270: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       288: 1
       290: q+1
       291: q+1
       292: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       300: q+1
       301: q+1
       302: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: q+1
       332: 1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       347: q+1
       348: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       376: q+1
       377: 1
       380: 1
       381: 1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       397: 1
       399: 1
       405: 1
       407: q+1
       408: 1
       412: 1
       414: q+1
       415: q+1
       416: 1
       435: 1
       437: q+1
       438: 1
       442: 1
       444: q+1
       445: q+1
       446: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: q+1
       505: 1
       509: 1
       511: q+1
       512: q+1
       513: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: q+1
       539: 1
       543: 1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       554: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: q+1
       586: 1
       612: 1
       614: 1
       620: 1
       622: q+1
       623: 1
       627: 1
       629: q+1
       630: q+1
       631: 1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: q+1
       699: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: 1
       750: q+1
       751: q+1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       829: q+1
       830: 1
       854: 1
       861: 1
       862: 1
       868: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       906: 1
       907: 1
       913: 1
       914: 1
       915: 1
       916: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: q+1
       956: 1
       980: 1
      1026: 1
      1035: 1
      1037: 1
      1071: 1
      1086: 1
      1087: 1
      1093: 1
      1106: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1237: 1
      1286: 1
      1315: 1
      1330: 1
      1331: 1
      1337: 1
      1350: 1
      1501: 1

1502:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: 2q+1
        60: q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: q^2+2q+1
        76: 2q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: 2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       112: q+1
       113: q^2+2q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: 1
       123: q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: 2q+1
       127: q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q^2+2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: q+1
       191: q+1
       192: 2q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: 1
       213: q+1
       214: q^2+2q+1
       215: 2q+1
       216: 2q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: 1
       224: q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: 1
       236: q+1
       237: q^2+2q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: 1
       247: q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: 2q+1
       251: q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       272: 1
       273: q+1
       276: 1
       277: q+1
       283: q+1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: q+1
       302: q+1
       303: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: 2q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q+1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       354: 1
       355: q+1
       356: 1
       357: q+1
       358: q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       380: q+1
       381: q^2+2q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: q+1
       418: 1
       431: q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: q+1
       452: 1
       453: q+1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: q+1
       633: 1
       646: q+1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       756: 1
       758: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       872: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
      1015: 1
      1017: 1
      1072: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1097: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1131: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1287: 1
      1316: 1
      1331: 1
      1332: 1
      1336: 1
      1339: 1
      1341: 1
      1502: 1

1503:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       165: 1
       167: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       183: 1
       184: 1
       185: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       273: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       298: 1
       300: 1
       302: 1
       309: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       412: 1
       435: 1
       437: 1
       438: 1
       442: 1
       449: 1
       452: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       566: 1
       612: 1
       614: 1
       627: 1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       688: 1
       690: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       810: 1
       856: 1
       862: 1
       864: 1
       866: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       890: 1
       907: 1
       909: 1
       911: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       945: 1
       947: 1
      1073: 1
      1087: 1
      1089: 1
      1091: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1149: 1
      1288: 1
      1317: 1
      1331: 1
      1333: 1
      1335: 1
      1503: 1

1504:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        92: 1
        94: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       173: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       395: 1
       396: 1
       402: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       564: 1
       610: 1
       611: 1
       617: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       808: 1
       857: 1
       863: 1
       864: 1
       865: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       943: 1
       944: 1
       950: 1
      1074: 1
      1088: 1
      1089: 1
      1090: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: 1
      1289: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1504: 1

1505:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       674: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       889: 1
       890: 1
       891: 1
       895: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       931: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
      1017: 1
      1075: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1290: 1
      1319: 1
      1334: 1
      1335: 1
      1336: 1
      1341: 1
      1505: 1

1506:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       312: 1
       314: 1
       316: 1
       317: 1
       318: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       469: 1
       471: 1
       472: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: 1
       521: 1
       523: 1
       524: 1
       525: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       654: 1
       656: 1
       662: 1
       664: 1
       665: 1
       669: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       708: 1
       710: 1
       711: 1
       715: 1
       717: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       829: 1
       830: 1
       859: 1
       866: 1
       868: 1
       883: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       911: 1
       913: 1
       919: 1
       921: 1
       922: 1
       926: 1
       936: 1
       938: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       980: 1
      1026: 1
      1035: 1
      1037: 1
      1076: 1
      1091: 1
      1093: 1
      1106: 1
      1118: 1
      1125: 1
      1127: 1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1237: 1
      1291: 1
      1320: 1
      1335: 1
      1337: 1
      1350: 1
      1506: 1

1507:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       470: 1
       471: 1
       472: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       525: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       571: 1
       572: 1
       576: 1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       655: 1
       656: 1
       663: 1
       664: 1
       665: 1
       670: 1
       674: 1
       675: 1
       680: 1
       682: 1
       683: 1
       684: 1
       685: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       709: 1
       710: 1
       711: 1
       716: 1
       718: 1
       719: 1
       720: 1
       721: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       763: 1
       768: 1
       777: 1
       778: 1
       780: 1
       811: 1
       815: 1
       816: 1
       820: 1
       821: 1
       823: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: 1
       860: 1
       867: 1
       868: 1
       877: 1
       884: 1
       885: 1
       886: 1
       891: 1
       895: 1
       896: 1
       900: 1
       901: 1
       903: 1
       912: 1
       913: 1
       920: 1
       921: 1
       922: 1
       927: 1
       931: 1
       932: 1
       937: 1
       939: 1
       940: 1
       941: 1
       942: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       981: 1
      1022: 1
      1027: 1
      1036: 1
      1037: 1
      1039: 1
      1077: 1
      1092: 1
      1093: 1
      1102: 1
      1107: 1
      1119: 1
      1126: 1
      1127: 1
      1136: 1
      1143: 1
      1144: 1
      1145: 1
      1150: 1
      1154: 1
      1155: 1
      1159: 1
      1160: 1
      1162: 1
      1238: 1
      1292: 1
      1321: 1
      1336: 1
      1337: 1
      1346: 1
      1351: 1
      1507: 1

1508:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 1
        85: q^2+2q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q^2+2q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q^2+2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q^2+2q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q^2+2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       431: q+1
       432: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       455: q+1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: q+1
       524: 1
       525: 1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: q+1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: q+1
       646: q+1
       647: q+1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: q+1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       763: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: q+1
       861: 1
       869: 1
       870: 1
       877: 1
       878: 1
       879: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       906: 1
       914: 1
       915: 1
       922: 1
       923: 1
       924: 1
       925: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       960: 1
       979: 1
      1014: 1
      1015: 1
      1022: 1
      1025: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1105: 1
      1120: 1
      1128: 1
      1129: 1
      1136: 1
      1137: 1
      1138: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1217: 1
      1236: 1
      1293: 1
      1322: 1
      1330: 1
      1338: 1
      1339: 1
      1346: 1
      1349: 1
      1508: 1

1509:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: 2q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q+1
        24: q^2+q+1
        25: q^2+2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: 2q+1
        39: q^2+2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q^2+q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: q^2+2q+1
        66: q+1
        67: q^2+2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q^2+2q+1
        72: q+1
        73: q+1
        74: q+1
        75: q^2+q+1
        76: q^2+2q+1
        77: q+1
        78: q^2+2q+1
        79: 2q+1
        80: 2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: 2q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: q+1
       104: q+1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: q^2+q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q^2+2q+1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: q+1
       135: q^2+q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: q+1
       141: q^2+2q+1
       142: q+1
       143: q+1
       144: q+1
       145: q^2+q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: q^2+2q+1
       150: q+1
       151: q^2+2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q^2+q+1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 2q+1
       227: 2q+1
       228: q+1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: q+1
       237: q^2+q+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: q^2+2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q^2+q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: 2q+1
       276: q+1
       277: 1
       278: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: 2q+1
       298: q+1
       299: 1
       300: 2q+1
       302: 2q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: 2q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: q+1
       365: q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: q+1
       374: 1
       375: q+1
       376: q+1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q^2+q+1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: q+1
       391: 1
       392: 2q+1
       394: 2q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       420: 1
       426: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       449: 2q+1
       452: q+1
       453: 1
       454: q+1
       458: 1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q+1
       535: 1
       536: 1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: q+1
       552: 1
       553: q+1
       554: q+1
       555: 1
       556: 1
       557: 1
       558: 2q+1
       561: q+1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: q+1
       628: 1
       633: 1
       635: 1
       641: q+1
       645: 1
       646: q+1
       648: q+1
       650: 1
       658: 1
       659: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       710: 1
       712: q+1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       754: 1
       756: 1
       757: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: q+1
       853: 1
       862: 1
       870: 1
       871: 1
       876: 1
       879: 1
       880: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       915: 1
       916: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: 1
       977: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1060: 1
      1079: 1
      1087: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1121: 1
      1129: 1
      1130: 1
      1135: 1
      1138: 1
      1139: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1218: 1
      1234: 1
      1294: 1
      1323: 1
      1331: 1
      1339: 1
      1340: 1
      1345: 1
      1347: 1
      1509: 1

1510:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: 1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: 1
       555: 1
       556: q+1
       557: 1
       558: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       761: 1
       774: 1
       801: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       863: 1
       871: 1
       872: 1
       875: 1
       880: 1
       881: 1
       884: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       897: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       959: 1
       962: 1
      1016: 1
      1017: 1
      1020: 1
      1033: 1
      1060: 1
      1080: 1
      1088: 1
      1096: 1
      1097: 1
      1100: 1
      1122: 1
      1130: 1
      1131: 1
      1134: 1
      1139: 1
      1140: 1
      1143: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1156: 1
      1219: 1
      1295: 1
      1324: 1
      1332: 1
      1340: 1
      1341: 1
      1344: 1
      1510: 1

1511:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: q^2+2q+1
        37: 2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+2q+1
        50: 2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: q^2+2q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: 2q+1
        88: 1
        89: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+q+1
        95: q+1
        96: q^2+q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: 2q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       165: q+1
       166: 1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q^2+q+1
       174: q+1
       175: q^2+q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 1
       181: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+q+1
       187: q+1
       188: q^2+q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 2q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: 2q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: 1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 1
       248: 2q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       272: 1
       273: q+1
       276: q+1
       277: 1
       278: q+1
       281: q+1
       282: 1
       283: q+1
       285: q+1
       286: q^2+q+1
       287: q+1
       288: 2q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q^2+q+1
       307: q+1
       308: q^2+q+1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: 1
       356: q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 2q+1
       374: 1
       375: q+1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: 2q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: 1
       386: q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: 1
       392: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       411: 1
       412: q+1
       413: 1
       418: 1
       419: q+1
       420: 1
       425: 1
       426: q+1
       429: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       449: q+1
       452: q+1
       453: 1
       454: q+1
       457: q+1
       458: 1
       459: q+1
       461: q+1
       462: q^2+q+1
       463: q+1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: 2q+1
       552: 1
       553: q+1
       554: 1
       555: q+1
       556: 1
       557: 1
       558: q+1
       561: q+1
       562: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: q+1
       599: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: q+1
       628: 1
       633: 1
       634: q+1
       635: 1
       640: 1
       641: q+1
       644: q+1
       645: 1
       646: q+1
       648: q+1
       652: 1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: 1
       707: 1
       708: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: q+1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       754: 1
       757: 1
       759: 1
       760: 1
       774: 1
       783: 1
       792: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: q+1
       843: 1
       848: 1
       849: q+1
       852: q+1
       853: 1
       864: 1
       871: 1
       873: 1
       874: 1
       880: 1
       882: 1
       883: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       897: 1
       909: 1
       916: 1
       918: 1
       919: 1
       924: 1
       925: 1
       926: 1
       928: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       959: 1
       963: 1
       997: 1
      1006: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1059: q+1
      1060: 1
      1065: 1
      1081: 1
      1089: 1
      1096: 1
      1098: 1
      1099: 1
      1123: 1
      1130: 1
      1132: 1
      1133: 1
      1139: 1
      1141: 1
      1142: 1
      1147: 1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1156: 1
      1208: 1
      1220: 1
      1254: 1
      1263: 1
      1270: 1
      1296: 1
      1325: 1
      1333: 1
      1340: 1
      1342: 1
      1343: 1
      1447: 1
      1511: 1

1512:    0: q^4+3q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: q^4+3q^2+2q+1
         4: q^4+3q^2+2q+1
         5: q^4+3q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: q^4+3q^2+2q+1
        12: q^4+3q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^4+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: q^4+3q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: q^4+3q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: q^4+3q^2+2q+1
        39: q^4+3q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: q^4+3q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: q^2+2q+1
       141: q+1
       142: q^2+2q+1
       143: 2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 2q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+2q+1
       153: 2q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: q^2+2q+1
       243: q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q+1
       249: q^2+2q+1
       250: 2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: 1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       298: q+1
       299: q+1
       300: q+1
       302: q+1
       303: q+1
       305: 1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: 2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 1
       354: q+1
       355: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: q+1
       370: q+1
       371: 2q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: q^2+2q+1
       387: q+1
       388: q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q+1
       394: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: 1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: q+1
       453: q+1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: 2q+1
       508: q+1
       509: 1
       510: 1
       515: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: q+1
       540: q+1
       541: 2q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: q+1
       548: q+1
       549: 2q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: q+1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       695: 1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: q+1
       745: q+1
       746: 2q+1
       747: q+1
       748: 1
       749: 1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       952: 1
       959: 1
       964: 1
      1006: 1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1082: 1
      1090: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1124: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1221: 1
      1263: 1
      1270: 1
      1297: 1
      1326: 1
      1334: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1512: 1

1513:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: 1
        47: 1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: q+1
        79: 1
        80: q+1
        81: 1
        82: q+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: q+1
        88: 1
        89: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: q+1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: q+1
       145: q+1
       146: 1
       147: 1
       148: q+1
       149: 1
       150: 1
       151: q+1
       152: 1
       153: q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: q+1
       166: 1
       167: 1
       169: q+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: q+1
       180: 1
       181: 1
       183: q+1
       184: 1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: 1
       227: q+1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: 1
       245: 1
       246: q+1
       247: 1
       248: 1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: 1
       254: 1
       255: q+1
       256: 1
       257: q+1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       272: 1
       273: 1
       276: q+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: q+1
       299: 1
       300: 1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: q+1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: q+1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: 1
       389: 1
       390: q+1
       391: 1
       392: 1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       412: 1
       418: 1
       419: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       449: 1
       452: q+1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       519: 1
       521: 1
       523: 1
       524: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q+1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: q+1
       562: 1
       566: 1
       568: 1
       570: 1
       571: 1
       581: 1
       589: 1
       597: 1
       598: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       627: 1
       633: 1
       634: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       654: 1
       662: 1
       664: 1
       669: 1
       671: 1
       673: 1
       674: 1
       679: 1
       681: 1
       683: 1
       684: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       708: 1
       710: 1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       754: 1
       760: 1
       762: 1
       782: 1
       791: 1
       799: 1
       800: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: 1
       825: 1
       833: 1
       841: 1
       842: 1
       848: 1
       849: 1
       852: 1
       853: 1
       866: 1
       874: 1
       876: 1
       883: 1
       885: 1
       890: 1
       892: 1
       894: 1
       895: 1
       905: 1
       911: 1
       919: 1
       921: 1
       926: 1
       928: 1
       930: 1
       931: 1
       936: 1
       938: 1
       940: 1
       941: 1
       945: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       959: 1
       965: 1
      1005: 1
      1013: 1
      1019: 1
      1021: 1
      1041: 1
      1050: 1
      1058: 1
      1059: 1
      1065: 1
      1083: 1
      1091: 1
      1099: 1
      1101: 1
      1125: 1
      1133: 1
      1135: 1
      1142: 1
      1144: 1
      1149: 1
      1151: 1
      1153: 1
      1154: 1
      1164: 1
      1216: 1
      1222: 1
      1262: 1
      1270: 1
      1298: 1
      1327: 1
      1335: 1
      1343: 1
      1345: 1
      1455: 1
      1513: 1

1514:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: 1
        12: q^2+1
        13: 1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: q^2+1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: 1
        30: 1
        31: q^2+1
        32: 1
        33: 1
        34: 1
        35: q^2+1
        36: 1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q^2+1
        76: 1
        77: 1
        78: q^2+1
        79: 1
        80: 1
        81: 1
        82: q^2+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       411: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       571: 1
       581: 1
       589: 1
       599: 1
       605: 1
       609: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       655: 1
       663: 1
       664: 1
       670: 1
       672: 1
       673: 1
       674: 1
       680: 1
       682: 1
       683: 1
       684: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       709: 1
       710: 1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       754: 1
       761: 1
       762: 1
       782: 1
       801: 1
       811: 1
       813: 1
       814: 1
       815: 1
       825: 1
       833: 1
       843: 1
       849: 1
       853: 1
       867: 1
       875: 1
       876: 1
       884: 1
       885: 1
       891: 1
       893: 1
       894: 1
       895: 1
       905: 1
       912: 1
       920: 1
       921: 1
       927: 1
       929: 1
       930: 1
       931: 1
       937: 1
       939: 1
       940: 1
       941: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       959: 1
       966: 1
      1020: 1
      1021: 1
      1041: 1
      1060: 1
      1084: 1
      1092: 1
      1100: 1
      1101: 1
      1126: 1
      1134: 1
      1135: 1
      1143: 1
      1144: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1164: 1
      1223: 1
      1299: 1
      1328: 1
      1336: 1
      1344: 1
      1345: 1
      1514: 1

1515:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: 2q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: 2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: 2q+1
        24: q^2+2q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: 2q+1
        33: q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: q^2+2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: 2q+1
        61: q^2+2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: q^2+2q+1
        74: 2q+1
        75: q^2+2q+1
        76: q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q+1
        80: 2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: q^2+2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q+1
       125: q+1
       126: q^2+2q+1
       127: 2q+1
       128: q^2+2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: q^2+2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: q^2+2q+1
       144: 2q+1
       145: q^2+2q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       208: q+1
       209: 1
       210: 2q+1
       211: q+1
       212: q+1
       215: q+1
       216: q+1
       217: 2q+1
       218: q^2+2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: 2q+1
       238: q+1
       239: q+1
       240: 2q+1
       241: q^2+2q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 2q+1
       246: 2q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+2q+1
       251: 2q+1
       252: q^2+2q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: 2q+1
       257: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       316: q+1
       317: 1
       318: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       346: q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: q+1
       355: 1
       360: q+1
       361: q+1
       362: q+1
       363: 2q+1
       364: q+1
       368: q+1
       369: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       375: q+1
       376: 1
       377: 2q+1
       378: q+1
       379: q+1
       382: q+1
       383: q+1
       384: 2q+1
       385: q^2+2q+1
       386: 2q+1
       387: q+1
       388: q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: 1
       393: q+1
       394: q+1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       471: 1
       472: 1
       480: q+1
       481: 1
       482: q+1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       523: q+1
       524: 1
       525: q+1
       530: q+1
       531: q+1
       532: q+1
       533: 2q+1
       534: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       553: q+1
       554: 1
       555: 2q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: q+1
       561: q+1
       562: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: q+1
       632: 1
       633: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       673: 1
       674: 1
       675: 1
       683: q+1
       684: 1
       685: q+1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       711: 1
       719: q+1
       720: 1
       721: q+1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       750: 1
       751: 1
       752: q+1
       753: 1
       754: 1
       762: 1
       763: 1
       771: 1
       773: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       802: 1
       805: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       868: 1
       876: 1
       877: 1
       885: 1
       886: 1
       894: 1
       895: 1
       896: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       913: 1
       921: 1
       922: 1
       930: 1
       931: 1
       932: 1
       940: q+1
       941: 1
       942: q+1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       967: 1
       984: 1
       986: 1
      1021: 1
      1022: 1
      1030: 1
      1032: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1061: 1
      1064: 1
      1085: 1
      1093: 1
      1101: 1
      1102: 1
      1110: 1
      1112: 1
      1127: 1
      1135: 1
      1136: 1
      1144: 1
      1145: 1
      1153: 1
      1154: 1
      1155: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1224: 1
      1241: 1
      1243: 1
      1300: 1
      1329: 1
      1337: 1
      1345: 1
      1346: 1
      1354: 1
      1356: 1
      1515: 1

1516:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^2+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^3+q^2+q+1
        10: q^2+1
        11: q+1
        12: q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^2+1
        15: q^3+q^2+q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: 1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q+1
        29: 1
        30: q^3+q^2+q+1
        31: q^2+1
        32: q+1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^3+q^2+q+1
        37: q^2+1
        38: q+1
        39: q^3+q^2+q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: q^2+1
        52: q^2+1
        54: 1
        55: q^2+1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: q+1
        69: 1
        70: q+1
        71: q^2+1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: q+1
        80: 1
        81: q^3+q^2+q+1
        82: q^2+1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q^2+1
       110: 1
       111: 1
       112: 1
       113: q^2+1
       114: q^2+1
       116: 1
       117: q^2+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q^2+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: q^2+1
       136: q^2+1
       138: 1
       139: q^2+1
       140: 1
       141: q^2+1
       142: q^2+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q^2+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: q^2+1
       215: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: q^2+1
       234: 1
       235: 1
       236: 1
       237: q^2+1
       238: q^2+1
       240: 1
       241: q^2+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q^2+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: q^2+1
       382: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       657: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       703: 1
       712: 1
       713: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       764: 1
       765: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: 1
       816: 1
       817: 1
       818: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       914: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       968: 1
       977: 1
       978: 1
       986: 1
      1008: 1
      1014: 1
      1023: 1
      1024: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1094: 1
      1103: 1
      1104: 1
      1112: 1
      1128: 1
      1137: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1180: 1
      1225: 1
      1234: 1
      1235: 1
      1243: 1
      1265: 1
      1301: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1419: 1
      1516: 1

1517:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+3q^2+3q+1
        10: q^3+3q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q^2+2q+1
        25: q^3+3q^2+3q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: q^3+3q^2+3q+1
        31: q^3+3q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^3+3q^2+3q+1
        37: q^3+3q^2+3q+1
        38: 2q^2+3q+1
        39: q^3+3q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        50: q+1
        51: q^2+2q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: q^2+2q+1
        62: 2q^2+3q+1
        63: q^2+2q+1
        64: 2q+1
        65: q^3+3q^2+3q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+3q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q^2+2q+1
        76: q^3+3q^2+3q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^3+3q^2+3q+1
        82: q^3+3q^2+3q+1
        83: 2q^2+3q+1
        84: 2q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: q^2+3q+1
        90: q+1
        91: 2q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: q+1
       113: q^2+2q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       128: q^2+2q+1
       129: 2q^2+3q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+3q+1
       133: q^2+3q+1
       134: q+1
       135: q^2+2q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: 2q+1
       149: q^3+3q^2+3q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+3q+1
       155: q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: q+1
       162: 2q+1
       163: q+1
       164: 1
       165: q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: 2q+1
       170: q^2+3q+1
       171: q+1
       172: q+1
       173: q^2+3q+1
       174: q^2+3q+1
       175: q^2+3q+1
       176: 2q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 2q+1
       181: q^2+3q+1
       182: q+1
       183: 2q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       206: q+1
       207: 2q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: q+1
       213: q+1
       214: q^2+2q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: q^2+3q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: q+1
       237: q^2+2q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q^2+2q+1
       253: 2q^2+3q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q+1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: q+1
       267: 2q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: 2q+1
       274: q+1
       275: 1
       276: q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: 1
       282: q+1
       283: q^2+3q+1
       284: q+1
       285: q+1
       286: q^2+3q+1
       287: q^2+3q+1
       288: q+1
       289: 2q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: q+1
       295: 2q+1
       296: q+1
       297: 1
       298: q+1
       299: 2q+1
       300: q^2+3q+1
       301: q+1
       302: 2q+1
       303: q^2+3q+1
       304: q+1
       305: q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       325: 1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: q+1
       351: 2q+1
       352: q+1
       353: 1
       354: q+1
       355: 2q+1
       356: 1
       357: 1
       358: 1
       359: q+1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: q+1
       374: 2q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: q+1
       380: q+1
       381: q^2+2q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: q+1
       387: 2q+1
       388: q^2+2q+1
       389: q+1
       390: q+1
       391: 2q+1
       392: q^2+3q+1
       393: q+1
       394: 2q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 2q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: q+1
       427: q+1
       428: 1
       430: q+1
       431: q^2+3q+1
       432: q+1
       433: q+1
       434: q+1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: q+1
       443: 2q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: 2q+1
       450: q+1
       451: 1
       452: q+1
       453: 2q+1
       454: q+1
       455: q+1
       456: 1
       458: q+1
       459: q^2+3q+1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       498: 1
       499: 1
       500: 1
       501: q+1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: q+1
       510: 2q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       532: 1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: q+1
       552: 2q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: q+1
       558: 2q+1
       559: q+1
       560: 1
       561: q+1
       562: 2q+1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: q+1
       600: 1
       601: 1
       603: 1
       605: q+1
       606: q+1
       607: 1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       616: 1
       617: 1
       618: 1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: 2q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: q+1
       643: 1
       645: q+1
       646: q^2+3q+1
       647: q+1
       648: q+1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       676: 1
       677: 1
       678: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       692: 1
       693: 1
       694: 1
       695: q+1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       737: 1
       738: 1
       739: 1
       740: q+1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: q+1
       749: 2q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: q+1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: q+1
       844: 1
       845: 1
       847: 1
       849: q+1
       850: q+1
       851: 1
       853: q+1
       870: 1
       879: 1
       887: 1
       888: 1
       889: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       915: 1
       923: 1
       924: 1
       925: 1
       931: 1
       933: 1
       934: 1
       935: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       949: 1
       950: 1
       951: 1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       969: 1
       977: 1
       978: 1
       979: 1
       985: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1015: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1053: 1
      1054: 1
      1056: 1
      1060: q+1
      1061: 1
      1062: 1
      1064: 1
      1095: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1129: 1
      1138: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1163: 1
      1164: 1
      1181: 1
      1211: 1
      1226: 1
      1234: 1
      1235: 1
      1236: 1
      1242: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1302: 1
      1339: 1
      1347: 1
      1348: 1
      1349: 1
      1355: 1
      1420: 1
      1450: 1
      1517: 1

1518:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: q^3+3q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: q^3+3q^2+3q+1
        37: q^2+3q+1
        38: 2q^2+3q+1
        39: q^3+3q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: q+1
        51: q+1
        52: q^2+3q+1
        53: q+1
        54: q+1
        55: q+1
        56: 1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q+1
        61: q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: q^2+3q+1
        79: 2q^2+3q+1
        80: q^2+3q+1
        81: q^3+3q^2+3q+1
        82: q^2+3q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       104: 1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: q^2+3q+1
       115: q+1
       116: q+1
       117: q+1
       118: 1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: q+1
       123: q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q+1
       128: q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q+1
       135: q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: q^2+3q+1
       142: q^2+3q+1
       143: q^2+3q+1
       144: q+1
       145: q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: q^2+3q+1
       150: q^2+3q+1
       151: q^2+3q+1
       152: 2q^2+3q+1
       153: q^2+3q+1
       154: 2q^2+3q+1
       155: q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: q+1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: q+1
       208: q^2+3q+1
       209: q+1
       210: q+1
       211: q+1
       212: 1
       213: q+1
       214: q+1
       215: q^2+3q+1
       216: q+1
       217: q+1
       218: q+1
       219: 1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q+1
       238: q^2+3q+1
       239: q+1
       240: q+1
       241: q+1
       242: 1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: q+1
       247: q+1
       248: q^2+3q+1
       249: q^2+3q+1
       250: q^2+3q+1
       251: q+1
       252: q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 2q^2+3q+1
       257: 2q+1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: 2q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: q+1
       299: 1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q+1
       350: 1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       374: q+1
       375: q^2+3q+1
       376: q+1
       377: q+1
       378: q+1
       379: 1
       380: q+1
       381: q+1
       382: q^2+3q+1
       383: q+1
       384: q+1
       385: q+1
       386: 1
       387: q^2+3q+1
       388: q^2+3q+1
       389: q^2+3q+1
       390: q+1
       391: q+1
       392: 2q+1
       393: 2q+1
       394: 2q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: 2q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       511: 2q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: q+1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: q+1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q+1
       552: q+1
       553: q^2+3q+1
       554: q+1
       555: q+1
       556: q+1
       557: 1
       558: 2q+1
       559: 2q+1
       560: 2q+1
       561: q+1
       562: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: 1
       629: 2q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       635: 1
       636: q+1
       639: 1
       641: q+1
       642: q+1
       643: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       750: 2q+1
       751: q+1
       752: q+1
       753: 1
       754: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       801: 1
       802: q+1
       805: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: q+1
       847: 1
       849: q+1
       850: q+1
       851: q+1
       853: 1
       871: 1
       880: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       916: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       970: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
      1008: 1
      1016: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1053: 1
      1060: 1
      1061: q+1
      1064: 1
      1096: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1130: 1
      1139: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1182: 1
      1227: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1265: 1
      1303: 1
      1340: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1421: 1
      1518: 1

1519:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       660: 1
       668: 1
       669: 1
       670: 1
       678: 1
       679: 1
       680: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       732: 1
       733: 1
       734: 1
       735: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       809: 1
       810: 1
       811: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: 1
       872: 1
       881: 1
       889: 1
       890: 1
       891: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       917: 1
       925: 1
       926: 1
       927: 1
       935: 1
       936: 1
       937: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1017: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1097: 1
      1105: 1
      1106: 1
      1107: 1
      1131: 1
      1140: 1
      1148: 1
      1149: 1
      1150: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1183: 1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1304: 1
      1341: 1
      1349: 1
      1350: 1
      1351: 1
      1422: 1
      1519: 1

1520:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: 2q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q+1
        79: 2q^2+2q+1
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: q^2+2q+1
        83: 2q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: 1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       152: 2q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: 1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       190: q+1
       191: 1
       192: 1
       194: 1
       195: 1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       311: 1
       314: 1
       315: 1
       320: q+1
       321: 1
       322: 1
       324: 1
       325: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       373: q+1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: q+1
       394: 1
       396: q+1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       468: 1
       475: 1
       478: 1
       479: 1
       484: q+1
       485: 1
       486: 1
       488: 1
       489: 1
       493: q+1
       494: 1
       495: 1
       497: 1
       498: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       521: 1
       522: 1
       527: q+1
       528: 1
       529: 1
       531: 1
       532: 1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       551: q+1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       596: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       661: 1
       668: 1
       671: 1
       672: 1
       678: 1
       681: 1
       682: 1
       687: q+1
       688: 1
       689: 1
       691: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       707: 1
       714: 1
       717: 1
       718: 1
       723: q+1
       724: 1
       725: 1
       727: 1
       728: 1
       732: q+1
       733: 1
       734: 1
       736: 1
       737: 1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       759: 1
       766: 1
       769: 1
       770: 1
       775: 1
       776: 1
       777: 1
       779: 1
       780: 1
       784: 1
       792: 1
       793: 1
       794: 1
       798: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       809: 1
       812: 1
       813: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       834: 1
       835: 1
       836: 1
       840: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       873: 1
       882: 1
       889: 1
       892: 1
       893: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       918: 1
       925: 1
       928: 1
       929: 1
       935: 1
       938: 1
       939: 1
       944: q+1
       945: 1
       946: 1
       948: 1
       949: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       972: 1
       979: 1
       982: 1
       983: 1
       998: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1018: 1
      1025: 1
      1028: 1
      1029: 1
      1034: 1
      1035: 1
      1036: 1
      1038: 1
      1039: 1
      1043: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1098: 1
      1105: 1
      1108: 1
      1109: 1
      1132: 1
      1141: 1
      1148: 1
      1151: 1
      1152: 1
      1157: 1
      1158: 1
      1159: 1
      1161: 1
      1162: 1
      1184: 1
      1209: 1
      1229: 1
      1236: 1
      1239: 1
      1240: 1
      1255: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1305: 1
      1342: 1
      1349: 1
      1352: 1
      1353: 1
      1423: 1
      1448: 1
      1520: 1

1521:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q^2+2q+1
        37: 2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+2q+1
        50: q+1
        52: q+1
        53: 1
        54: 2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+q+1
        95: 1
        96: q^2+q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: q+1
       114: q+1
       115: 1
       116: 2q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: 2q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       136: q+1
       137: 1
       138: 2q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q^2+q+1
       174: 1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+q+1
       187: 1
       188: q^2+q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       199: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       206: q+1
       208: q+1
       209: 1
       210: 2q+1
       211: q+1
       212: q+1
       213: q+1
       215: q+1
       216: 1
       217: 2q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       238: q+1
       239: 1
       240: 2q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: 2q+1
       246: 2q+1
       247: q+1
       248: q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q^2+q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q^2+q+1
       307: 1
       308: q^2+q+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       346: q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: q+1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       366: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       375: q+1
       376: 1
       377: 2q+1
       378: q+1
       379: q+1
       380: q+1
       382: q+1
       383: 1
       384: 2q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: 1
       393: q+1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+q+1
       463: 1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       494: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       536: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       544: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q+1
       551: q+1
       553: q+1
       554: 1
       555: 2q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: q+1
       561: q+1
       562: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       662: 1
       669: 1
       671: 1
       673: 1
       679: 1
       681: 1
       683: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 1
       715: 1
       717: 1
       719: 1
       724: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       733: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       741: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       750: 1
       751: 1
       752: q+1
       753: 1
       754: 1
       760: 1
       767: 1
       769: 1
       771: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       790: 1
       793: 1
       798: 1
       799: 1
       800: 1
       802: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       835: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       874: 1
       883: 1
       890: 1
       892: 1
       894: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       919: 1
       926: 1
       928: 1
       930: 1
       936: 1
       938: 1
       940: 1
       945: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       953: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       973: 1
       980: 1
       982: 1
       984: 1
      1004: 1
      1007: 1
      1012: 1
      1013: 1
      1019: 1
      1026: 1
      1028: 1
      1030: 1
      1035: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1049: 1
      1052: 1
      1057: 1
      1058: 1
      1059: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1099: 1
      1106: 1
      1108: 1
      1110: 1
      1133: 1
      1142: 1
      1149: 1
      1151: 1
      1153: 1
      1158: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1185: 1
      1215: 1
      1230: 1
      1237: 1
      1239: 1
      1241: 1
      1261: 1
      1264: 1
      1269: 1
      1270: 1
      1306: 1
      1343: 1
      1350: 1
      1352: 1
      1354: 1
      1424: 1
      1454: 1
      1521: 1

1522:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: 1
       214: q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: 1
       377: 1
       378: q+1
       379: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: q+1
       553: q+1
       554: 1
       555: 1
       556: q+1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       663: 1
       670: 1
       672: 1
       673: 1
       680: 1
       682: 1
       683: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 1
       716: 1
       718: 1
       719: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       761: 1
       768: 1
       770: 1
       771: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       801: 1
       802: 1
       805: 1
       811: 1
       813: 1
       814: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       875: 1
       884: 1
       891: 1
       893: 1
       894: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       920: 1
       927: 1
       929: 1
       930: 1
       937: 1
       939: 1
       940: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       974: 1
       981: 1
       983: 1
       984: 1
      1008: 1
      1020: 1
      1027: 1
      1029: 1
      1030: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1100: 1
      1107: 1
      1109: 1
      1110: 1
      1134: 1
      1143: 1
      1150: 1
      1152: 1
      1153: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1186: 1
      1231: 1
      1238: 1
      1240: 1
      1241: 1
      1265: 1
      1307: 1
      1344: 1
      1351: 1
      1353: 1
      1354: 1
      1425: 1
      1522: 1

1523:    0: 2q^2+q+1
         1: q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: 2q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: 2q^2+q+1
         9: q^2+q+1
        10: 2q^2+q+1
        11: q^2+q+1
        12: 2q^2+q+1
        13: q^2+q+1
        14: 2q^2+q+1
        15: 2q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q^2+1
        24: q^2+q+1
        25: q^2+q+1
        26: q+1
        27: 2q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q^2+q+1
        31: 2q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q+1
        35: 2q^2+q+1
        36: q^2+q+1
        37: 2q^2+q+1
        38: q^2+q+1
        39: 2q^2+q+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: q^2+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q^2+q+1
        65: q^2+q+1
        66: q+1
        67: 2q^2+q+1
        68: q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q+1
        73: q+1
        74: q^2+1
        75: q^2+q+1
        76: q^2+q+1
        77: q+1
        78: 2q^2+q+1
        79: q+1
        80: q^2+q+1
        81: q^2+q+1
        82: 2q^2+q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q^2+1
        88: q+1
        89: q+1
        90: 1
        91: q^2+q+1
        92: q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: q^2+q+1
       102: q^2+q+1
       103: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q^2+1
       123: q+1
       124: q^2+q+1
       125: q+1
       126: q+1
       127: q^2+1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q^2+q+1
       132: q+1
       133: q^2+q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q^2+q+1
       142: q+1
       143: q+1
       144: q^2+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q^2+q+1
       149: q^2+q+1
       150: q+1
       151: 2q^2+q+1
       152: q+1
       153: q^2+q+1
       154: q^2+q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q^2+1
       166: q+1
       167: q+1
       168: 1
       169: q^2+q+1
       170: q+1
       171: 1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q^2+1
       180: q+1
       181: q+1
       182: 1
       183: q^2+q+1
       184: q+1
       185: q^2+q+1
       186: q+1
       187: q+1
       188: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: 1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q^2+1
       224: q+1
       225: q+1
       226: 1
       227: q^2+q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q^2+1
       247: q+1
       248: q^2+q+1
       249: q+1
       250: q+1
       251: q^2+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q^2+q+1
       256: q+1
       257: q^2+q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q^2+1
       277: q+1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: q^2+1
       299: q+1
       300: q+1
       301: 1
       302: q^2+q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       316: 1
       317: 1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: q^2+1
       355: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: q^2+1
       391: q+1
       392: q+1
       393: 1
       394: q^2+q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       421: 1
       422: 1
       424: 1
       426: q+1
       427: 1
       428: 1
       430: q+1
       431: q+1
       432: 1
       433: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: q^2+1
       453: q+1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       471: 1
       480: 1
       481: 1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: 1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       523: 1
       524: 1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: 1
       560: 1
       561: q^2+1
       562: q+1
       570: 1
       571: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: q+1
       606: 1
       607: 1
       609: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: 1
       643: 1
       645: q+1
       646: q+1
       647: 1
       648: q+1
       664: 1
       673: 1
       674: 1
       683: 1
       684: 1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       719: 1
       720: 1
       726: 1
       727: q+1
       728: 1
       729: 1
       730: 1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       762: 1
       771: 1
       772: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       788: 1
       795: 1
       797: 1
       802: 1
       803: 1
       805: 1
       814: 1
       815: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       837: 1
       839: 1
       844: 1
       845: 1
       847: 1
       849: q+1
       850: 1
       851: 1
       853: q+1
       876: 1
       885: 1
       894: 1
       895: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       921: 1
       930: 1
       931: 1
       940: 1
       941: 1
       947: 1
       948: q+1
       949: 1
       950: 1
       951: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       975: 1
       984: 1
       985: 1
      1002: 1
      1009: 1
      1011: 1
      1021: 1
      1030: 1
      1031: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1047: 1
      1054: 1
      1056: 1
      1061: 1
      1062: 1
      1064: 1
      1101: 1
      1110: 1
      1111: 1
      1135: 1
      1144: 1
      1153: 1
      1154: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1187: 1
      1213: 1
      1232: 1
      1241: 1
      1242: 1
      1259: 1
      1266: 1
      1268: 1
      1308: 1
      1345: 1
      1354: 1
      1355: 1
      1426: 1
      1452: 1
      1523: 1

1524:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        21: q^2+1
        22: q^2+1
        23: 1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: q^2+1
        32: 1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: q^2+1
        54: 1
        55: q^2+1
        56: 1
        58: q^2+1
        59: q^2+1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: q^2+1
       110: 1
       111: 1
       115: q^2+1
       116: 1
       117: q^2+1
       118: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: q^2+1
       138: 1
       139: q^2+1
       140: 1
       142: q^2+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: q^2+1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       239: q^2+1
       240: 1
       241: q^2+1
       242: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: 1
       422: 1
       424: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       438: 1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: 1
       524: 1
       525: 1
       532: 1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       554: 1
       555: 1
       556: 1
       557: 1
       559: 1
       560: 1
       561: 1
       562: 1
       571: 1
       572: 1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       595: 1
       601: 1
       603: 1
       606: 1
       607: 1
       609: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       632: 1
       633: 1
       637: 1
       639: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       665: 1
       674: 1
       675: 1
       684: 1
       685: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       702: 1
       711: 1
       720: 1
       721: 1
       728: 1
       729: 1
       730: 1
       737: 1
       738: 1
       739: 1
       744: 1
       745: 1
       746: 1
       747: 1
       751: 1
       752: 1
       753: 1
       754: 1
       763: 1
       772: 1
       773: 1
       780: 1
       781: 1
       782: 1
       797: 1
       803: 1
       805: 1
       815: 1
       816: 1
       823: 1
       824: 1
       825: 1
       830: 1
       831: 1
       832: 1
       833: 1
       839: 1
       845: 1
       847: 1
       850: 1
       851: 1
       853: 1
       877: 1
       886: 1
       895: 1
       896: 1
       903: 1
       904: 1
       905: 1
       922: 1
       931: 1
       932: 1
       941: 1
       942: 1
       949: 1
       950: 1
       951: 1
       956: 1
       957: 1
       958: 1
       959: 1
       976: 1
       985: 1
       986: 1
      1011: 1
      1022: 1
      1031: 1
      1032: 1
      1039: 1
      1040: 1
      1041: 1
      1056: 1
      1062: 1
      1064: 1
      1102: 1
      1111: 1
      1112: 1
      1136: 1
      1145: 1
      1154: 1
      1155: 1
      1162: 1
      1163: 1
      1164: 1
      1188: 1
      1233: 1
      1242: 1
      1243: 1
      1268: 1
      1309: 1
      1346: 1
      1355: 1
      1356: 1
      1427: 1
      1524: 1

1525:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q^2+2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q+1
       262: q+1
       263: q+1
       264: q^2+2q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: q+1
       396: q^2+2q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: 1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: 1
       480: 1
       482: 1
       483: 1
       484: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       549: 1
       559: 1
       563: 1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: q+1
       661: 1
       662: 1
       663: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       755: 1
       756: 1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       840: 1
       850: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       898: 1
       906: 1
       918: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       977: 1
       978: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1014: 1
      1015: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1074: 1
      1094: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1209: 1
      1217: 1
      1229: 1
      1271: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1365: 1
      1385: 1
      1525: 1

1526:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: 1
        25: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: q^2+1
        51: 1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: 1
        56: 1
        57: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        64: q^2+1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: q^2+1
       106: 1
       107: q^2+1
       108: q^2+1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       113: 1
       118: 1
       119: q^2+1
       122: q^2+1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q^2+1
       156: 1
       157: q^2+1
       158: q^2+1
       159: q^2+1
       160: 1
       161: 1
       162: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       169: q^2+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q^2+1
       192: 1
       193: q^2+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: q^2+1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q^2+1
       260: 1
       261: q^2+1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       267: 1
       272: 1
       273: q^2+1
       276: q^2+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: q^2+1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q^2+1
       398: 1
       399: q^2+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q^2+1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q^2+1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       887: 1
       897: 1
       905: 1
       907: 1
       909: 1
       911: 1
       933: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1042: 1
      1050: 1
      1059: 1
      1068: 1
      1069: 1
      1103: 1
      1115: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1208: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1244: 1
      1272: 1
      1359: 1
      1360: 1
      1394: 1
      1406: 1
      1526: 1

1527:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 2q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^2+2q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^2+2q+1
        11: q^3+3q^2+3q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^2+2q+1
        30: q^2+3q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q+1
        38: 2q^2+3q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: q^3+3q^2+3q+1
        42: q^3+3q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: q+1
        54: q^3+3q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: 2q+1
        62: q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q^2+3q+1
        69: 2q+1
        70: q^2+3q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+3q+1
        74: 2q^2+3q+1
        75: q^2+3q+1
        76: 1
        77: q+1
        78: q+1
        79: 2q^2+3q+1
        80: q+1
        81: q^2+3q+1
        82: q+1
        83: q^2+3q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^3+3q^2+3q+1
        87: q^3+3q^2+3q+1
        88: q^2+3q+1
        89: q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^3+3q^2+3q+1
        93: q^2+2q+1
        94: q^2+3q+1
        95: 2q+1
        96: q^2+3q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: q+1
       102: 2q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+3q+1
       111: q^2+3q+1
       112: q+1
       113: 1
       114: q+1
       115: q+1
       116: q^2+2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: q^2+3q+1
       133: 1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: 1
       138: 2q^2+3q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q+1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: q+1
       151: q+1
       152: q^2+3q+1
       153: q+1
       154: q^2+3q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q+1
       159: q^3+3q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q+1
       163: q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: q^2+3q+1
       174: 2q+1
       175: q^2+3q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: q^2+3q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q^2+3q+1
       185: q+1
       186: q^2+3q+1
       187: q+1
       188: q^2+3q+1
       189: q+1
       190: q+1
       191: q+1
       192: 1
       193: q+1
       194: q+1
       195: q+1
       196: q^2+3q+1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: q+1
       207: 1
       208: q+1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: q+1
       214: 1
       215: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q^2+3q+1
       235: q^2+3q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: 1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: 1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q^2+3q+1
       265: q^2+3q+1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q^2+2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: q+1
       279: q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: q^2+3q+1
       287: 1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: 1
       292: 2q^2+3q+1
       293: q^2+3q+1
       294: q^2+3q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: q+1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: q+1
       305: q+1
       306: q^2+3q+1
       307: q+1
       308: q^2+3q+1
       310: q+1
       311: 1
       312: q+1
       313: 1
       314: q+1
       315: 1
       316: q+1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: 1
       328: 1
       329: q+1
       330: 1
       334: q+1
       335: q+1
       336: 1
       337: q+1
       338: 1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: 1
       346: q+1
       348: 2q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q^2+3q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: 1
       375: 1
       377: q+1
       380: 1
       381: 1
       382: 1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 1
       389: q+1
       390: q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: 1
       399: q+1
       400: q+1
       401: q+1
       402: q^2+3q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: q+1
       410: 2q+1
       411: 2q+1
       412: q+1
       413: 1
       414: q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: q+1
       427: q+1
       428: 2q+1
       429: 2q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q^2+3q+1
       441: q^2+3q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: q+1
       457: q+1
       458: q+1
       459: 1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: q+1
       470: 1
       471: 1
       472: 1
       474: 1
       475: 1
       476: q+1
       477: 1
       478: q+1
       479: 1
       480: q+1
       482: 1
       483: 1
       484: 1
       490: q+1
       491: 1
       492: 1
       493: 1
       499: 2q+1
       500: 1
       501: 1
       502: q+1
       503: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: q+1
       550: q+1
       551: 1
       553: 1
       555: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       564: q+1
       565: 1
       566: q+1
       567: 1
       568: q+1
       569: 1
       570: q+1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: q+1
       579: q+1
       580: 2q+1
       581: 1
       582: 1
       583: q+1
       584: 1
       588: q+1
       589: q+1
       590: 1
       591: q+1
       592: 1
       596: 2q+1
       597: 2q+1
       598: q+1
       599: 1
       600: q+1
       602: 2q+1
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+3q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: q+1
       626: q+1
       627: 1
       629: 1
       631: q+1
       634: 1
       635: 1
       636: 1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 1
       643: q+1
       644: q+1
       646: 1
       647: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       659: 1
       660: 1
       661: 1
       662: q+1
       663: 1
       667: 1
       675: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       738: q+1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       757: 1
       758: 1
       759: 1
       760: q+1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       769: q+1
       770: 1
       771: q+1
       773: 1
       774: 1
       775: 1
       781: q+1
       782: 1
       783: 1
       784: 1
       790: 2q+1
       791: 1
       792: 1
       793: q+1
       794: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: q+1
       825: 1
       827: 1
       834: 1
       835: 1
       836: 1
       840: q+1
       841: q+1
       842: 1
       844: 1
       846: q+1
       849: 1
       850: 1
       851: 1
       852: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       909: 1
       911: 1
       913: 1
       916: 1
       918: 1
       919: 1
       934: 1
       942: 1
       953: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       970: 1
       971: 1
       972: 1
       973: q+1
       974: 1
       978: 1
       986: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1049: q+1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1069: 1
      1070: 1
      1074: 1
      1104: 1
      1112: 1
      1118: 1
      1123: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1220: 1
      1222: 1
      1224: 1
      1227: 1
      1229: 1
      1230: 1
      1245: 1
      1253: 1
      1264: 1
      1273: 1
      1360: 1
      1361: 1
      1365: 1
      1395: 1
      1403: 1
      1409: 1
      1414: 1
      1527: 1

1528:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        81: q+1
        82: q+1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: q+1
       136: q+1
       137: q+1
       139: q+1
       141: q+1
       142: q+1
       143: q+1
       145: q+1
       149: q+1
       150: q+1
       151: 1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+q+1
       178: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       186: q+1
       187: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       230: q+1
       231: q+1
       233: q+1
       237: q+1
       238: q+1
       239: q+1
       241: q+1
       248: 1
       249: q+1
       250: 1
       252: 1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: q+1
       293: q+1
       295: q+1
       296: q+1
       297: q+1
       299: q+1
       303: q+1
       304: q+1
       305: 1
       309: q+1
       310: q+1
       311: q+1
       312: 1
       313: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       359: q+1
       361: 1
       367: q+1
       368: q+1
       370: q+1
       381: 1
       382: 1
       383: 1
       385: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       436: q+1
       437: q+1
       439: q+1
       443: q+1
       444: q+1
       445: q+1
       447: q+1
       454: 1
       455: q+1
       456: 1
       458: 1
       464: q+1
       465: q+1
       466: 1
       467: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: q+1
       531: 1
       545: 1
       546: 1
       548: 1
       563: q+1
       564: q+1
       565: q+1
       566: 1
       567: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       613: q+1
       615: 1
       621: q+1
       622: q+1
       624: q+1
       635: 1
       636: 1
       637: 1
       639: 1
       649: q+1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       682: 1
       689: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       755: q+1
       756: q+1
       757: 1
       758: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       813: 1
       820: q+1
       822: 1
       836: 1
       837: 1
       839: 1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       900: 1
       939: 1
       960: q+1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1029: 1
      1045: 1
      1047: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: 1
      1188: 1
      1211: 1
      1250: 1
      1274: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1528: 1

1529:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: q+1
       105: 2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: 2q+1
       113: q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       208: q+1
       209: q+1
       210: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       258: q+1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: 1
       266: 2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: 2q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: q+1
       331: q+1
       332: q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: 1
       396: q+1
       397: 2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: q+1
       415: q+1
       416: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       450: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: q+1
       487: q+1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: q+1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       563: 1
       564: 1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: q+1
       585: q+1
       586: q+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       665: 1
       669: q+1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       776: q+1
       778: q+1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: q+1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       878: 1
       879: 1
       882: 1
       886: 1
       899: 1
       906: 1
       918: 1
       935: 1
       938: 1
       939: 1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       976: 1
       980: q+1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       999: 1
      1007: 1
      1009: 1
      1010: 1
      1014: 1
      1015: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1086: 1
      1141: 1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: 1
      1177: 1
      1179: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1210: 1
      1217: 1
      1229: 1
      1246: 1
      1249: 1
      1250: 1
      1275: 1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1377: 1
      1432: 1
      1529: 1

1530:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       144: q+1
       145: q+1
       146: q+1
       149: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       242: q+1
       248: 1
       251: 1
       252: 1
       253: q+1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       298: q+1
       299: q+1
       300: q+1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       380: 1
       381: 1
       386: 1
       392: q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       448: q+1
       454: 1
       457: 1
       458: 1
       459: q+1
       462: q+1
       463: q+1
       465: q+1
       466: 1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       521: 1
       522: 1
       524: q+1
       543: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       634: 1
       635: 1
       640: 1
       646: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       707: 1
       756: q+1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       812: 1
       813: 1
       815: q+1
       834: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       872: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       895: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: q+1
      1018: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1095: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1183: 1
      1190: 1
      1193: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1276: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1386: 1
      1530: 1

1531:    0: 3q^3+8q^2+5q+1
         1: q^3+7q^2+5q+1
         2: 3q^3+8q^2+5q+1
         3: 3q^3+8q^2+5q+1
         4: q^3+6q^2+5q+1
         5: 3q^3+8q^2+5q+1
         6: 5q^2+5q+1
         7: q^3+7q^2+5q+1
         8: 3q^3+8q^2+5q+1
         9: q^3+7q^2+5q+1
        10: 2q^3+6q^2+5q+1
        11: 2q^3+6q^2+5q+1
        12: 4q^2+5q+1
        13: 5q^2+5q+1
        14: q^3+6q^2+5q+1
        15: q^3+6q^2+5q+1
        16: q^3+7q^2+5q+1
        17: 3q^3+8q^2+5q+1
        18: 3q^3+8q^2+5q+1
        19: q^3+6q^2+5q+1
        20: 5q^2+5q+1
        21: 5q^2+5q+1
        22: q^3+7q^2+5q+1
        23: 2q^3+6q^2+5q+1
        24: 4q^2+5q+1
        25: 3q^2+5q+1
        26: 3q^2+4q+1
        27: 2q^3+6q^2+5q+1
        28: q^3+5q^2+5q+1
        29: q^3+4q^2+5q+1
        30: 3q^2+5q+1
        31: 3q^2+5q+1
        32: 3q^2+5q+1
        33: 4q^2+5q+1
        34: 5q^2+5q+1
        35: q^3+6q^2+5q+1
        36: 5q^2+5q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 4q^2+5q+1
        40: 5q^2+5q+1
        41: q^3+7q^2+5q+1
        42: 3q^3+8q^2+5q+1
        43: q^3+7q^2+5q+1
        44: 2q^3+6q^2+5q+1
        45: 2q^3+6q^2+5q+1
        46: 4q^2+5q+1
        47: 5q^2+5q+1
        48: q^3+6q^2+5q+1
        49: q^3+6q^2+5q+1
        50: 2q^2+3q+1
        51: q^2+3q+1
        52: 5q^2+5q+1
        53: 3q^2+5q+1
        54: q^3+5q^2+5q+1
        55: 3q^2+5q+1
        56: 3q^2+5q+1
        57: 3q^2+5q+1
        58: q^2+4q+1
        59: 3q^2+4q+1
        60: q^3+4q^2+5q+1
        61: 3q^2+5q+1
        62: 2q^2+5q+1
        63: q^2+4q+1
        64: q^3+4q^2+5q+1
        65: q^2+5q+1
        66: q^2+4q+1
        67: 3q^2+5q+1
        68: 2q^2+5q+1
        69: 2q^2+5q+1
        70: 3q^2+5q+1
        71: 4q^2+5q+1
        72: 4q^2+5q+1
        73: 5q^2+5q+1
        74: 2q^2+3q+1
        75: 4q^2+5q+1
        76: q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q+1
        81: 3q^2+5q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: 5q^2+5q+1
        85: 5q^2+5q+1
        86: q^3+7q^2+5q+1
        87: 2q^3+6q^2+5q+1
        88: 4q^2+5q+1
        89: 3q^2+5q+1
        90: 3q^2+4q+1
        91: 2q^3+6q^2+5q+1
        92: q^3+5q^2+5q+1
        93: q^3+4q^2+5q+1
        94: 3q^2+5q+1
        95: 3q^2+5q+1
        96: 3q^2+5q+1
        97: 4q^2+5q+1
        98: 5q^2+5q+1
        99: q^3+6q^2+5q+1
       100: 5q^2+5q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: 4q^2+5q+1
       104: 2q+1
       105: 2q^2+3q+1
       106: q^2+3q+1
       107: 3q^2+5q+1
       108: 2q^2+5q+1
       109: q^2+5q+1
       110: 2q^2+5q+1
       111: 3q^2+5q+1
       112: q^2+3q+1
       113: 3q+1
       114: q^2+4q+1
       115: q^2+4q+1
       116: q^2+4q+1
       117: q^2+4q+1
       118: 2q^2+5q+1
       119: 2q^2+5q+1
       120: 4q+1
       121: q^2+4q+1
       122: q^3+4q^2+5q+1
       123: q^2+3q+1
       124: q^2+5q+1
       125: 4q+1
       126: q^2+4q+1
       127: 2q+1
       128: 3q^2+5q+1
       129: q^2+5q+1
       130: 4q+1
       131: 2q^2+5q+1
       132: 2q^2+5q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+3q+1
       136: 4q^2+5q+1
       137: q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+5q+1
       140: q^2+3q+1
       141: q^2+3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       148: 2q+1
       149: 3q+1
       151: q^2+3q+1
       152: q^2+3q+1
       153: 2q+1
       154: q^2+3q+1
       155: 2q^2+3q+1
       156: q^2+3q+1
       157: 5q^2+5q+1
       158: 3q^2+5q+1
       159: q^3+5q^2+5q+1
       160: 3q^2+5q+1
       161: 3q^2+5q+1
       162: 3q^2+5q+1
       163: q^2+4q+1
       164: 3q^2+4q+1
       165: q^3+4q^2+5q+1
       166: 3q^2+5q+1
       167: 2q^2+5q+1
       168: q^2+4q+1
       169: q^3+4q^2+5q+1
       170: q^2+5q+1
       171: q^2+4q+1
       172: 3q^2+5q+1
       173: 2q^2+5q+1
       174: 2q^2+5q+1
       175: 3q^2+5q+1
       176: 4q^2+5q+1
       177: 4q^2+5q+1
       178: 5q^2+5q+1
       179: 2q^2+3q+1
       180: 4q^2+5q+1
       181: q^2+3q+1
       183: 2q^2+3q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: 3q^2+5q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: 2q+1
       190: 2q+1
       191: q^2+3q+1
       192: 3q+1
       193: 2q^2+5q+1
       194: q^2+5q+1
       195: q^2+5q+1
       196: 2q^2+5q+1
       197: 2q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: q^2+4q+1
       202: 4q+1
       203: 4q+1
       204: 4q+1
       205: 2q^2+5q+1
       206: q^2+3q+1
       207: 2q+1
       208: 4q+1
       209: 2q+1
       210: q^2+4q+1
       211: 2q+1
       212: q^2+3q+1
       213: q+1
       214: 3q+1
       215: 4q+1
       216: 2q+1
       217: 2q+1
       218: q^2+4q+1
       219: 2q+1
       220: q^2+5q+1
       221: 4q+1
       222: 4q+1
       223: 2q+1
       224: q^2+3q+1
       225: 2q+1
       227: 2q+1
       228: q+1
       229: q^2+2q+1
       230: q^2+3q+1
       231: q^2+3q+1
       232: 2q+1
       233: 3q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: q+1
       237: 2q+1
       242: 2q+1
       243: 2q+1
       246: 2q+1
       248: 3q+1
       251: q+1
       252: q^2+3q+1
       253: 2q+1
       255: 2q+1
       256: q^2+3q+1
       257: q+1
       258: 2q+1
       259: 2q^2+3q+1
       260: q^2+3q+1
       261: 3q^2+5q+1
       262: 2q^2+5q+1
       263: q^2+5q+1
       264: 2q^2+5q+1
       265: 3q^2+5q+1
       266: q^2+3q+1
       267: 3q+1
       268: q^2+4q+1
       269: q^2+4q+1
       270: q^2+4q+1
       271: q^2+4q+1
       272: 2q^2+5q+1
       273: 2q^2+5q+1
       274: 4q+1
       275: q^2+4q+1
       276: q^3+4q^2+5q+1
       277: q^2+3q+1
       278: q^2+5q+1
       279: 4q+1
       280: q^2+4q+1
       281: 2q+1
       282: 3q^2+5q+1
       283: q^2+5q+1
       284: 4q+1
       285: 2q^2+5q+1
       286: 2q^2+5q+1
       287: 2q+1
       288: q^2+2q+1
       289: q^2+3q+1
       290: 4q^2+5q+1
       291: q^2+3q+1
       292: 2q^2+3q+1
       293: 3q^2+5q+1
       294: q^2+3q+1
       295: q^2+3q+1
       298: 2q+1
       299: q^2+3q+1
       300: 2q+1
       302: 2q+1
       303: 3q+1
       305: q^2+3q+1
       306: q^2+3q+1
       307: 2q+1
       308: q^2+3q+1
       310: 2q+1
       311: 2q+1
       312: q^2+3q+1
       313: 2q+1
       314: q+1
       315: 3q+1
       316: q^2+5q+1
       317: 2q+1
       319: 2q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: 4q+1
       324: 4q+1
       325: 4q+1
       326: 4q+1
       327: 2q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: 2q+1
       335: q^2+3q+1
       336: 1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: 2q+1
       346: 4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: 2q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       361: 3q+1
       362: 2q+1
       363: q^2+3q+1
       364: q+1
       365: q+1
       372: 2q+1
       373: q+1
       380: 1
       381: 2q+1
       386: q+1
       387: 2q+1
       390: q+1
       392: q+1
       394: q+1
       395: 2q+1
       396: 2q+1
       397: q^2+3q+1
       398: 3q+1
       399: 2q^2+5q+1
       400: q^2+5q+1
       401: q^2+5q+1
       402: 2q^2+5q+1
       403: 2q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: q^2+4q+1
       408: 4q+1
       409: 4q+1
       410: 4q+1
       411: 2q^2+5q+1
       412: q^2+3q+1
       413: 2q+1
       414: 4q+1
       415: 2q+1
       416: q^2+4q+1
       417: 2q+1
       418: q^2+3q+1
       419: q+1
       420: 3q+1
       421: 4q+1
       422: 2q+1
       423: 2q+1
       424: q^2+4q+1
       425: 2q+1
       426: q^2+5q+1
       427: 4q+1
       428: 4q+1
       429: 2q+1
       430: q^2+3q+1
       431: 2q+1
       433: 2q+1
       434: q+1
       435: q^2+2q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: 2q+1
       439: 3q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: q+1
       443: 2q+1
       448: 2q+1
       449: 2q+1
       452: 2q+1
       454: 3q+1
       457: q+1
       458: q^2+3q+1
       459: 2q+1
       461: 2q+1
       462: q^2+3q+1
       463: q+1
       466: 2q+1
       467: q+1
       468: 1
       469: q+1
       470: 2q+1
       471: 2q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 4q+1
       481: q+1
       483: q+1
       484: 1
       485: q+1
       486: 1
       487: 2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: 2q+1
       498: q+1
       499: 2q+1
       500: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       515: 1
       517: q+1
       518: q+1
       519: q+1
       521: 1
       522: 2q+1
       523: 2q+1
       524: q+1
       526: q+1
       534: q+1
       543: 1
       550: q+1
       551: 1
       558: q+1
       561: 1
       564: 2q+1
       565: 2q+1
       566: q^2+3q+1
       567: 2q+1
       568: q+1
       569: 3q+1
       570: q^2+5q+1
       571: 2q+1
       573: 2q+1
       574: q+1
       575: 2q+1
       576: 2q+1
       577: 4q+1
       578: 4q+1
       579: 4q+1
       580: 4q+1
       581: 2q+1
       582: q+1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: 2q+1
       589: q^2+3q+1
       590: 1
       591: q+1
       592: 2q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       597: 2q+1
       598: q+1
       599: 2q+1
       600: 4q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: q+1
       605: 2q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: 2q+1
       614: 2q+1
       615: 3q+1
       616: 2q+1
       617: q^2+3q+1
       618: q+1
       619: q+1
       626: 2q+1
       627: q+1
       634: 1
       635: 2q+1
       640: q+1
       641: 2q+1
       644: q+1
       646: q+1
       648: q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: q+1
       674: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: q+1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: q+1
       707: 1
       708: 1
       710: q+1
       731: 1
       739: 1
       748: 1
       757: 2q+1
       758: q+1
       759: 1
       760: q+1
       761: 2q+1
       762: 2q+1
       765: q+1
       766: q+1
       767: 2q+1
       768: q+1
       769: q+1
       770: 2q+1
       771: 4q+1
       772: q+1
       774: q+1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: 2q+1
       789: q+1
       790: 2q+1
       791: 1
       792: 1
       793: q+1
       794: q+1
       795: q+1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       806: 1
       808: q+1
       809: q+1
       810: q+1
       812: 1
       813: 2q+1
       814: 2q+1
       815: q+1
       817: q+1
       825: q+1
       834: 1
       841: q+1
       842: 1
       849: q+1
       852: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       875: 1
       876: 1
       880: 1
       882: 1
       883: 1
       885: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       909: 1
       911: 1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       970: q+1
       971: 1
       972: 1
       973: q+1
       974: q+1
       975: q+1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: q+1
       985: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: q+1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1013: 1
      1016: q+1
      1018: 1
      1019: 1
      1021: q+1
      1042: 1
      1050: 1
      1059: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1084: 1
      1089: 1
      1091: 1
      1096: 1
      1101: 1
      1168: 1
      1169: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1220: 1
      1222: 1
      1277: 1
      1360: 1
      1365: 1
      1366: 1
      1371: 1
      1375: 1
      1380: 1
      1382: 1
      1387: 1
      1392: 1
      1531: 1

1532:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^2+3q+1
        19: q^3+3q^2+3q+1
        20: q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q+1
        68: q^2+3q+1
        69: q^2+3q+1
        70: q+1
        71: q+1
        72: q^3+3q^2+3q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q^2+3q+1
       118: q^2+3q+1
       119: 1
       120: q^2+3q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q^2+3q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+3q+1
       169: q+1
       170: q^2+3q+1
       171: q^2+3q+1
       172: q+1
       173: q^2+3q+1
       174: q^2+3q+1
       175: q+1
       176: q+1
       177: q^3+3q^2+3q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q^2+3q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q^2+3q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       244: 2q+1
       248: 1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q^2+3q+1
       263: q^2+3q+1
       264: q^2+3q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q^2+3q+1
       270: q^2+3q+1
       271: q^2+3q+1
       272: q^2+3q+1
       273: 1
       274: q^2+3q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q^2+3q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+3q+1
       284: q^2+3q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q^2+3q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       388: 2q+1
       392: q+1
       393: q+1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       400: 1
       401: q^2+3q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q^2+3q+1
       409: q^2+3q+1
       410: q^2+3q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q^2+3q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       450: 2q+1
       454: 1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       462: q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: q+1
       521: 1
       522: 1
       524: q+1
       525: q+1
       527: q+1
       528: q+1
       529: q+1
       531: 1
       532: 2q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       559: q+1
       565: q+1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q^2+3q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       642: 2q+1
       646: q+1
       647: q+1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       707: 1
       711: q+1
       714: q+1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: q+1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: q+1
       812: 1
       813: 1
       815: q+1
       816: q+1
       818: q+1
       819: q+1
       820: q+1
       822: 1
       823: 2q+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       850: q+1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: 1
       877: 1
       882: 1
       886: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       918: 1
       935: 1
       938: 1
       939: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       979: 1
       980: 1
       981: 1
       985: 1
       986: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1018: 1
      1022: q+1
      1025: q+1
      1028: 1
      1029: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: q+1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1102: 1
      1105: 1
      1141: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1183: 1
      1188: 1
      1193: 1
      1197: 1
      1200: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1229: 1
      1246: 1
      1249: 1
      1250: 1
      1278: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1393: 1
      1396: 1
      1432: 1
      1532: 1

1533:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        81: q+1
        82: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       135: 1
       136: q+1
       137: q+1
       139: 1
       141: q+1
       142: q+1
       143: q+1
       145: 1
       149: q+1
       150: q+1
       151: q+1
       155: 1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       186: q+1
       187: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       214: 1
       215: q+1
       216: q+1
       218: 1
       220: q+1
       221: q+1
       222: q+1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       230: 1
       231: q+1
       233: 1
       237: 1
       238: q+1
       239: q+1
       241: 1
       248: q+1
       249: q+1
       250: q+1
       252: 1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       289: 1
       290: q+1
       291: q+1
       293: 1
       295: q+1
       296: q+1
       297: q+1
       299: 1
       303: q+1
       304: q+1
       305: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: q+1
       341: 1
       345: 1
       346: q+1
       347: q+1
       349: 1
       351: q+1
       352: q+1
       353: q+1
       355: 1
       359: 1
       361: 1
       367: 1
       368: q+1
       370: 1
       381: 1
       382: q+1
       383: q+1
       385: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: 1
       420: 1
       421: q+1
       422: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       436: 1
       437: q+1
       439: 1
       443: 1
       444: q+1
       445: q+1
       447: 1
       454: q+1
       455: q+1
       456: q+1
       458: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: q+1
       506: 1
       510: 1
       511: q+1
       512: q+1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: q+1
       548: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: q+1
       595: 1
       599: 1
       600: q+1
       601: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       613: 1
       615: 1
       621: 1
       622: q+1
       624: 1
       635: 1
       636: q+1
       637: q+1
       639: 1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: q+1
       700: 1
       718: 1
       734: 1
       736: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: q+1
       797: 1
       801: 1
       802: q+1
       803: q+1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       837: q+1
       839: 1
       854: 1
       861: 1
       862: 1
       868: 1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       939: 1
       960: 1
       961: 1
       967: 1
       968: 1
       969: 1
       970: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: q+1
      1011: 1
      1029: 1
      1045: 1
      1047: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1109: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1250: 1
      1279: 1
      1362: 1
      1369: 1
      1370: 1
      1376: 1
      1400: 1
      1533: 1

1534:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       145: 1
       149: 1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       183: 1
       186: 1
       187: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       248: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       299: 1
       303: 1
       305: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: 1
       361: 1
       381: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       454: 1
       458: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       522: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: 1
       615: 1
       635: 1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       813: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       893: 1
       961: 1
       962: 1
       966: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1204: 1
      1280: 1
      1363: 1
      1370: 1
      1371: 1
      1375: 1
      1534: 1

1535:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q+1
        89: 2q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: q^2+2q+1
       113: q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+2q+1
       123: q+1
       124: q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: 2q+1
       165: q^2+2q+1
       166: q+1
       167: 2q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: q+1
       191: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: q^2+2q+1
       207: q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: q+1
       214: 1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       242: 1
       248: q+1
       251: q+1
       252: 1
       253: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: 1
       266: q^2+2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: q^2+2q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q+1
       278: q+1
       279: q^2+2q+1
       280: q+1
       281: q+1
       282: 1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: 2q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: q+1
       381: 1
       386: 1
       392: q+1
       395: 1
       396: q+1
       397: 2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: q^2+2q+1
       413: q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       454: q+1
       457: q+1
       458: 1
       459: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: q+1
       485: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: q+1
       635: 1
       640: 1
       646: q+1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       707: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: q+1
       776: 2q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       856: 1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: 1
      1018: 1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1095: 1
      1098: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1190: 1
      1193: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1281: 1
      1364: 1
      1370: 1
      1372: 1
      1374: 1
      1386: 1
      1389: 1
      1535: 1

1536:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        79: 1
        81: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       152: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       184: 1
       186: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       256: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       306: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: 1
       357: 1
       363: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       462: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       610: 1
       611: 1
       617: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: 1
       686: 1
       687: 1
       693: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       808: 1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       888: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1199: 1
      1282: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1536: 1

1537:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       678: 1
       681: 1
       682: 1
       684: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       707: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       882: 1
       889: 1
       892: 1
       893: 1
       895: 1
       964: 1
       965: 1
       966: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       989: 1
       992: 1
       993: 1
       995: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1018: 1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1098: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1193: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1283: 1
      1366: 1
      1373: 1
      1374: 1
      1375: 1
      1389: 1
      1537: 1

1538:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       199: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       318: 1
       321: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       358: 1
       361: 1
       362: 1
       363: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       397: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       403: 1
       405: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       469: 1
       471: 1
       472: 1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       521: 1
       524: 1
       525: 1
       528: 1
       531: 1
       532: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       566: 1
       568: 1
       570: 1
       571: 1
       572: 1
       575: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       617: 1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       654: 1
       656: 1
       662: 1
       664: 1
       665: 1
       669: 1
       671: 1
       673: 1
       674: 1
       675: 1
       681: 1
       684: 1
       685: 1
       688: 1
       691: 1
       692: 1
       693: 1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       711: 1
       717: 1
       733: 1
       736: 1
       737: 1
       760: 1
       762: 1
       763: 1
       767: 1
       769: 1
       771: 1
       772: 1
       773: 1
       776: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       812: 1
       815: 1
       816: 1
       819: 1
       822: 1
       823: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: 1
       859: 1
       866: 1
       868: 1
       874: 1
       876: 1
       877: 1
       886: 1
       892: 1
       895: 1
       896: 1
       899: 1
       902: 1
       903: 1
       938: 1
       965: 1
       967: 1
       973: 1
       975: 1
       976: 1
       980: 1
       982: 1
       984: 1
       985: 1
       986: 1
       992: 1
       995: 1
       996: 1
       999: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1022: 1
      1028: 1
      1044: 1
      1047: 1
      1048: 1
      1076: 1
      1083: 1
      1085: 1
      1102: 1
      1108: 1
      1170: 1
      1177: 1
      1179: 1
      1185: 1
      1187: 1
      1188: 1
      1197: 1
      1203: 1
      1206: 1
      1207: 1
      1210: 1
      1213: 1
      1214: 1
      1249: 1
      1284: 1
      1367: 1
      1374: 1
      1376: 1
      1393: 1
      1399: 1
      1538: 1

1539:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       470: 1
       471: 1
       472: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       637: 1
       639: 1
       655: 1
       656: 1
       663: 1
       664: 1
       665: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       761: 1
       762: 1
       763: 1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       837: 1
       839: 1
       860: 1
       867: 1
       868: 1
       875: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       939: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1029: 1
      1045: 1
      1047: 1
      1077: 1
      1084: 1
      1085: 1
      1109: 1
      1171: 1
      1178: 1
      1179: 1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1250: 1
      1285: 1
      1368: 1
      1375: 1
      1376: 1
      1400: 1
      1539: 1

1540:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: q^3+5q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: 2q^3+5q^2+4q+1
         5: 3q^3+6q^2+4q+1
         6: q^3+5q^2+4q+1
         7: q^3+5q^2+4q+1
         8: q^3+5q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: 4q^2+4q+1
        11: 2q^3+5q^2+4q+1
        12: 2q^2+3q+1
        13: 2q^3+5q^2+4q+1
        14: q^3+4q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^3+6q^2+4q+1
        17: q^3+5q^2+4q+1
        18: 3q^3+6q^2+4q+1
        19: 2q^3+5q^2+4q+1
        20: q^3+5q^2+4q+1
        21: q^3+5q^2+4q+1
        22: q^3+5q^2+4q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: 4q^2+4q+1
        26: 4q^2+4q+1
        27: 4q^2+4q+1
        28: 2q^3+5q^2+4q+1
        29: 3q^2+4q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+4q^2+4q+1
        34: q^3+4q^2+4q+1
        35: q^3+4q^2+4q+1
        36: 2q^3+5q^2+4q+1
        37: 2q^2+3q+1
        38: q^3+3q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+5q^2+4q+1
        41: q^3+5q^2+4q+1
        42: q^3+5q^2+4q+1
        43: 3q^3+6q^2+4q+1
        44: 4q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 2q^2+3q+1
        47: 2q^3+5q^2+4q+1
        48: q^3+4q^2+4q+1
        49: 2q^3+5q^2+4q+1
        50: 2q^2+3q+1
        51: 2q+1
        52: q^3+5q^2+4q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q+1
        56: 2q+1
        57: 4q^2+4q+1
        58: 4q^2+4q+1
        59: 4q^2+4q+1
        60: q^2+3q+1
        61: 2q+1
        62: 3q^2+4q+1
        63: 3q^2+4q+1
        64: 3q^2+4q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+4q^2+4q+1
        74: q^2+2q+1
        75: 2q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: q^3+3q^2+3q+1
        80: q^2+2q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^3+5q^2+4q+1
        85: q^3+5q^2+4q+1
        86: q^3+5q^2+4q+1
        87: 2q^2+3q+1
        88: 2q+1
        89: 4q^2+4q+1
        90: 4q^2+4q+1
        91: 4q^2+4q+1
        92: 2q^3+5q^2+4q+1
        93: 3q^2+4q+1
        94: 2q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+4q+1
        98: q^3+4q^2+4q+1
        99: q^3+4q^2+4q+1
       100: 2q^3+5q^2+4q+1
       101: 2q^2+3q+1
       102: q^3+3q^2+3q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: 2q^2+3q+1
       106: 2q+1
       107: 2q^2+3q+1
       108: 2q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: q^2+3q+1
       113: 2q+1
       114: 4q^2+4q+1
       115: 2q^2+3q+1
       116: q^2+3q+1
       117: 2q+1
       118: 2q+1
       119: 3q^2+4q+1
       120: 3q^2+4q+1
       121: 3q^2+4q+1
       122: q^2+3q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q^2+2q+1
       135: 2q+1
       136: q^3+4q^2+4q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q+1
       140: q+1
       141: 2q^2+3q+1
       142: 2q^2+3q+1
       143: 2q^2+3q+1
       144: q+1
       145: q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 2q^2+3q+1
       156: 2q+1
       157: q^3+5q^2+4q+1
       158: 2q^2+3q+1
       159: 2q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: 4q^2+4q+1
       163: 4q^2+4q+1
       164: 4q^2+4q+1
       165: q^2+3q+1
       166: 2q+1
       167: 3q^2+4q+1
       168: 3q^2+4q+1
       169: 3q^2+4q+1
       170: q^2+3q+1
       171: q^2+3q+1
       172: q^2+3q+1
       173: 2q^2+3q+1
       174: q^2+3q+1
       175: 2q^2+3q+1
       176: q^3+4q^2+4q+1
       177: q^3+4q^2+4q+1
       178: q^3+4q^2+4q+1
       179: q^2+2q+1
       180: 2q+1
       181: 2q^2+3q+1
       182: 2q^2+3q+1
       183: 2q^2+3q+1
       184: q^3+3q^2+3q+1
       185: q^2+2q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: 2q+1
       192: q+1
       193: 2q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: q^2+3q+1
       200: 2q+1
       201: 2q^2+3q+1
       202: 2q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: q^2+3q+1
       208: 3q^2+4q+1
       209: q^2+2q+1
       210: q^2+3q+1
       213: q+1
       214: 2q+1
       215: q^2+3q+1
       216: q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q+1
       229: q^2+2q+1
       230: 2q+1
       231: q^2+2q+1
       232: q+1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: 2q^2+3q+1
       239: q^2+2q+1
       240: q+1
       241: q+1
       242: 1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: 2q+1
       259: 2q^2+3q+1
       260: 2q+1
       261: 2q^2+3q+1
       262: 2q+1
       263: q+1
       264: 2q+1
       265: 2q+1
       266: q^2+3q+1
       267: 2q+1
       268: 4q^2+4q+1
       269: 2q^2+3q+1
       270: q^2+3q+1
       271: 2q+1
       272: 2q+1
       273: 3q^2+4q+1
       274: 3q^2+4q+1
       275: 3q^2+4q+1
       276: q^2+3q+1
       278: q^2+3q+1
       279: q^2+3q+1
       280: q^2+3q+1
       281: q+1
       282: 2q+1
       283: q^2+3q+1
       284: q^2+3q+1
       285: q^2+3q+1
       286: 2q^2+3q+1
       287: 2q+1
       288: q^2+2q+1
       289: 2q+1
       290: q^3+4q^2+4q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: 2q+1
       294: q+1
       295: 2q^2+3q+1
       296: 2q^2+3q+1
       297: 2q^2+3q+1
       298: q+1
       299: q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: 2q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: q+1
       323: 2q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       329: q^2+3q+1
       331: q^2+2q+1
       332: q+1
       336: q+1
       337: q+1
       338: 2q+1
       339: q+1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       356: q+1
       357: q+1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: q+1
       367: q+1
       368: q^2+2q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q^2+2q+1
       377: q+1
       380: 1
       381: q+1
       382: 2q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       395: 2q+1
       396: 2q+1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: q+1
       401: q+1
       402: 2q+1
       403: q+1
       404: 2q+1
       405: q^2+3q+1
       406: 2q+1
       407: 2q^2+3q+1
       408: 2q+1
       409: q+1
       410: 2q+1
       411: 2q+1
       412: q^2+3q+1
       414: 3q^2+4q+1
       415: q^2+2q+1
       416: q^2+3q+1
       419: q+1
       420: 2q+1
       421: q^2+3q+1
       422: q+1
       423: q+1
       424: 2q+1
       425: q+1
       426: q^2+3q+1
       427: q^2+3q+1
       428: q^2+3q+1
       429: q+1
       431: 2q+1
       432: 2q+1
       433: 2q+1
       434: q+1
       435: q^2+2q+1
       436: 2q+1
       437: q^2+2q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: 2q^2+3q+1
       445: q^2+2q+1
       446: q+1
       447: q+1
       448: 1
       449: q^2+2q+1
       450: q^2+2q+1
       451: q^2+2q+1
       452: q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: 2q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       485: q+1
       487: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       502: q+1
       504: q+1
       505: 1
       509: 1
       511: 2q+1
       512: q+1
       513: 1
       516: 1
       517: q+1
       518: 1
       519: q+1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       563: q+1
       564: 2q+1
       565: q+1
       566: 2q+1
       569: q+1
       570: q+1
       571: 1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: q+1
       577: 2q+1
       578: q+1
       579: q+1
       580: 2q+1
       581: q+1
       583: q^2+3q+1
       585: q^2+2q+1
       586: q+1
       590: q+1
       591: q+1
       592: 2q+1
       593: q+1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       600: q^2+3q+1
       601: q+1
       602: q+1
       605: 2q+1
       606: 2q+1
       607: 2q+1
       608: 1
       610: q+1
       611: q+1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: q+1
       621: q+1
       622: q^2+2q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q^2+2q+1
       631: q+1
       634: 1
       635: q+1
       636: 2q+1
       637: q+1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       664: 1
       665: 1
       669: q+1
       676: 1
       677: q+1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: q+1
       699: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: q+1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: q+1
       752: 1
       755: q+1
       756: 1
       757: q+1
       762: 1
       763: 1
       764: q+1
       765: 2q+1
       766: q+1
       767: 2q+1
       770: q+1
       771: q+1
       772: 1
       773: q+1
       776: q+1
       778: q+1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       793: q+1
       795: q+1
       796: 1
       800: 1
       802: 2q+1
       803: q+1
       804: 1
       807: 1
       808: q+1
       809: 1
       810: q+1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: q+1
       846: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       854: 1
       861: 1
       862: 1
       868: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       906: 1
       907: 1
       913: 1
       914: 1
       916: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       942: 1
       953: 1
       960: 1
       961: 1
       967: 1
       968: q+1
       969: 1
       970: q+1
       975: 1
       976: 1
       980: q+1
       987: 1
       988: q+1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       996: 1
       999: 1
      1001: 1
      1007: 1
      1009: q+1
      1010: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: q+1
      1063: 1
      1071: 1
      1086: 1
      1087: 1
      1093: 1
      1106: 1
      1113: 1
      1137: 1
      1139: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1189: 1
      1190: 1
      1191: 1
      1196: 1
      1197: 1
      1201: 1
      1210: 1
      1212: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1227: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1253: 1
      1264: 1
      1286: 1
      1362: 1
      1377: 1
      1378: 1
      1384: 1
      1397: 1
      1404: 1
      1428: 1
      1430: 1
      1540: 1

1541:    0: 2q^3+6q^2+4q+1
         1: 2q^3+6q^2+4q+1
         2: 2q^3+6q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+6q^2+4q+1
         5: 2q^3+6q^2+4q+1
         6: 2q^3+6q^2+4q+1
         7: q^3+3q^2+3q+1
         8: 4q^2+4q+1
         9: 5q^2+4q+1
        10: 5q^2+4q+1
        11: 4q^2+4q+1
        12: 5q^2+4q+1
        13: 2q^3+6q^2+4q+1
        14: 2q^3+6q^2+4q+1
        15: 4q^2+4q+1
        16: 2q^3+6q^2+4q+1
        17: 2q^3+6q^2+4q+1
        18: 5q^2+4q+1
        19: 2q^3+6q^2+4q+1
        20: 4q^2+4q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: 2q^2+3q+1
        24: 4q^2+4q+1
        25: 5q^2+4q+1
        26: q^2+2q+1
        27: 4q^2+4q+1
        28: 4q^2+4q+1
        29: 4q^2+4q+1
        30: 5q^2+4q+1
        31: 5q^2+4q+1
        32: 4q^2+4q+1
        33: 2q^3+6q^2+4q+1
        34: q^3+3q^2+3q+1
        35: 3q^2+4q+1
        36: 4q^2+4q+1
        37: 4q^2+4q+1
        38: 2q^2+3q+1
        39: 4q^2+4q+1
        40: 2q^3+6q^2+4q+1
        41: q^3+3q^2+3q+1
        42: 4q^2+4q+1
        43: 5q^2+4q+1
        44: 5q^2+4q+1
        45: 4q^2+4q+1
        46: 5q^2+4q+1
        47: 2q^3+6q^2+4q+1
        48: 2q^3+6q^2+4q+1
        49: 4q^2+4q+1
        50: 2q^2+3q+1
        51: 4q^2+4q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: 2q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: 4q^2+4q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q^2+3q+1
        61: 4q^2+4q+1
        62: 4q^2+4q+1
        63: q^2+2q+1
        64: 2q^2+3q+1
        65: 5q^2+4q+1
        66: q^2+2q+1
        67: q^2+3q+1
        68: 4q^2+4q+1
        69: 4q^2+4q+1
        70: 2q^2+3q+1
        71: 3q^2+4q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: 2q+1
        75: 3q^2+4q+1
        76: 4q^2+4q+1
        78: 3q^2+4q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 4q^2+4q+1
        82: 4q^2+4q+1
        83: 2q^2+3q+1
        84: 4q^2+4q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: 2q^2+3q+1
        88: 4q^2+4q+1
        89: 5q^2+4q+1
        90: q^2+2q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: 4q^2+4q+1
        94: 5q^2+4q+1
        95: 5q^2+4q+1
        96: 4q^2+4q+1
        97: 2q^3+6q^2+4q+1
        98: q^3+3q^2+3q+1
        99: 3q^2+4q+1
       100: 4q^2+4q+1
       101: 4q^2+4q+1
       102: 2q^2+3q+1
       103: 4q^2+4q+1
       104: 2q^2+3q+1
       105: 2q+1
       106: q^2+3q+1
       107: q^2+3q+1
       108: 2q+1
       109: q^2+3q+1
       110: 2q+1
       111: q^2+2q+1
       112: 2q^2+3q+1
       113: 4q^2+4q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: 2q^2+3q+1
       119: 2q^2+3q+1
       120: q^2+2q+1
       121: q+1
       122: q^2+2q+1
       123: 2q^2+3q+1
       124: q^2+3q+1
       125: q^2+2q+1
       126: 2q+1
       127: q+1
       128: q^2+3q+1
       129: 4q^2+4q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q^2+3q+1
       133: 2q^2+3q+1
       134: 2q+1
       135: 3q^2+4q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 3q^2+4q+1
       144: 2q+1
       145: 3q^2+4q+1
       146: 2q^2+3q+1
       148: q^2+2q+1
       149: 4q^2+4q+1
       151: q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+2q+1
       155: 2q^2+3q+1
       156: 4q^2+4q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: 2q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: 4q^2+4q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q^2+3q+1
       166: 4q^2+4q+1
       167: 4q^2+4q+1
       168: q^2+2q+1
       169: 2q^2+3q+1
       170: 5q^2+4q+1
       171: q^2+2q+1
       172: q^2+3q+1
       173: 4q^2+4q+1
       174: 4q^2+4q+1
       175: 2q^2+3q+1
       176: 3q^2+4q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: 2q+1
       180: 3q^2+4q+1
       181: 4q^2+4q+1
       183: 3q^2+4q+1
       184: 2q^2+3q+1
       185: 2q^2+3q+1
       186: 4q^2+4q+1
       187: 4q^2+4q+1
       188: 2q^2+3q+1
       189: q^2+2q+1
       190: 2q+1
       191: 2q+1
       192: q^2+3q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q^2+2q+1
       198: 2q^2+3q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: q+1
       206: q^2+2q+1
       207: 2q^2+3q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: q^2+2q+1
       213: q+1
       214: q^2+3q+1
       215: 2q+1
       216: 2q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: 1
       224: 2q+1
       225: 2q^2+3q+1
       227: 2q+1
       228: 2q+1
       229: 2q+1
       230: q^2+3q+1
       231: q^2+3q+1
       232: 2q+1
       233: q^2+3q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 3q^2+4q+1
       242: 2q+1
       243: q^2+2q+1
       246: q+1
       247: q^2+2q+1
       248: q^2+3q+1
       251: q+1
       252: q^2+3q+1
       253: 2q^2+3q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q^2+3q+1
       259: 2q+1
       260: q^2+3q+1
       261: q^2+3q+1
       262: 2q+1
       263: q^2+3q+1
       264: 2q+1
       265: q^2+2q+1
       266: 2q^2+3q+1
       267: 4q^2+4q+1
       268: 2q+1
       269: 2q+1
       270: q+1
       271: 2q+1
       272: 2q^2+3q+1
       273: 2q^2+3q+1
       274: q^2+2q+1
       275: q+1
       276: q^2+2q+1
       277: 2q^2+3q+1
       278: q^2+3q+1
       279: q^2+2q+1
       280: 2q+1
       281: q+1
       282: q^2+3q+1
       283: 4q^2+4q+1
       284: q^2+2q+1
       285: 2q+1
       286: 2q^2+3q+1
       287: 2q^2+3q+1
       288: 2q+1
       289: 3q^2+4q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: 2q+1
       293: q^2+3q+1
       294: 2q+1
       295: 3q^2+4q+1
       298: 2q+1
       299: 3q^2+4q+1
       300: 2q^2+3q+1
       302: q^2+2q+1
       303: 4q^2+4q+1
       305: q^2+3q+1
       306: 2q^2+3q+1
       307: 2q^2+3q+1
       308: q^2+2q+1
       309: q^2+2q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       315: q+1
       316: 1
       317: q+1
       319: q+1
       320: q+1
       321: q+1
       322: 2q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: q+1
       328: q^2+2q+1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: q+1
       336: q+1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q+1
       343: 1
       344: 1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: 2q+1
       354: 1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: q^2+3q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       372: 1
       373: q+1
       374: q^2+2q+1
       379: q+1
       380: q+1
       381: q^2+3q+1
       386: q+1
       387: q+1
       390: 1
       391: q+1
       392: q^2+2q+1
       394: q+1
       395: q^2+2q+1
       396: 2q+1
       397: 2q+1
       398: q^2+3q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q^2+2q+1
       404: 2q^2+3q+1
       405: q+1
       406: 2q+1
       407: 2q+1
       408: q+1
       409: 2q+1
       410: q+1
       411: q+1
       412: q^2+2q+1
       413: 2q^2+3q+1
       414: q+1
       415: q+1
       416: 1
       417: q+1
       418: q^2+2q+1
       419: q+1
       420: q^2+3q+1
       421: 2q+1
       422: 2q+1
       423: q+1
       424: 2q+1
       425: q+1
       426: 2q+1
       427: q^2+2q+1
       428: q+1
       429: 1
       430: 2q+1
       431: 2q^2+3q+1
       433: 2q+1
       434: 2q+1
       435: 2q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: 2q+1
       439: q^2+3q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 3q^2+4q+1
       448: 2q+1
       449: q^2+2q+1
       452: q+1
       453: q^2+2q+1
       454: q^2+3q+1
       457: q+1
       458: q^2+3q+1
       459: 2q^2+3q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: 1
       467: q+1
       470: 1
       471: 1
       473: q+1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: q+1
       487: 1
       489: 1
       490: 1
       491: q+1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: 2q+1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       534: 1
       535: q+1
       542: 1
       543: q+1
       550: 1
       551: 1
       552: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       563: q^2+2q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       569: q+1
       570: 1
       571: q+1
       573: q+1
       574: q+1
       575: q+1
       576: 2q+1
       577: 1
       578: q+1
       579: q+1
       580: 1
       581: q+1
       582: q^2+2q+1
       583: 1
       584: q+1
       585: q+1
       586: 1
       587: q+1
       588: 1
       589: q+1
       590: q+1
       591: q+1
       592: 2q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: q+1
       597: 1
       598: 1
       599: 2q+1
       600: q+1
       601: q+1
       602: 1
       603: q+1
       604: 1
       605: 2q+1
       608: 1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: q^2+3q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       626: 1
       627: q+1
       628: q^2+2q+1
       633: q+1
       634: q+1
       635: q^2+3q+1
       640: q+1
       641: q+1
       644: 1
       645: q+1
       646: q^2+2q+1
       648: q+1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       706: q+1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       756: q+1
       757: 1
       758: q+1
       761: 1
       762: 1
       764: q+1
       765: 1
       766: q+1
       767: 1
       768: 1
       770: q+1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: q+1
       778: 1
       780: 1
       781: 1
       782: q+1
       783: 1
       784: q+1
       785: q+1
       786: 2q+1
       787: 1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: q+1
       796: 1
       797: q+1
       798: 1
       799: 1
       800: 1
       801: 2q+1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       825: 1
       826: q+1
       833: 1
       834: q+1
       841: 1
       842: 1
       843: q+1
       848: 1
       849: q+1
       852: 1
       853: q+1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       872: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       907: 1
       908: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       961: 1
       962: 1
       966: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: q+1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       987: 1
       988: 1
       989: q+1
       990: 1
       991: 1
       993: q+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: q+1
      1016: 1
      1017: q+1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: q+1
      1065: 1
      1072: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1097: 1
      1114: 1
      1146: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1183: 1
      1190: 1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1218: 1
      1219: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1287: 1
      1363: 1
      1378: 1
      1379: 1
      1383: 1
      1386: 1
      1388: 1
      1405: 1
      1437: 1
      1541: 1

1542:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        61: 1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       148: q+1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       242: 1
       243: q+1
       246: q+1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       302: q+1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: q+1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       449: q+1
       452: q+1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: q+1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       688: 1
       690: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       772: 1
       776: 1
       778: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       856: 1
       862: 1
       864: 1
       866: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       890: 1
       907: 1
       909: 1
       911: 1
       933: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       980: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       999: 1
      1001: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1042: 1
      1050: 1
      1059: 1
      1073: 1
      1087: 1
      1089: 1
      1091: 1
      1115: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1201: 1
      1218: 1
      1220: 1
      1222: 1
      1244: 1
      1288: 1
      1364: 1
      1378: 1
      1380: 1
      1382: 1
      1406: 1
      1542: 1

1543:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       722: 1
       731: 1
       740: 1
       747: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       857: 1
       863: 1
       864: 1
       865: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: 1
       908: 1
       909: 1
       910: 1
       943: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       997: 1
       998: 1
      1004: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1074: 1
      1088: 1
      1089: 1
      1090: 1
      1116: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1199: 1
      1219: 1
      1220: 1
      1221: 1
      1254: 1
      1289: 1
      1365: 1
      1379: 1
      1380: 1
      1381: 1
      1407: 1
      1543: 1

1544:    0: 2q^2+2q+1
         1: q^2+2q+1
         2: 2q^2+2q+1
         3: q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: 2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: 2q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q+1
        63: q+1
        64: q^2+q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 2q+1
        90: q+1
        91: q^2+2q+1
        92: 2q+1
        93: q^2+2q+1
        94: 2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+2q+1
       119: q+1
       120: q+1
       121: 1
       122: q^2+q+1
       123: q^2+q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       148: q+1
       149: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: q^2+2q+1
       162: q+1
       163: q+1
       164: q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: 2q+1
       168: q+1
       169: q^2+q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: q^2+2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q^2+q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       242: 2q+1
       243: q+1
       246: q+1
       247: q+1
       248: 1
       251: q+1
       252: q+1
       253: 2q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q^2+2q+1
       273: q+1
       274: q+1
       275: 1
       276: q^2+q+1
       277: q^2+q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       365: q+1
       372: 1
       373: q+1
       374: q+1
       379: q+1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q^2+q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       448: 2q+1
       449: q+1
       452: q+1
       453: q+1
       454: 1
       457: q+1
       458: q+1
       459: 2q+1
       461: 1
       462: q+1
       463: q+1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: 1
       523: 1
       524: q+1
       534: 1
       535: q+1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       626: 1
       627: q+1
       628: q+1
       633: q+1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       674: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       706: q+1
       707: 1
       708: 1
       709: 1
       710: 1
       730: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: 1
       814: 1
       815: q+1
       825: 1
       826: q+1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       889: 1
       890: 1
       891: 1
       895: 1
       910: 1
       911: 1
       912: 1
       951: 1
       952: 1
       964: 1
       965: 1
       966: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       985: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1017: q+1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1041: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1075: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1117: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1221: 1
      1222: 1
      1223: 1
      1262: 1
      1263: 1
      1290: 1
      1366: 1
      1381: 1
      1382: 1
      1383: 1
      1388: 1
      1408: 1
      1544: 1

1545:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: 2q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: 2q^2+2q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q+1
        62: 2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: q+1
        89: 2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q+1
       105: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: q+1
       112: 2q+1
       114: 2q+1
       115: 2q+1
       116: q^2+2q+1
       117: q+1
       118: q+1
       119: 2q+1
       120: 2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: 2q^2+2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: 2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: 2q+1
       193: 2q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       199: 2q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: q+1
       206: 2q+1
       208: 2q+1
       209: q+1
       210: q^2+2q+1
       213: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       229: q^2+2q+1
       231: q+1
       232: q+1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q+1
       268: 2q+1
       269: 2q+1
       270: q^2+2q+1
       271: q+1
       272: q+1
       273: 2q+1
       274: 2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 2q+1
       314: q+1
       316: q+1
       317: 1
       318: 1
       321: 2q+1
       323: 2q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       329: 2q+1
       331: q+1
       332: q+1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       358: q+1
       360: q+1
       361: 1
       362: 1
       363: q+1
       364: 1
       366: q+1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       377: q+1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 2q+1
       399: 2q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       405: 2q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: q+1
       412: 2q+1
       414: 2q+1
       415: q+1
       416: q^2+2q+1
       419: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       431: 1
       432: 1
       433: 1
       435: q^2+2q+1
       437: q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       469: q+1
       471: 1
       472: 1
       476: 2q+1
       478: q+1
       480: q+1
       481: 1
       482: 1
       485: q+1
       487: q+1
       494: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       502: q+1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: q+1
       521: 1
       523: 1
       524: 1
       525: 1
       528: q+1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 2q+1
       568: q+1
       570: q+1
       571: 1
       572: 1
       575: 2q+1
       577: 2q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       583: 2q+1
       585: q+1
       586: q+1
       591: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       600: q+1
       601: 1
       602: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       612: q+1
       614: q+1
       615: 1
       616: 1
       617: q+1
       618: 1
       620: q+1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       631: q+1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       654: 1
       656: 1
       662: q+1
       664: 1
       665: 1
       669: q+1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       708: 1
       710: 1
       711: 1
       715: q+1
       717: 1
       719: 1
       721: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       760: q+1
       762: 1
       763: 1
       767: 2q+1
       769: q+1
       771: q+1
       772: 1
       773: 1
       776: q+1
       778: q+1
       785: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       793: q+1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       810: q+1
       812: 1
       814: 1
       815: 1
       816: 1
       819: q+1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       859: 1
       866: 1
       868: 1
       883: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       911: 1
       913: 1
       919: 1
       936: 1
       938: 1
       940: 1
       942: 1
       953: 1
       965: 1
       967: 1
       973: q+1
       975: 1
       976: 1
       980: q+1
       990: 1
       992: 1
       994: 1
       995: 1
       996: 1
       999: 1
      1001: 1
      1007: 1
      1009: 1
      1010: 1
      1019: 1
      1021: 1
      1022: 1
      1026: q+1
      1028: 1
      1030: 1
      1032: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1076: 1
      1091: 1
      1093: 1
      1106: 1
      1118: 1
      1142: 1
      1170: 1
      1177: 1
      1179: 1
      1194: 1
      1196: 1
      1197: 1
      1201: 1
      1210: 1
      1212: 1
      1222: 1
      1224: 1
      1230: 1
      1247: 1
      1249: 1
      1251: 1
      1253: 1
      1264: 1
      1291: 1
      1367: 1
      1382: 1
      1384: 1
      1397: 1
      1409: 1
      1433: 1
      1545: 1

1546:    0: 2q^3+6q^2+4q+1
         1: 2q^3+6q^2+4q+1
         2: 2q^3+6q^2+4q+1
         3: 5q^2+4q+1
         4: 2q^3+6q^2+4q+1
         5: 2q^3+6q^2+4q+1
         6: q^3+3q^2+3q+1
         7: 2q^3+6q^2+4q+1
         8: 5q^2+4q+1
         9: 5q^2+4q+1
        10: 4q^2+4q+1
        11: 4q^2+4q+1
        12: 5q^2+4q+1
        13: 2q^3+6q^2+4q+1
        14: 2q^3+6q^2+4q+1
        15: 4q^2+4q+1
        16: 2q^3+6q^2+4q+1
        17: 2q^3+6q^2+4q+1
        18: 5q^2+4q+1
        19: 2q^3+6q^2+4q+1
        20: q^2+2q+1
        21: q^3+3q^2+3q+1
        22: 5q^2+4q+1
        23: 4q^2+4q+1
        24: 5q^2+4q+1
        25: q^2+3q+1
        26: 4q^2+4q+1
        27: 4q^2+4q+1
        28: 4q^2+4q+1
        29: 3q^2+4q+1
        30: 5q^2+4q+1
        31: 4q^2+4q+1
        32: 4q^2+4q+1
        33: q^3+3q^2+3q+1
        34: 2q^3+6q^2+4q+1
        35: 4q^2+4q+1
        36: 4q^2+4q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 4q^2+4q+1
        40: q^3+3q^2+3q+1
        41: 2q^3+6q^2+4q+1
        42: 5q^2+4q+1
        43: 5q^2+4q+1
        44: 4q^2+4q+1
        45: 4q^2+4q+1
        46: 5q^2+4q+1
        47: 2q^3+6q^2+4q+1
        48: 2q^3+6q^2+4q+1
        49: 4q^2+4q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+3q+1
        54: 4q^2+4q+1
        55: 5q^2+4q+1
        56: 4q^2+4q+1
        57: 2q+1
        58: q^2+3q+1
        59: 4q^2+4q+1
        60: 3q^2+4q+1
        61: 4q^2+4q+1
        62: q^2+3q+1
        63: 3q^2+4q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: 4q^2+4q+1
        67: 2q^2+3q+1
        68: 4q^2+4q+1
        69: 3q^2+4q+1
        70: 2q^2+3q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: 4q^2+4q+1
        74: 2q^2+3q+1
        75: 4q^2+4q+1
        76: 2q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q+1
        81: 4q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^2+2q+1
        85: q^3+3q^2+3q+1
        86: 5q^2+4q+1
        87: 4q^2+4q+1
        88: 5q^2+4q+1
        89: q^2+3q+1
        90: 4q^2+4q+1
        91: 4q^2+4q+1
        92: 4q^2+4q+1
        93: 3q^2+4q+1
        94: 5q^2+4q+1
        95: 4q^2+4q+1
        96: 4q^2+4q+1
        97: q^3+3q^2+3q+1
        98: 2q^3+6q^2+4q+1
        99: 4q^2+4q+1
       100: 4q^2+4q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: 4q^2+4q+1
       106: q^2+2q+1
       107: 2q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: 4q^2+4q+1
       111: 2q^2+3q+1
       113: 2q+1
       114: 2q+1
       115: q^2+3q+1
       116: 3q^2+4q+1
       117: 4q^2+4q+1
       118: 3q^2+4q+1
       119: 2q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: q^2+3q+1
       124: q+1
       125: q^2+3q+1
       126: 2q^2+3q+1
       127: q^2+2q+1
       128: 2q^2+3q+1
       129: q^2+3q+1
       130: 3q^2+4q+1
       131: 2q+1
       132: 2q^2+3q+1
       133: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: 2q^2+3q+1
       139: 4q^2+4q+1
       140: 2q^2+3q+1
       141: q+1
       142: 2q+1
       143: 2q^2+3q+1
       144: 2q+1
       145: 2q^2+3q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       152: 2q^2+3q+1
       153: 2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+3q+1
       159: 4q^2+4q+1
       160: 5q^2+4q+1
       161: 4q^2+4q+1
       162: 2q+1
       163: q^2+3q+1
       164: 4q^2+4q+1
       165: 3q^2+4q+1
       166: 4q^2+4q+1
       167: q^2+3q+1
       168: 3q^2+4q+1
       169: q^2+3q+1
       170: q^2+3q+1
       171: 4q^2+4q+1
       172: 2q^2+3q+1
       173: 4q^2+4q+1
       174: 3q^2+4q+1
       175: 2q^2+3q+1
       176: q^2+2q+1
       177: q^3+3q^2+3q+1
       178: 4q^2+4q+1
       179: 2q^2+3q+1
       180: 4q^2+4q+1
       181: 2q+1
       182: 2q^2+3q+1
       183: 2q^2+3q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: 4q^2+4q+1
       187: 2q^2+3q+1
       188: 2q^2+3q+1
       192: 2q+1
       193: 2q+1
       194: q+1
       195: q^2+3q+1
       196: 2q^2+3q+1
       197: q^2+2q+1
       200: 2q+1
       201: 2q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: 3q^2+4q+1
       205: 2q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q^2+3q+1
       211: q^2+3q+1
       212: q^2+3q+1
       214: q+1
       215: q+1
       216: q+1
       217: q^2+2q+1
       218: 2q^2+3q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+3q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q^2+2q+1
       227: q+1
       230: q^2+2q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q^2+3q+1
       235: q^2+2q+1
       237: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q^2+3q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: 2q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       260: q^2+2q+1
       261: 2q+1
       262: q^2+3q+1
       263: q^2+3q+1
       264: 4q^2+4q+1
       265: 2q^2+3q+1
       267: 2q+1
       268: 2q+1
       269: q^2+3q+1
       270: 3q^2+4q+1
       271: 4q^2+4q+1
       272: 3q^2+4q+1
       273: 2q+1
       274: q^2+3q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: q^2+3q+1
       278: q+1
       279: q^2+3q+1
       280: 2q^2+3q+1
       281: q^2+2q+1
       282: 2q^2+3q+1
       283: q^2+3q+1
       284: 3q^2+4q+1
       285: 2q+1
       286: 2q^2+3q+1
       287: q^2+2q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: 2q^2+3q+1
       293: 4q^2+4q+1
       294: 2q^2+3q+1
       295: q+1
       296: 2q+1
       297: 2q^2+3q+1
       298: 2q+1
       299: 2q^2+3q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q^2+3q+1
       305: q^2+2q+1
       306: 2q^2+3q+1
       307: 2q+1
       308: q^2+2q+1
       313: 2q+1
       315: q+1
       316: q+1
       317: q+1
       318: q^2+2q+1
       322: 2q+1
       323: 2q+1
       324: q+1
       325: q^2+3q+1
       326: 2q+1
       327: q+1
       330: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+3q+1
       335: 2q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       374: q+1
       375: q+1
       377: q+1
       378: q+1
       379: q+1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       398: 2q+1
       399: 2q+1
       400: q+1
       401: q^2+3q+1
       402: 2q^2+3q+1
       403: q^2+2q+1
       406: 2q+1
       407: 2q+1
       408: q^2+3q+1
       409: q^2+3q+1
       410: 3q^2+4q+1
       411: 2q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: q^2+3q+1
       417: q^2+3q+1
       418: q^2+3q+1
       420: q+1
       421: q+1
       422: q+1
       423: q^2+2q+1
       424: 2q^2+3q+1
       425: q^2+2q+1
       426: q+1
       427: q^2+3q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: q+1
       432: q^2+2q+1
       433: q+1
       436: q^2+2q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q^2+3q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: 2q+1
       456: q^2+2q+1
       457: q+1
       458: q^2+2q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       470: q+1
       471: 1
       472: q+1
       477: 2q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       486: q+1
       487: q+1
       489: q+1
       490: 2q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: q+1
       522: 1
       523: 1
       524: q+1
       525: q+1
       529: q+1
       530: q+1
       531: 1
       532: 2q+1
       533: 1
       534: 1
       537: q+1
       541: q+1
       542: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       567: 2q+1
       569: q+1
       570: q+1
       571: q+1
       572: q^2+2q+1
       576: 2q+1
       577: 2q+1
       578: q+1
       579: q^2+3q+1
       580: 2q+1
       581: q+1
       584: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: q^2+3q+1
       589: 2q+1
       592: q+1
       593: 1
       594: q+1
       595: q+1
       596: q^2+2q+1
       597: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: 2q+1
       604: q+1
       605: 1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       628: q+1
       629: q+1
       631: q+1
       632: q+1
       633: q+1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q^2+2q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       655: 1
       656: 1
       663: q+1
       664: 1
       665: 1
       670: q+1
       674: 1
       675: q+1
       680: 1
       682: 1
       683: 1
       684: 1
       685: 1
       689: 1
       690: 1
       692: 1
       693: q+1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       709: 1
       710: 1
       711: q+1
       716: q+1
       718: 1
       719: 1
       721: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       742: 1
       746: 1
       747: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       761: q+1
       762: 1
       763: q+1
       768: 2q+1
       770: q+1
       771: q+1
       772: 1
       773: q+1
       777: q+1
       778: q+1
       780: q+1
       781: 2q+1
       782: q+1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       791: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       801: 1
       802: 1
       803: 1
       804: 1
       805: q+1
       806: 1
       811: q+1
       813: 1
       814: 1
       815: q+1
       816: q+1
       820: q+1
       821: q+1
       822: 1
       823: 2q+1
       824: 1
       825: 1
       828: q+1
       832: q+1
       833: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       860: 1
       867: 1
       868: 1
       877: 1
       884: 1
       885: 1
       886: 1
       891: 1
       895: 1
       896: 1
       900: 1
       901: 1
       903: 1
       912: 1
       913: 1
       920: 1
       932: 1
       937: 1
       939: 1
       940: 1
       942: 1
       950: 1
       951: 1
       954: 1
       958: 1
       966: 1
       967: 1
       974: q+1
       975: 1
       976: 1
       981: q+1
       985: 1
       986: q+1
       991: 1
       993: 1
       994: 1
       995: 1
       996: 1
      1000: 1
      1001: 1
      1003: 1
      1004: q+1
      1005: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1020: 1
      1021: 1
      1022: q+1
      1027: q+1
      1029: 1
      1030: 1
      1032: 1
      1040: 1
      1041: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1053: 1
      1057: 1
      1058: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1077: 1
      1092: 1
      1093: 1
      1102: 1
      1107: 1
      1119: 1
      1143: 1
      1155: 1
      1171: 1
      1178: 1
      1179: 1
      1188: 1
      1195: 1
      1196: 1
      1197: 1
      1202: 1
      1206: 1
      1207: 1
      1211: 1
      1212: 1
      1214: 1
      1223: 1
      1224: 1
      1231: 1
      1243: 1
      1248: 1
      1250: 1
      1251: 1
      1253: 1
      1261: 1
      1262: 1
      1265: 1
      1269: 1
      1292: 1
      1368: 1
      1383: 1
      1384: 1
      1393: 1
      1398: 1
      1410: 1
      1434: 1
      1446: 1
      1546: 1

1547:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: 1
        72: q^2+2q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q^2+2q+1
       126: 1
       127: 1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q+1
       165: q+1
       166: q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: 1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q+1
       176: 1
       177: q^2+2q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q^2+2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q^2+2q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q^2+2q+1
       280: 1
       281: 1
       282: 1
       283: q^2+2q+1
       284: q^2+2q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       392: q+1
       393: q+1
       395: 1
       396: q+1
       397: q+1
       398: q+1
       401: q+1
       402: 1
       403: 1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q^2+2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: q+1
       563: 1
       564: 1
       565: q+1
       571: 1
       572: 1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: q+1
       646: q+1
       647: q+1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: 1
       704: 1
       711: 1
       714: 1
       732: 1
       733: 1
       734: 1
       737: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: q+1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       823: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: q+1
       861: 1
       869: 1
       870: 1
       877: 1
       878: 1
       879: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       906: 1
       935: 1
       960: 1
       968: 1
       969: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1014: 1
      1015: 1
      1022: 1
      1025: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1105: 1
      1172: 1
      1180: 1
      1181: 1
      1188: 1
      1189: 1
      1190: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1217: 1
      1246: 1
      1293: 1
      1369: 1
      1377: 1
      1385: 1
      1386: 1
      1393: 1
      1396: 1
      1547: 1

1548:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: 2q+1
        20: q^2+2q+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q+1
        25: q^2+2q+1
        26: q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        41: q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q^2+q+1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: q+1
        57: q^2+2q+1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q+1
        62: q^2+2q+1
        63: q+1
        64: q^2+2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q^2+2q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: q+1
        89: q^2+2q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       104: q+1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q^2+q+1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: q+1
       119: q^2+2q+1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: 2q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: q+1
       162: q^2+2q+1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: q+1
       167: q^2+2q+1
       168: q+1
       169: q^2+2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 2q+1
       183: 2q+1
       184: q+1
       185: q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q^2+q+1
       207: q+1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: 2q+1
       227: 2q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       248: 2q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: q+1
       266: q^2+q+1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: q+1
       273: q^2+2q+1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 1
       282: q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       287: 2q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: 2q+1
       298: 1
       299: q+1
       300: q+1
       302: q+1
       303: 2q+1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: q+1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: 2q+1
       354: 1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       392: q+1
       394: q+1
       395: q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: q+1
       404: q+1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: q^2+q+1
       413: q+1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: q+1
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: 2q+1
       427: q+1
       428: q+1
       429: 1
       430: q+1
       431: 2q+1
       433: 2q+1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: q+1
       452: 1
       454: 2q+1
       457: 1
       458: q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: q+1
       561: 1
       563: q+1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q+1
       582: q+1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: q+1
       590: 1
       591: 1
       592: 1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: q+1
       600: q+1
       601: q+1
       602: 1
       603: 1
       604: 1
       605: 2q+1
       608: 1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: q+1
       640: 1
       641: q+1
       644: 1
       646: q+1
       648: q+1
       650: 1
       658: 1
       659: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       762: 1
       764: q+1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: q+1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: q+1
       852: 1
       862: 1
       870: 1
       871: 1
       876: 1
       879: 1
       880: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       933: 1
       961: 1
       969: 1
       970: 1
       975: 1
       977: q+1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1042: 1
      1050: 1
      1059: 1
      1079: 1
      1087: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1173: 1
      1181: 1
      1182: 1
      1187: 1
      1190: 1
      1191: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: 1
      1244: 1
      1294: 1
      1370: 1
      1378: 1
      1386: 1
      1387: 1
      1392: 1
      1394: 1
      1548: 1

1549:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+q+1
        39: q^2+2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: q^2+2q+1
        44: 2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+2q+1
        50: q+1
        51: 2q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: 2q+1
        76: q+1
        78: q+1
        79: q^2+q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+q+1
       103: q^2+2q+1
       104: q+1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       112: q+1
       113: 2q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: 1
       135: 2q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       144: 1
       145: q+1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q^2+q+1
       153: q+1
       154: q^2+q+1
       155: q+1
       156: 2q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       180: 2q+1
       181: q+1
       183: q+1
       184: q^2+q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+q+1
       189: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: q+1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 2q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: q+1
       213: 1
       214: 2q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       242: 1
       243: q+1
       246: 1
       247: q+1
       248: q+1
       251: 1
       252: q+1
       253: q+1
       255: q+1
       256: q^2+q+1
       257: q+1
       258: q+1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       266: q+1
       267: 2q+1
       268: q+1
       269: 1
       270: 1
       271: q+1
       272: q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: q+1
       277: 2q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: 1
       289: 2q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q^2+q+1
       307: q+1
       308: q^2+q+1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: q+1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 2q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: q+1
       354: 1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       374: q+1
       379: 1
       380: 1
       381: q+1
       386: 1
       387: q+1
       390: 1
       391: q+1
       392: q+1
       394: q+1
       395: q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: q+1
       405: 1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: q+1
       413: 2q+1
       414: q+1
       415: 1
       416: 1
       417: q+1
       418: q+1
       419: 1
       420: 2q+1
       421: q+1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 2q+1
       427: q+1
       428: q+1
       429: 1
       430: 2q+1
       431: q+1
       433: q+1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: q+1
       452: 1
       453: q+1
       454: q+1
       457: 1
       458: q+1
       459: q+1
       461: q+1
       462: q^2+q+1
       463: q+1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: q+1
       583: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       590: 1
       591: 1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 2q+1
       600: q+1
       601: 1
       602: 1
       603: q+1
       604: 1
       605: q+1
       608: 1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       628: q+1
       633: 1
       634: 1
       635: q+1
       640: 1
       641: q+1
       644: 1
       645: q+1
       646: q+1
       648: q+1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: 1
       706: 1
       709: 1
       722: 1
       731: 1
       740: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       757: 1
       758: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: q+1
       806: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: q+1
       848: 1
       849: q+1
       852: 1
       853: q+1
       863: 1
       871: 1
       872: 1
       875: 1
       880: 1
       881: 1
       884: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       897: 1
       908: 1
       943: 1
       952: 1
       959: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       991: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1013: 1
      1016: 1
      1017: 1
      1020: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1059: 1
      1060: q+1
      1065: 1
      1080: 1
      1088: 1
      1096: 1
      1097: 1
      1100: 1
      1156: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1191: 1
      1192: 1
      1195: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1208: 1
      1219: 1
      1254: 1
      1263: 1
      1270: 1
      1295: 1
      1371: 1
      1379: 1
      1387: 1
      1388: 1
      1391: 1
      1447: 1
      1549: 1

1550:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       422: 1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: 1
       602: q+1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       652: 1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: 1
       707: 1
       708: 1
       731: 1
       748: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       864: 1
       871: 1
       873: 1
       874: 1
       880: 1
       882: 1
       883: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       897: 1
       909: 1
       963: 1
       970: 1
       972: 1
       973: 1
       978: 1
       979: 1
       980: 1
       982: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1042: 1
      1059: 1
      1081: 1
      1089: 1
      1096: 1
      1098: 1
      1099: 1
      1175: 1
      1182: 1
      1184: 1
      1185: 1
      1191: 1
      1193: 1
      1194: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1208: 1
      1220: 1
      1296: 1
      1372: 1
      1380: 1
      1387: 1
      1389: 1
      1390: 1
      1550: 1

1551:    0: q^4+3q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: q^4+3q^2+2q+1
         4: q^4+3q^2+2q+1
         5: q^4+3q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: q^4+3q^2+2q+1
        12: q^4+3q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^4+3q^2+2q+1
        19: q^4+3q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: q^4+3q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: q^4+3q^2+2q+1
        46: q^4+3q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^4+3q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 1
       144: q+1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: q^2+2q+1
       162: q+1
       163: q^2+2q+1
       164: 2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: q^2+2q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: q^2+2q+1
       273: q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       298: q+1
       299: q+1
       300: q+1
       302: 1
       303: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: 2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 1
       354: q+1
       355: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: q+1
       409: q+1
       410: 2q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: q^2+2q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: q+1
       427: q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: 1
       453: 1
       454: 1
       457: q+1
       458: q+1
       459: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: 2q+1
       508: q+1
       509: 1
       510: 1
       515: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: q+1
       587: q+1
       588: 2q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: q+1
       595: q+1
       596: 2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 1
       608: q+1
       609: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       695: 1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: q+1
       797: q+1
       798: 2q+1
       799: q+1
       800: 1
       801: 1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       910: 1
       952: 1
       959: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1006: 1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1082: 1
      1090: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1221: 1
      1263: 1
      1270: 1
      1297: 1
      1373: 1
      1381: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1551: 1

1552:    0: q^2+1
         1: 1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: 1
         7: 1
         8: q^2+1
         9: 1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: q^2+1
        18: q^2+1
        19: 1
        20: 1
        21: 1
        22: 1
        23: q^2+1
        24: 1
        25: 1
        26: 1
        27: q^2+1
        28: 1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: q^2+1
        43: 1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: q^2+1
        61: 1
        62: 1
        63: 1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q^2+1
        88: 1
        89: 1
        90: 1
        91: q^2+1
        92: 1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: q^2+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: q^2+1
       166: 1
       167: 1
       168: 1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       373: 1
       380: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       519: 1
       521: 1
       523: 1
       524: 1
       534: 1
       550: 1
       551: 1
       558: 1
       561: 1
       566: 1
       568: 1
       570: 1
       571: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       627: 1
       634: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       654: 1
       662: 1
       664: 1
       669: 1
       671: 1
       673: 1
       674: 1
       679: 1
       681: 1
       683: 1
       684: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       708: 1
       710: 1
       739: 1
       748: 1
       760: 1
       762: 1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: 1
       825: 1
       841: 1
       842: 1
       849: 1
       852: 1
       866: 1
       874: 1
       876: 1
       883: 1
       885: 1
       890: 1
       892: 1
       894: 1
       895: 1
       905: 1
       911: 1
       965: 1
       973: 1
       975: 1
       980: 1
       982: 1
       984: 1
       985: 1
       990: 1
       992: 1
       994: 1
       995: 1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1013: 1
      1019: 1
      1021: 1
      1050: 1
      1059: 1
      1083: 1
      1091: 1
      1099: 1
      1101: 1
      1177: 1
      1185: 1
      1187: 1
      1194: 1
      1196: 1
      1201: 1
      1203: 1
      1205: 1
      1206: 1
      1216: 1
      1222: 1
      1298: 1
      1374: 1
      1382: 1
      1390: 1
      1392: 1
      1552: 1

1553:    0: q+1
         1: 1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: q+1
         9: 1
        10: q+1
        11: q+1
        12: q+1
        13: 1
        14: q+1
        15: q+1
        16: 1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: q+1
        28: 1
        29: q+1
        30: 1
        31: q+1
        32: q+1
        33: 1
        34: 1
        35: q+1
        36: 1
        37: q+1
        38: 1
        39: q+1
        40: 1
        41: 1
        42: q+1
        43: 1
        44: q+1
        45: q+1
        46: q+1
        47: 1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: 1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: q+1
        68: 1
        69: q+1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: q+1
        76: 1
        78: q+1
        79: 1
        80: 1
        81: 1
        82: q+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: q+1
        92: 1
        93: q+1
        94: 1
        95: q+1
        96: q+1
        97: 1
        98: 1
        99: q+1
       100: 1
       101: q+1
       102: 1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: 1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: q+1
       129: 1
       130: 1
       131: q+1
       132: 1
       133: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: q+1
       146: 1
       148: 1
       149: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: q+1
       166: q+1
       167: 1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: q+1
       173: 1
       174: q+1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: q+1
       181: 1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: q+1
       188: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: q+1
       225: 1
       227: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: q+1
       253: 1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: 1
       274: 1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: q+1
       283: 1
       284: 1
       285: q+1
       286: 1
       287: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: q+1
       300: 1
       302: 1
       303: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       313: 1
       315: 1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       372: 1
       374: 1
       379: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: q+1
       431: 1
       433: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: q+1
       459: 1
       461: 1
       462: 1
       463: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       534: 1
       542: 1
       550: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       571: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       626: 1
       628: 1
       633: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       655: 1
       663: 1
       664: 1
       670: 1
       672: 1
       673: 1
       674: 1
       680: 1
       682: 1
       683: 1
       684: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       709: 1
       710: 1
       730: 1
       739: 1
       747: 1
       749: 1
       754: 1
       761: 1
       762: 1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       801: 1
       806: 1
       811: 1
       813: 1
       814: 1
       815: 1
       825: 1
       833: 1
       841: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       867: 1
       875: 1
       876: 1
       884: 1
       885: 1
       891: 1
       893: 1
       894: 1
       895: 1
       905: 1
       912: 1
       951: 1
       959: 1
       966: 1
       974: 1
       975: 1
       981: 1
       983: 1
       984: 1
       985: 1
       991: 1
       993: 1
       994: 1
       995: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1013: 1
      1020: 1
      1021: 1
      1041: 1
      1050: 1
      1058: 1
      1060: 1
      1065: 1
      1084: 1
      1092: 1
      1100: 1
      1101: 1
      1164: 1
      1178: 1
      1186: 1
      1187: 1
      1195: 1
      1196: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1216: 1
      1223: 1
      1262: 1
      1270: 1
      1299: 1
      1375: 1
      1383: 1
      1391: 1
      1392: 1
      1455: 1
      1553: 1

1554:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: 2q+1
         5: q^2+2q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: 2q+1
        25: q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        52: q+1
        53: q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: 2q+1
        62: q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       114: q+1
       115: q+1
       116: q^2+2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: 2q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       157: q+1
       158: q+1
       159: q^2+2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       208: q+1
       209: q+1
       210: q^2+2q+1
       211: 2q+1
       212: 2q+1
       215: q+1
       216: 1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: 1
       226: q+1
       227: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       261: q+1
       262: q+1
       263: q+1
       264: 2q+1
       265: 2q+1
       268: q+1
       269: q+1
       270: q^2+2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: 2q+1
       281: q+1
       282: 2q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       316: q+1
       317: 1
       318: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       346: q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: q+1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: q+1
       400: q+1
       401: q+1
       402: 2q+1
       403: q+1
       407: q+1
       408: q+1
       409: q+1
       410: 2q+1
       411: 2q+1
       414: q+1
       415: q+1
       416: q^2+2q+1
       417: 2q+1
       418: 2q+1
       421: q+1
       422: 1
       423: q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: 1
       432: q+1
       433: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: q+1
       457: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       471: 1
       472: 1
       480: q+1
       481: 1
       482: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       570: q+1
       571: 1
       572: q+1
       577: q+1
       578: q+1
       579: q+1
       580: 2q+1
       581: q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       600: q+1
       601: 1
       602: q+1
       603: 2q+1
       604: q+1
       605: 1
       606: 1
       607: q+1
       608: 1
       609: q+1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       631: 1
       636: 1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       673: q+1
       674: 1
       675: q+1
       683: 1
       684: 1
       685: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       711: 1
       719: 1
       721: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       750: 1
       752: 1
       762: 1
       763: 1
       771: q+1
       772: 1
       773: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       802: 1
       803: 1
       804: 1
       805: q+1
       806: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       868: 1
       876: 1
       877: 1
       885: 1
       886: 1
       894: 1
       895: 1
       896: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       913: 1
       940: 1
       942: 1
       967: 1
       975: 1
       976: 1
       984: q+1
       985: 1
       986: q+1
       994: 1
       995: 1
       996: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1021: 1
      1022: 1
      1030: 1
      1032: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1061: 1
      1063: 1
      1085: 1
      1093: 1
      1101: 1
      1102: 1
      1110: 1
      1112: 1
      1179: 1
      1187: 1
      1188: 1
      1196: 1
      1197: 1
      1205: 1
      1206: 1
      1207: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1224: 1
      1251: 1
      1253: 1
      1300: 1
      1376: 1
      1384: 1
      1392: 1
      1393: 1
      1401: 1
      1403: 1
      1554: 1

1555:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^2+1
         3: q^3+q^2+q+1
         4: q+1
         5: q^3+q^2+q+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^3+q^2+q+1
        10: q^2+1
        11: q^3+q^2+q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q^3+q^2+q+1
        17: q^2+1
        18: q^3+q^2+q+1
        19: q+1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: 1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^3+q^2+q+1
        29: q^2+1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^3+q^2+q+1
        44: q^2+1
        45: q^3+q^2+q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: q^2+1
        51: 1
        52: q^2+1
        54: q^2+1
        55: 1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q^2+1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^3+q^2+q+1
        93: q^2+1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: q^2+1
       106: 1
       110: 1
       111: 1
       112: q^2+1
       113: 1
       114: q^2+1
       116: q^2+1
       117: 1
       118: 1
       119: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^2+1
       156: 1
       157: q^2+1
       159: q^2+1
       160: 1
       161: 1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: q^2+1
       200: 1
       204: 1
       205: 1
       206: q^2+1
       207: 1
       208: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: q^2+1
       260: 1
       264: 1
       265: 1
       266: q^2+1
       267: 1
       268: q^2+1
       270: q^2+1
       271: 1
       272: 1
       273: q^2+1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       328: 1
       329: q^2+1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: q^2+1
       406: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: 1
       580: 1
       581: 1
       582: 1
       583: q^2+1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       657: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       703: 1
       712: 1
       713: 1
       721: 1
       731: 1
       732: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       764: 1
       765: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       816: 1
       817: 1
       818: 1
       824: 1
       825: 1
       827: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       914: 1
       933: 1
       934: 1
       942: 1
       953: 1
       968: 1
       977: 1
       978: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1014: 1
      1023: 1
      1024: 1
      1032: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1094: 1
      1103: 1
      1104: 1
      1112: 1
      1137: 1
      1180: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1225: 1
      1244: 1
      1245: 1
      1253: 1
      1264: 1
      1301: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1428: 1
      1555: 1

1556:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 2q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+3q^2+3q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q+1
        23: q^2+2q+1
        24: q+1
        25: q^3+3q^2+3q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+3q^2+3q+1
        29: q^3+3q^2+3q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        50: q^2+2q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q+1
        60: q^2+2q+1
        61: q+1
        62: q^3+3q^2+3q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+3q+1
        66: q^2+2q+1
        67: 2q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+3q+1
        71: 2q+1
        72: q^2+2q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: q^2+3q+1
        77: q+1
        78: 2q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q+1
        87: q^2+2q+1
        88: q+1
        89: q^3+3q^2+3q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^3+3q^2+3q+1
        93: q^3+3q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q^2+2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q+1
       122: q^2+2q+1
       123: q+1
       124: 2q+1
       125: q^2+2q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q^2+3q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+3q+1
       133: q^2+3q+1
       134: 2q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: q+1
       141: 2q+1
       142: q+1
       143: 1
       144: 2q+1
       145: q+1
       146: q^2+3q+1
       147: q+1
       148: q+1
       149: q^2+3q+1
       150: q+1
       151: 2q+1
       152: q^2+3q+1
       153: q^2+3q+1
       154: q^2+3q+1
       155: q^2+2q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q+1
       165: q^2+2q+1
       166: q+1
       167: q^3+3q^2+3q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q^2+3q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+3q+1
       176: 2q+1
       177: q^2+2q+1
       178: q+1
       179: 2q+1
       180: q+1
       181: q^2+3q+1
       182: q+1
       183: 2q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q^2+2q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: q+1
       213: 2q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q^2+2q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: q^2+3q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: 2q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       248: 2q+1
       249: q+1
       250: 1
       251: 2q+1
       252: q+1
       253: q^2+3q+1
       254: q+1
       255: q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q+1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q^2+2q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: q+1
       273: q^2+2q+1
       274: q^2+2q+1
       275: q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       279: q^2+2q+1
       280: q+1
       281: 2q+1
       282: q+1
       283: 2q^2+3q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+3q+1
       287: q^2+3q+1
       288: 2q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: q+1
       295: 2q+1
       296: q+1
       297: 1
       298: 2q+1
       299: q+1
       300: q^2+3q+1
       301: q+1
       302: q+1
       303: q^2+3q+1
       304: q+1
       305: 2q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       325: 1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: 2q+1
       345: q+1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 2q+1
       355: q+1
       356: 1
       357: 1
       358: q+1
       359: 1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: 2q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: q+1
       388: q+1
       389: 1
       390: q+1
       392: q^2+3q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q^2+2q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: q+1
       419: 2q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: q+1
       426: 2q+1
       427: q^2+2q+1
       428: q+1
       429: 2q+1
       430: q+1
       431: q^2+3q+1
       432: q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: 2q+1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       454: 2q+1
       455: q+1
       456: 1
       457: 2q+1
       458: q+1
       459: q^2+3q+1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       498: 1
       499: 1
       500: 1
       501: q+1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: 2q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q+1
       553: 1
       554: 1
       555: 1
       558: q+1
       559: q+1
       560: 1
       561: q+1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       579: 1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: 2q+1
       599: q+1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: q+1
       605: 2q+1
       606: q+1
       607: 1
       608: 2q+1
       609: q+1
       610: 1
       611: 1
       612: q+1
       613: 1
       616: 1
       617: 1
       618: 1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: 2q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       646: q^2+3q+1
       647: q+1
       648: q+1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       676: 1
       677: 1
       678: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       692: 1
       693: 1
       694: 1
       695: q+1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       724: 1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: q+1
       750: 1
       751: 1
       752: 1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       789: 1
       790: 1
       791: 1
       792: q+1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: 2q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       807: 1
       808: 1
       809: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: 1
       845: 1
       846: 1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       870: 1
       879: 1
       887: 1
       888: 1
       889: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       915: 1
       933: 1
       934: 1
       935: 1
       941: 1
       945: 1
       953: 1
       955: 1
       956: 1
       969: 1
       977: 1
       978: 1
       979: 1
       985: 1
       987: 1
       988: 1
       989: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1015: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1035: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: q+1
      1061: 1
      1062: 1
      1063: 1
      1095: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1138: 1
      1158: 1
      1181: 1
      1190: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1215: 1
      1216: 1
      1226: 1
      1244: 1
      1245: 1
      1246: 1
      1252: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1302: 1
      1386: 1
      1394: 1
      1395: 1
      1396: 1
      1402: 1
      1429: 1
      1449: 1
      1556: 1

1557:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 2q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: q^3+3q^2+3q+1
        10: q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^2+3q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q+1
        24: q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: q^3+3q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: q+1
        51: q+1
        52: q^2+3q+1
        53: q+1
        54: q+1
        55: q+1
        56: 1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q+1
        61: q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: q+1
        88: q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^3+3q^2+3q+1
        93: q^2+3q+1
        94: 2q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+3q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: q^2+2q+1
       103: 2q^2+3q+1
       104: 1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: q^2+3q+1
       115: q+1
       116: q+1
       117: q+1
       118: 1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: q+1
       123: q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q+1
       128: q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q+1
       135: q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q+1
       166: q+1
       167: q^2+3q+1
       168: q^2+3q+1
       169: q^2+3q+1
       170: q^2+3q+1
       171: q^2+3q+1
       172: q^2+3q+1
       173: 2q^2+3q+1
       174: q^2+3q+1
       175: 2q^2+3q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: q^2+2q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: q+1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: q+1
       208: q^2+3q+1
       209: q+1
       210: q+1
       211: q+1
       212: 1
       213: q+1
       214: q+1
       215: q^2+3q+1
       216: q+1
       217: q+1
       218: q+1
       219: 1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: 2q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: q+1
       268: q^2+3q+1
       269: q+1
       270: q+1
       271: q+1
       272: 1
       273: q^2+3q+1
       274: q^2+3q+1
       275: q^2+3q+1
       276: q+1
       277: q+1
       278: q^2+3q+1
       279: q^2+3q+1
       280: q^2+3q+1
       281: q+1
       282: q+1
       283: q^2+3q+1
       284: q^2+3q+1
       285: q^2+3q+1
       286: 2q^2+3q+1
       287: 2q+1
       288: q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q+1
       350: 1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       377: 1
       380: 1
       381: q+1
       382: 2q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: q+1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: q+1
       414: q^2+3q+1
       415: q+1
       416: q+1
       417: q+1
       418: 1
       419: q+1
       420: q+1
       421: q^2+3q+1
       422: q+1
       423: q+1
       424: q+1
       425: 1
       426: q^2+3q+1
       427: q^2+3q+1
       428: q^2+3q+1
       429: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       433: 2q+1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: 2q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: q+1
       511: 2q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: q+1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: q+1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: q+1
       600: q^2+3q+1
       601: q+1
       602: q+1
       603: q+1
       604: 1
       605: 2q+1
       606: 2q+1
       607: 2q+1
       608: 1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: q+1
       631: 1
       634: 1
       635: q+1
       636: 2q+1
       637: q+1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       646: q+1
       647: q+1
       648: q+1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       748: 1
       750: q+1
       752: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: q+1
       794: q+1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: q+1
       802: 2q+1
       803: q+1
       804: 1
       805: q+1
       806: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: q+1
       846: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       871: 1
       880: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       916: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       953: 1
       970: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: 1
      1059: 1
      1061: q+1
      1063: 1
      1096: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1139: 1
      1182: 1
      1191: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1227: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1264: 1
      1303: 1
      1387: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1430: 1
      1557: 1

1558:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: 2q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: 1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q+1
        92: 2q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+2q+1
        95: q^2+2q+1
        96: 2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q+1
       165: q+1
       166: q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: 2q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: 1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       195: 1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       266: q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q^2+2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q^2+2q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       311: 1
       312: 1
       313: 1
       320: q+1
       321: 1
       322: 1
       323: 1
       325: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       412: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: 1
       475: 1
       476: 1
       477: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       489: 1
       493: q+1
       494: 1
       495: 1
       496: 1
       498: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       574: q+1
       575: 1
       576: 1
       577: 1
       579: 1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       660: 1
       668: 1
       669: 1
       670: 1
       678: 1
       679: 1
       680: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       732: 1
       733: 1
       734: 1
       735: 1
       737: 1
       740: 1
       741: 1
       742: 1
       746: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: q+1
       776: 1
       777: 1
       778: 1
       780: 1
       784: q+1
       785: 1
       786: 1
       787: 1
       789: 1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: 1
       810: 1
       811: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       832: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       872: 1
       881: 1
       889: 1
       890: 1
       891: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       917: 1
       935: 1
       936: 1
       937: 1
       944: 1
       952: 1
       953: 1
       954: 1
       958: 1
       971: 1
       979: 1
       980: 1
       981: 1
       989: 1
       990: 1
       991: 1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1017: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1048: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1097: 1
      1105: 1
      1106: 1
      1107: 1
      1140: 1
      1157: 1
      1183: 1
      1192: 1
      1200: 1
      1201: 1
      1202: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1214: 1
      1228: 1
      1246: 1
      1247: 1
      1248: 1
      1255: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1304: 1
      1388: 1
      1396: 1
      1397: 1
      1398: 1
      1431: 1
      1448: 1
      1558: 1

1559:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       468: 1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       521: 1
       522: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       661: 1
       668: 1
       671: 1
       672: 1
       678: 1
       681: 1
       682: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       707: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       759: 1
       766: 1
       769: 1
       770: 1
       775: 1
       776: 1
       777: 1
       779: 1
       780: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: 1
       812: 1
       813: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: 1
       873: 1
       882: 1
       889: 1
       892: 1
       893: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       918: 1
       935: 1
       938: 1
       939: 1
       972: 1
       979: 1
       982: 1
       983: 1
       989: 1
       992: 1
       993: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1018: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1098: 1
      1105: 1
      1108: 1
      1109: 1
      1141: 1
      1184: 1
      1193: 1
      1200: 1
      1203: 1
      1204: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1229: 1
      1246: 1
      1249: 1
      1250: 1
      1305: 1
      1389: 1
      1396: 1
      1399: 1
      1400: 1
      1432: 1
      1559: 1

1560:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       405: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       421: q+1
       422: 1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       600: q+1
       601: 1
       602: q+1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       662: 1
       669: 1
       671: 1
       673: 1
       679: 1
       681: 1
       683: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 1
       715: 1
       717: 1
       719: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       748: 1
       750: 1
       752: 1
       760: 1
       767: 1
       769: 1
       771: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       874: 1
       883: 1
       890: 1
       892: 1
       894: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       919: 1
       936: 1
       938: 1
       940: 1
       953: 1
       973: 1
       980: 1
       982: 1
       984: 1
       990: 1
       992: 1
       994: 1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1026: 1
      1028: 1
      1030: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1099: 1
      1106: 1
      1108: 1
      1110: 1
      1142: 1
      1185: 1
      1194: 1
      1201: 1
      1203: 1
      1205: 1
      1210: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1230: 1
      1247: 1
      1249: 1
      1251: 1
      1264: 1
      1306: 1
      1390: 1
      1397: 1
      1399: 1
      1401: 1
      1433: 1
      1560: 1

1561:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+q+1
        39: q^2+2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: q^2+2q+1
        44: 2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+2q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: 2q+1
        56: q+1
        57: q+1
        58: q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: q^2+q+1
        80: 1
        81: q^2+2q+1
        82: q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+q+1
       103: q^2+2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: 2q+1
       118: q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: q+1
       123: 2q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q^2+q+1
       153: 1
       154: q^2+q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: 2q+1
       161: q+1
       162: q+1
       163: q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q^2+q+1
       185: 1
       186: q^2+2q+1
       187: q+1
       188: q^2+q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: 2q+1
       212: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: 1
       226: q+1
       227: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q^2+q+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: 2q+1
       272: q+1
       273: q+1
       274: q+1
       275: 2q+1
       276: q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: 2q+1
       281: q+1
       282: 2q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q^2+q+1
       307: 1
       308: q^2+q+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: 2q+1
       418: q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: 1
       432: q+1
       433: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: q+1
       457: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q^2+q+1
       463: 1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: 2q+1
       604: q+1
       605: 1
       606: 1
       607: q+1
       608: 1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       663: 1
       670: 1
       672: 1
       673: 1
       680: 1
       682: 1
       683: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 1
       716: 1
       718: 1
       719: 1
       729: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       742: 1
       746: 1
       747: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       761: 1
       768: 1
       770: 1
       771: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       801: 1
       802: 1
       803: 1
       804: 1
       805: q+1
       806: 1
       811: 1
       813: 1
       814: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       828: 1
       832: 1
       833: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       875: 1
       884: 1
       891: 1
       893: 1
       894: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       920: 1
       937: 1
       939: 1
       940: 1
       950: 1
       954: 1
       958: 1
       959: 1
       974: 1
       981: 1
       983: 1
       984: 1
       991: 1
       993: 1
       994: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1020: 1
      1027: 1
      1029: 1
      1030: 1
      1040: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1053: 1
      1057: 1
      1058: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1100: 1
      1107: 1
      1109: 1
      1110: 1
      1143: 1
      1163: 1
      1186: 1
      1195: 1
      1202: 1
      1204: 1
      1205: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1231: 1
      1248: 1
      1250: 1
      1251: 1
      1261: 1
      1265: 1
      1269: 1
      1270: 1
      1307: 1
      1391: 1
      1398: 1
      1400: 1
      1401: 1
      1434: 1
      1454: 1
      1561: 1

1562:    0: 2q^2+q+1
         1: q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: q^2+q+1
         5: 2q^2+q+1
         6: q^2+q+1
         7: q+1
         8: 2q^2+q+1
         9: q^2+q+1
        10: 2q^2+q+1
        11: 2q^2+q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: 2q^2+q+1
        18: 2q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q^2+1
        25: q^2+q+1
        26: q+1
        27: 2q^2+q+1
        28: q^2+q+1
        29: 2q^2+q+1
        30: q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q+1
        42: 2q^2+q+1
        43: q^2+q+1
        44: 2q^2+q+1
        45: 2q^2+q+1
        46: q^2+q+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+1
        62: q^2+q+1
        63: q+1
        64: 2q^2+q+1
        65: q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q^2+1
        76: q+1
        77: 1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q+1
        82: q^2+q+1
        83: q+1
        84: q^2+q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: q^2+1
        89: q^2+q+1
        90: q+1
        91: 2q^2+q+1
        92: q^2+q+1
        93: 2q^2+q+1
        94: q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: q^2+q+1
       102: q+1
       103: q^2+q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q^2+q+1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: q^2+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+1
       129: q+1
       130: q+1
       131: q^2+q+1
       132: q+1
       133: q^2+q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: q^2+1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: q^2+1
       167: q^2+q+1
       168: q+1
       169: 2q^2+q+1
       170: q+1
       171: q+1
       172: q^2+q+1
       173: q+1
       174: q^2+q+1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q^2+1
       181: q+1
       182: 1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: q+1
       187: q^2+q+1
       188: q+1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q^2+1
       225: q+1
       226: 1
       227: q^2+q+1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: q+1
       249: 1
       250: 1
       251: q+1
       252: q^2+1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q^2+q+1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: q^2+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q^2+1
       283: q+1
       284: q+1
       285: q^2+q+1
       286: q+1
       287: q^2+q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: q^2+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q^2+q+1
       306: q+1
       307: q+1
       308: q+1
       316: 1
       317: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q^2+1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: 1
       389: 1
       390: q+1
       392: q+1
       393: 1
       394: q+1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q^2+1
       431: q+1
       432: 1
       433: q^2+q+1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: q+1
       455: 1
       456: 1
       457: q+1
       458: q^2+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       471: 1
       480: 1
       481: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       523: 1
       524: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       558: q+1
       559: 1
       560: 1
       561: q+1
       570: 1
       571: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: 1
       607: 1
       608: q+1
       609: q^2+1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: q+1
       642: 1
       643: 1
       644: q+1
       646: q+1
       647: 1
       648: q+1
       664: 1
       673: 1
       674: 1
       683: 1
       684: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       719: 1
       720: 1
       726: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       750: 1
       751: 1
       752: 1
       762: 1
       771: 1
       772: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       787: q+1
       788: 1
       789: 1
       790: 1
       791: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       814: 1
       815: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       845: 1
       846: 1
       849: q+1
       850: 1
       851: 1
       852: q+1
       876: 1
       885: 1
       894: 1
       895: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       921: 1
       940: 1
       941: 1
       947: 1
       955: 1
       956: 1
       975: 1
       984: 1
       985: 1
       994: 1
       995: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1021: 1
      1030: 1
      1031: 1
      1037: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1054: 1
      1055: 1
      1061: 1
      1062: 1
      1063: 1
      1101: 1
      1110: 1
      1111: 1
      1144: 1
      1160: 1
      1187: 1
      1196: 1
      1205: 1
      1206: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1232: 1
      1251: 1
      1252: 1
      1258: 1
      1266: 1
      1267: 1
      1308: 1
      1392: 1
      1401: 1
      1402: 1
      1435: 1
      1451: 1
      1562: 1

1563:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: 1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: 1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        53: q^2+1
        54: q^2+1
        55: 1
        56: 1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: q^2+1
       109: 1
       110: 1
       111: 1
       115: q^2+1
       116: q^2+1
       117: 1
       118: 1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: q^2+1
       159: q^2+1
       160: 1
       161: 1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: q^2+1
       203: 1
       204: 1
       205: 1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       245: 1
       246: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       269: q^2+1
       270: q^2+1
       271: 1
       272: 1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       438: 1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       451: 1
       452: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: 1
       524: 1
       525: 1
       532: 1
       533: 1
       534: 1
       539: 1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       559: 1
       560: 1
       561: 1
       571: 1
       572: 1
       579: 1
       580: 1
       581: 1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       603: 1
       604: 1
       606: 1
       607: 1
       608: 1
       609: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       665: 1
       674: 1
       675: 1
       684: 1
       685: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       702: 1
       711: 1
       720: 1
       721: 1
       737: 1
       738: 1
       739: 1
       744: 1
       751: 1
       752: 1
       763: 1
       772: 1
       773: 1
       780: 1
       781: 1
       782: 1
       789: 1
       790: 1
       791: 1
       796: 1
       797: 1
       798: 1
       799: 1
       803: 1
       804: 1
       805: 1
       806: 1
       815: 1
       816: 1
       823: 1
       824: 1
       825: 1
       830: 1
       838: 1
       839: 1
       840: 1
       841: 1
       845: 1
       846: 1
       850: 1
       851: 1
       852: 1
       877: 1
       886: 1
       895: 1
       896: 1
       903: 1
       904: 1
       905: 1
       922: 1
       941: 1
       942: 1
       956: 1
       976: 1
       985: 1
       986: 1
       995: 1
       996: 1
      1003: 1
      1004: 1
      1005: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1022: 1
      1031: 1
      1032: 1
      1048: 1
      1049: 1
      1050: 1
      1055: 1
      1062: 1
      1063: 1
      1102: 1
      1111: 1
      1112: 1
      1145: 1
      1188: 1
      1197: 1
      1206: 1
      1207: 1
      1214: 1
      1215: 1
      1216: 1
      1233: 1
      1252: 1
      1253: 1
      1267: 1
      1309: 1
      1393: 1
      1402: 1
      1403: 1
      1436: 1
      1563: 1

1564:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: 1
        30: q^2+2q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: 1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q^2+2q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: q+1
       108: 1
       109: q+1
       110: q+1
       111: q+1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q^2+2q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: q+1
       262: 1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       338: q+1
       345: 1
       346: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       385: q+1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: q+1
       480: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       503: 1
       510: 1
       511: 1
       514: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       545: q+1
       552: 1
       553: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: q+1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: 1
       663: 1
       666: 1
       667: 1
       675: 1
       697: 1
       703: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       742: 1
       749: 1
       750: 1
       753: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: q+1
       771: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: q+1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       854: 1
       855: 1
       860: 1
       863: 1
       869: 1
       906: 1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       920: 1
       923: 1
       924: 1
       932: 1
       954: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1066: 1
      1113: 1
      1114: 1
      1119: 1
      1122: 1
      1128: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1265: 1
      1310: 1
      1357: 1
      1404: 1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1564: 1

1565:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q+1
        31: 1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: q+1
       108: q+1
       109: 1
       110: q+1
       111: q+1
       112: q+1
       113: 1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: q+1
       210: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: q+1
       232: q+1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: q+1
       262: q+1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       329: q+1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: q+1
       357: q+1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       377: q+1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       416: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: q+1
       478: 1
       479: 1
       480: 1
       482: 1
       492: 1
       493: 1
       499: 1
       500: 1
       502: 1
       509: 1
       511: 1
       513: 1
       516: 1
       517: q+1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: q+1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       583: q+1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       610: q+1
       611: q+1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       631: q+1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       659: 1
       661: 1
       662: 1
       676: 1
       677: 1
       685: 1
       696: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       769: 1
       770: 1
       771: 1
       773: 1
       783: 1
       784: 1
       790: 1
       791: 1
       793: 1
       800: 1
       802: 1
       804: 1
       807: 1
       808: q+1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       854: 1
       856: 1
       859: 1
       864: 1
       878: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       942: 1
       953: 1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       970: 1
       972: 1
       973: 1
       987: 1
       988: 1
       996: 1
      1007: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1067: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1165: 1
      1167: 1
      1170: 1
      1175: 1
      1189: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1227: 1
      1229: 1
      1230: 1
      1244: 1
      1245: 1
      1253: 1
      1264: 1
      1311: 1
      1358: 1
      1404: 1
      1406: 1
      1409: 1
      1414: 1
      1428: 1
      1565: 1

1566:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        64: q+1
        65: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       118: 2q+1
       119: q+1
       122: q+1
       123: q+1
       124: q+1
       127: q+1
       128: q+1
       129: 2q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       148: q+1
       149: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       169: q+1
       170: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       205: 1
       206: q+1
       207: q+1
       212: q+1
       213: q+1
       214: q+1
       219: q+1
       220: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       242: 2q+1
       243: q+1
       246: q+1
       247: q+1
       248: q+1
       251: q+1
       252: q+1
       253: 2q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       272: 2q+1
       273: q+1
       276: q+1
       277: q+1
       278: q+1
       281: q+1
       282: q+1
       283: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       327: 1
       328: q+1
       335: 1
       336: q+1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       372: 1
       373: q+1
       374: q+1
       379: q+1
       380: q+1
       381: q+1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       411: 1
       412: q+1
       413: q+1
       418: q+1
       419: q+1
       420: q+1
       425: q+1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       448: 2q+1
       449: q+1
       452: q+1
       453: q+1
       454: q+1
       457: q+1
       458: q+1
       459: 2q+1
       461: 1
       462: q+1
       463: q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       534: 1
       535: q+1
       542: 1
       543: q+1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       581: 1
       582: q+1
       589: 1
       590: q+1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       626: 1
       627: q+1
       628: q+1
       633: q+1
       634: q+1
       635: q+1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       825: 1
       826: q+1
       833: 1
       834: q+1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       887: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1068: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1312: 1
      1359: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1566: 1

1567:    0: q^2+q+1
         1: q^2+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: 1
         7: q^2+1
         8: q^2+q+1
         9: q^2+1
        10: q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: 1
        21: 1
        22: q^2+1
        23: q^2+q+1
        24: q^2+q+1
        25: 1
        27: q+1
        28: q^2+1
        29: q+1
        30: q^2+1
        31: q+1
        32: q^2+q+1
        33: 1
        34: q^2+1
        35: q^2+q+1
        36: q^2+1
        37: q+1
        38: q^2+q+1
        39: q^2+q+1
        40: 1
        41: q^2+1
        42: q^2+q+1
        43: q^2+1
        44: q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+1
        48: q^2+q+1
        49: q^2+q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: q^2+1
        55: q^2+1
        56: q^2+q+1
        57: 1
        60: q+1
        61: q+1
        62: 1
        64: q+1
        65: 1
        67: q+1
        68: q^2+1
        69: q+1
        70: q^2+q+1
        71: 1
        72: 1
        73: q^2+1
        74: q^2+q+1
        75: q^2+q+1
        76: 1
        78: q+1
        79: q^2+1
        80: q+1
        81: q^2+1
        82: q+1
        83: q^2+q+1
        84: 1
        85: 1
        86: q^2+1
        87: q^2+q+1
        88: q^2+q+1
        89: 1
        91: q+1
        92: q^2+1
        93: q+1
        94: q^2+1
        95: q+1
        96: q^2+q+1
        97: 1
        98: q^2+1
        99: q^2+q+1
       100: q^2+1
       101: q+1
       102: q^2+q+1
       103: q^2+q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: q^2+1
       111: q^2+q+1
       112: 1
       113: 1
       118: q+1
       119: 1
       122: q+1
       123: q+1
       124: 1
       127: q+1
       128: q+1
       129: 1
       131: q+1
       132: q^2+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: q^2+1
       139: q^2+1
       140: q^2+q+1
       141: 1
       144: q+1
       145: q+1
       146: 1
       148: q+1
       149: 1
       151: q+1
       152: q^2+1
       153: q+1
       154: q^2+q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: q^2+1
       160: q^2+1
       161: q^2+q+1
       162: 1
       165: q+1
       166: q+1
       167: 1
       169: q+1
       170: 1
       172: q+1
       173: q^2+1
       174: q+1
       175: q^2+q+1
       176: 1
       177: 1
       178: q^2+1
       179: q^2+q+1
       180: q^2+q+1
       181: 1
       183: q+1
       184: q^2+1
       185: q+1
       186: q^2+1
       187: q+1
       188: q^2+q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q^2+1
       197: 1
       198: 1
       205: q+1
       206: 1
       207: 1
       212: q+1
       213: 1
       214: 1
       219: q+1
       220: 1
       223: q+1
       224: q+1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q^2+1
       235: q^2+q+1
       236: 1
       237: 1
       242: q+1
       243: 1
       246: q+1
       247: q+1
       248: 1
       251: q+1
       252: q+1
       253: 1
       255: q+1
       256: q^2+1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: q^2+1
       265: q^2+q+1
       266: 1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: q+1
       282: q+1
       283: 1
       285: q+1
       286: q^2+1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: q^2+1
       293: q^2+1
       294: q^2+q+1
       295: 1
       298: q+1
       299: q+1
       300: 1
       302: q+1
       303: 1
       305: q+1
       306: q^2+1
       307: q+1
       308: q^2+q+1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: q+1
       336: 1
       343: q+1
       344: 1
       345: 1
       350: q+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q^2+1
       364: 1
       365: 1
       372: q+1
       373: 1
       374: 1
       379: q+1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: q+1
       391: q+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q^2+1
       403: 1
       404: 1
       411: q+1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: q+1
       426: 1
       429: q+1
       430: q+1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q^2+1
       441: q^2+q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: q+1
       453: q+1
       454: 1
       457: q+1
       458: q+1
       459: 1
       461: q+1
       462: q^2+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: q+1
       543: 1
       550: q+1
       551: 1
       552: 1
       557: q+1
       558: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: q+1
       590: 1
       597: q+1
       598: 1
       599: 1
       604: q+1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+1
       618: 1
       619: 1
       626: q+1
       627: 1
       628: 1
       633: q+1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: q+1
       645: q+1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       686: 1
       694: 1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: q+1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: q+1
       800: 1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: q+1
       834: 1
       841: q+1
       842: 1
       843: 1
       848: q+1
       849: 1
       852: 1
       853: 1
       857: 1
       858: 1
       897: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       943: 1
       951: 1
       952: 1
       959: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: q+1
      1059: 1
      1060: 1
      1065: 1
      1069: 1
      1116: 1
      1117: 1
      1156: 1
      1164: 1
      1168: 1
      1169: 1
      1208: 1
      1216: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1313: 1
      1360: 1
      1407: 1
      1408: 1
      1447: 1
      1455: 1
      1567: 1

1568:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+2q+1
         7: 2q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: 2q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+3q+1
        29: 2q+1
        30: q^2+3q+1
        31: 2q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: 2q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: 2q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: q^2+2q+1
        41: 2q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: 2q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: 1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: 2q+1
        67: q+1
        68: q^2+3q+1
        69: 2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: q^2+3q+1
        80: 2q+1
        81: q^2+3q+1
        82: 2q+1
        83: q^2+3q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+3q+1
        93: 2q+1
        94: q^2+3q+1
        95: 2q+1
        96: q^2+3q+1
        97: q^2+2q+1
        98: 2q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: 2q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: q^2+3q+1
       111: q^2+2q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q^2+3q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: 1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: 2q+1
       151: q+1
       152: q^2+3q+1
       153: 2q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: 1
       163: q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: 2q+1
       172: q+1
       173: q^2+3q+1
       174: 2q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: q^2+3q+1
       181: q+1
       182: 2q+1
       183: 2q+1
       184: q^2+3q+1
       185: 2q+1
       186: q^2+3q+1
       187: 2q+1
       188: q^2+3q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q^2+2q+1
       197: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: q^2+3q+1
       235: q^2+2q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: 2q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: q^2+3q+1
       265: q^2+2q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: 2q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q^2+3q+1
       293: q^2+3q+1
       294: q^2+3q+1
       295: 1
       296: q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q+1
       301: 2q+1
       302: q+1
       303: q+1
       304: 2q+1
       305: q+1
       306: q^2+3q+1
       307: 2q+1
       308: q^2+2q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q^2+2q+1
       364: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: 2q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q^2+2q+1
       403: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: 2q+1
       411: 1
       412: 1
       413: 1
       414: 1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: q^2+3q+1
       441: q^2+2q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: 2q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       482: 1
       484: 1
       490: 1
       491: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q^2+2q+1
       618: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: 2q+1
       626: 1
       627: 1
       628: 1
       629: 1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       675: 1
       685: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       723: 1
       729: 1
       730: 1
       732: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       775: 1
       781: 1
       782: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: 1
       896: 1
       898: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       932: 1
       942: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       986: 1
       996: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1034: 1
      1040: 1
      1041: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1155: 1
      1157: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1207: 1
      1209: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1243: 1
      1253: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1314: 1
      1361: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1446: 1
      1448: 1
      1568: 1

1569:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: 1
        12: 1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: 1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: 1
        39: 1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: 1
        46: 1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: 1
        51: 1
        52: q^2+q+1
        53: q^2+q+1
        54: 1
        55: 1
        56: 1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: 1
        75: 1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: 1
        88: 1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: q^2+q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q^2+q+1
       115: q^2+q+1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: q^2+q+1
       137: q^2+q+1
       138: 1
       139: 1
       140: 1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: q^2+q+1
       158: q^2+q+1
       159: 1
       160: 1
       161: 1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: 1
       180: 1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q^2+q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: q^2+q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q^2+q+1
       239: q^2+q+1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: q^2+q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q^2+q+1
       269: q^2+q+1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: q^2+q+1
       291: q^2+q+1
       292: 1
       293: 1
       294: 1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       338: 1
       339: 1
       341: 1
       346: 1
       347: 1
       351: 1
       352: 1
       353: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q^2+q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       381: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q^2+q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: q^2+q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q^2+q+1
       445: q^2+q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       495: 1
       497: 1
       504: 1
       511: 1
       512: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       545: 1
       546: 1
       548: 1
       553: 1
       554: 1
       558: 1
       559: 1
       560: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       592: 1
       593: 1
       595: 1
       600: 1
       601: 1
       605: 1
       606: 1
       607: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q^2+q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       669: 1
       682: 1
       698: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       734: 1
       736: 1
       743: 1
       750: 1
       751: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       773: 1
       776: 1
       778: 1
       786: 1
       788: 1
       795: 1
       802: 1
       803: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       850: 1
       851: 1
       854: 1
       861: 1
       862: 1
       868: 1
       906: 1
       907: 1
       913: 1
       914: 1
       915: 1
       916: 1
       921: 1
       922: 1
       926: 1
       939: 1
       955: 1
       960: 1
       961: 1
       967: 1
       968: 1
       969: 1
       970: 1
       975: 1
       976: 1
       980: 1
       993: 1
      1009: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1045: 1
      1047: 1
      1054: 1
      1061: 1
      1062: 1
      1071: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1237: 1
      1250: 1
      1266: 1
      1315: 1
      1362: 1
      1404: 1
      1411: 1
      1412: 1
      1418: 1
      1569: 1

1570:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: 2q+1
        12: q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^2+3q+1
        19: q^3+3q^2+3q+1
        20: q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: 2q+1
        24: q^2+3q+1
        25: q^2+3q+1
        26: q+1
        27: q^2+3q+1
        28: 2q+1
        29: 2q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: 2q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: 2q+1
        39: q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: 2q+1
        46: q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: q^2+3q+1
        50: 2q+1
        51: q^2+3q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: 2q+1
        55: q^2+3q+1
        56: 2q+1
        57: q^2+3q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q^2+3q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: q^2+3q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: 2q+1
        75: q^2+3q+1
        76: q^2+3q+1
        77: q+1
        78: q^2+3q+1
        79: 2q+1
        80: 2q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: 2q+1
        84: q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q+1
        91: q^2+3q+1
        92: 2q+1
        93: 2q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: 2q+1
       103: q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: q^2+3q+1
       107: q^2+3q+1
       108: 2q+1
       109: q^2+3q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: q^2+3q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: q^2+3q+1
       140: 2q+1
       141: q^2+3q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: q^2+3q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: 2q+1
       160: q^2+3q+1
       161: 2q+1
       162: q^2+3q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: q^2+3q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: q^2+3q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: 2q+1
       180: q^2+3q+1
       181: q^2+3q+1
       182: q+1
       183: q^2+3q+1
       184: 2q+1
       185: 2q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: 2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: q^2+3q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: q^2+3q+1
       231: q^2+3q+1
       232: 2q+1
       233: q^2+3q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: q^2+3q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q^2+3q+1
       262: 2q+1
       263: q^2+3q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: q^2+3q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: 1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: 2q+1
       293: q^2+3q+1
       294: 2q+1
       295: q^2+3q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: q^2+3q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: q^2+3q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: q^2+3q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: q+1
       394: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: q^2+3q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: 2q+1
       439: q^2+3q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: q^2+3q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: 1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       465: q+1
       466: 1
       467: q+1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: q^2+3q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       648: 1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       682: 1
       689: 1
       704: q+1
       705: 1
       706: q+1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       756: q+1
       757: 1
       758: q+1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       853: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       872: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       939: 1
       946: 1
       961: 1
       962: 1
       966: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       993: 1
      1000: 1
      1015: q+1
      1016: 1
      1017: q+1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1072: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1131: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1183: 1
      1218: 1
      1219: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1250: 1
      1257: 1
      1316: 1
      1363: 1
      1405: 1
      1412: 1
      1413: 1
      1417: 1
      1420: 1
      1422: 1
      1570: 1

1571:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: 2q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^2+3q+1
        19: q^3+3q^2+3q+1
        20: q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: 2q+1
        25: q^2+3q+1
        26: q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: 2q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: 2q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: 2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: 2q+1
        56: 2q+1
        57: q^2+3q+1
        58: q+1
        59: q+1
        60: q^2+3q+1
        61: 2q+1
        62: q^2+3q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: 2q+1
        76: q^2+3q+1
        77: q+1
        78: q^2+3q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: 2q+1
        89: q^2+3q+1
        90: q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+3q+1
       103: 2q+1
       104: 2q+1
       105: q^2+3q+1
       106: 2q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+3q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: 2q+1
       140: 2q+1
       141: q^2+3q+1
       142: q+1
       143: q+1
       144: q^2+3q+1
       145: 2q+1
       146: q^2+3q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q^2+3q+1
       156: 2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q^2+3q+1
       163: q+1
       164: q+1
       165: q^2+3q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: 2q+1
       181: q^2+3q+1
       182: q+1
       183: q^2+3q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: q+1
       190: 2q+1
       191: q^2+3q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       227: 1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q^2+3q+1
       232: q^2+3q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q^2+3q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       259: q^2+3q+1
       260: 2q+1
       261: q^2+3q+1
       262: q^2+3q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q^2+3q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q^2+3q+1
       289: 2q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: q^2+3q+1
       293: 2q+1
       294: 2q+1
       295: q^2+3q+1
       296: q+1
       297: q+1
       298: q^2+3q+1
       299: 2q+1
       300: q^2+3q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: q+1
       357: 2q+1
       358: q^2+3q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       394: 1
       395: q+1
       396: 2q+1
       397: q^2+3q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: q+1
       433: 1
       434: 2q+1
       435: q^2+3q+1
       436: 2q+1
       437: q^2+3q+1
       438: q^2+3q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q^2+3q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       465: q+1
       466: 1
       468: q+1
       469: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       610: q+1
       611: 2q+1
       612: q^2+3q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       648: 1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       688: 1
       704: q+1
       705: 1
       707: q+1
       708: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       756: q+1
       757: 1
       759: q+1
       760: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: 1
       769: 1
       770: 1
       771: 1
       772: 1
       776: 1
       778: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       852: 1
       856: 1
       862: 1
       864: 1
       866: 1
       879: 1
       882: 1
       907: 1
       909: 1
       911: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       926: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       945: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       980: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       999: 1
      1015: q+1
      1016: 1
      1018: q+1
      1019: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1073: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1138: 1
      1141: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1190: 1
      1193: 1
      1218: 1
      1220: 1
      1222: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1256: 1
      1317: 1
      1364: 1
      1406: 1
      1412: 1
      1414: 1
      1416: 1
      1429: 1
      1432: 1
      1571: 1

1572:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: 1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: 2q+1
        21: 2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 1
        26: 1
        27: 1
        28: 2q+1
        29: 1
        30: 2q+1
        31: 1
        32: 2q+1
        33: 2q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: 1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: 1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 2q+1
        69: 1
        70: 2q+1
        71: 2q+1
        72: 2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 1
        77: 1
        78: 1
        79: 2q+1
        80: 1
        81: 2q+1
        82: 1
        83: 2q+1
        84: 2q+1
        85: 2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 1
        90: 1
        91: 1
        92: 2q+1
        93: 1
        94: 2q+1
        95: 1
        96: 2q+1
        97: 2q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: 1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 1
       108: 1
       109: 1
       110: 2q+1
       111: 2q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 2q+1
       153: 1
       154: 2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 2q+1
       174: 1
       175: 2q+1
       176: 2q+1
       177: 2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 1
       182: 1
       183: 1
       184: 2q+1
       185: 1
       186: 2q+1
       187: 1
       188: 2q+1
       189: 2q+1
       190: 2q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 2q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 1
       232: 1
       233: 1
       234: 2q+1
       235: 2q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 2q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 1
       262: 1
       263: 1
       264: 2q+1
       265: 2q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 2q+1
       307: 1
       308: 2q+1
       310: 2q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: 2q+1
       357: 2q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 2q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       395: 2q+1
       396: 2q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 2q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 1
       438: 1
       439: 1
       440: 2q+1
       441: 2q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 2q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: 2q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       564: 2q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       610: 2q+1
       611: 2q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 2q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       808: 2q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       857: 1
       863: 1
       864: 1
       865: 1
       888: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       934: 1
       943: 1
       944: 1
       950: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1040: 1
      1042: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1074: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1147: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1199: 1
      1219: 1
      1220: 1
      1221: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1245: 1
      1254: 1
      1255: 1
      1261: 1
      1318: 1
      1365: 1
      1407: 1
      1413: 1
      1414: 1
      1415: 1
      1438: 1
      1572: 1

1573:    0: q^4+2q^3+6q^2+5q+1
         1: q^3+5q^2+5q+1
         2: q^4+2q^3+6q^2+5q+1
         3: 2q^2+5q+1
         4: q^4+2q^3+6q^2+5q+1
         5: q^4+2q^3+6q^2+5q+1
         6: q^3+5q^2+5q+1
         7: q^3+5q^2+5q+1
         8: 2q^2+5q+1
         9: q^2+5q+1
        10: 2q^2+5q+1
        11: 2q^2+5q+1
        12: 2q^2+5q+1
        13: q^3+5q^2+5q+1
        14: q^4+2q^3+6q^2+5q+1
        15: 2q^2+5q+1
        16: q^3+5q^2+5q+1
        17: q^4+2q^3+6q^2+5q+1
        18: 2q^2+5q+1
        19: q^4+2q^3+6q^2+5q+1
        20: 3q+1
        21: q^3+5q^2+5q+1
        22: q^2+5q+1
        23: 2q^2+5q+1
        24: 2q^2+5q+1
        25: q^2+5q+1
        26: 3q+1
        27: 2q^2+5q+1
        28: q^2+5q+1
        29: 2q^2+5q+1
        30: q^2+5q+1
        31: 2q^2+5q+1
        32: 2q^2+5q+1
        33: q^3+5q^2+5q+1
        34: q^3+5q^2+5q+1
        35: 2q^2+5q+1
        36: q^2+5q+1
        37: 2q^2+5q+1
        38: 2q^2+5q+1
        39: 2q^2+5q+1
        40: q^3+5q^2+5q+1
        41: q^3+5q^2+5q+1
        42: 2q^2+5q+1
        43: q^2+5q+1
        44: 2q^2+5q+1
        45: 2q^2+5q+1
        46: 2q^2+5q+1
        47: q^3+5q^2+5q+1
        48: q^4+2q^3+6q^2+5q+1
        49: 2q^2+5q+1
        50: 3q+1
        51: 3q+1
        52: 3q+1
        53: q^2+5q+1
        54: q^2+5q+1
        55: q^2+5q+1
        56: 2q^2+5q+1
        57: 3q+1
        58: 3q+1
        59: 3q+1
        60: 2q^2+5q+1
        61: 2q^2+5q+1
        62: q^2+5q+1
        63: 3q+1
        64: q^2+2q+1
        65: q^2+5q+1
        66: 3q+1
        67: q^2+2q+1
        68: q^2+5q+1
        69: 2q^2+5q+1
        70: 2q+1
        71: 3q+1
        72: q^3+5q^2+5q+1
        73: q^2+5q+1
        74: 2q^2+5q+1
        75: 2q^2+5q+1
        76: q^2+5q+1
        77: 3q+1
        78: 2q^2+5q+1
        79: q^2+5q+1
        80: 2q^2+5q+1
        81: q^2+5q+1
        82: 2q^2+5q+1
        83: 2q^2+5q+1
        84: 3q+1
        85: q^3+5q^2+5q+1
        86: q^2+5q+1
        87: 2q^2+5q+1
        88: 2q^2+5q+1
        89: q^2+5q+1
        90: 3q+1
        91: 2q^2+5q+1
        92: q^2+5q+1
        93: 2q^2+5q+1
        94: q^2+5q+1
        95: 2q^2+5q+1
        96: 2q^2+5q+1
        97: q^3+5q^2+5q+1
        98: q^3+5q^2+5q+1
        99: 2q^2+5q+1
       100: q^2+5q+1
       101: 2q^2+5q+1
       102: 2q^2+5q+1
       103: 2q^2+5q+1
       104: 3q+1
       105: 3q+1
       106: 3q+1
       107: 3q+1
       108: q^2+5q+1
       109: q^2+5q+1
       110: q^2+5q+1
       111: 2q+1
       112: 3q+1
       113: 3q+1
       114: q+1
       115: 3q+1
       116: 3q+1
       117: 3q+1
       118: 2q^2+5q+1
       119: q+1
       120: 3q+1
       121: q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q+1
       125: 3q+1
       126: q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+5q+1
       130: 3q+1
       131: 1
       132: 2q+1
       133: 2q+1
       134: 3q+1
       135: 3q+1
       136: 3q+1
       137: q^2+5q+1
       138: q^2+5q+1
       139: q^2+5q+1
       140: 2q^2+5q+1
       141: 3q+1
       142: 3q+1
       143: 3q+1
       144: 2q^2+5q+1
       145: 2q^2+5q+1
       146: q^2+5q+1
       147: 3q+1
       148: q^2+2q+1
       149: q^2+5q+1
       150: 3q+1
       151: q^2+2q+1
       152: q^2+5q+1
       153: 2q^2+5q+1
       154: 2q+1
       155: 3q+1
       156: 3q+1
       157: 3q+1
       158: q^2+5q+1
       159: q^2+5q+1
       160: q^2+5q+1
       161: 2q^2+5q+1
       162: 3q+1
       163: 3q+1
       164: 3q+1
       165: 2q^2+5q+1
       166: 2q^2+5q+1
       167: q^2+5q+1
       168: 3q+1
       169: q^2+2q+1
       170: q^2+5q+1
       171: 3q+1
       172: q^2+2q+1
       173: q^2+5q+1
       174: 2q^2+5q+1
       175: 2q+1
       176: 3q+1
       177: q^3+5q^2+5q+1
       178: q^2+5q+1
       179: 2q^2+5q+1
       180: 2q^2+5q+1
       181: q^2+5q+1
       182: 3q+1
       183: 2q^2+5q+1
       184: q^2+5q+1
       185: 2q^2+5q+1
       186: q^2+5q+1
       187: 2q^2+5q+1
       188: 2q^2+5q+1
       190: 3q+1
       191: 3q+1
       192: 3q+1
       193: q+1
       194: q+1
       195: q^2+5q+1
       196: 2q+1
       197: 2q+1
       198: 3q+1
       199: q+1
       200: q+1
       201: q+1
       202: 3q+1
       203: 3q+1
       204: 3q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q^2+2q+1
       213: q+1
       214: q+1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+2q+1
       220: 1
       221: 3q+1
       222: 1
       223: 1
       224: 1
       225: 2q+1
       227: 1
       228: 3q+1
       229: 3q+1
       230: 3q+1
       231: 3q+1
       232: q^2+5q+1
       233: q^2+5q+1
       234: q^2+5q+1
       235: 2q+1
       236: 3q+1
       237: 3q+1
       238: q+1
       239: 3q+1
       240: 3q+1
       241: 3q+1
       242: 2q^2+5q+1
       243: q+1
       244: 3q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q+1
       249: 3q+1
       250: q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+5q+1
       254: 3q+1
       255: 1
       256: 2q+1
       257: 2q+1
       258: 3q+1
       259: 3q+1
       260: 3q+1
       261: 3q+1
       262: q^2+5q+1
       263: q^2+5q+1
       264: q^2+5q+1
       265: 2q+1
       266: 3q+1
       267: 3q+1
       268: q+1
       269: 3q+1
       270: 3q+1
       271: 3q+1
       272: 2q^2+5q+1
       273: q+1
       274: 3q+1
       275: q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q+1
       279: 3q+1
       280: q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: q^2+5q+1
       284: 3q+1
       285: 1
       286: 2q+1
       287: 2q+1
       288: 3q+1
       289: 3q+1
       290: 3q+1
       291: q^2+5q+1
       292: q^2+5q+1
       293: q^2+5q+1
       294: 2q^2+5q+1
       295: 3q+1
       296: 3q+1
       297: 3q+1
       298: 2q^2+5q+1
       299: 2q^2+5q+1
       300: q^2+5q+1
       301: 3q+1
       302: q^2+2q+1
       303: q^2+5q+1
       304: 3q+1
       305: q^2+2q+1
       306: q^2+5q+1
       307: 2q^2+5q+1
       308: 2q+1
       311: 3q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: 2q+1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: 3q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: 3q+1
       358: 3q+1
       359: 3q+1
       360: q+1
       361: q+1
       362: q^2+5q+1
       363: 2q+1
       364: 2q+1
       365: 3q+1
       366: q+1
       367: q+1
       368: q+1
       369: 3q+1
       370: 3q+1
       371: 3q+1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q^2+2q+1
       380: q+1
       381: q+1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q^2+2q+1
       387: 1
       388: 3q+1
       389: 1
       390: 1
       391: 1
       392: 2q+1
       394: 1
       396: 3q+1
       397: 3q+1
       398: 3q+1
       399: q+1
       400: q+1
       401: q^2+5q+1
       402: 2q+1
       403: 2q+1
       404: 3q+1
       405: q+1
       406: q+1
       407: q+1
       408: 3q+1
       409: 3q+1
       410: 3q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q^2+2q+1
       419: q+1
       420: q+1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q^2+2q+1
       426: 1
       427: 3q+1
       428: 1
       429: 1
       430: 1
       431: 2q+1
       433: 1
       434: 3q+1
       435: 3q+1
       436: 3q+1
       437: 3q+1
       438: q^2+5q+1
       439: q^2+5q+1
       440: q^2+5q+1
       441: 2q+1
       442: 3q+1
       443: 3q+1
       444: q+1
       445: 3q+1
       446: 3q+1
       447: 3q+1
       448: 2q^2+5q+1
       449: q+1
       450: 3q+1
       451: q+1
       452: q^2+2q+1
       453: q^2+2q+1
       454: q+1
       455: 3q+1
       456: q+1
       457: q^2+2q+1
       458: q^2+2q+1
       459: q^2+5q+1
       460: 3q+1
       461: 1
       462: 2q+1
       463: 2q+1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: 3q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: 2q+1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: 3q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 3q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: 2q+1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: 3q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 3q+1
       612: 3q+1
       613: 3q+1
       614: q+1
       615: q+1
       616: q^2+5q+1
       617: 2q+1
       618: 2q+1
       619: 3q+1
       620: q+1
       621: q+1
       622: q+1
       623: 3q+1
       624: 3q+1
       625: 3q+1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q^2+2q+1
       634: q+1
       635: q+1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q^2+2q+1
       641: 1
       642: 3q+1
       643: 1
       644: 1
       645: 1
       646: 2q+1
       648: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       674: 1
       678: 1
       681: 1
       682: 1
       684: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       714: q+1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: q+1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       766: q+1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: 3q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: 2q+1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: 3q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       882: 1
       889: 1
       895: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       931: 1
       935: 1
       938: 1
       939: 1
       941: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       964: 1
       965: 1
       966: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       985: 1
       989: 1
       992: 1
       993: 1
       995: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1075: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1141: 1
      1148: 1
      1154: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1193: 1
      1200: 1
      1206: 1
      1221: 1
      1222: 1
      1223: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1319: 1
      1366: 1
      1408: 1
      1415: 1
      1416: 1
      1417: 1
      1422: 1
      1432: 1
      1439: 1
      1445: 1
      1573: 1

1574:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: q+1
       105: q+1
       107: q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 1
       120: 2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: q+1
       140: q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: q+1
       187: q+1
       188: q+1
       191: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       199: q+1
       201: q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       229: q+1
       231: q+1
       232: 2q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 1
       244: 2q+1
       245: q+1
       246: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: 1
       274: 2q+1
       275: q+1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: q+1
       294: q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       312: 1
       314: 1
       316: 1
       317: q+1
       318: q+1
       321: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       358: q+1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       366: q+1
       368: q+1
       369: 2q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       375: 1
       376: q+1
       377: q+1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       397: q+1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       405: q+1
       407: q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       414: 1
       415: q+1
       416: q+1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: q+1
       432: q+1
       433: 1
       435: q+1
       437: q+1
       438: 2q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: q+1
       448: q+1
       449: 1
       450: 2q+1
       451: q+1
       452: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       469: 1
       471: 1
       472: q+1
       476: 1
       478: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: 1
       521: 1
       523: 1
       524: q+1
       525: q+1
       528: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: q+1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       566: 1
       568: 1
       570: 1
       571: q+1
       572: q+1
       575: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       612: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       620: q+1
       622: q+1
       623: 2q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       629: 1
       630: q+1
       631: q+1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       647: q+1
       648: 1
       654: 1
       656: 1
       662: 1
       664: 1
       665: 1
       669: 1
       681: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       708: 1
       710: 1
       711: q+1
       715: 1
       717: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       733: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       760: 1
       762: 1
       763: q+1
       767: 1
       769: 1
       771: 1
       772: 1
       773: 1
       776: 1
       778: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       810: 1
       812: 1
       814: 1
       815: q+1
       816: q+1
       819: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: q+1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       859: 1
       866: 1
       868: 1
       886: 1
       899: 1
       911: 1
       913: 1
       919: 1
       921: 1
       922: 1
       926: 1
       938: 1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       965: 1
       967: 1
       973: 1
       975: 1
       976: 1
       980: 1
       992: 1
       995: 1
       996: 1
       999: 1
      1007: 1
      1009: 1
      1010: 1
      1019: 1
      1021: 1
      1022: q+1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1044: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1076: 1
      1118: 1
      1125: 1
      1127: 1
      1145: 1
      1158: 1
      1170: 1
      1177: 1
      1179: 1
      1197: 1
      1210: 1
      1222: 1
      1224: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1249: 1
      1252: 1
      1253: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1320: 1
      1367: 1
      1409: 1
      1416: 1
      1418: 1
      1436: 1
      1449: 1
      1574: 1

1575:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: 2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: q+1
        93: q+1
        94: 2q+1
        95: 2q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       106: q+1
       107: q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: 1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: q+1
       160: 2q+1
       161: q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: q+1
       168: q+1
       169: 1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q+1
       185: q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       200: q+1
       201: q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       230: q+1
       231: q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: q+1
       237: q+1
       238: q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 2q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       260: q+1
       261: q+1
       262: q+1
       263: 2q+1
       264: q+1
       265: q+1
       267: q+1
       268: q+1
       269: 2q+1
       270: q+1
       271: 2q+1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 2q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: q+1
       293: 2q+1
       294: q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: q+1
       299: 2q+1
       300: q+1
       301: q+1
       302: 1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       313: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       359: q+1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       367: q+1
       368: q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: q+1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       398: q+1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       406: q+1
       407: q+1
       408: q+1
       409: 2q+1
       410: q+1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: q+1
       424: q+1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       436: q+1
       437: q+1
       438: q+1
       439: 2q+1
       440: q+1
       441: q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: q+1
       447: 2q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 2q+1
       456: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       470: 1
       471: 1
       472: q+1
       477: 1
       479: 1
       480: 1
       481: 1
       482: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       520: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: q+1
       560: 1
       562: 1
       567: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: q+1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       613: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       621: q+1
       622: q+1
       623: q+1
       624: 2q+1
       625: q+1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: q+1
       639: q+1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       655: 1
       656: 1
       663: 1
       664: 1
       665: 1
       670: 1
       674: 1
       675: 1
       682: 1
       689: 1
       697: 1
       698: 1
       700: 1
       709: 1
       710: 1
       711: q+1
       716: 1
       718: 1
       719: 1
       720: 1
       721: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       761: 1
       762: 1
       763: q+1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       811: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: q+1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: q+1
       851: 1
       853: 1
       860: 1
       867: 1
       868: 1
       877: 1
       900: 1
       912: 1
       913: 1
       920: 1
       921: 1
       922: 1
       927: 1
       931: 1
       932: 1
       939: 1
       946: 1
       954: 1
       955: 1
       957: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       981: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1020: 1
      1021: 1
      1022: q+1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1077: 1
      1119: 1
      1126: 1
      1127: 1
      1136: 1
      1159: 1
      1171: 1
      1178: 1
      1179: 1
      1188: 1
      1211: 1
      1223: 1
      1224: 1
      1231: 1
      1232: 1
      1233: 1
      1238: 1
      1242: 1
      1243: 1
      1250: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1321: 1
      1368: 1
      1410: 1
      1417: 1
      1418: 1
      1427: 1
      1450: 1
      1575: 1

1576:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: 1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: 1
        75: q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q^2+2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q^2+2q+1
       164: q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q+1
       184: q+1
       185: q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q^2+2q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q^2+2q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q^2+2q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: q+1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       383: q+1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       422: q+1
       424: q+1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q^2+2q+1
       456: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       495: q+1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: q+1
       560: 1
       562: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: q+1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: q+1
       593: q+1
       595: q+1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       637: q+1
       639: q+1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       689: 1
       697: 1
       698: 1
       700: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       734: q+1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       786: q+1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: q+1
       837: q+1
       839: q+1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: q+1
       851: 1
       853: 1
       861: 1
       869: 1
       870: 1
       877: 1
       900: 1
       906: 1
       914: 1
       915: 1
       922: 1
       923: 1
       924: 1
       925: 1
       931: 1
       932: 1
       946: 1
       954: 1
       955: 1
       957: 1
       960: 1
       968: 1
       969: 1
       976: 1
       977: 1
       978: 1
       979: 1
       985: 1
       986: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1014: 1
      1015: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1040: 1
      1041: 1
      1045: q+1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1078: 1
      1120: 1
      1128: 1
      1129: 1
      1136: 1
      1159: 1
      1172: 1
      1180: 1
      1181: 1
      1188: 1
      1211: 1
      1217: 1
      1225: 1
      1226: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1242: 1
      1243: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1322: 1
      1369: 1
      1411: 1
      1419: 1
      1420: 1
      1427: 1
      1450: 1
      1576: 1

1577:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: q^2+q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+1
        24: q+1
        25: 2q^2+2q+1
        26: q+1
        27: 2q^2+2q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: q^2+q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: q^2+q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+1
        51: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: 1
        55: q+1
        56: 1
        57: 2q^2+2q+1
        58: q+1
        59: q+1
        60: q^2+1
        61: q+1
        62: q^2+q+1
        63: q+1
        64: q^2+q+1
        65: q^2+2q+1
        66: q+1
        67: q^2+2q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+1
        75: q+1
        76: 2q^2+2q+1
        77: q+1
        78: 2q^2+2q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: 2q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+1
        88: q+1
        89: 2q^2+2q+1
        90: q+1
        91: 2q^2+2q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: q^2+q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: q+1
       107: q^2+2q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: q^2+1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q^2+q+1
       120: q+1
       121: q+1
       122: q^2+1
       123: 1
       124: q^2+2q+1
       125: q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q^2+1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 1
       139: q+1
       140: 1
       141: 2q^2+2q+1
       142: q+1
       143: q+1
       144: q^2+1
       145: q+1
       146: q^2+q+1
       147: q+1
       148: q^2+q+1
       149: q^2+2q+1
       150: q+1
       151: q^2+2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: 1
       160: q+1
       161: 1
       162: 2q^2+2q+1
       163: q+1
       164: q+1
       165: q^2+1
       166: q+1
       167: q^2+q+1
       168: q+1
       169: q^2+q+1
       170: q^2+2q+1
       171: q+1
       172: q^2+2q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+1
       180: q+1
       181: 2q^2+2q+1
       182: q+1
       183: 2q^2+2q+1
       184: q^2+q+1
       185: q^2+q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       216: q+1
       218: 1
       220: q+1
       221: q+1
       222: q+1
       224: 1
       225: q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: q^2+1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: q^2+q+1
       244: q+1
       245: q+1
       246: q^2+1
       247: 1
       248: q^2+2q+1
       249: q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q^2+2q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: q^2+1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q^2+q+1
       274: q+1
       275: q+1
       276: q^2+1
       277: 1
       278: q^2+2q+1
       279: q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q^2+1
       289: q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: 1
       293: q+1
       294: 1
       295: 2q^2+2q+1
       296: q+1
       297: q+1
       298: q^2+1
       299: q+1
       300: q^2+q+1
       301: q+1
       302: q^2+q+1
       303: q^2+2q+1
       304: q+1
       305: q^2+2q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: q+1
       341: 1
       345: 1
       346: q+1
       347: q+1
       349: 1
       351: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q^2+1
       374: 1
       375: q+1
       376: q+1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       383: q+1
       385: 1
       387: q+1
       388: q+1
       389: q+1
       391: 1
       392: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       422: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: 1
       436: q+1
       437: q^2+2q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: q^2+1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: q^2+q+1
       450: q+1
       451: q+1
       452: q^2+1
       453: 1
       454: q^2+2q+1
       455: q+1
       456: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: q+1
       506: 1
       510: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: q+1
       548: 1
       552: 1
       553: q+1
       554: q+1
       556: 1
       558: q+1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: q+1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: q+1
       595: 1
       599: 1
       600: q+1
       601: q+1
       603: 1
       605: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q^2+1
       628: 1
       629: q+1
       630: q+1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       637: q+1
       639: 1
       641: q+1
       642: q+1
       643: q+1
       645: 1
       646: q+1
       648: q+1
       650: 1
       658: 1
       659: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       704: 1
       705: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: q+1
       745: 1
       749: 1
       756: 1
       757: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: q+1
       797: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: q+1
       839: 1
       843: 1
       844: q+1
       845: q+1
       847: 1
       849: q+1
       853: 1
       862: 1
       870: 1
       871: 1
       876: 1
       893: 1
       907: 1
       915: 1
       916: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       939: 1
       946: 1
       948: 1
       961: 1
       969: 1
       970: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: q+1
      1056: 1
      1060: 1
      1079: 1
      1121: 1
      1129: 1
      1130: 1
      1135: 1
      1152: 1
      1173: 1
      1181: 1
      1182: 1
      1187: 1
      1204: 1
      1218: 1
      1226: 1
      1227: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1242: 1
      1250: 1
      1257: 1
      1259: 1
      1323: 1
      1370: 1
      1412: 1
      1420: 1
      1421: 1
      1426: 1
      1443: 1
      1577: 1

1578:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: q+1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: q+1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: q+1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: 1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: q+1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       345: 1
       346: 1
       349: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       503: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       552: 1
       553: 1
       556: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       742: 1
       757: 1
       758: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       863: 1
       871: 1
       872: 1
       875: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
      1016: 1
      1017: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1053: 1
      1080: 1
      1122: 1
      1130: 1
      1131: 1
      1134: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1219: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1324: 1
      1371: 1
      1413: 1
      1421: 1
      1422: 1
      1425: 1
      1578: 1

1579:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: q+1
        38: 2q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: 1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: 2q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: 2q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 2q^2+2q+1
       101: q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: q+1
       113: 1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+2q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: 1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: 1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: 2q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       237: 1
       238: q+1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: 1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       310: q+1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       348: q+1
       349: 1
       350: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       374: 1
       375: q+1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: q+1
       381: 1
       382: q+1
       384: q+1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: 1
       444: q+1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       507: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: q+1
       545: 1
       549: 1
       550: 1
       551: q+1
       552: 1
       553: q+1
       555: q+1
       556: 1
       557: 1
       564: q+1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: 1
       629: q+1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: q+1
       635: 1
       636: q+1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 1
       652: 1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       686: 1
       687: 1
       693: 1
       705: 1
       707: 1
       708: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       738: 1
       740: 1
       741: q+1
       742: 1
       746: 1
       747: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: q+1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: q+1
       836: 1
       840: 1
       841: 1
       842: q+1
       843: 1
       844: q+1
       846: q+1
       847: 1
       848: 1
       864: 1
       871: 1
       873: 1
       874: 1
       888: 1
       909: 1
       916: 1
       918: 1
       919: 1
       924: 1
       925: 1
       926: 1
       928: 1
       929: 1
       930: 1
       934: 1
       943: 1
       944: 1
       950: 1
       963: 1
       970: 1
       972: 1
       973: 1
       978: 1
       979: 1
       980: 1
       982: 1
       983: 1
       984: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1016: 1
      1018: 1
      1019: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: 1
      1043: 1
      1049: 1
      1051: 1
      1052: q+1
      1053: 1
      1057: 1
      1058: 1
      1081: 1
      1123: 1
      1130: 1
      1132: 1
      1133: 1
      1147: 1
      1175: 1
      1182: 1
      1184: 1
      1185: 1
      1199: 1
      1220: 1
      1227: 1
      1229: 1
      1230: 1
      1235: 1
      1236: 1
      1237: 1
      1239: 1
      1240: 1
      1241: 1
      1245: 1
      1254: 1
      1255: 1
      1261: 1
      1325: 1
      1372: 1
      1414: 1
      1421: 1
      1423: 1
      1424: 1
      1438: 1
      1579: 1

1580:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: 1
       152: 2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       687: 1
       693: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       944: 1
       950: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       998: 1
      1004: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1082: 1
      1124: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1221: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1255: 1
      1261: 1
      1326: 1
      1373: 1
      1415: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1580: 1

1581:    0: 2q^2+2q+1
         1: q^2+2q+1
         2: 2q^2+2q+1
         3: q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q+1
        13: q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: q^2+2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q^2+q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^2+2q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: q^2+2q+1
        79: 2q+1
        80: q^2+2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: q^2+2q+1
        92: 2q+1
        93: q^2+2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 2q+1
       105: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: 1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q^2+q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q^2+q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q^2+2q+1
       180: 2q+1
       181: 2q+1
       182: q+1
       183: q^2+2q+1
       184: 2q+1
       185: q^2+2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       191: q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       199: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       229: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: 1
       244: q+1
       245: q+1
       246: q^2+q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: 1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: q+1
       298: q^2+2q+1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: q^2+q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       312: 1
       314: q+1
       316: 1
       317: q+1
       321: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       358: q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       366: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       397: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       405: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       435: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: 1
       450: q+1
       451: q+1
       452: q^2+q+1
       453: q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       494: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       515: 1
       519: 1
       521: q+1
       523: 1
       524: q+1
       528: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       566: 1
       568: q+1
       570: 1
       571: q+1
       575: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       612: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       620: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       654: 1
       662: 1
       664: 1
       669: 1
       671: 1
       673: 1
       674: 1
       681: 1
       684: 1
       688: 1
       691: 1
       692: 1
       693: 1
       694: 1
       708: 1
       710: 1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       727: 1
       728: q+1
       729: 1
       730: 1
       733: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       754: 1
       760: 1
       762: 1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       806: 1
       810: 1
       812: q+1
       814: 1
       815: q+1
       819: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       866: 1
       874: 1
       876: 1
       892: 1
       895: 1
       911: 1
       919: 1
       921: 1
       926: 1
       928: 1
       930: 1
       931: 1
       938: 1
       941: 1
       945: 1
       948: 1
       949: 1
       950: 1
       951: 1
       965: 1
       973: 1
       975: 1
       980: 1
       982: 1
       984: 1
       985: 1
       992: 1
       995: 1
       999: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1019: 1
      1021: 1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1044: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1065: 1
      1083: 1
      1125: 1
      1133: 1
      1135: 1
      1151: 1
      1154: 1
      1177: 1
      1185: 1
      1187: 1
      1203: 1
      1206: 1
      1222: 1
      1230: 1
      1232: 1
      1237: 1
      1239: 1
      1241: 1
      1242: 1
      1249: 1
      1252: 1
      1256: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1327: 1
      1374: 1
      1416: 1
      1424: 1
      1426: 1
      1442: 1
      1445: 1
      1581: 1

1582:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: 1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: 1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       648: 1
       655: 1
       663: 1
       664: 1
       670: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       709: 1
       710: 1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       761: 1
       762: 1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       853: 1
       867: 1
       875: 1
       876: 1
       893: 1
       912: 1
       920: 1
       921: 1
       927: 1
       929: 1
       930: 1
       931: 1
       939: 1
       946: 1
       948: 1
       966: 1
       974: 1
       975: 1
       981: 1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1020: 1
      1021: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1084: 1
      1126: 1
      1134: 1
      1135: 1
      1152: 1
      1178: 1
      1186: 1
      1187: 1
      1204: 1
      1223: 1
      1231: 1
      1232: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1250: 1
      1257: 1
      1259: 1
      1328: 1
      1375: 1
      1417: 1
      1425: 1
      1426: 1
      1443: 1
      1582: 1

1583:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: q+1
       216: q+1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: q+1
       341: q+1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       382: q+1
       383: q+1
       385: q+1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       421: q+1
       422: q+1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       497: q+1
       504: 1
       506: 1
       511: 1
       512: 1
       514: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: q+1
       548: q+1
       553: 1
       554: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: q+1
       595: q+1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       636: q+1
       637: q+1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       673: 1
       674: 1
       675: 1
       691: 1
       698: 1
       700: 1
       710: 1
       711: 1
       719: 1
       720: 1
       721: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       736: q+1
       743: 1
       745: 1
       750: 1
       751: 1
       753: 1
       762: 1
       763: 1
       771: 1
       772: 1
       773: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       788: q+1
       795: 1
       797: 1
       802: 1
       803: 1
       805: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       837: q+1
       839: q+1
       844: 1
       845: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       868: 1
       876: 1
       877: 1
       902: 1
       913: 1
       921: 1
       922: 1
       930: 1
       931: 1
       932: 1
       948: 1
       955: 1
       957: 1
       967: 1
       975: 1
       976: 1
       984: 1
       985: 1
       986: 1
      1002: 1
      1009: 1
      1011: 1
      1021: 1
      1022: 1
      1030: 1
      1031: 1
      1032: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1047: q+1
      1054: 1
      1056: 1
      1061: 1
      1062: 1
      1064: 1
      1085: 1
      1127: 1
      1135: 1
      1136: 1
      1161: 1
      1179: 1
      1187: 1
      1188: 1
      1213: 1
      1224: 1
      1232: 1
      1233: 1
      1241: 1
      1242: 1
      1243: 1
      1259: 1
      1266: 1
      1268: 1
      1329: 1
      1376: 1
      1418: 1
      1426: 1
      1427: 1
      1452: 1
      1583: 1

1584:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q^2+2q+1
        59: q+1
        60: q+1
        61: 1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: 1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q^2+2q+1
       143: q+1
       144: q+1
       145: 1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q^2+2q+1
       164: q+1
       165: q+1
       166: 1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: q+1
       209: q+1
       210: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q^2+2q+1
       275: q+1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q^2+2q+1
       297: q+1
       298: q+1
       299: 1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       325: 1
       326: 1
       327: 1
       329: q+1
       331: q+1
       332: q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       376: q+1
       377: q+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       415: q+1
       416: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q^2+2q+1
       451: q+1
       452: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       485: q+1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       538: q+1
       539: q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       579: 1
       580: 1
       581: 1
       583: q+1
       585: q+1
       586: q+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       630: q+1
       631: q+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       647: q+1
       648: 1
       649: 1
       657: 1
       658: 1
       665: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: 1
       720: 1
       721: 1
       724: q+1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: 1
       772: 1
       773: 1
       776: q+1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       829: q+1
       830: q+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       861: 1
       878: 1
       879: 1
       886: 1
       899: 1
       906: 1
       914: 1
       915: 1
       922: 1
       933: 1
       934: 1
       935: 1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       960: 1
       968: 1
       969: 1
       976: 1
       987: 1
       988: 1
       989: 1
       995: 1
       996: 1
       999: 1
      1007: 1
      1009: 1
      1010: 1
      1014: 1
      1015: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1032: 1
      1035: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1086: 1
      1120: 1
      1137: 1
      1138: 1
      1145: 1
      1158: 1
      1172: 1
      1189: 1
      1190: 1
      1197: 1
      1210: 1
      1217: 1
      1225: 1
      1226: 1
      1233: 1
      1244: 1
      1245: 1
      1246: 1
      1252: 1
      1253: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1330: 1
      1377: 1
      1411: 1
      1428: 1
      1429: 1
      1436: 1
      1449: 1
      1584: 1

1585:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: q^2+q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q^2+1
        25: 2q^2+2q+1
        26: q+1
        27: 2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: q^2+2q+1
        39: q^2+q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: q^2+2q+1
        46: q^2+q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q+1
        51: q^2+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: 1
        57: 2q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q^2+1
        62: q^2+2q+1
        63: q+1
        64: q^2+2q+1
        65: q^2+q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+1
        76: 2q^2+2q+1
        77: q+1
        78: 2q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: 2q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+1
        89: 2q^2+2q+1
        90: q+1
        91: 2q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: q^2+2q+1
       103: q^2+q+1
       104: 1
       105: q+1
       106: 1
       107: q^2+2q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q^2+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q^2+2q+1
       120: q+1
       121: q+1
       122: q+1
       124: q^2+q+1
       125: q+1
       126: q+1
       127: 1
       128: q^2+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q^2+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 1
       140: 1
       141: 2q^2+2q+1
       142: q+1
       143: q+1
       144: q+1
       145: q^2+1
       146: q^2+2q+1
       147: q+1
       148: q^2+2q+1
       149: q^2+q+1
       150: q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q^2+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: 1
       162: 2q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+1
       167: q^2+2q+1
       168: q+1
       169: q^2+2q+1
       170: q^2+q+1
       171: q+1
       172: q^2+q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+1
       181: 2q^2+2q+1
       182: q+1
       183: 2q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+q+1
       187: q^2+q+1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: q+1
       209: q+1
       210: 1
       213: 1
       214: q^2+1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       225: q+1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q^2+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: q^2+2q+1
       244: q+1
       245: q+1
       246: q+1
       248: q^2+q+1
       249: q+1
       250: q+1
       251: 1
       252: q^2+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: q^2+2q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: q^2+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q^2+2q+1
       274: q+1
       275: q+1
       276: q+1
       278: q^2+q+1
       279: q+1
       280: q+1
       281: 1
       282: q^2+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q^2+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q+1
       293: 1
       294: 1
       295: 2q^2+2q+1
       296: q+1
       297: q+1
       298: q+1
       299: q^2+1
       300: q^2+2q+1
       301: q+1
       302: q^2+2q+1
       303: q^2+q+1
       304: q+1
       305: q^2+q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: q+1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: q+1
       332: 1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       347: q+1
       348: 1
       351: q+1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       376: q+1
       377: 1
       380: 1
       381: q^2+1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       394: q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       415: q+1
       416: 1
       419: 1
       420: q^2+1
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       431: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q^2+2q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: q^2+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: q^2+2q+1
       450: q+1
       451: q+1
       452: q+1
       454: q^2+q+1
       455: q+1
       456: q+1
       457: 1
       458: q^2+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: q+1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: q+1
       539: 1
       543: 1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       554: q+1
       555: 1
       558: q+1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: q+1
       586: 1
       590: 1
       591: 1
       592: 1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: q+1
       601: q+1
       602: 1
       605: q+1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       630: q+1
       631: 1
       634: 1
       635: q^2+1
       636: q+1
       637: q+1
       638: 1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       646: q+1
       648: q+1
       650: 1
       658: 1
       659: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       688: 1
       690: 1
       704: 1
       705: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: 1
       756: 1
       757: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       776: 1
       778: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: q+1
       796: 1
       800: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       813: 1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: q+1
       830: 1
       834: 1
       835: 1
       836: 1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: q+1
       845: q+1
       846: 1
       849: q+1
       852: 1
       862: 1
       879: 1
       880: 1
       885: 1
       890: 1
       907: 1
       915: 1
       916: 1
       921: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       945: 1
       947: 1
       961: 1
       969: 1
       970: 1
       975: 1
       980: 1
       987: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       999: 1
      1001: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: q+1
      1055: 1
      1059: 1
      1087: 1
      1121: 1
      1138: 1
      1139: 1
      1144: 1
      1149: 1
      1173: 1
      1190: 1
      1191: 1
      1196: 1
      1201: 1
      1218: 1
      1226: 1
      1227: 1
      1232: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1252: 1
      1256: 1
      1258: 1
      1331: 1
      1378: 1
      1412: 1
      1429: 1
      1430: 1
      1435: 1
      1440: 1
      1585: 1

1586:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q^2+2q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: 2q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 1
        54: q+1
        55: q^2+2q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: 2q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 2q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+2q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: 2q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: q+1
       268: q+1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       348: 1
       349: q+1
       350: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: 1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: q+1
       414: q+1
       416: 1
       417: q+1
       418: 1
       419: 1
       420: q+1
       421: q+1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: q+1
       444: q+1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       507: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: q+1
       588: 1
       589: 1
       590: 1
       591: 1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: q+1
       600: q+1
       602: 1
       603: q+1
       604: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: q+1
       629: q+1
       631: 1
       632: q+1
       633: 1
       634: 1
       635: q+1
       636: q+1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: q+1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       757: 1
       758: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: 1
       775: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: 1
       794: q+1
       798: 1
       799: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: q+1
       832: 1
       833: 1
       834: 1
       835: 1
       836: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: q+1
       844: q+1
       846: 1
       847: q+1
       848: 1
       863: 1
       880: 1
       881: 1
       884: 1
       888: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: 1
       940: 1
       943: 1
       944: 1
       950: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: 1
       988: 1
       989: 1
       990: 1
       991: 1
       993: 1
       994: 1
       997: 1
       998: 1
      1004: 1
      1016: 1
      1017: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1040: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: 1
      1053: q+1
      1057: 1
      1058: 1
      1088: 1
      1122: 1
      1139: 1
      1140: 1
      1143: 1
      1147: 1
      1174: 1
      1191: 1
      1192: 1
      1195: 1
      1199: 1
      1219: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1261: 1
      1332: 1
      1379: 1
      1413: 1
      1430: 1
      1431: 1
      1434: 1
      1438: 1
      1586: 1

1587:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       348: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       416: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       652: 1
       659: 1
       661: 1
       662: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       705: 1
       707: 1
       708: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       864: 1
       880: 1
       882: 1
       883: 1
       909: 1
       916: 1
       918: 1
       919: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       963: 1
       970: 1
       972: 1
       973: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
      1016: 1
      1018: 1
      1019: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: 1
      1089: 1
      1123: 1
      1139: 1
      1141: 1
      1142: 1
      1175: 1
      1191: 1
      1193: 1
      1194: 1
      1220: 1
      1227: 1
      1229: 1
      1230: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1333: 1
      1380: 1
      1414: 1
      1430: 1
      1432: 1
      1433: 1
      1587: 1

1588:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: q+1
        30: 2q+1
        31: q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: q+1
        81: 2q+1
        82: q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: 2q+1
        95: q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: 2q+1
       187: q+1
       188: 2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: 1
       490: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: 1
       693: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: 1
       729: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: 1
       781: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       865: 1
       881: 1
       882: 1
       883: 1
       884: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       944: 1
       950: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       998: 1
      1004: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1034: 1
      1040: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1090: 1
      1124: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1176: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1221: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1255: 1
      1261: 1
      1334: 1
      1381: 1
      1415: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1588: 1

1589:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        61: 1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: 1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: 1
       146: q+1
       147: 1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: q+1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       229: q+1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: q+1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: 1
       300: q+1
       301: 1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: q+1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       358: q+1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       397: q+1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       435: q+1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       519: q+1
       521: 1
       523: 1
       524: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       566: q+1
       568: 1
       570: 1
       571: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       612: q+1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       648: 1
       654: 1
       662: 1
       664: 1
       669: 1
       679: 1
       681: 1
       683: 1
       684: 1
       688: 1
       690: 1
       708: 1
       710: 1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       760: 1
       762: 1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       810: q+1
       812: 1
       814: 1
       815: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       852: 1
       866: 1
       883: 1
       885: 1
       890: 1
       911: 1
       919: 1
       921: 1
       926: 1
       936: 1
       938: 1
       940: 1
       941: 1
       945: 1
       947: 1
       965: 1
       973: 1
       975: 1
       980: 1
       990: 1
       992: 1
       994: 1
       995: 1
       999: 1
      1001: 1
      1019: 1
      1021: 1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1091: 1
      1125: 1
      1142: 1
      1144: 1
      1149: 1
      1177: 1
      1194: 1
      1196: 1
      1201: 1
      1222: 1
      1230: 1
      1232: 1
      1237: 1
      1247: 1
      1249: 1
      1251: 1
      1252: 1
      1256: 1
      1258: 1
      1335: 1
      1382: 1
      1416: 1
      1433: 1
      1435: 1
      1440: 1
      1589: 1

1590:    0: 2q^2+2q+1
         1: q^2+2q+1
         2: 2q^2+2q+1
         3: q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q+1
        10: q^2+2q+1
        11: 2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q^2+2q+1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: q^2+2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q+1
        37: q^2+2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q+1
        44: q^2+2q+1
        45: 2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q^2+2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q^2+q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: q^2+2q+1
        76: 2q+1
        77: q+1
        78: q^2+2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: q^2+2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q^2+2q+1
        89: 2q+1
        90: q+1
        91: q^2+2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: q^2+2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 2q+1
       101: q^2+2q+1
       102: 2q+1
       103: q^2+2q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       113: q+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: q^2+2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q^2+q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: q^2+2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q^2+q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q^2+2q+1
       181: 2q+1
       182: q+1
       183: q^2+2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: q^2+2q+1
       188: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       237: q+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q^2+q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       267: q+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q^2+q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: q^2+2q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q^2+q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       313: q+1
       315: 1
       316: 1
       317: q+1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       398: q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       443: q+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q^2+q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       515: 1
       520: q+1
       522: 1
       523: 1
       524: q+1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       567: q+1
       569: 1
       570: 1
       571: q+1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       655: 1
       663: 1
       664: 1
       670: 1
       674: 1
       680: 1
       682: 1
       683: 1
       684: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       709: 1
       710: 1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       754: 1
       761: 1
       762: 1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       801: 1
       806: 1
       811: q+1
       813: 1
       814: 1
       815: q+1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       867: 1
       884: 1
       885: 1
       891: 1
       895: 1
       912: 1
       920: 1
       921: 1
       927: 1
       931: 1
       937: 1
       939: 1
       940: 1
       941: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       966: 1
       974: 1
       975: 1
       981: 1
       985: 1
       991: 1
       993: 1
       994: 1
       995: 1
      1000: 1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1020: 1
      1021: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1060: 1
      1065: 1
      1092: 1
      1126: 1
      1143: 1
      1144: 1
      1150: 1
      1154: 1
      1178: 1
      1195: 1
      1196: 1
      1202: 1
      1206: 1
      1223: 1
      1231: 1
      1232: 1
      1238: 1
      1242: 1
      1248: 1
      1250: 1
      1251: 1
      1252: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1336: 1
      1383: 1
      1417: 1
      1434: 1
      1435: 1
      1441: 1
      1445: 1
      1590: 1

1591:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       208: q+1
       209: q+1
       210: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       318: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       331: q+1
       332: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       375: q+1
       376: q+1
       377: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       414: q+1
       415: q+1
       416: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: q+1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       511: 1
       512: 1
       513: 1
       523: 1
       524: 1
       525: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       538: q+1
       539: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       570: 1
       571: 1
       572: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       585: q+1
       586: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       629: q+1
       630: q+1
       631: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       683: 1
       684: 1
       685: 1
       690: 1
       698: 1
       699: 1
       710: 1
       711: 1
       719: 1
       720: 1
       721: 1
       726: q+1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       750: 1
       751: 1
       752: 1
       762: 1
       763: 1
       771: 1
       772: 1
       773: 1
       778: q+1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       795: 1
       796: 1
       802: 1
       803: 1
       804: 1
       814: 1
       815: 1
       816: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       829: q+1
       830: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       868: 1
       885: 1
       886: 1
       901: 1
       913: 1
       921: 1
       922: 1
       940: 1
       941: 1
       942: 1
       947: 1
       955: 1
       956: 1
       967: 1
       975: 1
       976: 1
       994: 1
       995: 1
       996: 1
      1001: 1
      1009: 1
      1010: 1
      1021: 1
      1022: 1
      1030: 1
      1031: 1
      1032: 1
      1037: q+1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1054: 1
      1055: 1
      1061: 1
      1062: 1
      1063: 1
      1093: 1
      1127: 1
      1144: 1
      1145: 1
      1160: 1
      1179: 1
      1196: 1
      1197: 1
      1212: 1
      1224: 1
      1232: 1
      1233: 1
      1251: 1
      1252: 1
      1253: 1
      1258: 1
      1266: 1
      1267: 1
      1337: 1
      1384: 1
      1418: 1
      1435: 1
      1436: 1
      1451: 1
      1591: 1

1592:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^2+2q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^2+2q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^2+2q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q^2+3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 2q+1
        32: 2q^2+3q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^2+2q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: 2q^2+3q+1
        69: 2q+1
        70: q^2+2q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q^2+3q+1
        80: 2q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q+1
        96: 2q^2+3q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: 2q+1
       131: 1
       132: q^2+2q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q^2+3q+1
       153: 2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q^2+3q+1
       174: 2q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: 2q^2+3q+1
       189: q+1
       190: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       204: 2q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q^2+3q+1
       307: 2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       318: q+1
       319: 1
       320: 2q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       410: 2q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       464: q+1
       473: 1
       474: 1
       482: 1
       483: 1
       484: q+1
       490: 1
       491: 1
       492: 1
       493: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       525: q+1
       526: 1
       527: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       572: q+1
       573: 1
       574: 2q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       657: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       703: q+1
       712: 1
       713: 1
       721: 1
       722: 1
       723: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       764: 1
       765: 1
       773: 1
       774: 1
       775: q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       816: q+1
       817: 1
       818: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       898: 1
       914: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       968: 1
       977: 1
       978: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1014: q+1
      1023: 1
      1024: 1
      1032: 1
      1033: 1
      1034: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1094: 1
      1128: 1
      1137: 1
      1146: 1
      1147: 1
      1155: 1
      1157: 1
      1180: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1209: 1
      1225: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1338: 1
      1385: 1
      1419: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1448: 1
      1592: 1

1593:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: q^2+3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: q^2+3q+1
        19: 2q^2+3q+1
        20: 2q+1
        21: q^2+2q+1
        22: q+1
        23: 2q+1
        24: 2q+1
        25: q^2+3q+1
        26: q+1
        27: 2q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: 2q^2+3q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: 2q^2+3q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: q^2+3q+1
        50: 2q+1
        51: 2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: 1
        60: 2q+1
        61: 2q+1
        62: q^2+3q+1
        63: q+1
        64: q+1
        65: q^2+3q+1
        66: q+1
        67: q+1
        68: q^2+3q+1
        69: q^2+3q+1
        70: q^2+2q+1
        71: 2q+1
        72: q^2+2q+1
        73: q+1
        74: 2q+1
        75: 2q+1
        76: q^2+3q+1
        77: q+1
        78: 2q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: 2q+1
        85: q^2+2q+1
        86: q+1
        87: 2q+1
        88: 2q+1
        89: q^2+3q+1
        90: q+1
        91: 2q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: 2q^2+3q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: 2q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: q^2+3q+1
       130: q+1
       131: 1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 2q+1
       141: 2q+1
       142: q+1
       143: 1
       144: 2q+1
       145: 2q+1
       146: q^2+3q+1
       147: q+1
       148: q+1
       149: q^2+3q+1
       150: q+1
       151: q+1
       152: q^2+3q+1
       153: q^2+3q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: 2q+1
       162: 2q+1
       163: q+1
       164: 1
       165: 2q+1
       166: 2q+1
       167: q^2+3q+1
       168: q+1
       169: q+1
       170: q^2+3q+1
       171: q+1
       172: q+1
       173: q^2+3q+1
       174: q^2+3q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^2+2q+1
       178: q+1
       179: 2q+1
       180: 2q+1
       181: q^2+3q+1
       182: q+1
       183: 2q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       195: q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q^2+2q+1
       227: 1
       228: 2q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: q^2+3q+1
       254: q+1
       255: 1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: q^2+3q+1
       284: q+1
       285: 1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: 2q+1
       295: 2q+1
       296: q+1
       297: 1
       298: 2q+1
       299: 2q+1
       300: q^2+3q+1
       301: q+1
       302: q+1
       303: q^2+3q+1
       304: q+1
       305: q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q+1
       317: q+1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       362: q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q^2+2q+1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       401: q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q^2+2q+1
       433: 1
       434: 2q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: q^2+3q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       524: q+1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       571: q+1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       616: q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q^2+2q+1
       648: 1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       676: 1
       677: 1
       678: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       712: 1
       713: 1
       714: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: q+1
       764: 1
       765: 1
       766: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       815: q+1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       870: 1
       879: 1
       887: 1
       888: 1
       889: 1
       895: 1
       915: 1
       923: 1
       924: 1
       925: 1
       931: 1
       933: 1
       934: 1
       935: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       969: 1
       977: 1
       978: 1
       979: 1
       985: 1
       987: 1
       988: 1
       989: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: q+1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1095: 1
      1129: 1
      1138: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1181: 1
      1190: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1226: 1
      1234: 1
      1235: 1
      1236: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1339: 1
      1386: 1
      1420: 1
      1429: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1593: 1

1594:    0: 2q^3+7q^2+5q+1
         1: 2q^3+7q^2+5q+1
         2: q^3+5q^2+5q+1
         3: 2q^3+7q^2+5q+1
         4: 2q^3+7q^2+5q+1
         5: 2q^3+7q^2+5q+1
         6: q^3+5q^2+5q+1
         7: 3q^2+4q+1
         8: q^3+5q^2+5q+1
         9: 2q^3+7q^2+5q+1
        10: 3q^2+5q+1
        11: q^3+5q^2+5q+1
        12: q^3+5q^2+5q+1
        13: 2q^3+7q^2+5q+1
        14: q^3+5q^2+5q+1
        15: 2q^3+7q^2+5q+1
        16: 2q^3+7q^2+5q+1
        17: q^3+5q^2+5q+1
        18: 2q^3+7q^2+5q+1
        19: 2q^3+7q^2+5q+1
        20: q^3+5q^2+5q+1
        21: 3q^2+4q+1
        22: 3q^2+4q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 3q^2+5q+1
        26: 3q+1
        27: 3q^2+5q+1
        28: q^3+5q^2+5q+1
        29: 2q^2+5q+1
        30: q^3+5q^2+5q+1
        31: 2q^2+5q+1
        32: 3q^2+5q+1
        33: q^3+5q^2+5q+1
        34: 3q^2+4q+1
        35: q^3+5q^2+5q+1
        36: 2q^3+7q^2+5q+1
        37: 3q^2+5q+1
        38: q^3+5q^2+5q+1
        39: q^3+5q^2+5q+1
        40: q^3+5q^2+5q+1
        41: 3q^2+4q+1
        42: q^3+5q^2+5q+1
        43: 2q^3+7q^2+5q+1
        44: 3q^2+5q+1
        45: q^3+5q^2+5q+1
        46: q^3+5q^2+5q+1
        47: 2q^3+7q^2+5q+1
        48: q^3+5q^2+5q+1
        49: 2q^3+7q^2+5q+1
        50: 2q^2+3q+1
        51: 2q^2+3q+1
        52: 3q^2+4q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: 2q+1
        57: 3q^2+5q+1
        58: 3q+1
        59: 3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: 2q^2+5q+1
        63: 3q+1
        64: 2q^2+5q+1
        65: 2q^2+5q+1
        66: 3q+1
        67: 2q^2+5q+1
        68: 3q^2+5q+1
        69: q^2+5q+1
        70: 3q^2+5q+1
        71: q^3+5q^2+5q+1
        72: 3q^2+4q+1
        73: 3q^2+4q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 3q^2+5q+1
        77: 3q+1
        78: 3q^2+5q+1
        79: q^3+5q^2+5q+1
        80: 2q^2+5q+1
        81: q^3+5q^2+5q+1
        82: 2q^2+5q+1
        83: 3q^2+5q+1
        84: q^3+5q^2+5q+1
        85: 3q^2+4q+1
        86: 3q^2+4q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 3q^2+5q+1
        90: 3q+1
        91: 3q^2+5q+1
        92: q^3+5q^2+5q+1
        93: 2q^2+5q+1
        94: q^3+5q^2+5q+1
        95: 2q^2+5q+1
        96: 3q^2+5q+1
        97: q^3+5q^2+5q+1
        98: 3q^2+4q+1
        99: q^3+5q^2+5q+1
       100: 2q^3+7q^2+5q+1
       101: 3q^2+5q+1
       102: q^3+5q^2+5q+1
       103: q^3+5q^2+5q+1
       104: 2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: 3q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: 2q^2+5q+1
       120: 3q+1
       121: 3q+1
       122: q^2+3q+1
       123: 2q+1
       124: 2q^2+5q+1
       125: 3q+1
       126: 3q+1
       127: 2q+1
       128: q^2+3q+1
       129: q^2+5q+1
       130: 3q+1
       131: q^2+5q+1
       132: 3q^2+5q+1
       133: 3q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: 3q^2+4q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 2q+1
       141: 3q^2+5q+1
       142: 3q+1
       143: 3q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: 2q^2+5q+1
       147: 3q+1
       148: 2q^2+5q+1
       149: 2q^2+5q+1
       150: 3q+1
       151: 2q^2+5q+1
       152: 3q^2+5q+1
       153: q^2+5q+1
       154: 3q^2+5q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 3q^2+4q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: 2q+1
       162: 3q^2+5q+1
       163: 3q+1
       164: 3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+5q+1
       168: 3q+1
       169: 2q^2+5q+1
       170: 2q^2+5q+1
       171: 3q+1
       172: 2q^2+5q+1
       173: 3q^2+5q+1
       174: q^2+5q+1
       175: 3q^2+5q+1
       176: q^3+5q^2+5q+1
       177: 3q^2+4q+1
       178: 3q^2+4q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: 3q^2+5q+1
       182: 3q+1
       183: 3q^2+5q+1
       184: q^3+5q^2+5q+1
       185: 2q^2+5q+1
       186: q^3+5q^2+5q+1
       187: 2q^2+5q+1
       188: 3q^2+5q+1
       189: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 2q+1
       206: q^2+3q+1
       207: 2q+1
       208: 3q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: q^2+3q+1
       215: 3q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: q^2+5q+1
       221: 3q+1
       222: 3q+1
       223: 2q+1
       224: 2q+1
       225: 3q+1
       227: 3q+1
       228: 2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: q+1
       235: 2q+1
       236: q^2+3q+1
       237: q^2+3q+1
       238: 3q+1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: 2q^2+5q+1
       244: 3q+1
       245: 3q+1
       246: q^2+3q+1
       247: 2q+1
       248: 2q^2+5q+1
       249: 3q+1
       250: 3q+1
       251: 2q+1
       252: q^2+3q+1
       253: q^2+5q+1
       254: 3q+1
       255: q^2+5q+1
       256: 3q^2+5q+1
       257: 3q+1
       258: 2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: q+1
       263: q+1
       264: q+1
       265: 2q+1
       266: q^2+3q+1
       267: q^2+3q+1
       268: 3q+1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: 2q^2+5q+1
       274: 3q+1
       275: 3q+1
       276: q^2+3q+1
       277: 2q+1
       278: 2q^2+5q+1
       279: 3q+1
       280: 3q+1
       281: 2q+1
       282: q^2+3q+1
       283: q^2+5q+1
       284: 3q+1
       285: q^2+5q+1
       286: 3q^2+5q+1
       287: 3q+1
       288: 2q^2+3q+1
       289: 2q^2+3q+1
       290: 3q^2+4q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: 2q+1
       295: 3q^2+5q+1
       296: 3q+1
       297: 3q+1
       298: q^2+3q+1
       299: q^2+3q+1
       300: 2q^2+5q+1
       301: 3q+1
       302: 2q^2+5q+1
       303: 2q^2+5q+1
       304: 3q+1
       305: 2q^2+5q+1
       306: 3q^2+5q+1
       307: q^2+5q+1
       308: 3q^2+5q+1
       310: q+1
       311: q+1
       312: q+1
       315: q+1
       316: q+1
       319: 2q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: 3q+1
       347: q+1
       348: q+1
       349: q+1
       350: 1
       351: 3q+1
       354: q+1
       355: q+1
       356: 2q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 2q+1
       373: q^2+3q+1
       374: 2q+1
       375: 3q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: q^2+3q+1
       382: 3q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: q^2+5q+1
       388: 3q+1
       389: 3q+1
       390: 2q+1
       391: 2q+1
       392: 3q+1
       394: 3q+1
       395: 2q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 2q+1
       412: q^2+3q+1
       413: 2q+1
       414: 3q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 2q+1
       420: q^2+3q+1
       421: 3q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q^2+5q+1
       427: 3q+1
       428: 3q+1
       429: 2q+1
       430: 2q+1
       431: 3q+1
       433: 3q+1
       434: 2q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q^2+2q+1
       438: q+1
       439: q+1
       440: q+1
       441: 2q+1
       442: q^2+3q+1
       443: q^2+3q+1
       444: 3q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: 2q^2+5q+1
       450: 3q+1
       451: 3q+1
       452: q^2+3q+1
       453: 2q+1
       454: 2q^2+5q+1
       455: 3q+1
       456: 3q+1
       457: 2q+1
       458: q^2+3q+1
       459: q^2+5q+1
       460: 3q+1
       461: q^2+5q+1
       462: 3q^2+5q+1
       463: 3q+1
       466: q+1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: q+1
       515: 1
       517: q+1
       518: q+1
       519: q+1
       522: q+1
       523: q+1
       526: 2q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: 2q+1
       552: 2q+1
       553: 3q+1
       554: q+1
       555: q+1
       556: q+1
       557: 1
       558: 3q+1
       561: q+1
       562: q+1
       564: q+1
       565: q+1
       566: q+1
       569: q+1
       570: q+1
       573: 2q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: q+1
       598: 2q+1
       599: 2q+1
       600: 3q+1
       601: q+1
       602: q+1
       603: q+1
       604: 1
       605: 3q+1
       608: q+1
       609: q+1
       610: 2q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 2q+1
       627: q^2+3q+1
       628: 2q+1
       629: 3q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 2q+1
       635: q^2+3q+1
       636: 3q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: q^2+5q+1
       642: 3q+1
       643: 3q+1
       644: 2q+1
       645: 2q+1
       646: 3q+1
       648: 3q+1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: q+1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       722: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: q+1
       754: 1
       757: q+1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: q+1
       794: q+1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: q+1
       806: 1
       808: q+1
       809: q+1
       810: q+1
       813: q+1
       814: q+1
       817: 2q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: q+1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: 2q+1
       843: 2q+1
       844: 3q+1
       845: q+1
       846: q+1
       847: q+1
       848: 1
       849: 3q+1
       852: q+1
       853: q+1
       871: 1
       880: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       897: 1
       916: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       959: 1
       970: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1013: 1
      1016: q+1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: q+1
      1053: q+1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1065: 1
      1096: 1
      1130: 1
      1139: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1156: 1
      1182: 1
      1191: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1208: 1
      1227: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1263: 1
      1270: 1
      1340: 1
      1387: 1
      1421: 1
      1430: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1447: 1
      1594: 1

1595:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: 1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 2q+1
       182: q+1
       183: q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       195: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 1
       298: q+1
       299: q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: 1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       312: q+1
       313: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       362: q+1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       401: q+1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       442: q+1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       467: q+1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: q+1
       519: q+1
       520: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: q+1
       566: q+1
       567: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       616: q+1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       660: 1
       668: 1
       669: 1
       670: 1
       678: 1
       679: 1
       680: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       695: 1
       706: q+1
       714: 1
       715: 1
       716: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       732: 1
       733: 1
       734: 1
       735: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       754: 1
       758: q+1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       784: 1
       785: 1
       786: 1
       787: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       806: 1
       809: q+1
       810: q+1
       811: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       872: 1
       881: 1
       889: 1
       890: 1
       891: 1
       917: 1
       925: 1
       926: 1
       927: 1
       935: 1
       936: 1
       937: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       952: 1
       971: 1
       979: 1
       980: 1
       981: 1
       989: 1
       990: 1
       991: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1006: 1
      1017: q+1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1048: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1059: 1
      1060: 1
      1065: 1
      1097: 1
      1131: 1
      1140: 1
      1148: 1
      1149: 1
      1150: 1
      1183: 1
      1192: 1
      1200: 1
      1201: 1
      1202: 1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1246: 1
      1247: 1
      1248: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1263: 1
      1341: 1
      1388: 1
      1422: 1
      1431: 1
      1439: 1
      1440: 1
      1441: 1
      1595: 1

1596:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q+1
        23: q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: 1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 2q+1
       182: q+1
       183: q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       194: q+1
       195: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: 1
       298: q+1
       299: q+1
       300: 2q+1
       301: q+1
       302: 1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       314: q+1
       315: q+1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       361: q+1
       362: q+1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       400: q+1
       401: q+1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       442: q+1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       468: q+1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       515: 1
       518: q+1
       521: q+1
       522: q+1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: q+1
       568: q+1
       569: q+1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       615: q+1
       616: q+1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       661: 1
       668: 1
       671: 1
       672: 1
       678: 1
       681: 1
       682: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       695: 1
       707: q+1
       714: 1
       717: 1
       718: 1
       723: 1
       724: 1
       725: 1
       727: 1
       728: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       754: 1
       759: q+1
       766: 1
       769: 1
       770: 1
       775: 1
       776: 1
       777: 1
       779: 1
       780: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       806: 1
       809: q+1
       812: q+1
       813: q+1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       873: 1
       882: 1
       889: 1
       892: 1
       893: 1
       918: 1
       925: 1
       928: 1
       929: 1
       935: 1
       938: 1
       939: 1
       944: 1
       945: 1
       946: 1
       948: 1
       949: 1
       952: 1
       972: 1
       979: 1
       982: 1
       983: 1
       989: 1
       992: 1
       993: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1006: 1
      1018: q+1
      1025: 1
      1028: 1
      1029: 1
      1034: 1
      1035: 1
      1036: 1
      1038: 1
      1039: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1059: 1
      1060: 1
      1065: 1
      1098: 1
      1132: 1
      1141: 1
      1148: 1
      1151: 1
      1152: 1
      1184: 1
      1193: 1
      1200: 1
      1203: 1
      1204: 1
      1229: 1
      1236: 1
      1239: 1
      1240: 1
      1246: 1
      1249: 1
      1250: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1263: 1
      1342: 1
      1389: 1
      1423: 1
      1432: 1
      1439: 1
      1442: 1
      1443: 1
      1596: 1

1597:    0: q^4+3q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: q^4+3q^2+2q+1
         4: q^4+3q^2+2q+1
         5: q^4+3q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: q^4+3q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^4+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^4+3q^2+2q+1
        19: q^4+3q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: 2q^2+2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: q^4+3q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: q^4+3q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^4+3q^2+2q+1
        50: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: q^2+2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q^2+2q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: 2q^2+2q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: q^4+3q^2+2q+1
       103: q^2+2q+1
       105: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 2q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: q^2+2q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: q^2+2q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q^2+2q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: q^2+2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: 2q^2+2q+1
       180: q+1
       181: 2q+1
       182: q+1
       183: q^2+2q+1
       184: 2q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       191: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       199: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 2q+1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       227: q+1
       229: q^2+2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 2q+1
       238: q+1
       239: 1
       240: q+1
       241: 1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: 1
       248: 2q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       259: q^2+2q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q+1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: q^2+2q+1
       277: 1
       278: 2q+1
       279: q+1
       280: q+1
       281: 2q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: q^2+2q+1
       299: q+1
       300: 2q+1
       301: q+1
       302: q^2+2q+1
       303: 2q+1
       304: q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       312: q+1
       314: q+1
       316: q+1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: 1
       358: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       366: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 2q+1
       375: q+1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: 2q+1
       382: q+1
       383: 1
       384: q+1
       385: 1
       386: q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: 1
       392: q+1
       394: q+1
       397: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       405: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: 2q+1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 2q+1
       421: q+1
       422: 1
       423: q+1
       424: 1
       425: q+1
       426: 2q+1
       427: q+1
       428: q+1
       429: 2q+1
       430: 1
       431: q+1
       433: q+1
       435: q^2+2q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 2q+1
       444: q+1
       445: 1
       446: q+1
       447: 1
       448: q+1
       449: 2q+1
       450: q+1
       451: q+1
       452: q^2+2q+1
       453: 1
       454: 2q+1
       455: q+1
       456: q+1
       457: 2q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       469: q+1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       515: 1
       519: q+1
       521: q+1
       523: q+1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       544: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: 2q+1
       553: q+1
       554: 1
       555: q+1
       556: 1
       557: 1
       558: q+1
       561: q+1
       562: 1
       566: q+1
       568: q+1
       570: q+1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q+1
       598: 2q+1
       600: q+1
       601: 1
       602: q+1
       603: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       612: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       620: q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q+1
       627: 2q+1
       629: q+1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: 2q+1
       636: q+1
       637: 1
       638: q+1
       639: 1
       640: q+1
       641: 2q+1
       642: q+1
       643: q+1
       644: 2q+1
       645: 1
       646: q+1
       648: q+1
       662: 1
       669: 1
       671: 1
       673: 1
       679: 1
       681: 1
       683: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       708: q+1
       715: 1
       717: 1
       719: 1
       724: 1
       726: 1
       727: 1
       728: 1
       729: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       754: 1
       760: q+1
       767: 1
       769: 1
       771: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       806: 1
       810: q+1
       812: q+1
       814: q+1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: q+1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       835: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: 2q+1
       844: q+1
       845: 1
       846: q+1
       847: 1
       848: 1
       849: q+1
       852: q+1
       853: 1
       874: 1
       883: 1
       890: 1
       892: 1
       894: 1
       919: 1
       926: 1
       928: 1
       930: 1
       936: 1
       938: 1
       940: 1
       945: 1
       947: 1
       948: 1
       949: 1
       950: 1
       959: 1
       973: 1
       980: 1
       982: 1
       984: 1
       990: 1
       992: 1
       994: 1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1013: 1
      1019: q+1
      1026: 1
      1028: 1
      1030: 1
      1035: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1065: 1
      1099: 1
      1133: 1
      1142: 1
      1149: 1
      1151: 1
      1153: 1
      1185: 1
      1194: 1
      1201: 1
      1203: 1
      1205: 1
      1230: 1
      1237: 1
      1239: 1
      1241: 1
      1247: 1
      1249: 1
      1251: 1
      1256: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1270: 1
      1343: 1
      1390: 1
      1424: 1
      1433: 1
      1440: 1
      1442: 1
      1444: 1
      1597: 1

1598:    0: q^4+3q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: q^4+3q^2+2q+1
         4: q^4+3q^2+2q+1
         5: q^4+3q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^4+3q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^4+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^4+3q^2+2q+1
        19: q^4+3q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: 2q^2+2q+1
        25: 2q+1
        26: q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^4+3q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^4+3q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^4+3q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: q^2+2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: 2q^2+2q+1
        76: 2q+1
        77: q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: 2q^2+2q+1
        89: 2q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^4+3q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       113: 2q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: q^2+2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: q+1
       145: q^2+2q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q+1
       150: q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: q^2+2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: 2q^2+2q+1
       181: 2q+1
       182: q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: 2q+1
       186: 2q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       207: 2q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: q+1
       214: 2q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q+1
       227: q+1
       230: q^2+2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       237: 2q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: 1
       252: q^2+2q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       260: q^2+2q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       267: 2q+1
       268: q+1
       269: 1
       270: 1
       271: q+1
       272: q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: q+1
       277: 2q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 1
       282: q^2+2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: q+1
       299: q^2+2q+1
       300: 2q+1
       301: q+1
       302: 2q+1
       303: 2q+1
       304: q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       313: q+1
       315: q+1
       316: q+1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: 2q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: q+1
       354: 1
       355: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       374: 2q+1
       375: q+1
       376: 1
       377: 1
       378: q+1
       379: q+1
       381: 2q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 2q+1
       388: q+1
       389: q+1
       390: 1
       391: 2q+1
       392: q+1
       394: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       413: 2q+1
       414: q+1
       415: 1
       416: 1
       417: q+1
       418: q+1
       420: 2q+1
       421: q+1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 2q+1
       427: q+1
       428: q+1
       429: 1
       430: 2q+1
       431: q+1
       433: q+1
       436: q^2+2q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       443: 2q+1
       444: q+1
       445: 1
       446: 1
       447: q+1
       448: q+1
       449: 2q+1
       450: q+1
       451: q+1
       452: q+1
       453: 2q+1
       454: 2q+1
       455: q+1
       456: q+1
       457: 1
       458: q^2+2q+1
       459: 2q+1
       460: q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       470: q+1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: q+1
       515: 1
       520: q+1
       522: q+1
       523: q+1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: 2q+1
       553: q+1
       554: 1
       555: 1
       556: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       567: q+1
       569: q+1
       570: q+1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       599: 2q+1
       600: q+1
       601: 1
       602: 1
       603: q+1
       604: 1
       605: q+1
       608: 1
       609: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       621: q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q+1
       628: 2q+1
       629: q+1
       630: 1
       631: 1
       632: q+1
       633: q+1
       635: 2q+1
       636: q+1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 2q+1
       642: q+1
       643: q+1
       644: 1
       645: 2q+1
       646: q+1
       648: q+1
       663: 1
       670: 1
       672: 1
       673: 1
       680: 1
       682: 1
       683: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       702: 1
       709: q+1
       716: 1
       718: 1
       719: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: q+1
       754: 1
       761: q+1
       768: 1
       770: 1
       771: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       801: q+1
       806: 1
       811: q+1
       813: q+1
       814: q+1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       828: q+1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       836: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       843: 2q+1
       844: q+1
       845: 1
       846: 1
       847: q+1
       848: 1
       849: q+1
       852: 1
       853: q+1
       875: 1
       884: 1
       891: 1
       893: 1
       894: 1
       920: 1
       927: 1
       929: 1
       930: 1
       937: 1
       939: 1
       940: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       959: 1
       974: 1
       981: 1
       983: 1
       984: 1
       991: 1
       993: 1
       994: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1013: 1
      1020: q+1
      1027: 1
      1029: 1
      1030: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1060: q+1
      1065: 1
      1100: 1
      1134: 1
      1143: 1
      1150: 1
      1152: 1
      1153: 1
      1186: 1
      1195: 1
      1202: 1
      1204: 1
      1205: 1
      1231: 1
      1238: 1
      1240: 1
      1241: 1
      1248: 1
      1250: 1
      1251: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1270: 1
      1344: 1
      1391: 1
      1425: 1
      1434: 1
      1441: 1
      1443: 1
      1444: 1
      1598: 1

1599:    0: 2q^2+2q+1
         1: q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q+1
         7: q+1
         8: 2q^2+2q+1
         9: q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q+1
        22: q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q+1
        26: 1
        27: 2q^2+2q+1
        28: q+1
        29: q^2+2q+1
        30: q+1
        31: q^2+2q+1
        32: 2q+1
        33: q+1
        34: q+1
        35: 2q^2+2q+1
        36: q+1
        37: 2q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q+1
        42: 2q^2+2q+1
        43: q+1
        44: 2q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: q+1
        58: 1
        59: 1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q+1
        63: 1
        64: q^2+2q+1
        65: q+1
        66: 1
        67: q^2+2q+1
        68: q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q+1
        77: 1
        78: 2q^2+2q+1
        79: q+1
        80: q^2+2q+1
        81: q+1
        82: q^2+2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q+1
        90: 1
        91: 2q^2+2q+1
        92: q+1
        93: q^2+2q+1
        94: q+1
        95: q^2+2q+1
        96: 2q+1
        97: q+1
        98: q+1
        99: 2q^2+2q+1
       100: q+1
       101: 2q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 2q+1
       119: q+1
       120: 1
       121: 1
       122: q^2+2q+1
       123: q+1
       124: q+1
       125: 1
       126: 1
       127: q+1
       128: q^2+2q+1
       129: q+1
       130: 1
       131: 2q+1
       132: q+1
       133: 2q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: 2q+1
       141: q+1
       142: 1
       143: 1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q+1
       147: 1
       148: q^2+2q+1
       149: q+1
       150: 1
       151: q^2+2q+1
       152: q+1
       153: 2q+1
       154: 2q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: 2q+1
       162: q+1
       163: 1
       164: 1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q+1
       168: 1
       169: q^2+2q+1
       170: q+1
       171: 1
       172: q^2+2q+1
       173: q+1
       174: 2q+1
       175: 2q+1
       176: q+1
       177: q+1
       178: q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: q+1
       182: 1
       183: 2q^2+2q+1
       184: q+1
       185: q^2+2q+1
       186: q+1
       187: q^2+2q+1
       188: 2q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 2q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: q+1
       221: 1
       222: 1
       223: q+1
       224: q+1
       225: q+1
       227: 2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 2q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 2q+1
       243: q+1
       244: 1
       245: 1
       246: q^2+2q+1
       247: q+1
       248: q+1
       249: 1
       250: 1
       251: q+1
       252: q^2+2q+1
       253: q+1
       254: 1
       255: 2q+1
       256: q+1
       257: 2q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: 2q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 2q+1
       273: q+1
       274: 1
       275: 1
       276: q^2+2q+1
       277: q+1
       278: q+1
       279: 1
       280: 1
       281: q+1
       282: q^2+2q+1
       283: q+1
       284: 1
       285: 2q+1
       286: q+1
       287: 2q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: 2q+1
       295: q+1
       296: 1
       297: 1
       298: q^2+2q+1
       299: q^2+2q+1
       300: q+1
       301: 1
       302: q^2+2q+1
       303: q+1
       304: 1
       305: q^2+2q+1
       306: q+1
       307: 2q+1
       308: 2q+1
       316: q+1
       317: q+1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 2q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: 2q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 2q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: q+1
       388: 1
       389: 1
       390: q+1
       391: q+1
       392: q+1
       394: 2q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: 2q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 2q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q+1
       427: 1
       428: 1
       429: q+1
       430: q+1
       431: q+1
       433: 2q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: 2q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 2q+1
       449: q+1
       450: 1
       451: 1
       452: q^2+2q+1
       453: q+1
       454: q+1
       455: 1
       456: 1
       457: q+1
       458: q^2+2q+1
       459: q+1
       460: 1
       461: 2q+1
       462: q+1
       463: 2q+1
       471: q+1
       480: 1
       481: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       515: 1
       523: q+1
       524: q+1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 2q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: q+1
       561: q+1
       562: q+1
       570: q+1
       571: q+1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 2q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: q+1
       608: q+1
       609: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: 2q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 2q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: 1
       643: 1
       644: q+1
       645: q+1
       646: q+1
       648: 2q+1
       664: 1
       673: 1
       674: 1
       683: 1
       684: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       710: q+1
       719: 1
       720: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: q+1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       754: 1
       762: q+1
       771: 1
       772: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       787: 1
       788: 1
       789: 1
       790: 1
       791: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       806: 1
       814: q+1
       815: q+1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 2q+1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+1
       852: q+1
       853: q+1
       876: 1
       885: 1
       894: 1
       895: 1
       905: 1
       921: 1
       930: 1
       931: 1
       940: 1
       941: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       959: 1
       975: 1
       984: 1
       985: 1
       994: 1
       995: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1013: 1
      1021: q+1
      1030: 1
      1031: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q+1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1065: 1
      1101: 1
      1135: 1
      1144: 1
      1153: 1
      1154: 1
      1164: 1
      1187: 1
      1196: 1
      1205: 1
      1206: 1
      1216: 1
      1232: 1
      1241: 1
      1242: 1
      1251: 1
      1252: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1270: 1
      1345: 1
      1392: 1
      1426: 1
      1435: 1
      1444: 1
      1445: 1
      1455: 1
      1599: 1

1600:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       120: 2q+1
       121: q+1
       122: q+1
       123: q+1
       125: 2q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       195: 2q+1
       196: q+1
       197: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q+1
       257: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q+1
       287: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       317: q+1
       318: q+1
       325: 2q+1
       326: 1
       327: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       362: 2q+1
       363: q+1
       364: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       401: 2q+1
       402: q+1
       403: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q+1
       463: q+1
       472: q+1
       481: 1
       482: 1
       489: q+1
       490: 1
       491: 1
       498: q+1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: 1
       524: q+1
       525: q+1
       532: 2q+1
       533: 1
       534: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       554: 1
       555: 1
       556: 1
       557: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       571: q+1
       572: q+1
       579: 2q+1
       580: 1
       581: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       601: 1
       602: 1
       603: 1
       604: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       616: 2q+1
       617: q+1
       618: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       665: 1
       674: 1
       675: 1
       684: 1
       685: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       711: q+1
       720: 1
       721: 1
       728: q+1
       729: 1
       730: 1
       737: q+1
       738: 1
       739: 1
       744: 1
       745: 1
       746: 1
       747: 1
       751: 1
       752: 1
       753: 1
       754: 1
       763: q+1
       772: 1
       773: 1
       780: q+1
       781: 1
       782: 1
       789: q+1
       790: 1
       791: 1
       796: 1
       797: 1
       798: 1
       799: 1
       803: 1
       804: 1
       805: 1
       806: 1
       815: q+1
       816: q+1
       823: 2q+1
       824: 1
       825: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       845: 1
       846: 1
       847: 1
       848: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       877: 1
       886: 1
       895: 1
       896: 1
       903: 1
       922: 1
       931: 1
       932: 1
       941: 1
       942: 1
       949: 1
       950: 1
       951: 1
       956: 1
       957: 1
       958: 1
       976: 1
       985: 1
       986: 1
       995: 1
       996: 1
      1003: 1
      1004: 1
      1005: 1
      1010: 1
      1011: 1
      1012: 1
      1022: q+1
      1031: 1
      1032: 1
      1039: q+1
      1040: 1
      1041: 1
      1048: q+1
      1049: 1
      1050: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1102: 1
      1136: 1
      1145: 1
      1154: 1
      1155: 1
      1162: 1
      1188: 1
      1197: 1
      1206: 1
      1207: 1
      1214: 1
      1233: 1
      1242: 1
      1243: 1
      1252: 1
      1253: 1
      1260: 1
      1261: 1
      1262: 1
      1267: 1
      1268: 1
      1269: 1
      1346: 1
      1393: 1
      1427: 1
      1436: 1
      1445: 1
      1446: 1
      1453: 1
      1600: 1

1601:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       702: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       817: 1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       887: 1
       897: 1
       905: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1103: 1
      1146: 1
      1156: 1
      1164: 1
      1198: 1
      1208: 1
      1216: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1347: 1
      1394: 1
      1437: 1
      1447: 1
      1455: 1
      1601: 1

1602:    0: q^2+q+1
         1: q^2+q+1
         2: 1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: 1
         7: 1
         8: 1
         9: q^2+q+1
        10: 1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: 1
        15: q^2+q+1
        16: q^2+q+1
        17: 1
        18: q^2+q+1
        19: q^2+q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q^2+q+1
        29: 1
        30: q^2+q+1
        31: 1
        32: q^2+q+1
        33: 1
        34: 1
        35: 1
        36: q^2+q+1
        37: 1
        38: q^2+q+1
        39: q^2+q+1
        40: 1
        41: 1
        42: 1
        43: q^2+q+1
        44: 1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: 1
        49: q^2+q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q^2+q+1
        69: 1
        70: q^2+q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q^2+q+1
        80: 1
        81: q^2+q+1
        82: 1
        83: q^2+q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q^2+q+1
        93: 1
        94: q^2+q+1
        95: 1
        96: q^2+q+1
        97: 1
        98: 1
        99: 1
       100: q^2+q+1
       101: 1
       102: q^2+q+1
       103: q^2+q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q^2+q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q^2+q+1
       153: 1
       154: q^2+q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q^2+q+1
       174: 1
       175: q^2+q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q^2+q+1
       185: 1
       186: q^2+q+1
       187: 1
       188: q^2+q+1
       189: 1
       190: 1
       196: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q^2+q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+q+1
       307: 1
       308: q^2+q+1
       310: 1
       319: 1
       320: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+q+1
       463: 1
       474: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       517: 1
       526: 1
       527: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: 1
       573: 1
       574: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       617: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       667: 1
       677: 1
       686: 1
       687: 1
       693: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       713: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       765: 1
       774: 1
       775: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: 1
       817: 1
       818: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       888: 1
       897: 1
       898: 1
       904: 1
       924: 1
       934: 1
       943: 1
       944: 1
       950: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       978: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1024: 1
      1033: 1
      1034: 1
      1040: 1
      1042: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1104: 1
      1147: 1
      1156: 1
      1157: 1
      1163: 1
      1199: 1
      1208: 1
      1209: 1
      1215: 1
      1235: 1
      1245: 1
      1254: 1
      1255: 1
      1261: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1348: 1
      1395: 1
      1438: 1
      1447: 1
      1448: 1
      1454: 1
      1602: 1

1603:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: 2q+1
         8: 1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: 1
        21: 2q+1
        22: 1
        23: 1
        24: 1
        25: 2q+1
        26: 2q+1
        27: 1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: 2q+1
        35: 1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: 2q+1
        42: 1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 2q+1
        59: 1
        60: 1
        61: 1
        62: 2q+1
        63: 2q+1
        64: 1
        65: 2q+1
        66: 2q+1
        67: 1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 1
        72: 2q+1
        73: 1
        74: 1
        75: 1
        76: 2q+1
        77: 2q+1
        78: 1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 1
        85: 2q+1
        86: 1
        87: 1
        88: 1
        89: 2q+1
        90: 2q+1
        91: 1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: 2q+1
        99: 1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 2q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 2q+1
       126: 1
       127: 1
       128: 1
       129: 2q+1
       130: 2q+1
       131: 1
       132: 2q+1
       133: 2q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 2q+1
       143: 1
       144: 1
       145: 1
       146: 2q+1
       147: 2q+1
       148: 1
       149: 2q+1
       150: 2q+1
       151: 1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 2q+1
       164: 1
       165: 1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 1
       170: 2q+1
       171: 2q+1
       172: 1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 1
       177: 2q+1
       178: 1
       179: 1
       180: 1
       181: 2q+1
       182: 2q+1
       183: 1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: 1
       191: 1
       192: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: 2q+1
       226: 2q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 2q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 2q+1
       250: 1
       251: 1
       252: 1
       253: 2q+1
       254: 2q+1
       255: 1
       256: 2q+1
       257: 2q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 2q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 2q+1
       280: 1
       281: 1
       282: 1
       283: 2q+1
       284: 2q+1
       285: 1
       286: 2q+1
       287: 2q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 2q+1
       297: 1
       298: 1
       299: 1
       300: 2q+1
       301: 2q+1
       302: 1
       303: 2q+1
       304: 2q+1
       305: 1
       306: 2q+1
       307: 2q+1
       308: 2q+1
       311: 1
       320: 1
       321: 1
       322: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 2q+1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: 2q+1
       393: 2q+1
       394: 1
       396: 1
       397: 1
       398: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: 2q+1
       432: 2q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 2q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 2q+1
       456: 1
       457: 1
       458: 1
       459: 2q+1
       460: 2q+1
       461: 1
       462: 2q+1
       463: 2q+1
       475: 1
       484: 1
       485: 1
       486: 1
       489: 1
       493: 1
       494: 1
       495: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       527: 1
       528: 1
       529: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 2q+1
       560: 1
       561: 1
       562: 1
       565: 1
       574: 1
       575: 1
       576: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 2q+1
       607: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: 2q+1
       647: 2q+1
       648: 1
       668: 1
       678: 1
       687: 1
       688: 1
       689: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       714: 1
       723: 1
       724: 1
       725: 1
       728: 1
       732: 1
       733: 1
       734: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       766: 1
       775: 1
       776: 1
       777: 1
       780: 1
       784: 1
       785: 1
       786: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: 1
       818: 1
       819: 1
       820: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 2q+1
       851: 1
       852: 1
       853: 1
       889: 1
       898: 1
       899: 1
       900: 1
       903: 1
       925: 1
       935: 1
       944: 1
       945: 1
       946: 1
       949: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       979: 1
       989: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1025: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1105: 1
      1148: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1200: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1236: 1
      1246: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1349: 1
      1396: 1
      1439: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1603: 1

1604:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        52: 1
        53: 1
        54: 1
        57: 1
        58: 1
        59: 1
        60: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
       112: 1
       114: 1
       115: 1
       116: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       141: 1
       142: 1
       143: 1
       144: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: 1
       193: 1
       199: 1
       201: 1
       202: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       215: 1
       216: 1
       217: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: 1
       231: 1
       232: 1
       236: 1
       238: 1
       239: 1
       240: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       278: 1
       279: 1
       280: 1
       281: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       321: 1
       323: 1
       329: 1
       331: 1
       332: 1
       337: 1
       339: 1
       340: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: 1
       360: 1
       366: 1
       368: 1
       369: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       419: 1
       421: 1
       422: 1
       423: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       476: 1
       485: 1
       487: 1
       494: 1
       496: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: 1
       528: 1
       530: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       591: 1
       593: 1
       594: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       669: 1
       679: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       715: 1
       724: 1
       726: 1
       733: 1
       735: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       767: 1
       776: 1
       778: 1
       785: 1
       787: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       810: 1
       819: 1
       821: 1
       827: 1
       829: 1
       830: 1
       835: 1
       837: 1
       838: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       890: 1
       899: 1
       901: 1
       926: 1
       936: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       980: 1
       990: 1
       999: 1
      1001: 1
      1007: 1
      1009: 1
      1010: 1
      1026: 1
      1035: 1
      1037: 1
      1044: 1
      1046: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1106: 1
      1149: 1
      1158: 1
      1160: 1
      1201: 1
      1210: 1
      1212: 1
      1237: 1
      1247: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1267: 1
      1350: 1
      1397: 1
      1440: 1
      1449: 1
      1451: 1
      1604: 1

1605:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       192: 1
       193: 1
       195: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       313: 1
       322: 1
       323: 1
       325: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       359: 1
       360: 1
       362: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       398: 1
       399: 1
       401: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       477: 1
       486: 1
       487: 1
       489: 1
       495: 1
       496: 1
       498: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       520: 1
       529: 1
       530: 1
       532: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       567: 1
       576: 1
       577: 1
       579: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       613: 1
       614: 1
       616: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       670: 1
       680: 1
       689: 1
       690: 1
       692: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       716: 1
       725: 1
       726: 1
       728: 1
       734: 1
       735: 1
       737: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       768: 1
       777: 1
       778: 1
       780: 1
       786: 1
       787: 1
       789: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       811: 1
       820: 1
       821: 1
       823: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       891: 1
       900: 1
       901: 1
       903: 1
       927: 1
       937: 1
       946: 1
       947: 1
       949: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       981: 1
       991: 1
      1000: 1
      1001: 1
      1003: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1027: 1
      1036: 1
      1037: 1
      1039: 1
      1045: 1
      1046: 1
      1048: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1107: 1
      1150: 1
      1159: 1
      1160: 1
      1162: 1
      1202: 1
      1211: 1
      1212: 1
      1214: 1
      1238: 1
      1248: 1
      1257: 1
      1258: 1
      1260: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1351: 1
      1398: 1
      1441: 1
      1450: 1
      1451: 1
      1453: 1
      1605: 1

1606:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       191: 1
       194: 1
       195: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       314: 1
       321: 1
       324: 1
       325: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       358: 1
       361: 1
       362: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       397: 1
       400: 1
       401: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       478: 1
       485: 1
       488: 1
       489: 1
       494: 1
       497: 1
       498: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       521: 1
       528: 1
       531: 1
       532: 1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       568: 1
       575: 1
       578: 1
       579: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       612: 1
       615: 1
       616: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       671: 1
       681: 1
       688: 1
       691: 1
       692: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       717: 1
       724: 1
       727: 1
       728: 1
       733: 1
       736: 1
       737: 1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       769: 1
       776: 1
       779: 1
       780: 1
       785: 1
       788: 1
       789: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       812: 1
       819: 1
       822: 1
       823: 1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       892: 1
       899: 1
       902: 1
       903: 1
       928: 1
       938: 1
       945: 1
       948: 1
       949: 1
       953: 1
       955: 1
       956: 1
       957: 1
       958: 1
       982: 1
       992: 1
       999: 1
      1002: 1
      1003: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1028: 1
      1035: 1
      1038: 1
      1039: 1
      1044: 1
      1047: 1
      1048: 1
      1052: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1108: 1
      1151: 1
      1158: 1
      1161: 1
      1162: 1
      1203: 1
      1210: 1
      1213: 1
      1214: 1
      1239: 1
      1249: 1
      1256: 1
      1259: 1
      1260: 1
      1264: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1352: 1
      1399: 1
      1442: 1
      1449: 1
      1452: 1
      1453: 1
      1606: 1

1607:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: 1
        52: 1
        53: 1
        55: 1
        57: 1
        58: 1
        59: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: 1
       107: 1
       109: 1
       113: 1
       114: 1
       115: 1
       117: 1
       119: 1
       120: 1
       121: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       158: 1
       160: 1
       162: 1
       163: 1
       164: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: 1
       194: 1
       200: 1
       201: 1
       203: 1
       207: 1
       208: 1
       209: 1
       211: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       243: 1
       244: 1
       245: 1
       247: 1
       248: 1
       249: 1
       250: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       263: 1
       267: 1
       268: 1
       269: 1
       271: 1
       273: 1
       274: 1
       275: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       315: 1
       322: 1
       324: 1
       330: 1
       331: 1
       333: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       374: 1
       375: 1
       376: 1
       378: 1
       381: 1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       400: 1
       406: 1
       407: 1
       409: 1
       413: 1
       414: 1
       415: 1
       417: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       449: 1
       450: 1
       451: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       479: 1
       486: 1
       488: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       537: 1
       538: 1
       540: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       569: 1
       576: 1
       578: 1
       584: 1
       585: 1
       587: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       628: 1
       629: 1
       630: 1
       632: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       672: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       718: 1
       725: 1
       727: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       770: 1
       777: 1
       779: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       813: 1
       820: 1
       822: 1
       828: 1
       829: 1
       831: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       893: 1
       900: 1
       902: 1
       929: 1
       939: 1
       946: 1
       948: 1
       954: 1
       955: 1
       957: 1
       983: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1029: 1
      1036: 1
      1038: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1109: 1
      1152: 1
      1159: 1
      1161: 1
      1204: 1
      1211: 1
      1213: 1
      1240: 1
      1250: 1
      1257: 1
      1259: 1
      1265: 1
      1266: 1
      1268: 1
      1353: 1
      1400: 1
      1443: 1
      1450: 1
      1452: 1
      1607: 1

1608:    0: q^2+2q+1
         1: q^2+2q+1
         2: 2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: 2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: 2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: q+1
        24: q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: q^2+2q+1
        37: 2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: q^2+2q+1
        44: 2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: 2q+1
        49: q^2+2q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: 2q+1
        60: q+1
        61: q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: q+1
        88: q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: q^2+2q+1
       101: 2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: 2q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: 2q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: 2q+1
       144: q+1
       145: q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: 2q+1
       165: q+1
       166: q+1
       167: q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: q+1
       181: q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: 2q+1
       186: q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       193: 1
       194: 1
       195: 1
       196: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: 1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: q+1
       225: q+1
       226: 2q+1
       227: 2q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: 2q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 2q+1
       251: q+1
       252: q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: 2q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: 2q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: 2q+1
       281: q+1
       282: q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: 2q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: 2q+1
       298: q+1
       299: q+1
       300: q+1
       301: 2q+1
       302: 2q+1
       303: q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       316: 1
       323: 1
       324: 1
       325: 1
       326: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: 1
       351: q+1
       352: q+1
       353: 2q+1
       354: q+1
       355: q+1
       360: 1
       361: 1
       362: 1
       363: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: 1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: 2q+1
       390: q+1
       391: q+1
       392: q+1
       393: 2q+1
       394: 2q+1
       399: 1
       400: 1
       401: 1
       402: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: 1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: 2q+1
       429: q+1
       430: q+1
       431: q+1
       432: 2q+1
       433: 2q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: q+1
       445: 1
       446: q+1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: 2q+1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: 2q+1
       457: q+1
       458: q+1
       459: q+1
       460: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: 2q+1
       480: 1
       487: 1
       488: 1
       489: 1
       490: 1
       496: 1
       497: 1
       498: 1
       499: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       511: q+1
       512: 1
       513: q+1
       514: q+1
       515: 1
       523: 1
       530: 1
       531: 1
       532: 1
       533: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: 2q+1
       561: q+1
       562: q+1
       570: 1
       577: 1
       578: 1
       579: 1
       580: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: 1
       605: q+1
       606: q+1
       607: 2q+1
       608: q+1
       609: q+1
       614: 1
       615: 1
       616: 1
       617: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: q+1
       630: 1
       631: q+1
       632: q+1
       633: 1
       636: q+1
       637: 1
       638: q+1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: 2q+1
       644: q+1
       645: q+1
       646: q+1
       647: 2q+1
       648: 2q+1
       673: 1
       683: 1
       690: 1
       691: 1
       692: 1
       693: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       719: 1
       726: 1
       727: 1
       728: 1
       729: 1
       735: 1
       736: 1
       737: 1
       738: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       750: q+1
       751: 1
       752: q+1
       753: q+1
       754: 1
       771: 1
       778: 1
       779: 1
       780: 1
       781: 1
       787: 1
       788: 1
       789: 1
       790: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       802: q+1
       803: 1
       804: q+1
       805: q+1
       806: 1
       814: 1
       821: 1
       822: 1
       823: 1
       824: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: 1
       849: q+1
       850: q+1
       851: 2q+1
       852: q+1
       853: q+1
       894: 1
       901: 1
       902: 1
       903: 1
       904: 1
       930: 1
       940: 1
       947: 1
       948: 1
       949: 1
       950: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       984: 1
       994: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1030: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1061: q+1
      1062: 1
      1063: q+1
      1064: q+1
      1065: 1
      1110: 1
      1153: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1205: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1241: 1
      1251: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1354: 1
      1401: 1
      1444: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1608: 1

1609:    0: q^2+q+1
         1: q^2+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+1
         7: 1
         8: q+1
         9: q^2+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        21: 1
        22: 1
        23: q+1
        24: q+1
        25: q^2+1
        26: 1
        27: q+1
        28: q^2+1
        29: q^2+q+1
        30: q^2+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+1
        34: 1
        35: q+1
        36: q^2+1
        37: q^2+q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q^2+1
        41: 1
        42: q+1
        43: q^2+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+1
        48: q^2+q+1
        49: q^2+q+1
        53: 1
        54: 1
        55: 1
        56: q+1
        58: 1
        59: 1
        60: q+1
        61: q+1
        62: q^2+1
        63: 1
        64: q+1
        65: q^2+1
        66: 1
        67: q+1
        68: q^2+1
        69: q^2+q+1
        70: q^2+q+1
        72: 1
        73: 1
        74: q+1
        75: q+1
        76: q^2+1
        77: 1
        78: q+1
        79: q^2+1
        80: q^2+q+1
        81: q^2+1
        82: q^2+q+1
        83: q^2+q+1
        85: 1
        86: 1
        87: q+1
        88: q+1
        89: q^2+1
        90: 1
        91: q+1
        92: q^2+1
        93: q^2+q+1
        94: q^2+1
        95: q^2+q+1
        96: q^2+q+1
        97: q^2+1
        98: 1
        99: q+1
       100: q^2+1
       101: q^2+q+1
       102: q^2+q+1
       103: q^2+q+1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       120: 1
       121: 1
       122: q+1
       123: q+1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: q^2+1
       130: 1
       131: q+1
       132: q^2+1
       133: q^2+q+1
       137: 1
       138: 1
       139: 1
       140: q+1
       142: 1
       143: 1
       144: q+1
       145: q+1
       146: q^2+1
       147: 1
       148: q+1
       149: q^2+1
       150: 1
       151: q+1
       152: q^2+1
       153: q^2+q+1
       154: q^2+q+1
       158: 1
       159: 1
       160: 1
       161: q+1
       163: 1
       164: 1
       165: q+1
       166: q+1
       167: q^2+1
       168: 1
       169: q+1
       170: q^2+1
       171: 1
       172: q+1
       173: q^2+1
       174: q^2+q+1
       175: q^2+q+1
       177: 1
       178: 1
       179: q+1
       180: q+1
       181: q^2+1
       182: 1
       183: q+1
       184: q^2+1
       185: q^2+q+1
       186: q^2+1
       187: q^2+q+1
       188: q^2+q+1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       216: 1
       217: 1
       218: 1
       219: q+1
       221: 1
       222: 1
       223: q+1
       224: q+1
       225: q^2+1
       226: 1
       227: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: q^2+1
       254: 1
       255: q+1
       256: q^2+1
       257: q^2+q+1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       279: 1
       280: 1
       281: q+1
       282: q+1
       283: q^2+1
       284: 1
       285: q+1
       286: q^2+1
       287: q^2+q+1
       291: 1
       292: 1
       293: 1
       294: q+1
       296: 1
       297: 1
       298: q+1
       299: q+1
       300: q^2+1
       301: 1
       302: q+1
       303: q^2+1
       304: 1
       305: q+1
       306: q^2+1
       307: q^2+q+1
       308: q^2+q+1
       317: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       383: 1
       384: 1
       385: 1
       386: q+1
       388: 1
       389: 1
       390: q+1
       391: q+1
       392: q^2+1
       393: 1
       394: q+1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       422: 1
       423: 1
       424: 1
       425: q+1
       427: 1
       428: 1
       429: q+1
       430: q+1
       431: q^2+1
       432: 1
       433: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       450: 1
       451: 1
       452: q+1
       453: q+1
       455: 1
       456: 1
       457: q+1
       458: q+1
       459: q^2+1
       460: 1
       461: q+1
       462: q^2+1
       463: q^2+q+1
       481: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       524: 1
       532: 1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       556: 1
       557: q+1
       559: 1
       560: 1
       561: q+1
       562: q+1
       571: 1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       603: 1
       604: q+1
       606: 1
       607: 1
       608: q+1
       609: q+1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       637: 1
       638: 1
       639: 1
       640: q+1
       642: 1
       643: 1
       644: q+1
       645: q+1
       646: q^2+1
       647: 1
       648: q+1
       674: 1
       684: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       702: 1
       720: 1
       728: 1
       729: 1
       730: 1
       737: 1
       738: 1
       739: 1
       744: 1
       745: 1
       746: 1
       747: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       772: 1
       780: 1
       781: 1
       782: 1
       789: 1
       790: 1
       791: 1
       796: 1
       797: 1
       798: 1
       799: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       815: 1
       823: 1
       824: 1
       825: 1
       830: 1
       831: 1
       832: 1
       833: 1
       838: 1
       839: 1
       840: 1
       841: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       850: 1
       851: 1
       852: q+1
       853: q+1
       895: 1
       903: 1
       904: 1
       905: 1
       931: 1
       941: 1
       949: 1
       950: 1
       951: 1
       956: 1
       957: 1
       958: 1
       959: 1
       985: 1
       995: 1
      1003: 1
      1004: 1
      1005: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1031: 1
      1039: 1
      1040: 1
      1041: 1
      1048: 1
      1049: 1
      1050: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1111: 1
      1154: 1
      1162: 1
      1163: 1
      1164: 1
      1206: 1
      1214: 1
      1215: 1
      1216: 1
      1242: 1
      1252: 1
      1260: 1
      1261: 1
      1262: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1355: 1
      1402: 1
      1445: 1
      1453: 1
      1454: 1
      1455: 1
      1609: 1

1610:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        22: 1
        23: 1
        24: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        54: 1
        55: 1
        56: 1
        59: 1
        60: 1
        61: 1
        63: 1
        64: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        73: 1
        74: 1
        75: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        86: 1
        87: 1
        88: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       110: 1
       111: 1
       116: 1
       117: 1
       118: 1
       121: 1
       122: 1
       123: 1
       126: 1
       127: 1
       128: 1
       130: 1
       131: 1
       132: 1
       133: 1
       138: 1
       139: 1
       140: 1
       143: 1
       144: 1
       145: 1
       147: 1
       148: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       159: 1
       160: 1
       161: 1
       164: 1
       165: 1
       166: 1
       168: 1
       169: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       178: 1
       179: 1
       180: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       196: 1
       197: 1
       204: 1
       205: 1
       210: 1
       211: 1
       212: 1
       217: 1
       218: 1
       219: 1
       222: 1
       223: 1
       224: 1
       226: 1
       227: 1
       234: 1
       235: 1
       240: 1
       241: 1
       242: 1
       245: 1
       246: 1
       247: 1
       250: 1
       251: 1
       252: 1
       254: 1
       255: 1
       256: 1
       257: 1
       264: 1
       265: 1
       270: 1
       271: 1
       272: 1
       275: 1
       276: 1
       277: 1
       280: 1
       281: 1
       282: 1
       284: 1
       285: 1
       286: 1
       287: 1
       292: 1
       293: 1
       294: 1
       297: 1
       298: 1
       299: 1
       301: 1
       302: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       318: 1
       326: 1
       327: 1
       334: 1
       335: 1
       342: 1
       343: 1
       348: 1
       349: 1
       350: 1
       353: 1
       354: 1
       355: 1
       363: 1
       364: 1
       371: 1
       372: 1
       377: 1
       378: 1
       379: 1
       384: 1
       385: 1
       386: 1
       389: 1
       390: 1
       391: 1
       393: 1
       394: 1
       402: 1
       403: 1
       410: 1
       411: 1
       416: 1
       417: 1
       418: 1
       423: 1
       424: 1
       425: 1
       428: 1
       429: 1
       430: 1
       432: 1
       433: 1
       440: 1
       441: 1
       446: 1
       447: 1
       448: 1
       451: 1
       452: 1
       453: 1
       456: 1
       457: 1
       458: 1
       460: 1
       461: 1
       462: 1
       463: 1
       482: 1
       490: 1
       491: 1
       499: 1
       500: 1
       507: 1
       508: 1
       513: 1
       514: 1
       515: 1
       525: 1
       533: 1
       534: 1
       541: 1
       542: 1
       549: 1
       550: 1
       555: 1
       556: 1
       557: 1
       560: 1
       561: 1
       562: 1
       572: 1
       580: 1
       581: 1
       588: 1
       589: 1
       596: 1
       597: 1
       602: 1
       603: 1
       604: 1
       607: 1
       608: 1
       609: 1
       617: 1
       618: 1
       625: 1
       626: 1
       631: 1
       632: 1
       633: 1
       638: 1
       639: 1
       640: 1
       643: 1
       644: 1
       645: 1
       647: 1
       648: 1
       675: 1
       685: 1
       693: 1
       694: 1
       701: 1
       702: 1
       721: 1
       729: 1
       730: 1
       738: 1
       739: 1
       746: 1
       747: 1
       752: 1
       753: 1
       754: 1
       773: 1
       781: 1
       782: 1
       790: 1
       791: 1
       798: 1
       799: 1
       804: 1
       805: 1
       806: 1
       816: 1
       824: 1
       825: 1
       832: 1
       833: 1
       840: 1
       841: 1
       846: 1
       847: 1
       848: 1
       851: 1
       852: 1
       853: 1
       896: 1
       904: 1
       905: 1
       932: 1
       942: 1
       950: 1
       951: 1
       958: 1
       959: 1
       986: 1
       996: 1
      1004: 1
      1005: 1
      1012: 1
      1013: 1
      1032: 1
      1040: 1
      1041: 1
      1049: 1
      1050: 1
      1057: 1
      1058: 1
      1063: 1
      1064: 1
      1065: 1
      1112: 1
      1155: 1
      1163: 1
      1164: 1
      1207: 1
      1215: 1
      1216: 1
      1243: 1
      1253: 1
      1261: 1
      1262: 1
      1269: 1
      1270: 1
      1356: 1
      1403: 1
      1446: 1
      1454: 1
      1455: 1
      1610: 1

1611:    0: q^4+2q^3+3q^2+2q+1
         1: q^4+2q^3+3q^2+2q+1
         2: q^4+2q^3+3q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^4+2q^3+3q^2+2q+1
         7: q^4+2q^3+3q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^4+2q^3+3q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^3+2q^2+2q+1
        58: q^3+2q^2+2q+1
        59: q^3+2q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^3+2q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^3+2q^2+2q+1
       115: q^3+2q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q^2+2q+1
       126: q+1
       127: 1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q+1
       148: 1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^3+2q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^3+2q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: 1
       224: 1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: q^2+2q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+2q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: q+1
       241: q^2+2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: q+1
       249: q^2+2q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: q^2+2q+1
       262: q^2+2q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+2q+1
       267: q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q^2+2q+1
       271: q+1
       272: q+1
       273: q+1
       274: q^2+2q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q+1
       293: q+1
       294: q+1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q^2+2q+1
       310: q^2+2q+1
       311: q^2+2q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q^2+2q+1
       318: q^2+2q+1
       319: q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q^2+2q+1
       353: q+1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+2q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q+1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q^2+2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q^2+2q+1
       406: q+1
       407: q^2+2q+1
       408: q^2+2q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q^2+2q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q^2+2q+1
       465: q^2+2q+1
       466: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: q+1
       472: q^2+2q+1
       473: q+1
       474: q+1
       475: q^2+2q+1
       476: q+1
       477: 1
       478: 1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       521: 1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q^2+2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q^2+2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q^2+2q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       646: q+1
       647: q+1
       648: 1
       649: q^2+2q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: 1
       707: 1
       708: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       717: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       736: q+1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: q+1
       756: q+1
       757: 1
       758: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       850: q+1
       851: 1
       854: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: q+1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       960: q+1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1014: q+1
      1015: q+1
      1016: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1045: 1
      1047: 1
      1054: 1
      1061: 1
      1062: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1141: 1
      1145: 1
      1158: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: 1
      1188: 1
      1211: 1
      1217: q+1
      1218: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1237: 1
      1250: 1
      1266: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1293: 1
      1301: 1
      1302: 1
      1309: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1404: 1
      1411: 1
      1412: 1
      1418: 1
      1456: 1
      1457: 1
      1458: 1
      1478: 1
      1490: 1
      1528: 1
      1569: 1
      1611: 1

1612:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^3+2q^2+2q+1
        58: q^3+2q^2+2q+1
        59: q^3+2q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: q^2+2q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^3+2q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^3+2q^2+2q+1
       115: q^3+2q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: q^2+2q+1
       197: q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^3+2q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: q^2+2q+1
       206: q^2+2q+1
       207: q+1
       208: q^2+2q+1
       209: q+1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: q+1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: q+1
       262: q+1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: q+1
       310: q^2+2q+1
       311: q^2+2q+1
       312: q^2+2q+1
       313: q+1
       314: q+1
       315: q^2+2q+1
       316: q^2+2q+1
       317: q+1
       318: q+1
       319: q^2+2q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: q^2+2q+1
       326: q^2+2q+1
       327: q+1
       328: q+1
       329: q^2+2q+1
       330: q+1
       331: q+1
       332: q+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q^2+2q+1
       339: q+1
       340: 1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: q+1
       465: q+1
       466: q^2+2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q^2+2q+1
       475: q^2+2q+1
       476: q^2+2q+1
       477: q+1
       478: q+1
       479: q^2+2q+1
       480: q^2+2q+1
       481: q+1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: q+1
       565: 1
       566: q+1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       649: q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: q+1
       657: q+1
       658: q+1
       659: q^2+2q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       666: 1
       667: q+1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: q+1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       836: 1
       844: 1
       849: 1
       850: 1
       851: 1
       854: q+1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: q+1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: 1
       942: 1
       953: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1032: 1
      1061: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1139: 1
      1141: 1
      1142: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1182: 1
      1183: 1
      1186: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1227: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1303: 1
      1311: 1
      1333: 1
      1357: 1
      1371: 1
      1404: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1467: 1
      1471: 1
      1612: 1

1613:    0: q^4+3q^3+2q^2+4q+1
         1: q^3+2q^2+4q+1
         2: q^4+3q^3+2q^2+4q+1
         3: q^4+3q^3+2q^2+4q+1
         4: q^3+q^2+4q+1
         5: q^3+q^2+4q+1
         6: q^3+2q^2+4q+1
         7: q^3+2q^2+4q+1
         8: q^4+3q^3+2q^2+4q+1
         9: q^3+2q^2+4q+1
        10: q^4+3q^3+2q^2+4q+1
        11: q^3+q^2+4q+1
        12: q^3+q^2+4q+1
        13: q^2+4q+1
        14: q^3+q^2+4q+1
        15: q^3+q^2+4q+1
        16: q^2+4q+1
        17: q^3+q^2+4q+1
        18: q^3+q^2+4q+1
        19: q^2+4q+1
        20: q^3+2q^2+4q+1
        21: q^3+2q^2+4q+1
        22: q^3+2q^2+4q+1
        23: q^3+q^2+4q+1
        24: q^3+q^2+4q+1
        25: q^3+2q^2+4q+1
        26: q^3+2q^2+4q+1
        27: q^4+3q^3+2q^2+4q+1
        28: q^2+4q+1
        29: q^3+q^2+4q+1
        30: q^2+4q+1
        31: q^3+q^2+4q+1
        32: q^2+4q+1
        33: q^2+4q+1
        34: q^2+4q+1
        35: q^3+q^2+4q+1
        36: q^2+4q+1
        37: q^3+q^2+4q+1
        38: 2q+1
        39: q^3+q^2+4q+1
        40: q^2+4q+1
        41: q^2+4q+1
        42: q^3+q^2+4q+1
        43: q^2+4q+1
        44: q^3+q^2+4q+1
        45: q^3+q^2+4q+1
        46: 2q+1
        47: q^2+4q+1
        48: q^2+4q+1
        49: q^2+4q+1
        50: 2q+1
        51: 2q+1
        52: q^3+2q^2+4q+1
        53: q^3+2q^2+4q+1
        54: q^2+4q+1
        55: q^2+4q+1
        56: q^2+4q+1
        57: q^3+2q^2+4q+1
        58: q^3+2q^2+4q+1
        59: q^3+2q^2+4q+1
        60: q^3+q^2+4q+1
        61: q^3+q^2+4q+1
        62: q^2+4q+1
        63: q^2+4q+1
        64: q^3+q^2+4q+1
        65: q^2+4q+1
        66: q^2+4q+1
        67: q^3+q^2+4q+1
        68: q^2+4q+1
        69: q^2+4q+1
        70: q^2+4q+1
        71: q^2+4q+1
        72: q^2+4q+1
        73: q^2+4q+1
        74: 2q+1
        75: q^3+q^2+4q+1
        76: q^2+4q+1
        77: 2q+1
        78: q^3+q^2+4q+1
        79: 2q+1
        80: 2q+1
        81: q^2+4q+1
        82: q^3+q^2+4q+1
        83: 2q+1
        84: q^2+4q+1
        85: q^2+4q+1
        86: q^2+4q+1
        87: q^3+q^2+4q+1
        88: 2q+1
        89: q^2+4q+1
        90: 2q+1
        91: q^3+q^2+4q+1
        92: q^2+4q+1
        93: q^3+q^2+4q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+4q+1
        98: q^2+4q+1
        99: q^2+4q+1
       100: q^2+4q+1
       101: q^2+4q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: 2q+1
       106: 2q+1
       107: q^3+2q^2+4q+1
       108: q^2+4q+1
       109: q^2+4q+1
       110: q^2+4q+1
       111: q^2+4q+1
       112: 2q+1
       113: 2q+1
       114: q^3+2q^2+4q+1
       115: q^3+2q^2+4q+1
       116: q^2+4q+1
       117: q^2+4q+1
       118: q^2+4q+1
       119: q^2+4q+1
       120: q^2+4q+1
       121: q^2+4q+1
       122: q^3+q^2+4q+1
       123: 2q+1
       124: q^2+4q+1
       125: q^2+4q+1
       126: q^2+4q+1
       127: 2q+1
       128: q^3+q^2+4q+1
       129: q^2+4q+1
       130: q^2+4q+1
       131: q^2+4q+1
       132: q^2+4q+1
       133: q^2+4q+1
       134: q+1
       135: 2q+1
       136: q^2+4q+1
       137: q^2+4q+1
       138: 2q+1
       139: q^2+4q+1
       140: 2q+1
       141: q^2+4q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: q^3+q^2+4q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: q^2+4q+1
       150: 2q+1
       151: q^3+q^2+4q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: 2q+1
       156: q+1
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^2+4q+1
       160: 2q+1
       161: 2q+1
       162: q^2+4q+1
       163: 2q+1
       164: 2q+1
       165: q^3+q^2+4q+1
       166: 2q+1
       167: q^2+4q+1
       168: 2q+1
       169: q^3+q^2+4q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: q^2+4q+1
       177: q^2+4q+1
       178: q^2+4q+1
       179: 2q+1
       180: 2q+1
       181: q^2+4q+1
       182: q+1
       183: q^2+4q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: 2q+1
       193: q^2+4q+1
       194: q^2+4q+1
       195: q^2+4q+1
       196: q^2+4q+1
       197: q^2+4q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       201: q^3+2q^2+4q+1
       202: q^2+4q+1
       203: q^2+4q+1
       204: q^2+4q+1
       205: q^2+4q+1
       206: 2q+1
       207: q+1
       208: q^2+4q+1
       209: q^2+4q+1
       210: q^2+4q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: 2q+1
       215: q^2+4q+1
       216: q^2+4q+1
       217: 2q+1
       218: q^2+4q+1
       219: 2q+1
       220: q^2+4q+1
       221: q^2+4q+1
       222: q^2+4q+1
       223: 2q+1
       224: 2q+1
       225: q^2+4q+1
       226: q+1
       227: q^2+4q+1
       228: 1
       229: q+1
       230: 2q+1
       231: q^2+4q+1
       232: 2q+1
       233: q^2+4q+1
       234: 2q+1
       235: 2q+1
       236: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: 2q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: 2q+1
       248: q^2+4q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: q^3+q^2+4q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       258: 1
       259: 2q+1
       260: q+1
       261: q^2+4q+1
       262: q^2+4q+1
       263: 2q+1
       264: 2q+1
       265: 2q+1
       266: 2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: 2q+1
       273: q^2+4q+1
       274: 2q+1
       275: 2q+1
       276: q^3+q^2+4q+1
       277: 2q+1
       278: 2q+1
       279: q+1
       280: q+1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       287: 2q+1
       288: q+1
       289: q+1
       290: q^2+4q+1
       291: q^2+4q+1
       292: 2q+1
       293: 2q+1
       294: q+1
       295: q^2+4q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 1
       302: 2q+1
       303: 2q+1
       304: 1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: q^2+4q+1
       317: q^2+4q+1
       318: q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: q^2+4q+1
       324: q^2+4q+1
       325: q^2+4q+1
       326: q^2+4q+1
       327: q^2+4q+1
       328: 1
       329: 2q+1
       330: q+1
       331: q^2+4q+1
       332: q^2+4q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: q+1
       338: 2q+1
       339: q^2+4q+1
       340: 2q+1
       341: q^2+4q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: q+1
       346: q^2+4q+1
       347: q^2+4q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: q^2+4q+1
       352: q+1
       353: q+1
       354: 2q+1
       355: 2q+1
       356: 1
       357: 1
       358: q+1
       359: 2q+1
       360: 2q+1
       361: q^2+4q+1
       362: 2q+1
       363: 2q+1
       364: 2q+1
       365: 1
       366: 1
       367: q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 2q+1
       373: q+1
       375: q+1
       376: q+1
       377: q+1
       380: q+1
       381: 2q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: 2q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: 2q+1
       392: 2q+1
       393: 1
       394: 2q+1
       395: 1
       396: 1
       397: 2q+1
       398: q+1
       399: q^2+4q+1
       400: 2q+1
       401: 2q+1
       402: 2q+1
       403: 2q+1
       404: 1
       405: q+1
       406: 1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 2q+1
       412: 2q+1
       413: q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: 2q+1
       420: q+1
       421: q+1
       422: q+1
       424: q+1
       426: 2q+1
       427: q+1
       428: q+1
       430: 2q+1
       431: 2q+1
       432: 1
       433: 2q+1
       434: 1
       435: q+1
       436: q+1
       437: q^2+4q+1
       438: 2q+1
       439: 2q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: q+1
       449: 2q+1
       450: 1
       451: 1
       452: 2q+1
       454: 2q+1
       455: 1
       456: 1
       458: 2q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: q+1
       470: q+1
       471: q^2+4q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: q^2+4q+1
       481: q^2+4q+1
       482: q+1
       483: 1
       484: 1
       485: 2q+1
       486: q+1
       487: q^2+4q+1
       488: 2q+1
       489: 2q+1
       490: 2q+1
       491: 2q+1
       492: 1
       493: 1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: q^2+4q+1
       498: 2q+1
       499: 2q+1
       500: 2q+1
       501: 1
       502: q+1
       503: q+1
       504: q^2+4q+1
       505: 2q+1
       506: 2q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: q+1
       522: 2q+1
       523: 2q+1
       524: 2q+1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: 2q+1
       532: q+1
       533: q+1
       534: 2q+1
       536: 1
       538: q+1
       539: q+1
       543: 1
       544: 1
       545: q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 2q+1
       551: q+1
       553: q+1
       554: q+1
       555: q+1
       558: 2q+1
       559: 1
       560: 1
       561: 2q+1
       563: 1
       564: 1
       565: 1
       566: 2q+1
       567: q+1
       569: q+1
       570: 2q+1
       571: 2q+1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: 2q+1
       578: q+1
       579: q+1
       580: q+1
       581: 2q+1
       582: 1
       583: q+1
       584: 1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 2q+1
       592: 1
       593: q+1
       595: q+1
       599: q+1
       600: q+1
       601: q+1
       603: q+1
       605: 2q+1
       606: 1
       607: 1
       609: 2q+1
       610: 1
       611: 1
       612: q+1
       613: q+1
       614: 2q+1
       615: 2q+1
       616: q+1
       617: q+1
       618: q+1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: q+1
       627: q+1
       629: 1
       630: 1
       631: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: 1
       643: 1
       646: q+1
       647: 1
       648: q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: q+1
       655: q+1
       656: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: q^2+4q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: 2q+1
       670: q+1
       672: q+1
       673: 2q+1
       674: 2q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       681: q+1
       682: 2q+1
       683: 2q+1
       684: 2q+1
       685: 1
       686: 1
       687: 1
       688: q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: 1
       705: 1
       707: 1
       708: q+1
       710: 2q+1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: q+1
       719: q+1
       720: q+1
       721: 1
       724: 1
       726: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: 2q+1
       737: q+1
       738: q+1
       739: 2q+1
       741: 1
       743: q+1
       744: q+1
       748: q+1
       750: 1
       751: 1
       752: 1
       756: 1
       757: 1
       758: 1
       761: q+1
       762: 2q+1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       770: 1
       771: q+1
       772: q+1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       779: q+1
       780: q+1
       781: q+1
       782: 2q+1
       786: 1
       788: q+1
       794: 1
       795: q+1
       797: q+1
       801: q+1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       813: q+1
       814: q+1
       815: q+1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: q+1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: q+1
       850: 1
       851: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: q+1
       867: q+1
       868: q+1
       870: 1
       871: 1
       872: 1
       875: q+1
       876: 2q+1
       877: 1
       879: 1
       880: 1
       882: 1
       883: q+1
       885: 2q+1
       886: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       893: q+1
       894: q+1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: q+1
       907: 1
       909: 1
       911: q+1
       913: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: q+1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: q+1
       941: q+1
       942: 1
       945: 1
       947: q+1
       953: 1
       955: 1
       956: 1
       961: 1
       962: 1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: q+1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: q+1
       985: q+1
       986: 1
       993: 1
      1000: 1
      1002: q+1
      1008: 1
      1009: 1
      1011: 1
      1015: 1
      1016: 1
      1021: q+1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1045: 1
      1047: 1
      1054: 1
      1061: 1
      1062: 1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1079: 1
      1080: 1
      1084: q+1
      1085: 1
      1087: 1
      1089: 1
      1091: q+1
      1093: 1
      1095: 1
      1096: 1
      1101: q+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1115: 1
      1118: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: q+1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1166: 1
      1171: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: q+1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1218: 1
      1224: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1237: 1
      1250: 1
      1266: 1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: 1
      1285: 1
      1288: 1
      1291: 1
      1294: 1
      1300: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1317: 1
      1320: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1363: 1
      1368: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1412: 1
      1418: 1
      1457: 1
      1459: 1
      1460: 1
      1479: 1
      1485: 1
      1503: 1
      1506: 1
      1534: 1
      1539: 1
      1613: 1

1614:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: q^2+2q+1
       194: q+1
       195: q^2+2q+1
       196: q+1
       197: 1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: q+1
       206: q^2+2q+1
       207: q^2+2q+1
       208: q^2+2q+1
       209: q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: q+1
       257: 1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q+1
       262: q+1
       263: q+1
       264: q^2+2q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q^2+2q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: q^2+2q+1
       324: q+1
       325: q^2+2q+1
       326: q+1
       327: 1
       328: q^2+2q+1
       329: q^2+2q+1
       330: q^2+2q+1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: q+1
       396: q^2+2q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: 1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q^2+2q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q^2+2q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q^2+2q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       563: 1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q^2+2q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       755: 1
       756: 1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       840: 1
       850: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       906: 1
       918: 1
       935: 1
       938: 1
       939: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1014: 1
      1015: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1094: 1
      1095: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1141: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1209: 1
      1217: 1
      1229: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1293: 1
      1305: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1385: 1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1525: 1
      1536: 1
      1614: 1

1615:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: 1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: q^2+1
        51: 1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: 1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: q^2+1
       106: 1
       107: q^2+1
       108: q^2+1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       113: 1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: 1
       118: 1
       119: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q^2+1
       156: 1
       157: q^2+1
       158: q^2+1
       159: q^2+1
       160: 1
       161: 1
       162: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       169: q^2+1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q^2+1
       192: 1
       193: q^2+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q^2+1
       200: 1
       201: q^2+1
       202: q^2+1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       207: 1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q^2+1
       260: 1
       261: q^2+1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       267: 1
       272: 1
       273: q^2+1
       276: q^2+1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: q^2+1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: q^2+1
       322: 1
       323: q^2+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q^2+1
       330: 1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q^2+1
       398: 1
       399: q^2+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: q^2+1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: q^2+1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q^2+1
       486: 1
       487: q^2+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q^2+1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q^2+1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       909: 1
       911: 1
       933: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1042: 1
      1050: 1
      1059: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1115: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1208: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1244: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1359: 1
      1360: 1
      1394: 1
      1406: 1
      1459: 1
      1463: 1
      1464: 1
      1473: 1
      1526: 1
      1615: 1

1616:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: q^3+3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 2q^2+2q+1
         5: q^3+3q^2+2q+1
         6: q^2+2q+1
         7: q^3+3q^2+2q+1
         8: q^3+3q^2+2q+1
         9: q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: q^3+3q^2+2q+1
        17: q^3+3q^2+2q+1
        18: q^3+3q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^3+3q^2+2q+1
        23: q^3+3q^2+2q+1
        24: 2q^2+2q+1
        25: q^2+2q+1
        26: q^3+3q^2+2q+1
        27: q^3+3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: q^3+3q^2+2q+1
        42: q^3+3q^2+2q+1
        43: q^3+3q^2+2q+1
        44: q^2+q+1
        45: q^3+3q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^3+3q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^3+3q^2+2q+1
        60: q^3+3q^2+2q+1
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: q^3+3q^2+2q+1
        64: q^3+3q^2+2q+1
        65: q^2+2q+1
        66: 2q^2+2q+1
        67: 2q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: 2q^2+2q+1
        75: 2q^2+2q+1
        76: 1
        77: q^2+1
        78: q^2+1
        79: 2q^2+2q+1
        80: q^2+1
        81: 2q^2+2q+1
        82: q^2+1
        83: 2q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^3+3q^2+2q+1
        87: q^3+3q^2+2q+1
        88: q^2+2q+1
        89: q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^3+3q^2+2q+1
        93: q^2+q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 1
       102: 2q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+2q+1
       111: 2q^2+2q+1
       112: q^2+2q+1
       113: q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^3+3q^2+2q+1
       117: 2q^2+2q+1
       118: 2q^2+2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^3+3q^2+2q+1
       122: q^3+3q^2+2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: 2q^2+2q+1
       128: 2q^2+2q+1
       129: q^2+2q+1
       130: 2q^2+2q+1
       131: 2q^2+2q+1
       132: 2q^2+2q+1
       133: 1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: 1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: 2q^2+2q+1
       141: 1
       142: 1
       143: q^2+1
       144: q^2+1
       145: q^2+1
       146: 1
       147: q^2+1
       148: q^2+1
       149: 1
       150: q^2+1
       151: q^2+1
       152: 2q^2+2q+1
       153: q^2+1
       154: 2q^2+2q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q+1
       159: q^3+3q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q+1
       163: q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: 2q^2+2q+1
       180: q^2+2q+1
       181: 1
       182: 1
       183: 1
       184: 2q^2+2q+1
       185: 1
       186: q^2+2q+1
       187: 1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q^2+2q+1
       192: q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: 2q^2+2q+1
       197: 1
       198: q+1
       199: q^2+2q+1
       200: q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 2q^2+2q+1
       205: 2q^2+2q+1
       206: q^2+2q+1
       207: q+1
       208: q^2+2q+1
       209: q+1
       210: q^3+3q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q^2+2q+1
       214: q+1
       215: q^2+2q+1
       216: 1
       217: 2q^2+2q+1
       218: 2q^2+2q+1
       219: 2q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 2q^2+2q+1
       223: 2q^2+2q+1
       224: q^2+2q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 2q^2+2q+1
       235: 2q^2+2q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: q^2+1
       241: q^2+1
       242: q^2+1
       243: 1
       244: 1
       245: q^2+1
       246: q^2+1
       248: 1
       249: 1
       250: q^2+1
       251: q^2+1
       252: q^2+1
       253: 1
       254: q^2+1
       255: q^2+1
       256: 2q^2+2q+1
       257: 1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: 1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: 1
       292: 2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: q^2+2q+1
       313: q+1
       314: q^2+2q+1
       315: q+1
       316: q^2+2q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q^2+2q+1
       322: q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: q^2+2q+1
       326: 2q^2+2q+1
       327: 1
       328: q+1
       329: q^2+2q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: q^2+2q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 2q^2+2q+1
       343: 2q^2+2q+1
       344: q^2+2q+1
       345: q+1
       346: q^2+2q+1
       347: 1
       348: 2q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 2q^2+2q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q^2+1
       372: q^2+1
       373: 1
       375: 1
       377: q^2+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: q^2+1
       385: q^2+1
       386: q^2+1
       387: 1
       388: 1
       389: q^2+1
       390: q^2+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: 1
       399: q+1
       400: q+1
       401: q+1
       402: q^2+2q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+2q+1
       463: 1
       466: q+1
       467: q+1
       468: q+1
       469: q^2+2q+1
       470: q+1
       471: 1
       472: 1
       474: q+1
       475: q+1
       476: q^2+2q+1
       477: q+1
       478: q^2+2q+1
       479: q+1
       480: q^2+2q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: q+1
       486: 1
       487: q+1
       488: q+1
       489: q+1
       490: q^2+2q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 2q^2+2q+1
       500: 1
       501: q+1
       502: q^2+2q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q^2+2q+1
       508: q^2+2q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q^2+1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: q^2+1
       550: q^2+1
       551: 1
       553: 1
       555: q^2+1
       558: 1
       559: 1
       560: 1
       561: 1
       564: q+1
       565: 1
       566: q+1
       567: 1
       568: q+1
       569: 1
       570: q+1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: 1
       591: q+1
       592: 1
       596: q+1
       597: q+1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+2q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       659: q+1
       660: q+1
       661: q+1
       662: q^2+2q+1
       663: q+1
       664: 1
       665: 1
       667: q+1
       668: 1
       669: q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: 1
       675: 1
       677: q+1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+2q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q^2+1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       757: 1
       758: 1
       759: 1
       760: q+1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       769: q+1
       770: 1
       771: q+1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: 1
       784: 1
       790: q+1
       791: 1
       792: 1
       793: q+1
       794: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       888: q+1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       909: 1
       911: 1
       913: 1
       916: 1
       918: 1
       919: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       942: 1
       953: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       970: 1
       971: 1
       972: 1
       973: q+1
       974: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       986: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1069: 1
      1070: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1093: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1118: 1
      1123: 1
      1139: 1
      1141: 1
      1142: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1220: 1
      1222: 1
      1224: 1
      1227: 1
      1229: 1
      1230: 1
      1245: 1
      1253: 1
      1264: 1
      1273: 1
      1277: 1
      1278: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1291: 1
      1296: 1
      1298: 1
      1300: 1
      1303: 1
      1305: 1
      1306: 1
      1333: 1
      1360: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1395: 1
      1403: 1
      1409: 1
      1414: 1
      1460: 1
      1464: 1
      1465: 1
      1476: 1
      1481: 1
      1527: 1
      1536: 1
      1616: 1

1617:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q+1
       133: 1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: q+1
       197: 1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q^2+2q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q^2+2q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q^2+2q+1
       312: q+1
       313: q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: q+1
       324: q^2+2q+1
       325: q^2+2q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: q^2+2q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q^2+2q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       468: q^2+2q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q^2+2q+1
       476: q+1
       477: q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       489: 1
       490: q+1
       491: 1
       492: q+1
       493: q^2+2q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       661: q^2+2q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       832: 1
       850: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       960: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1014: 1
      1015: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1157: 1
      1183: 1
      1217: 1
      1228: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1304: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1338: 1
      1458: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1486: 1
      1504: 1
      1617: 1

1618:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: 1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: q^2+1
        32: 1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: 1
        55: q^2+1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q^2+1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: q^2+1
       107: q^2+1
       108: 1
       109: q^2+1
       110: 1
       111: 1
       112: 1
       113: q^2+1
       114: q^2+1
       115: q^2+1
       116: 1
       117: q^2+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q^2+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q^2+1
       136: q^2+1
       137: q^2+1
       138: 1
       139: q^2+1
       140: 1
       141: q^2+1
       144: 1
       145: q^2+1
       146: 1
       148: 1
       149: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: q^2+1
       193: 1
       194: q^2+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q^2+1
       201: q^2+1
       202: 1
       203: q^2+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: q^2+1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q^2+1
       231: q^2+1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       236: 1
       237: q^2+1
       242: 1
       243: 1
       246: 1
       247: 1
       248: q^2+1
       251: 1
       252: q^2+1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q^2+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: q^2+1
       323: 1
       324: q^2+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q^2+1
       360: 1
       361: q^2+1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: q^2+1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: q^2+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: q^2+1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: q^2+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1060: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1156: 1
      1164: 1
      1166: 1
      1218: 1
      1219: 1
      1223: 1
      1234: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1299: 1
      1312: 1
      1313: 1
      1347: 1
      1405: 1
      1459: 1
      1468: 1
      1469: 1
      1472: 1
      1487: 1
      1618: 1

1619:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: q^3+3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: q^3+3q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^3+3q^2+2q+1
         8: q^3+3q^2+2q+1
         9: q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: 2q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^3+3q^2+2q+1
        23: 2q^2+2q+1
        24: q^3+3q^2+2q+1
        25: q^2+2q+1
        26: q^3+3q^2+2q+1
        27: q^3+3q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: q^3+3q^2+2q+1
        35: q^3+3q^2+2q+1
        36: q^3+3q^2+2q+1
        37: q^2+q+1
        38: q^2+2q+1
        39: q^3+3q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: 2q^2+2q+1
        55: q^3+3q^2+2q+1
        56: 2q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^3+3q^2+2q+1
        60: 2q^2+2q+1
        61: q^3+3q^2+2q+1
        62: q^2+2q+1
        63: 2q^2+2q+1
        64: 2q^2+2q+1
        65: q^2+2q+1
        66: q^3+3q^2+2q+1
        67: q^3+3q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^3+3q^2+2q+1
        74: q^2+2q+1
        75: q^3+3q^2+2q+1
        76: q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q^2+2q+1
        80: q+1
        81: q^3+3q^2+2q+1
        82: q^2+q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^2+2q+1
        89: 1
        90: q^2+1
        91: q^2+1
        92: 2q^2+2q+1
        93: q^2+1
        94: 2q^2+2q+1
        95: q^2+1
        96: 2q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 1
       102: q^2+2q+1
       103: 2q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+2q+1
       111: 2q^2+2q+1
       112: q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: 2q^2+2q+1
       117: q^3+3q^2+2q+1
       118: 2q^2+2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: 2q^2+2q+1
       122: 2q^2+2q+1
       123: 2q^2+2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q^3+3q^2+2q+1
       127: q^2+2q+1
       128: q^3+3q^2+2q+1
       129: q^2+2q+1
       130: 2q^2+2q+1
       131: 2q^2+2q+1
       132: 2q^2+2q+1
       133: 1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q^3+3q^2+2q+1
       140: q^2+2q+1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 1
       159: 2q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 1
       163: 1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: 1
       168: q^2+1
       169: q^2+1
       170: 1
       171: q^2+1
       172: q^2+1
       173: 2q^2+2q+1
       174: q^2+1
       175: 2q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: q^2+2q+1
       180: 2q^2+2q+1
       181: 1
       182: 1
       183: 1
       184: q^2+2q+1
       185: 1
       186: 2q^2+2q+1
       187: 1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^2+2q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: 2q^2+2q+1
       197: 1
       198: q+1
       199: q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 2q^2+2q+1
       205: 2q^2+2q+1
       206: q+1
       207: q^2+2q+1
       208: q^2+2q+1
       209: 1
       210: 2q^2+2q+1
       211: 2q^2+2q+1
       212: 2q^2+2q+1
       213: q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: q+1
       217: q^2+2q+1
       218: q^3+3q^2+2q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: 2q^2+2q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: 1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: 1
       262: 1
       263: 1
       264: 2q^2+2q+1
       265: 2q^2+2q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: q^2+1
       271: q^2+1
       272: q^2+1
       273: 1
       274: 1
       275: q^2+1
       276: q^2+1
       277: q^2+1
       278: 1
       279: 1
       280: q^2+1
       282: q^2+1
       283: 1
       284: q^2+1
       285: q^2+1
       286: 2q^2+2q+1
       287: 1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 1
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q^2+2q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+2q+1
       307: 1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: q+1
       313: q^2+2q+1
       314: q+1
       315: q^2+2q+1
       316: q^2+2q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q^2+2q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: q^2+2q+1
       326: 2q^2+2q+1
       327: 1
       328: q+1
       329: q+1
       330: q^2+2q+1
       331: 1
       332: 1
       333: 1
       334: 2q^2+2q+1
       335: 2q^2+2q+1
       336: q+1
       337: q+1
       338: q^2+2q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q^2+2q+1
       344: q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q^2+2q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: 1
       374: q+1
       375: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 2q^2+2q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q^2+1
       411: q^2+1
       412: 1
       413: 1
       414: 1
       415: 1
       416: q^2+1
       417: q^2+1
       418: q^2+1
       420: 1
       421: 1
       424: q^2+1
       426: 1
       427: 1
       428: q^2+1
       430: q^2+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 1
       438: 1
       439: 1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+2q+1
       463: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q^2+2q+1
       471: 1
       472: 1
       474: q+1
       475: q+1
       476: q+1
       477: q^2+2q+1
       478: q+1
       479: q^2+2q+1
       480: q^2+2q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 2q^2+2q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q^2+2q+1
       500: 1
       501: q+1
       502: q+1
       503: q^2+2q+1
       504: 1
       505: 1
       506: 1
       507: q^2+2q+1
       508: q^2+2q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: q+1
       521: 1
       522: q+1
       523: q+1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: 1
       535: 1
       536: 1
       537: q+1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: 1
       552: q+1
       553: q+1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q^2+1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: q^2+1
       589: q^2+1
       592: 1
       599: 1
       600: 1
       603: q^2+1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+2q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q^2+2q+1
       664: 1
       665: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       677: q+1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+2q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: q+1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       716: q+1
       717: 1
       718: q+1
       719: q+1
       721: 1
       722: 1
       723: 1
       729: q+1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       740: 1
       741: 1
       742: q+1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q^2+1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: 1
       886: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       924: 1
       932: 1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q+1
       940: q+1
       942: 1
       943: 1
       944: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       962: 1
       966: 1
       967: 1
       970: 1
       971: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1069: 1
      1070: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1084: 1
      1085: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1171: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1219: 1
      1223: 1
      1224: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1243: 1
      1265: 1
      1273: 1
      1277: 1
      1278: 1
      1285: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1295: 1
      1299: 1
      1300: 1
      1303: 1
      1304: 1
      1307: 1
      1313: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1348: 1
      1356: 1
      1371: 1
      1410: 1
      1413: 1
      1460: 1
      1469: 1
      1470: 1
      1477: 1
      1480: 1
      1488: 1
      1504: 1
      1619: 1

1620:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 2q^2+3q+1
        23: 2q+1
        24: 2q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^3+3q^2+3q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^3+3q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: q^2+2q+1
        54: 2q+1
        55: 2q^2+3q+1
        56: 2q+1
        57: 2q^2+3q+1
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 2q+1
        61: 2q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: 2q^2+3q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: q+1
        75: 2q^2+3q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q+1
        81: q^3+3q^2+3q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q^2+3q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q+1
        96: 2q^2+3q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: q^2+2q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: 2q^2+3q+1
       107: q^2+2q+1
       108: q+1
       109: q^2+2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: 2q^2+3q+1
       114: 2q^2+3q+1
       115: q^2+2q+1
       116: 2q+1
       117: 2q^2+3q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: 2q+1
       123: q^2+3q+1
       124: 2q^2+3q+1
       125: 2q^2+3q+1
       126: 2q^2+3q+1
       127: q+1
       128: 2q^2+3q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: q+1
       138: q+1
       139: 2q^2+3q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: 1
       145: q^2+2q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 2q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: q+1
       159: 2q+1
       160: q^2+3q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: 2q+1
       171: 2q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q+1
       175: 2q^2+3q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q^2+3q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q^2+2q+1
       193: q+1
       194: q^2+2q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q^2+3q+1
       201: q^2+2q+1
       202: q+1
       203: q^2+2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: q^2+3q+1
       208: q^2+3q+1
       209: q+1
       210: 2q+1
       211: q^2+3q+1
       212: 2q+1
       213: q+1
       214: 2q^2+3q+1
       215: 2q^2+3q+1
       216: q+1
       217: q+1
       218: 2q^2+3q+1
       219: q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q^2+3q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: q^2+2q+1
       238: q^2+2q+1
       239: q+1
       240: 1
       241: q^2+2q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: 1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q+1
       262: 1
       263: q+1
       264: 2q+1
       265: 2q+1
       266: q+1
       267: 2q+1
       268: 2q+1
       269: q+1
       270: q+1
       271: 2q+1
       272: q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 2q+1
       278: 2q+1
       279: 2q+1
       280: 2q+1
       282: 2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: 2q^2+3q+1
       287: 2q+1
       288: q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q^2+3q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 1
       299: 2q+1
       300: q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q+1
       313: q+1
       315: q^2+2q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: q^2+2q+1
       323: q+1
       324: q^2+2q+1
       325: q+1
       326: 2q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: q^2+3q+1
       331: q+1
       332: 1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: 2q^2+3q+1
       339: q+1
       340: 1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: q^2+3q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+3q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q^2+2q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q^2+2q+1
       382: q^2+2q+1
       383: q+1
       384: 1
       385: q^2+2q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: 2q+1
       396: 2q+1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 2q+1
       403: q+1
       404: q+1
       405: q+1
       406: 2q+1
       407: q+1
       408: 1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: q+1
       417: 2q+1
       418: q+1
       420: 2q+1
       421: 2q+1
       424: 2q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       430: 2q+1
       431: 2q+1
       432: 2q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: q^2+3q+1
       437: q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: 2q+1
       444: 2q+1
       445: q+1
       446: 1
       447: 2q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       458: 2q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       467: q+1
       470: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q+1
       477: q+1
       479: q^2+2q+1
       480: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 2q+1
       491: q+1
       492: q+1
       493: q+1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q^2+3q+1
       504: q+1
       505: 1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 1
       514: 2q+1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+2q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       563: q+1
       564: 2q+1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       572: q+1
       573: q+1
       574: q+1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: q+1
       581: q+1
       582: q+1
       583: q+1
       584: 2q+1
       585: q+1
       586: 1
       587: q+1
       588: q+1
       589: q+1
       592: 2q+1
       599: 2q+1
       600: 2q+1
       603: 2q+1
       605: 2q+1
       606: 2q+1
       607: 2q+1
       609: 2q+1
       610: q+1
       611: q+1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 2q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: q+1
       629: q+1
       631: 1
       632: q+1
       633: 1
       635: 2q+1
       636: 2q+1
       639: 2q+1
       641: q+1
       642: q+1
       643: q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       651: q+1
       655: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       660: q+1
       663: q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: 1
       669: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       675: q+1
       676: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 2q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       752: 1
       753: q+1
       754: 1
       755: q+1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: q+1
       765: q+1
       766: 1
       767: 1
       768: 1
       770: q+1
       771: 1
       773: q+1
       774: q+1
       775: q+1
       776: 1
       777: q+1
       778: 1
       779: q+1
       780: 1
       781: q+1
       782: q+1
       794: 2q+1
       801: 2q+1
       802: 2q+1
       805: 2q+1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: q+1
       832: 1
       833: 1
       836: 2q+1
       843: q+1
       844: q+1
       847: q+1
       849: q+1
       850: q+1
       851: q+1
       853: q+1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       867: 1
       868: 1
       869: q+1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       902: q+1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: q+1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: q+1
       970: 1
       971: 1
       974: 1
       977: q+1
       978: q+1
       979: 1
       980: 1
       981: 1
       983: q+1
       984: 1
       986: q+1
      1008: 2q+1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1053: q+1
      1060: q+1
      1061: q+1
      1064: q+1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1119: 1
      1122: 1
      1128: 1
      1137: 1
      1139: 1
      1140: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: q+1
      1182: 1
      1183: 1
      1186: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1265: q+1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1307: 1
      1310: 1
      1332: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1357: 1
      1371: 1
      1404: 1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1461: 1
      1466: 1
      1471: 1
      1472: 1
      1477: 1
      1480: 1
      1516: 1
      1564: 1
      1620: 1

1621:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 2q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 2q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: q^3+3q^2+3q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q+1
        52: 2q^2+3q+1
        53: q^2+2q+1
        54: 2q^2+3q+1
        55: 2q+1
        56: 2q+1
        57: 2q^2+3q+1
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 2q^2+3q+1
        61: 2q+1
        62: 2q^2+3q+1
        63: 2q^2+3q+1
        64: 2q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q^2+3q+1
        80: 2q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^3+3q^2+3q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       104: 2q+1
       105: 2q^2+3q+1
       106: 2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: 2q^2+3q+1
       113: 2q+1
       114: 2q^2+3q+1
       115: q^2+2q+1
       116: 2q^2+3q+1
       117: 2q+1
       118: 2q+1
       119: 2q^2+3q+1
       120: 2q^2+3q+1
       121: 2q^2+3q+1
       122: 2q^2+3q+1
       123: q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q^2+3q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: q+1
       138: q^2+3q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       147: 2q+1
       148: 2q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: 2q^2+3q+1
       153: 2q+1
       154: 2q^2+3q+1
       155: 2q^2+3q+1
       156: q+1
       157: 2q^2+3q+1
       158: q+1
       159: 2q^2+3q+1
       160: q+1
       161: q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q^2+2q+1
       192: q+1
       193: q^2+2q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: 2q^2+3q+1
       200: 2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 2q^2+3q+1
       207: q+1
       208: 2q^2+3q+1
       209: q+1
       210: 2q^2+3q+1
       211: q+1
       212: q+1
       213: q^2+3q+1
       214: 2q+1
       215: q^2+3q+1
       216: q+1
       217: q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q+1
       232: q+1
       233: 1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q+1
       238: 2q+1
       239: q+1
       240: 2q+1
       241: q+1
       242: q+1
       243: 2q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: 2q^2+3q+1
       257: 2q+1
       258: q+1
       259: 2q^2+3q+1
       260: q+1
       261: q+1
       262: q+1
       263: 1
       264: q+1
       265: q+1
       266: q^2+2q+1
       267: 1
       268: q^2+2q+1
       269: q+1
       270: q^2+2q+1
       271: 1
       272: 1
       273: q^2+2q+1
       274: q^2+2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+3q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q^2+3q+1
       293: q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q^2+2q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q^2+2q+1
       322: q+1
       323: q^2+2q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: 2q^2+3q+1
       330: q+1
       331: q+1
       332: q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: q^2+3q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: 1
       342: 2q+1
       343: 2q+1
       344: q^2+3q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       348: q^2+3q+1
       349: q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 2q+1
       355: 1
       356: 2q+1
       357: 2q+1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 2q+1
       364: q+1
       365: q+1
       366: 2q+1
       367: q+1
       368: q+1
       369: q+1
       370: 1
       371: q+1
       372: q+1
       373: 2q+1
       375: 2q+1
       377: 2q+1
       380: 2q+1
       381: q+1
       382: 2q+1
       383: q+1
       384: 2q+1
       385: q+1
       386: q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: 2q+1
       392: 2q+1
       393: 2q+1
       394: 2q+1
       395: q+1
       396: q+1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q^2+2q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q^2+2q+1
       413: 1
       414: q^2+2q+1
       415: q+1
       416: q^2+2q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q^2+3q+1
       436: q+1
       437: q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       442: 2q+1
       443: 1
       444: 2q+1
       445: q+1
       446: 2q+1
       447: 1
       448: 1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       468: q+1
       469: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q^2+2q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 2q+1
       500: q+1
       501: q+1
       502: q^2+3q+1
       503: q+1
       504: q+1
       505: q+1
       506: 1
       507: q+1
       508: q+1
       509: 2q+1
       510: 1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: 1
       515: 1
       516: q+1
       517: 2q+1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: q+1
       534: q+1
       536: 2q+1
       543: q+1
       544: 2q+1
       545: q+1
       546: q+1
       547: q+1
       548: 1
       549: q+1
       550: q+1
       551: 2q+1
       553: 2q+1
       555: 2q+1
       558: 2q+1
       559: 2q+1
       560: 2q+1
       561: 2q+1
       563: 1
       564: q+1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q^2+2q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 2q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: 2q+1
       629: 2q+1
       631: 2q+1
       634: q+1
       635: 1
       636: q+1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       652: q+1
       654: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       661: q+1
       662: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 2q+1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 2q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: q+1
       713: q+1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       721: q+1
       731: q+1
       732: q+1
       733: q+1
       734: 1
       735: q+1
       736: 1
       737: 1
       738: q+1
       739: q+1
       741: 2q+1
       748: 2q+1
       750: 2q+1
       752: 2q+1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       804: q+1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 2q+1
       834: 1
       835: q+1
       836: 1
       840: 1
       841: 1
       842: q+1
       844: q+1
       846: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: q+1
       866: 1
       868: 1
       869: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: q+1
       916: 1
       918: 1
       919: 1
       933: q+1
       934: q+1
       935: 1
       936: q+1
       938: 1
       939: 1
       940: 1
       942: q+1
       953: 2q+1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       970: 1
       972: 1
       973: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       982: 1
       983: 1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1052: q+1
      1059: q+1
      1061: q+1
      1063: q+1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: q+1
      1139: 1
      1141: 1
      1142: 1
      1165: 1
      1167: 1
      1170: 1
      1175: 1
      1180: 1
      1182: 1
      1184: 1
      1185: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1227: 1
      1229: 1
      1230: 1
      1244: 1
      1245: 1
      1253: 1
      1264: q+1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1303: 1
      1305: 1
      1306: 1
      1311: 1
      1333: 1
      1358: 1
      1372: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1414: 1
      1428: 1
      1462: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1481: 1
      1555: 1
      1565: 1
      1621: 1

1622:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: 3q^2+3q+1
         7: q^2+2q+1
         8: 2q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: 2q^2+3q+1
        19: 3q^2+3q+1
        20: 2q^2+3q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 3q^2+3q+1
        26: q^2+2q+1
        27: 2q^2+3q+1
        28: 3q^2+3q+1
        29: 3q^2+3q+1
        30: 3q^2+3q+1
        31: 3q^2+3q+1
        32: 3q^2+3q+1
        33: 3q^2+3q+1
        34: q^2+2q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 3q^2+3q+1
        41: q^2+2q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 3q^2+3q+1
        48: 3q^2+3q+1
        49: q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+3q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q^2+3q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q^2+3q+1
        61: 2q^2+3q+1
        62: 3q^2+3q+1
        63: q^2+2q+1
        64: q^2+3q+1
        65: 3q^2+3q+1
        66: q^2+2q+1
        67: q^2+3q+1
        68: 3q^2+3q+1
        69: 3q^2+3q+1
        70: q^2+3q+1
        71: q^2+3q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: 2q^2+3q+1
        78: q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: 2q^2+3q+1
        91: q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: 3q^2+3q+1
        98: q^2+2q+1
        99: 3q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: 2q^2+3q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: 2q+1
       112: 2q^2+3q+1
       113: 2q^2+3q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q^2+3q+1
       119: q^2+3q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+3q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: q^2+2q+1
       126: 2q+1
       127: q^2+3q+1
       128: q^2+3q+1
       129: 3q^2+3q+1
       130: q^2+2q+1
       131: 3q+1
       132: q^2+3q+1
       133: q^2+3q+1
       134: q^2+3q+1
       135: q^2+3q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q^2+3q+1
       141: q^2+3q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       148: 2q+1
       149: 2q^2+3q+1
       151: q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+3q+1
       155: q^2+3q+1
       156: q^2+3q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: q^2+3q+1
       162: q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       169: q^2+3q+1
       170: 2q^2+3q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+3q+1
       176: 3q+1
       177: q^2+2q+1
       178: 2q+1
       179: 3q+1
       180: 3q+1
       181: q^2+3q+1
       183: 3q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: 2q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: 2q+1
       198: 2q^2+3q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: q^2+3q+1
       207: q^2+3q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: q^2+3q+1
       213: q^2+3q+1
       214: q^2+3q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: q^2+3q+1
       220: 3q+1
       221: q^2+2q+1
       222: 2q+1
       223: 3q+1
       224: 3q+1
       225: q^2+3q+1
       227: 3q+1
       228: q^2+3q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: q^2+3q+1
       237: q^2+3q+1
       242: q^2+3q+1
       243: 2q+1
       246: 2q+1
       247: 2q+1
       248: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: 2q^2+3q+1
       255: 2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: 2q+1
       266: q^2+3q+1
       267: q^2+3q+1
       272: q^2+3q+1
       273: q^2+3q+1
       276: q^2+3q+1
       277: q^2+3q+1
       278: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q^2+3q+1
       285: 2q+1
       286: q^2+3q+1
       287: q^2+3q+1
       288: 3q+1
       289: 3q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 3q+1
       295: 3q+1
       298: 3q+1
       299: 3q+1
       300: q^2+3q+1
       302: 2q+1
       303: q^2+3q+1
       305: 2q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: 2q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: 2q+1
       328: q^2+3q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: q^2+3q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: 3q+1
       345: 3q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 3q+1
       351: 3q+1
       354: 3q+1
       355: 3q+1
       356: 2q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: 2q+1
       365: q^2+3q+1
       372: q+1
       373: 2q+1
       374: 2q+1
       379: 2q+1
       380: q^2+3q+1
       381: q^2+3q+1
       386: q^2+3q+1
       387: 2q+1
       390: 2q+1
       391: 2q+1
       392: q^2+3q+1
       394: 2q+1
       395: 2q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: 2q+1
       404: q^2+3q+1
       411: q+1
       412: q^2+3q+1
       413: q^2+3q+1
       418: q^2+3q+1
       419: 2q+1
       420: 2q+1
       425: 2q+1
       426: 2q+1
       429: 2q+1
       430: 2q+1
       431: q^2+3q+1
       433: 2q+1
       434: 3q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: 2q+1
       442: 3q+1
       443: 3q+1
       448: 3q+1
       449: 2q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       457: 2q+1
       458: 2q+1
       459: q^2+3q+1
       461: q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 2q+1
       474: q+1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       483: 2q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: 2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: 2q+1
       501: 3q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: 2q+1
       509: 3q+1
       510: 3q+1
       515: 3q+1
       516: 2q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: q+1
       534: q+1
       535: 2q+1
       542: q+1
       543: q^2+3q+1
       550: q+1
       551: 2q+1
       552: 2q+1
       557: 2q+1
       558: 2q+1
       561: 2q+1
       562: 2q+1
       563: 2q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: q+1
       581: q+1
       582: q^2+3q+1
       589: q+1
       590: 2q+1
       597: q+1
       598: 2q+1
       599: 2q+1
       604: 2q+1
       605: 2q+1
       608: 2q+1
       609: 2q+1
       610: 2q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: 2q+1
       619: 3q+1
       626: 1
       627: 2q+1
       628: 2q+1
       633: 2q+1
       634: 2q+1
       635: 2q+1
       640: 2q+1
       641: q+1
       644: q+1
       645: q+1
       646: q^2+3q+1
       648: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: q+1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: 2q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       676: 2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       686: 2q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: 2q+1
       695: 3q+1
       702: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: q+1
       722: q+1
       730: q+1
       731: q+1
       739: q+1
       740: 2q+1
       747: q+1
       748: 2q+1
       749: 2q+1
       754: 2q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: q+1
       774: q+1
       782: q+1
       783: q+1
       791: q+1
       792: 2q+1
       799: q+1
       800: 2q+1
       801: 2q+1
       806: 2q+1
       807: 2q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       825: 1
       826: 2q+1
       833: 1
       834: 2q+1
       841: 1
       842: q+1
       843: q+1
       848: q+1
       849: q+1
       852: q+1
       853: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: 2q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       897: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: q+1
       933: q+1
       943: q+1
       951: q+1
       952: 2q+1
       959: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: q+1
       987: q+1
       997: q+1
      1005: q+1
      1006: 2q+1
      1013: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: q+1
      1058: 1
      1059: q+1
      1060: q+1
      1065: q+1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: q+1
      1156: 1
      1164: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: q+1
      1208: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: q+1
      1270: 1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1312: 1
      1347: 1
      1359: 1
      1394: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1447: 1
      1455: 1
      1463: 1
      1468: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1566: 1
      1601: 1
      1622: 1

1623:    0: 2q^2+1
         1: q^2+1
         2: 2q^2+1
         3: 2q^2+1
         4: 2q^2+1
         5: 2q^2+1
         6: 1
         7: q^2+1
         8: 2q^2+1
         9: q^2+1
        10: 2q^2+1
        11: 2q^2+1
        12: 2q^2+1
        13: q^2+1
        14: 2q^2+1
        15: 2q^2+1
        16: q^2+1
        17: 2q^2+1
        18: 2q^2+1
        19: 2q^2+1
        20: 1
        21: 1
        22: q^2+1
        23: 2q^2+1
        24: 2q^2+1
        25: 1
        26: q^2+1
        27: 2q^2+1
        28: q^2+1
        29: 2q^2+1
        30: q^2+1
        31: 2q^2+1
        32: 2q^2+1
        33: 1
        34: q^2+1
        35: 2q^2+1
        36: q^2+1
        37: q^2+1
        38: 2q^2+1
        39: 2q^2+1
        40: 1
        41: q^2+1
        42: 2q^2+1
        43: q^2+1
        44: q^2+1
        45: 2q^2+1
        46: 2q^2+1
        47: q^2+1
        48: 2q^2+1
        49: 2q^2+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: q^2+1
        55: q^2+1
        56: 2q^2+1
        57: 1
        58: 1
        59: q^2+1
        60: 2q^2+1
        61: 2q^2+1
        62: 1
        63: q^2+1
        64: 2q^2+1
        65: 1
        66: q^2+1
        67: 2q^2+1
        68: q^2+1
        69: 2q^2+1
        70: 2q^2+1
        71: 1
        72: 1
        73: q^2+1
        74: 2q^2+1
        75: 2q^2+1
        76: 1
        78: q^2+1
        79: q^2+1
        80: q^2+1
        81: q^2+1
        82: q^2+1
        83: 2q^2+1
        84: 1
        85: 1
        86: q^2+1
        87: 2q^2+1
        88: 2q^2+1
        89: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: 2q^2+1
        97: 1
        98: q^2+1
        99: 2q^2+1
       100: q^2+1
       101: 1
       102: 2q^2+1
       103: 2q^2+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: q^2+1
       111: 2q^2+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: q^2+1
       117: q^2+1
       118: 2q^2+1
       119: 1
       120: 1
       121: q^2+1
       122: 2q^2+1
       123: 2q^2+1
       124: 1
       125: 1
       126: q^2+1
       127: 2q^2+1
       128: 2q^2+1
       129: 1
       130: q^2+1
       131: 2q^2+1
       132: q^2+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: 1
       144: q^2+1
       145: q^2+1
       146: 1
       148: q^2+1
       149: 1
       151: q^2+1
       152: q^2+1
       153: q^2+1
       154: 2q^2+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: q^2+1
       160: q^2+1
       161: 2q^2+1
       162: 1
       165: q^2+1
       166: q^2+1
       167: 1
       169: q^2+1
       170: 1
       172: q^2+1
       173: q^2+1
       174: q^2+1
       175: 2q^2+1
       176: 1
       177: 1
       178: q^2+1
       179: 2q^2+1
       180: 2q^2+1
       181: 1
       183: 1
       184: q^2+1
       185: 1
       186: q^2+1
       187: 1
       188: 2q^2+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q^2+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: q^2+1
       205: 2q^2+1
       206: 1
       207: 1
       208: 1
       209: 1
       210: q^2+1
       211: q^2+1
       212: 2q^2+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: q^2+1
       218: q^2+1
       219: 2q^2+1
       220: 1
       221: 1
       222: q^2+1
       223: 2q^2+1
       224: 2q^2+1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q^2+1
       235: 2q^2+1
       236: 1
       237: 1
       242: q^2+1
       243: 1
       246: q^2+1
       247: q^2+1
       248: 1
       251: q^2+1
       252: q^2+1
       253: 1
       255: q^2+1
       256: q^2+1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: q^2+1
       265: 2q^2+1
       266: 1
       267: 1
       272: q^2+1
       273: 1
       276: q^2+1
       277: q^2+1
       278: 1
       281: q^2+1
       282: q^2+1
       283: 1
       285: q^2+1
       286: q^2+1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: q^2+1
       293: q^2+1
       294: 2q^2+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q^2+1
       307: 1
       308: 2q^2+1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q^2+1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: q^2+1
       335: 2q^2+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q^2+1
       343: 2q^2+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: q^2+1
       350: 2q^2+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q^2+1
       364: 1
       365: 1
       372: q^2+1
       373: 1
       374: 1
       379: q^2+1
       380: 1
       381: 1
       386: q^2+1
       387: 1
       390: q^2+1
       391: q^2+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q^2+1
       403: 1
       404: 1
       411: q^2+1
       412: 1
       413: 1
       418: q^2+1
       419: 1
       420: 1
       425: q^2+1
       426: 1
       429: q^2+1
       430: q^2+1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q^2+1
       441: 2q^2+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q^2+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q^2+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q^2+1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q^2+1
       508: 2q^2+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: q^2+1
       543: 1
       550: q^2+1
       551: 1
       552: 1
       557: q^2+1
       558: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: q^2+1
       590: 1
       597: q^2+1
       598: 1
       599: 1
       604: q^2+1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+1
       694: 1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: q^2+1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: q^2+1
       800: 1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       943: 1
       951: 1
       952: 1
       959: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1116: 1
      1117: 1
      1156: 1
      1164: 1
      1168: 1
      1169: 1
      1208: 1
      1216: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1277: 1
      1282: 1
      1283: 1
      1289: 1
      1290: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1313: 1
      1360: 1
      1407: 1
      1408: 1
      1447: 1
      1455: 1
      1464: 1
      1469: 1
      1474: 1
      1475: 1
      1567: 1
      1623: 1

1624:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: q^2+2q+1
         7: 3q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: 2q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: 2q^2+3q+1
        19: 3q^2+3q+1
        20: q+1
        21: q^2+2q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^2+2q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: 3q^2+3q+1
        29: 3q^2+3q+1
        30: 3q^2+3q+1
        31: 3q^2+3q+1
        32: 3q^2+3q+1
        33: q^2+2q+1
        34: 3q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+2q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: 3q^2+3q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 3q^2+3q+1
        48: 3q^2+3q+1
        49: q^2+3q+1
        50: q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: 3q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q+1
        58: q^2+2q+1
        59: 3q^2+3q+1
        60: 3q^2+3q+1
        61: 3q^2+3q+1
        62: q^2+2q+1
        63: 3q^2+3q+1
        64: 2q^2+3q+1
        65: q^2+2q+1
        66: 3q^2+3q+1
        67: 2q^2+3q+1
        68: 3q^2+3q+1
        69: 3q^2+3q+1
        70: q^2+3q+1
        71: q+1
        72: q^2+2q+1
        73: 2q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+3q+1
        80: q^2+2q+1
        81: 2q^2+3q+1
        82: q^2+2q+1
        83: 2q^2+3q+1
        84: q+1
        85: q^2+2q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+3q+1
        93: q^2+2q+1
        94: 2q^2+3q+1
        95: q^2+2q+1
        96: 2q^2+3q+1
        97: q^2+2q+1
        98: 3q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: 2q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 3q^2+3q+1
       111: q^2+3q+1
       112: q+1
       113: q+1
       114: q+1
       115: q^2+2q+1
       116: 3q^2+3q+1
       117: 3q^2+3q+1
       118: 3q^2+3q+1
       119: q+1
       120: q^2+2q+1
       121: 2q^2+3q+1
       122: 2q^2+3q+1
       123: 2q^2+3q+1
       124: q+1
       125: q^2+2q+1
       126: 2q^2+3q+1
       127: 2q^2+3q+1
       128: 2q^2+3q+1
       129: q^2+2q+1
       130: 3q^2+3q+1
       131: q^2+3q+1
       132: q^2+3q+1
       133: 2q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: 2q^2+3q+1
       141: 1
       142: q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q+1
       147: q^2+2q+1
       148: q+1
       149: q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+3q+1
       153: q^2+2q+1
       154: q^2+3q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 1
       163: q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: q^2+2q+1
       172: q+1
       173: 2q^2+3q+1
       174: q^2+2q+1
       175: q^2+3q+1
       176: q+1
       177: q^2+2q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: q^2+3q+1
       181: q+1
       182: 2q+1
       183: 2q+1
       184: q^2+3q+1
       185: 2q+1
       186: q^2+3q+1
       187: 2q+1
       188: q^2+3q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: q^2+3q+1
       197: 2q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 3q^2+3q+1
       205: q^2+3q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: 2q^2+3q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 2q^2+3q+1
       220: q+1
       221: q^2+2q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: q+1
       226: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q^2+3q+1
       235: q^2+3q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q^2+2q+1
       241: q^2+2q+1
       242: q^2+2q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q+1
       254: q^2+2q+1
       255: q+1
       256: q^2+3q+1
       257: 2q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q^2+3q+1
       265: q^2+3q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q^2+2q+1
       271: q^2+2q+1
       272: q^2+2q+1
       273: 1
       274: q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q^2+2q+1
       285: q+1
       286: q^2+3q+1
       287: 2q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q^2+3q+1
       293: q^2+3q+1
       294: q^2+3q+1
       295: 1
       296: q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q+1
       301: 2q+1
       302: q+1
       303: q+1
       304: 2q+1
       305: q+1
       306: q^2+3q+1
       307: 2q+1
       308: q^2+3q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       318: 2q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: q^2+3q+1
       327: 2q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: 2q^2+3q+1
       343: q^2+3q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 1
       352: q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q^2+3q+1
       364: 2q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q^2+2q+1
       372: q+1
       373: 1
       374: 1
       375: 1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q^2+2q+1
       385: q^2+2q+1
       386: q^2+2q+1
       387: 1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: 2q+1
       394: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q^2+3q+1
       403: 2q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q^2+2q+1
       411: q+1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q^2+2q+1
       417: q^2+2q+1
       418: q^2+2q+1
       419: 1
       420: 1
       421: 1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: 2q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: 2q+1
       461: 1
       462: q^2+3q+1
       463: 2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: 2q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q^2+3q+1
       491: 2q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q^2+3q+1
       500: 2q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: q^2+3q+1
       508: q^2+3q+1
       509: 1
       510: 1
       511: 1
       512: q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: 2q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: 1
       537: 1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q^2+2q+1
       550: q+1
       551: 1
       552: 1
       553: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: 2q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q^2+2q+1
       589: q+1
       590: 1
       591: 1
       592: 1
       596: q+1
       597: q+1
       598: 1
       599: 1
       600: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q^2+3q+1
       618: 2q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: 2q+1
       626: 1
       627: 1
       628: 1
       629: 1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: 2q+1
       648: 1
       653: q+1
       654: 1
       655: 1
       656: 1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: 2q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: q+1
       685: 2q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q^2+3q+1
       694: 2q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: 2q+1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: q+1
       723: 1
       729: q+1
       730: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       739: q+1
       740: 1
       741: 1
       742: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       752: q+1
       753: q+1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       782: q+1
       784: 1
       790: q+1
       791: q+1
       792: 1
       793: 1
       794: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       804: q+1
       805: q+1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: 2q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: q+1
       866: 1
       867: 1
       868: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: 2q+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       932: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       942: q+1
       944: 1
       950: q+1
       951: q+1
       952: 1
       953: 1
       954: 1
       958: q+1
       959: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       986: q+1
       996: q+1
       998: 1
      1004: q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: 1
      1012: q+1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1034: 1
      1040: 1
      1041: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1155: q+1
      1157: 1
      1163: 1
      1164: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1207: q+1
      1209: 1
      1215: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1243: 1
      1253: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1290: 1
      1291: 1
      1292: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1314: 1
      1334: 1
      1356: 1
      1361: 1
      1373: 1
      1403: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1446: 1
      1448: 1
      1454: 1
      1455: 1
      1465: 1
      1470: 1
      1475: 1
      1476: 1
      1477: 1
      1482: 1
      1568: 1
      1610: 1
      1624: 1

1625:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q+1
        24: q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q^3+2q^2+2q+1
        53: q^3+2q^2+2q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^3+2q^2+2q+1
        58: q^3+2q^2+2q+1
        59: q^3+2q^2+2q+1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 1
        75: q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: 1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q^3+2q^2+2q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q^3+2q^2+2q+1
       115: q^3+2q^2+2q+1
       116: q+1
       117: q+1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q+1
       123: 1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: 1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: 1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: 1
       180: 1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q^3+2q^2+2q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q^2+2q+1
       209: q^2+2q+1
       210: q+1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q^2+2q+1
       216: q^2+2q+1
       217: 1
       218: q+1
       219: 1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: 1
       224: 1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: 1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: q^2+2q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q+1
       271: 1
       272: 1
       273: q^2+2q+1
       274: q^2+2q+1
       275: q^2+2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: q^2+2q+1
       291: q^2+2q+1
       292: 1
       293: 1
       294: 1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q^2+2q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q^2+2q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q^2+2q+1
       347: q^2+2q+1
       348: 1
       349: 1
       350: 1
       351: q^2+2q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q^2+2q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       375: q+1
       376: q+1
       377: 1
       380: 1
       381: q+1
       382: q^2+2q+1
       383: q^2+2q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q^2+2q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q^2+2q+1
       415: q^2+2q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: q+1
       422: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: q^2+2q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q^2+2q+1
       445: q^2+2q+1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       454: q+1
       455: q+1
       456: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q^2+2q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q^2+2q+1
       512: q^2+2q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       536: 1
       538: q+1
       539: 1
       543: 1
       544: 1
       545: q+1
       546: q^2+2q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       553: q+1
       554: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q^2+2q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       592: 1
       593: q+1
       595: 1
       599: 1
       600: q+1
       601: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q^2+2q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: q+1
       630: q+1
       631: 1
       635: 1
       636: q+1
       637: q+1
       639: 1
       641: q+1
       642: q+1
       643: q+1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       664: q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q+1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q^2+2q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: 1
       750: q+1
       751: q+1
       752: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: q+1
       797: 1
       801: 1
       802: q+1
       803: q+1
       805: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: q+1
       830: 1
       836: 1
       837: q+1
       839: 1
       844: q+1
       845: q+1
       849: q+1
       850: q+1
       851: q+1
       854: q+1
       861: q+1
       862: q+1
       868: q+1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       913: 1
       914: 1
       915: 1
       916: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: q+1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: q+1
       956: 1
       960: 1
       961: 1
       967: 1
       968: 1
       969: 1
       970: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: q+1
      1011: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1045: 1
      1047: 1
      1054: q+1
      1061: q+1
      1062: q+1
      1071: q+1
      1078: 1
      1079: 1
      1085: 1
      1086: 1
      1087: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1237: 1
      1250: 1
      1266: q+1
      1279: 1
      1286: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1315: 1
      1330: 1
      1331: 1
      1337: 1
      1350: 1
      1362: 1
      1369: 1
      1370: 1
      1376: 1
      1400: 1
      1404: 1
      1411: 1
      1412: 1
      1418: 1
      1471: 1
      1478: 1
      1479: 1
      1485: 1
      1501: 1
      1533: 1
      1569: 1
      1625: 1

1626:    0: 2q^3+6q^2+4q+1
         1: 2q^3+6q^2+4q+1
         2: 2q^3+6q^2+4q+1
         3: 2q^3+6q^2+4q+1
         4: 2q^3+6q^2+4q+1
         5: q^3+5q^2+4q+1
         6: 2q^3+6q^2+4q+1
         7: q^3+4q^2+4q+1
         8: q^3+4q^2+4q+1
         9: 2q^3+6q^2+4q+1
        10: 2q^3+6q^2+4q+1
        11: q^3+5q^2+4q+1
        12: 2q^3+6q^2+4q+1
        13: 2q^3+6q^2+4q+1
        14: 2q^3+6q^2+4q+1
        15: q^3+4q^2+4q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: 3q^2+4q+1
        19: q^3+5q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+4q^2+4q+1
        22: 2q^2+4q+1
        23: 2q^2+3q+1
        24: q^3+4q^2+4q+1
        25: 2q^3+6q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: q^3+5q^2+4q+1
        29: q^3+5q^2+4q+1
        30: 2q^3+6q^2+4q+1
        31: 2q^3+6q^2+4q+1
        32: q^3+5q^2+4q+1
        33: 2q^3+6q^2+4q+1
        34: q^3+4q^2+4q+1
        35: 2q^2+4q+1
        36: q^3+4q^2+4q+1
        37: q^3+4q^2+4q+1
        38: 2q^2+3q+1
        39: q^3+4q^2+4q+1
        40: q^3+5q^2+4q+1
        41: q^3+4q^2+4q+1
        42: 2q^2+4q+1
        43: 3q^2+4q+1
        44: 3q^2+4q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: q^3+5q^2+4q+1
        48: q^3+5q^2+4q+1
        49: 2q^2+4q+1
        50: 2q^2+3q+1
        51: q^3+4q^2+4q+1
        52: 2q^2+4q+1
        53: 2q^2+4q+1
        54: q^2+3q+1
        55: 2q^2+4q+1
        56: 2q^2+3q+1
        57: q^3+4q^2+4q+1
        58: q^3+4q^2+4q+1
        59: 2q^2+4q+1
        60: 2q^2+3q+1
        61: q^3+4q^2+4q+1
        62: q^3+5q^2+4q+1
        63: q^3+4q^2+4q+1
        64: 2q^2+4q+1
        65: 2q^3+6q^2+4q+1
        66: q^3+4q^2+4q+1
        67: 2q^2+4q+1
        68: q^3+5q^2+4q+1
        69: q^3+5q^2+4q+1
        70: 2q^2+4q+1
        71: 2q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^2+4q+1
        74: 2q+1
        75: 2q^2+4q+1
        76: q^3+4q^2+4q+1
        77: q^2+2q+1
        78: 2q^2+4q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^3+4q^2+4q+1
        82: q^3+4q^2+4q+1
        83: 2q^2+3q+1
        84: 2q^2+4q+1
        85: q^3+4q^2+4q+1
        86: q^2+4q+1
        87: q^2+3q+1
        88: 2q^2+4q+1
        89: 3q^2+4q+1
        90: q^2+2q+1
        91: 2q^2+4q+1
        92: 3q^2+4q+1
        93: 3q^2+4q+1
        94: 3q^2+4q+1
        95: 3q^2+4q+1
        96: 3q^2+4q+1
        97: q^3+5q^2+4q+1
        98: q^3+4q^2+4q+1
        99: q^2+4q+1
       100: 2q^2+4q+1
       101: 2q^2+4q+1
       102: q^2+3q+1
       103: 2q^2+4q+1
       104: 2q^2+3q+1
       105: q^2+3q+1
       106: 2q^2+4q+1
       107: 2q^2+4q+1
       108: q^2+3q+1
       109: 2q^2+4q+1
       110: q^2+3q+1
       111: 2q+1
       112: 2q^2+3q+1
       113: q^3+4q^2+4q+1
       114: 2q^2+4q+1
       115: 2q^2+4q+1
       116: q^2+3q+1
       117: 2q^2+4q+1
       118: 2q^2+3q+1
       119: 2q^2+4q+1
       120: q^3+4q^2+4q+1
       121: q^2+4q+1
       122: q^2+3q+1
       123: 2q^2+4q+1
       124: 2q^2+4q+1
       125: q^3+4q^2+4q+1
       126: q^2+4q+1
       127: 2q+1
       128: 2q^2+4q+1
       129: q^3+5q^2+4q+1
       130: q^3+4q^2+4q+1
       131: q^2+4q+1
       132: 2q^2+4q+1
       133: 2q^2+4q+1
       134: 2q+1
       135: 2q^2+4q+1
       136: q^2+4q+1
       137: q^2+4q+1
       138: 2q+1
       139: q^2+4q+1
       140: 2q+1
       141: 2q^2+4q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q+1
       145: 2q^2+4q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: 2q+1
       149: q^3+4q^2+4q+1
       150: q^2+2q+1
       151: 2q^2+4q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+3q+1
       155: q^2+3q+1
       156: 2q^2+4q+1
       157: q^2+4q+1
       158: q^2+4q+1
       159: 3q+1
       160: q^2+4q+1
       161: q^2+3q+1
       162: 2q^2+4q+1
       163: q^2+2q+1
       164: 2q+1
       165: q^2+3q+1
       166: 2q^2+4q+1
       167: 3q^2+4q+1
       168: q^2+2q+1
       169: 2q^2+4q+1
       170: 3q^2+4q+1
       171: q^2+2q+1
       172: 2q+1
       173: 3q^2+4q+1
       174: 3q^2+4q+1
       175: 2q^2+4q+1
       176: q^2+4q+1
       177: q^3+4q^2+4q+1
       178: q^2+4q+1
       179: 2q+1
       180: q^2+4q+1
       181: 2q^2+4q+1
       182: q+1
       183: q^2+4q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: 2q^2+4q+1
       187: 2q^2+4q+1
       188: q^2+3q+1
       189: 2q+1
       190: q^2+3q+1
       191: q^2+3q+1
       192: 2q^2+4q+1
       193: 2q+1
       194: 2q+1
       195: q^2+3q+1
       196: 2q+1
       197: 2q+1
       198: 2q^2+3q+1
       199: q^2+3q+1
       200: 2q^2+4q+1
       201: 2q^2+4q+1
       202: q^2+3q+1
       203: 2q^2+4q+1
       204: q^2+3q+1
       205: 2q+1
       206: q^2+3q+1
       207: 2q^2+4q+1
       208: q^2+4q+1
       209: q^2+4q+1
       210: 3q+1
       211: q^2+4q+1
       212: q^2+3q+1
       213: 2q+1
       214: 2q^2+4q+1
       215: q^2+4q+1
       216: q^2+4q+1
       217: 2q+1
       218: q^2+4q+1
       219: 2q+1
       220: q^2+4q+1
       221: q^3+4q^2+4q+1
       222: q^2+4q+1
       223: 2q+1
       224: q^2+4q+1
       225: 2q^2+4q+1
       226: q+1
       227: q^2+4q+1
       228: 2q+1
       229: 2q+1
       230: q^2+4q+1
       231: q^2+4q+1
       232: 2q+1
       233: q^2+4q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q^2+4q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: 2q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q^2+4q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: 2q^2+4q+1
       253: 2q^2+3q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q^2+3q+1
       259: 3q+1
       260: q^2+4q+1
       261: q^2+4q+1
       262: 3q+1
       263: q^2+4q+1
       264: 3q+1
       265: 2q+1
       266: q^2+3q+1
       267: 2q^2+4q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: q^2+3q+1
       273: 2q^2+4q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+3q+1
       277: 2q^2+4q+1
       278: 2q+1
       279: q^2+2q+1
       280: q+1
       282: 2q+1
       283: 3q^2+4q+1
       284: q^2+2q+1
       285: 2q+1
       286: 2q^2+4q+1
       287: 2q^2+4q+1
       288: 2q+1
       289: q^2+4q+1
       290: q^2+4q+1
       291: q^2+4q+1
       292: 2q+1
       293: q^2+4q+1
       294: 2q+1
       295: q^2+4q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: q^2+4q+1
       300: q^2+3q+1
       301: q+1
       302: 2q+1
       303: 2q^2+4q+1
       304: q+1
       305: 2q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: 2q+1
       310: 2q+1
       311: q^2+3q+1
       312: 2q+1
       313: 2q+1
       315: 2q+1
       316: q+1
       317: 2q+1
       319: 2q+1
       320: q^2+3q+1
       321: q^2+3q+1
       322: 2q^2+4q+1
       323: 2q+1
       324: 2q+1
       325: q^2+3q+1
       326: 2q+1
       327: 2q+1
       328: q^2+3q+1
       329: 3q+1
       330: q^2+4q+1
       331: q^2+4q+1
       332: 3q+1
       333: q^2+4q+1
       334: 3q+1
       335: 2q+1
       336: 2q+1
       337: 2q+1
       338: q^2+4q+1
       339: q^2+4q+1
       340: 2q+1
       341: q^2+4q+1
       342: 2q+1
       343: q+1
       344: 2q+1
       345: q^2+4q+1
       346: q^2+4q+1
       347: q^2+4q+1
       348: 2q+1
       349: q^2+4q+1
       350: 2q+1
       351: q^2+4q+1
       352: q+1
       353: q+1
       354: 2q+1
       355: q^2+4q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: q^2+4q+1
       360: q+1
       361: 2q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: q+1
       374: 2q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: q+1
       380: 2q+1
       381: 2q^2+4q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: 2q+1
       387: 2q+1
       388: q^2+2q+1
       389: q+1
       390: q+1
       391: 2q+1
       392: q^2+3q+1
       393: q+1
       394: 2q+1
       395: 2q+1
       396: 3q+1
       397: 3q+1
       398: q^2+4q+1
       399: 2q+1
       400: q+1
       401: 3q+1
       402: 2q+1
       403: 2q+1
       404: q^2+3q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q+1
       412: q^2+3q+1
       413: 2q^2+4q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: q^2+3q+1
       420: 2q+1
       421: q+1
       422: q+1
       424: q+1
       426: 2q+1
       427: q^2+2q+1
       428: q+1
       430: 2q+1
       431: 2q^2+4q+1
       432: q+1
       433: 2q+1
       434: 2q+1
       435: 2q+1
       436: q^2+4q+1
       437: q^2+4q+1
       438: 2q+1
       439: q^2+4q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: q^2+4q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: 2q+1
       450: q+1
       451: 1
       452: q+1
       453: 2q+1
       454: 2q+1
       455: q+1
       456: 1
       458: 2q+1
       459: q^2+3q+1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: 2q+1
       466: q+1
       467: 2q+1
       470: q+1
       471: q+1
       473: 2q+1
       474: 2q+1
       475: q^2+3q+1
       476: 2q+1
       477: 2q+1
       479: 2q+1
       480: q+1
       481: 2q+1
       483: 2q+1
       484: 3q+1
       485: 3q+1
       486: q^2+4q+1
       487: 2q+1
       488: q+1
       489: 3q+1
       490: 2q+1
       491: 2q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: q^2+4q+1
       496: q+1
       497: 2q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: q^2+4q+1
       504: q^2+4q+1
       505: 2q+1
       506: q^2+4q+1
       507: 2q+1
       508: q+1
       509: 2q+1
       510: q^2+4q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       522: 2q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: 2q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 1
       551: q+1
       552: 2q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: q+1
       558: 2q+1
       559: q+1
       560: 1
       561: q+1
       562: 2q+1
       563: 2q+1
       564: 2q+1
       565: 3q+1
       566: 2q+1
       567: 2q+1
       569: q+1
       570: 1
       571: 2q+1
       573: q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: 1
       579: 2q+1
       580: q+1
       581: q+1
       582: q^2+3q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q+1
       592: q+1
       593: q+1
       595: q+1
       599: 2q+1
       600: q+1
       601: q+1
       603: q+1
       605: 2q+1
       606: q+1
       607: 1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: q^2+4q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: 2q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: 2q+1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: q+1
       643: 1
       645: q+1
       646: q^2+3q+1
       647: q+1
       648: q+1
       650: q+1
       651: q+1
       655: q+1
       658: 2q+1
       659: q+1
       660: 2q+1
       663: q+1
       664: q+1
       666: 2q+1
       667: 2q+1
       668: 3q+1
       669: 2q+1
       670: 2q+1
       672: q+1
       673: 1
       674: 2q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       682: 2q+1
       683: 1
       684: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: q^2+4q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       704: q+1
       705: 1
       706: q+1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: q+1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: q+1
       749: 2q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       756: 2q+1
       757: 1
       758: 2q+1
       761: 1
       762: 1
       764: q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       770: 1
       771: 1
       772: q+1
       774: q+1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: 1
       780: 2q+1
       781: q+1
       782: q+1
       786: q+1
       788: 1
       794: q+1
       795: q+1
       797: q+1
       801: 2q+1
       802: 1
       803: 1
       805: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: q+1
       844: 1
       845: 1
       847: 1
       849: q+1
       850: q+1
       851: 1
       853: q+1
       855: q+1
       862: q+1
       863: q+1
       867: q+1
       870: 2q+1
       871: 1
       872: 2q+1
       875: 1
       876: 1
       879: q+1
       880: 1
       881: q+1
       884: 1
       885: 1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       893: q+1
       894: 1
       895: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       961: 1
       962: 1
       966: 1
       969: q+1
       970: 1
       971: q+1
       974: 1
       975: 1
       977: q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       983: 1
       984: 1
       985: q+1
       993: 1
      1000: q+1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1015: q+1
      1016: 1
      1017: q+1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: q+1
      1061: 1
      1062: 1
      1064: 1
      1072: q+1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1092: 1
      1095: q+1
      1096: 1
      1097: q+1
      1100: 1
      1101: 1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1131: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: q+1
      1182: 1
      1183: q+1
      1186: 1
      1187: 1
      1204: 1
      1211: 1
      1213: 1
      1218: 1
      1219: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1250: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1280: 1
      1287: 1
      1294: 1
      1295: 1
      1299: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1316: 1
      1331: 1
      1332: 1
      1336: 1
      1339: 1
      1341: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1363: 1
      1370: 1
      1371: 1
      1375: 1
      1400: 1
      1405: 1
      1412: 1
      1413: 1
      1417: 1
      1420: 1
      1422: 1
      1450: 1
      1472: 1
      1479: 1
      1480: 1
      1484: 1
      1502: 1
      1517: 1
      1519: 1
      1534: 1
      1570: 1
      1626: 1

1627:    0: 2q^3+6q^2+4q+1
         1: 2q^3+6q^2+4q+1
         2: 2q^3+6q^2+4q+1
         3: 2q^3+6q^2+4q+1
         4: q^3+5q^2+4q+1
         5: 2q^3+6q^2+4q+1
         6: 2q^3+6q^2+4q+1
         7: q^3+4q^2+4q+1
         8: q^3+4q^2+4q+1
         9: 2q^3+6q^2+4q+1
        10: 2q^3+6q^2+4q+1
        11: 2q^3+6q^2+4q+1
        12: q^3+5q^2+4q+1
        13: q^3+5q^2+4q+1
        14: q^3+5q^2+4q+1
        15: 3q^2+4q+1
        16: 2q^3+6q^2+4q+1
        17: 2q^3+6q^2+4q+1
        18: q^3+4q^2+4q+1
        19: q^3+5q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+4q^2+4q+1
        22: 2q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 2q^2+3q+1
        25: 2q^3+6q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: 2q^3+6q^2+4q+1
        29: 2q^3+6q^2+4q+1
        30: q^3+5q^2+4q+1
        31: q^3+5q^2+4q+1
        32: q^3+5q^2+4q+1
        33: q^3+5q^2+4q+1
        34: q^3+4q^2+4q+1
        35: 2q^2+4q+1
        36: 3q^2+4q+1
        37: 3q^2+4q+1
        38: 3q^2+4q+1
        39: 3q^2+4q+1
        40: 2q^3+6q^2+4q+1
        41: q^3+4q^2+4q+1
        42: 2q^2+4q+1
        43: q^3+4q^2+4q+1
        44: q^3+4q^2+4q+1
        45: q^3+4q^2+4q+1
        46: 2q^2+3q+1
        47: q^3+5q^2+4q+1
        48: q^3+5q^2+4q+1
        49: 2q^2+4q+1
        50: q^3+4q^2+4q+1
        51: 2q^2+3q+1
        52: 2q^2+4q+1
        53: 2q^2+4q+1
        54: 2q^2+4q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: q^3+4q^2+4q+1
        58: q^3+4q^2+4q+1
        59: 2q^2+4q+1
        60: q^3+4q^2+4q+1
        61: 2q^2+3q+1
        62: 2q^3+6q^2+4q+1
        63: q^3+4q^2+4q+1
        64: 2q^2+4q+1
        65: q^3+5q^2+4q+1
        66: q^3+4q^2+4q+1
        67: 2q^2+4q+1
        68: q^3+5q^2+4q+1
        69: q^3+5q^2+4q+1
        70: 2q^2+4q+1
        71: 2q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^2+4q+1
        74: 2q^2+4q+1
        75: q^2+3q+1
        76: 3q^2+4q+1
        77: q^2+2q+1
        78: 2q^2+4q+1
        79: 3q^2+4q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+4q+1
        83: 3q^2+4q+1
        84: 2q^2+4q+1
        85: q^3+4q^2+4q+1
        86: q^2+4q+1
        87: 2q^2+4q+1
        88: 2q+1
        89: q^3+4q^2+4q+1
        90: q^2+2q+1
        91: 2q^2+4q+1
        92: q^3+4q^2+4q+1
        93: q^3+4q^2+4q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+5q^2+4q+1
        98: q^3+4q^2+4q+1
        99: q^2+4q+1
       100: 2q^2+4q+1
       101: 2q^2+4q+1
       102: 2q^2+4q+1
       103: q^2+3q+1
       104: 2q^2+3q+1
       105: 2q^2+4q+1
       106: q^2+3q+1
       107: 2q^2+4q+1
       108: 2q^2+4q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: 2q+1
       112: q^3+4q^2+4q+1
       113: 2q^2+3q+1
       114: 2q^2+4q+1
       115: 2q^2+4q+1
       116: 2q^2+4q+1
       117: q^2+3q+1
       118: 2q^2+3q+1
       119: 2q^2+4q+1
       120: q^3+4q^2+4q+1
       121: q^2+4q+1
       122: 2q^2+4q+1
       123: 2q+1
       124: 2q^2+4q+1
       125: q^3+4q^2+4q+1
       126: q^2+4q+1
       127: 2q^2+4q+1
       128: q^2+3q+1
       129: q^3+5q^2+4q+1
       130: q^3+4q^2+4q+1
       131: q^2+4q+1
       132: 2q^2+4q+1
       133: 2q^2+4q+1
       134: 2q^2+4q+1
       135: q^2+3q+1
       136: q^2+4q+1
       137: q^2+4q+1
       138: q^2+4q+1
       139: 3q+1
       140: q^2+3q+1
       141: 2q^2+4q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q^2+4q+1
       145: q^2+3q+1
       146: 3q^2+4q+1
       147: q^2+2q+1
       148: 2q+1
       149: 3q^2+4q+1
       150: q^2+2q+1
       151: 2q^2+4q+1
       152: 3q^2+4q+1
       153: 3q^2+4q+1
       154: 2q^2+4q+1
       155: 2q^2+4q+1
       156: 2q+1
       157: q^2+4q+1
       158: q^2+4q+1
       159: q^2+4q+1
       160: 2q+1
       161: 2q+1
       162: 2q^2+4q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q^2+4q+1
       166: 2q+1
       167: q^3+4q^2+4q+1
       168: q^2+2q+1
       169: 2q^2+4q+1
       170: 2q^2+3q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+3q+1
       176: q^2+4q+1
       177: q^3+4q^2+4q+1
       178: q^2+4q+1
       179: q^2+4q+1
       180: 2q+1
       181: 2q^2+4q+1
       182: q+1
       183: q^2+4q+1
       184: 2q^2+4q+1
       185: 2q^2+4q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: 2q+1
       190: q^2+3q+1
       191: 2q^2+4q+1
       192: q^2+3q+1
       193: 2q+1
       194: 2q+1
       195: q^2+3q+1
       196: 2q+1
       197: 2q+1
       198: 2q^2+3q+1
       199: 2q^2+4q+1
       200: q^2+3q+1
       201: 2q^2+4q+1
       202: 2q^2+4q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: 2q+1
       206: 2q^2+4q+1
       207: 2q+1
       208: q^2+4q+1
       209: q^2+4q+1
       210: q^2+4q+1
       211: 2q+1
       212: 2q+1
       213: 2q^2+4q+1
       214: q^2+3q+1
       215: q^2+4q+1
       216: q^2+4q+1
       217: q^2+4q+1
       218: 3q+1
       219: q^2+3q+1
       220: q^2+4q+1
       221: q^3+4q^2+4q+1
       222: q^2+4q+1
       223: q^2+4q+1
       224: 2q+1
       225: 2q^2+4q+1
       226: q+1
       227: q^2+4q+1
       228: q^2+3q+1
       229: q^2+4q+1
       230: 3q+1
       231: q^2+4q+1
       232: q^2+4q+1
       233: 3q+1
       234: 3q+1
       235: 2q+1
       236: 2q^2+4q+1
       237: q^2+3q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: q^2+3q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       248: 2q^2+4q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q^2+4q+1
       252: q^2+3q+1
       253: 3q^2+4q+1
       254: q^2+2q+1
       255: 2q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: 2q+1
       259: q^2+4q+1
       260: 2q+1
       261: q^2+4q+1
       262: q^2+4q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q^2+4q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: 2q+1
       273: 2q^2+4q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q^2+4q+1
       277: 2q+1
       278: 2q+1
       279: q^2+2q+1
       280: q+1
       281: 2q+1
       282: q+1
       283: 2q^2+3q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+3q+1
       287: q^2+3q+1
       288: q^2+4q+1
       289: 2q+1
       290: q^2+4q+1
       291: q^2+4q+1
       292: q^2+4q+1
       293: 2q+1
       294: 2q+1
       295: q^2+4q+1
       296: q+1
       297: q+1
       298: q^2+4q+1
       299: 2q+1
       300: 2q^2+4q+1
       301: q+1
       302: 2q+1
       303: q^2+3q+1
       304: q+1
       305: 2q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: 2q+1
       310: 2q+1
       311: q^2+3q+1
       312: 2q+1
       314: 2q+1
       315: 2q+1
       316: q+1
       317: 2q+1
       319: 2q+1
       320: q^2+3q+1
       321: 2q^2+4q+1
       322: q^2+3q+1
       323: 2q+1
       324: 2q+1
       325: q^2+3q+1
       326: 2q+1
       327: 2q+1
       328: 2q+1
       329: q^2+4q+1
       330: 2q+1
       331: q^2+4q+1
       332: q^2+4q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: q^2+3q+1
       337: q^2+4q+1
       338: 3q+1
       339: q^2+4q+1
       340: q^2+4q+1
       341: 3q+1
       342: 3q+1
       343: 2q+1
       344: q^2+4q+1
       345: 2q+1
       346: q^2+4q+1
       347: q^2+4q+1
       348: q^2+4q+1
       349: 2q+1
       350: 2q+1
       351: q^2+4q+1
       352: q+1
       353: q+1
       354: q^2+4q+1
       355: 2q+1
       356: 2q+1
       357: 3q+1
       358: q^2+4q+1
       359: 3q+1
       360: q+1
       361: 2q+1
       362: 3q+1
       363: 2q+1
       364: 2q+1
       365: q^2+3q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: 2q+1
       375: q+1
       376: q+1
       377: q+1
       380: 2q^2+4q+1
       381: q^2+3q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: q^2+3q+1
       387: 2q+1
       388: q^2+2q+1
       389: q+1
       390: 2q+1
       392: 2q^2+4q+1
       393: q+1
       394: 2q+1
       395: q+1
       396: 2q+1
       397: q^2+4q+1
       398: 2q+1
       399: 2q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: 2q^2+4q+1
       413: 2q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: 2q+1
       419: 2q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: q+1
       426: 2q+1
       427: q^2+2q+1
       428: q+1
       429: 2q+1
       430: q+1
       431: q^2+3q+1
       432: q+1
       433: 2q+1
       434: 2q+1
       435: q^2+4q+1
       436: 2q+1
       437: q^2+4q+1
       438: q^2+4q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q^2+4q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: 2q+1
       450: q+1
       451: 1
       452: 2q+1
       454: 2q+1
       455: q+1
       456: 1
       457: 2q+1
       458: q+1
       459: q^2+3q+1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: 2q+1
       466: q+1
       468: 2q+1
       469: q+1
       471: q+1
       473: 2q+1
       474: 2q+1
       475: q^2+3q+1
       476: 2q+1
       478: 2q+1
       479: 2q+1
       480: q+1
       481: 2q+1
       483: q+1
       484: 2q+1
       485: q^2+4q+1
       486: 2q+1
       487: 2q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: 2q+1
       493: 3q+1
       494: q^2+4q+1
       495: 3q+1
       496: q+1
       497: 2q+1
       498: 3q+1
       499: 2q+1
       500: 2q+1
       501: 2q+1
       502: q^2+4q+1
       503: 2q+1
       504: q^2+4q+1
       505: q^2+4q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: q^2+4q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2q+1
       516: 2q+1
       517: 2q+1
       518: 3q+1
       519: q+1
       521: 2q+1
       522: 2q+1
       523: 1
       524: 2q+1
       526: q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: 1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       536: q+1
       538: q+1
       539: q+1
       543: q^2+3q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: 2q+1
       553: q+1
       554: q+1
       555: q+1
       558: 2q+1
       559: q+1
       560: 1
       561: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: 2q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 2q+1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: 2q+1
       599: q+1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: q+1
       605: 2q+1
       606: q+1
       607: 1
       608: 2q+1
       609: q+1
       610: q+1
       611: 2q+1
       612: q^2+4q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 2q+1
       629: 1
       630: 1
       631: 1
       634: 2q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       646: q^2+3q+1
       647: q+1
       648: q+1
       650: q+1
       652: q+1
       654: q+1
       658: 2q+1
       659: q+1
       661: 2q+1
       662: q+1
       664: q+1
       666: q+1
       667: q+1
       668: 2q+1
       669: 2q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       676: 2q+1
       677: 2q+1
       678: 3q+1
       679: q+1
       681: 2q+1
       682: 2q+1
       683: 1
       684: 2q+1
       686: q+1
       687: 2q+1
       688: q^2+4q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       704: 2q+1
       705: 1
       707: 2q+1
       708: 1
       710: 1
       712: q+1
       713: q+1
       714: 2q+1
       715: 1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       724: q+1
       726: 1
       731: q+1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: 1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       741: q+1
       743: q+1
       744: q+1
       748: 2q+1
       750: 1
       751: 1
       752: 1
       756: q+1
       757: 1
       759: q+1
       760: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: q+1
       776: 2q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: q+1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: 2q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: 1
       845: 1
       846: 1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       856: q+1
       862: q+1
       864: q+1
       866: q+1
       870: q+1
       871: 1
       873: q+1
       874: 1
       876: 1
       879: 2q+1
       880: 1
       882: 2q+1
       883: 1
       885: 1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       907: 1
       909: 1
       911: 1
       915: q+1
       916: 1
       918: q+1
       919: 1
       921: 1
       926: 1
       933: q+1
       934: q+1
       935: 2q+1
       936: 1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       945: q+1
       947: 1
       953: 1
       955: 1
       956: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1015: q+1
      1016: 1
      1018: q+1
      1019: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: q+1
      1061: 1
      1062: 1
      1063: 1
      1073: q+1
      1079: 1
      1081: 1
      1083: 1
      1087: 1
      1089: 1
      1091: 1
      1095: q+1
      1096: 1
      1098: q+1
      1099: 1
      1101: 1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1138: q+1
      1139: 1
      1141: q+1
      1142: 1
      1144: 1
      1149: 1
      1158: 1
      1160: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1190: 1
      1193: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1281: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1317: 1
      1331: 1
      1333: 1
      1335: 1
      1350: 1
      1364: 1
      1370: 1
      1372: 1
      1374: 1
      1386: 1
      1389: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1406: 1
      1412: 1
      1414: 1
      1416: 1
      1429: 1
      1432: 1
      1449: 1
      1473: 1
      1479: 1
      1481: 1
      1483: 1
      1503: 1
      1535: 1
      1556: 1
      1559: 1
      1571: 1
      1627: 1

1628:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 3q+1
         7: 3q+1
         8: 3q+1
         9: 2q^2+3q+1
        10: 3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: 3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: 3q+1
        21: 3q+1
        22: 3q+1
        23: 3q+1
        24: 3q+1
        25: 3q+1
        26: 3q+1
        27: 3q+1
        28: 2q^2+3q+1
        29: 3q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 3q+1
        34: 3q+1
        35: 3q+1
        36: 2q^2+3q+1
        37: q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 3q+1
        41: 3q+1
        42: 3q+1
        43: 2q^2+3q+1
        44: q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 3q+1
        49: 2q^2+3q+1
        50: 3q+1
        51: 3q+1
        52: 3q+1
        53: q+1
        54: 3q+1
        55: 3q+1
        56: 3q+1
        57: 3q+1
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: 3q+1
        65: 3q+1
        66: 3q+1
        67: 3q+1
        68: 2q^2+3q+1
        69: 3q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 3q+1
        73: 3q+1
        74: 3q+1
        75: 3q+1
        76: q+1
        77: q+1
        78: q+1
        79: 2q^2+3q+1
        80: q+1
        81: 2q^2+3q+1
        82: q+1
        83: 2q^2+3q+1
        84: 3q+1
        85: 3q+1
        86: 3q+1
        87: 3q+1
        88: 3q+1
        89: q+1
        90: q+1
        91: q+1
        92: 2q^2+3q+1
        93: q+1
        94: 2q^2+3q+1
        95: q+1
        96: 2q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: 3q+1
       100: 2q^2+3q+1
       101: 1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 3q+1
       105: 3q+1
       106: 3q+1
       107: q+1
       108: q+1
       109: q+1
       110: 3q+1
       111: 3q+1
       112: 3q+1
       113: 3q+1
       114: 3q+1
       115: q+1
       116: 3q+1
       117: 3q+1
       118: 3q+1
       119: 3q+1
       120: 3q+1
       121: 3q+1
       122: 3q+1
       123: 3q+1
       124: 3q+1
       125: 3q+1
       126: 3q+1
       127: 3q+1
       128: 3q+1
       129: 3q+1
       130: 3q+1
       131: 3q+1
       132: 2q^2+3q+1
       133: 1
       134: 3q+1
       135: 3q+1
       136: 3q+1
       137: 1
       138: 3q+1
       139: 3q+1
       140: 3q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: 2q^2+3q+1
       153: q+1
       154: 2q^2+3q+1
       155: 3q+1
       156: 3q+1
       157: 3q+1
       158: 1
       159: 3q+1
       160: 3q+1
       161: 3q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: 2q^2+3q+1
       174: q+1
       175: 2q^2+3q+1
       176: 3q+1
       177: 3q+1
       178: 3q+1
       179: 3q+1
       180: 3q+1
       181: 1
       182: 1
       183: 1
       184: 2q^2+3q+1
       185: 1
       186: 2q^2+3q+1
       187: 1
       188: 2q^2+3q+1
       189: 3q+1
       190: 3q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 3q+1
       198: 3q+1
       199: 3q+1
       200: 3q+1
       201: q+1
       202: q+1
       203: q+1
       204: 3q+1
       205: 3q+1
       206: 3q+1
       207: 3q+1
       208: 3q+1
       209: 1
       210: 3q+1
       211: 3q+1
       212: 3q+1
       213: 3q+1
       214: 3q+1
       215: 3q+1
       216: 1
       217: 3q+1
       218: 3q+1
       219: 3q+1
       220: 3q+1
       221: 3q+1
       222: 3q+1
       223: 3q+1
       224: 3q+1
       225: 1
       226: 1
       227: 1
       228: 3q+1
       229: 3q+1
       230: 3q+1
       231: 1
       232: 1
       233: 1
       234: 3q+1
       235: 3q+1
       236: q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: 2q^2+3q+1
       257: 1
       258: 3q+1
       259: 3q+1
       260: 3q+1
       261: 1
       262: 1
       263: 1
       264: 3q+1
       265: 3q+1
       266: q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: 2q^2+3q+1
       287: 1
       288: 3q+1
       289: 3q+1
       290: 3q+1
       291: 1
       292: 3q+1
       293: 3q+1
       294: 3q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 2q^2+3q+1
       307: 1
       308: 2q^2+3q+1
       310: 3q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       319: 3q+1
       320: 3q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 3q+1
       328: 3q+1
       329: 3q+1
       330: 3q+1
       331: 1
       332: 1
       333: 1
       334: 3q+1
       335: 3q+1
       336: 3q+1
       337: 3q+1
       338: 3q+1
       339: 1
       340: 1
       341: 1
       342: 3q+1
       343: 3q+1
       344: 3q+1
       345: 3q+1
       346: 3q+1
       347: 1
       348: 3q+1
       349: 3q+1
       350: 3q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 3q+1
       357: 3q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 3q+1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: 3q+1
       396: 3q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 3q+1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: 3q+1
       435: 3q+1
       436: 3q+1
       437: 1
       438: 1
       439: 1
       440: 3q+1
       441: 3q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 2q^2+3q+1
       463: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       474: 3q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       483: 3q+1
       484: 3q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 3q+1
       492: 3q+1
       493: 3q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 3q+1
       501: 3q+1
       502: 3q+1
       503: 3q+1
       504: 1
       505: 1
       506: 1
       507: 3q+1
       508: 3q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: 3q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       535: q+1
       536: q+1
       537: q+1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: 3q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: q+1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       596: q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 3q+1
       611: 3q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 3q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: q+1
       652: q+1
       653: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       667: 3q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: 3q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: 3q+1
       687: 3q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 3q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: q+1
       723: q+1
       729: q+1
       731: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       740: q+1
       741: q+1
       742: q+1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: q+1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       783: q+1
       784: q+1
       790: q+1
       792: q+1
       793: q+1
       794: q+1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: 3q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       857: q+1
       863: q+1
       864: q+1
       865: q+1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: 3q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: q+1
       934: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       943: q+1
       944: q+1
       950: q+1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: q+1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       988: q+1
       997: q+1
       998: q+1
      1004: q+1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1040: 1
      1042: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1074: q+1
      1080: 1
      1081: 1
      1082: 1
      1088: 1
      1089: 1
      1090: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: q+1
      1156: 1
      1157: 1
      1163: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1199: q+1
      1208: 1
      1209: 1
      1215: 1
      1219: 1
      1220: 1
      1221: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1245: 1
      1254: 1
      1255: 1
      1261: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1282: 1
      1289: 1
      1295: 1
      1296: 1
      1297: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1348: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1395: 1
      1407: 1
      1413: 1
      1414: 1
      1415: 1
      1438: 1
      1447: 1
      1448: 1
      1454: 1
      1474: 1
      1480: 1
      1481: 1
      1482: 1
      1504: 1
      1536: 1
      1572: 1
      1602: 1
      1628: 1

1629:    0: q^4+4q^3+11q^2+6q+1
         1: 2q^3+10q^2+6q+1
         2: q^4+4q^3+11q^2+6q+1
         3: q^4+4q^3+11q^2+6q+1
         4: q^4+4q^3+11q^2+6q+1
         5: q^4+4q^3+11q^2+6q+1
         6: 2q^3+10q^2+6q+1
         7: q^3+8q^2+6q+1
         8: 2q^3+7q^2+6q+1
         9: 2q^3+10q^2+6q+1
        10: q^4+4q^3+11q^2+6q+1
        11: q^4+4q^3+11q^2+6q+1
        12: q^4+4q^3+11q^2+6q+1
        13: 2q^3+10q^2+6q+1
        14: q^4+4q^3+11q^2+6q+1
        15: 2q^3+7q^2+6q+1
        16: 2q^3+10q^2+6q+1
        17: q^4+4q^3+11q^2+6q+1
        18: 2q^3+7q^2+6q+1
        19: q^4+4q^3+11q^2+6q+1
        20: 3q^2+4q+1
        21: q^3+8q^2+6q+1
        22: 4q^2+6q+1
        23: 2q^3+7q^2+6q+1
        24: 2q^3+7q^2+6q+1
        25: 2q^3+10q^2+6q+1
        26: q^3+8q^2+6q+1
        27: 2q^3+7q^2+6q+1
        28: 2q^3+10q^2+6q+1
        29: q^4+4q^3+11q^2+6q+1
        30: 2q^3+10q^2+6q+1
        31: q^4+4q^3+11q^2+6q+1
        32: q^4+4q^3+11q^2+6q+1
        33: 2q^3+10q^2+6q+1
        34: q^3+8q^2+6q+1
        35: q^3+4q^2+6q+1
        36: q^3+6q^2+6q+1
        37: 2q^3+7q^2+6q+1
        38: 2q^3+7q^2+6q+1
        39: 2q^3+7q^2+6q+1
        40: 2q^3+10q^2+6q+1
        41: q^3+8q^2+6q+1
        42: q^3+4q^2+6q+1
        43: q^3+6q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+10q^2+6q+1
        48: q^4+4q^3+11q^2+6q+1
        49: 4q^2+6q+1
        50: 3q^2+4q+1
        51: 3q^2+4q+1
        52: q^2+4q+1
        53: 4q^2+6q+1
        54: 4q^2+6q+1
        55: 4q^2+6q+1
        56: 2q^3+7q^2+6q+1
        57: 3q^2+4q+1
        58: q^3+8q^2+6q+1
        59: 4q^2+6q+1
        60: 2q^3+7q^2+6q+1
        61: 2q^3+7q^2+6q+1
        62: 2q^3+10q^2+6q+1
        63: q^3+8q^2+6q+1
        64: q^3+4q^2+6q+1
        65: 2q^3+10q^2+6q+1
        66: q^3+8q^2+6q+1
        67: q^3+4q^2+6q+1
        68: 2q^3+10q^2+6q+1
        69: q^4+4q^3+11q^2+6q+1
        70: 4q^2+6q+1
        71: q^2+4q+1
        72: q^3+8q^2+6q+1
        73: 2q^2+6q+1
        74: q^3+4q^2+6q+1
        75: q^3+4q^2+6q+1
        76: q^3+6q^2+6q+1
        77: 3q^2+4q+1
        78: q^3+4q^2+6q+1
        79: q^3+6q^2+6q+1
        80: 2q^3+7q^2+6q+1
        81: q^3+6q^2+6q+1
        82: 2q^3+7q^2+6q+1
        83: 2q^3+7q^2+6q+1
        84: q^2+4q+1
        85: q^3+8q^2+6q+1
        86: 2q^2+6q+1
        87: q^3+4q^2+6q+1
        88: q^3+4q^2+6q+1
        89: q^3+6q^2+6q+1
        90: 3q^2+4q+1
        91: q^3+4q^2+6q+1
        92: q^3+6q^2+6q+1
        93: 2q^3+7q^2+6q+1
        94: q^3+6q^2+6q+1
        95: 2q^3+7q^2+6q+1
        96: 2q^3+7q^2+6q+1
        97: 2q^3+10q^2+6q+1
        98: q^3+8q^2+6q+1
        99: 2q^2+6q+1
       100: 3q^2+6q+1
       101: 4q^2+6q+1
       102: 4q^2+6q+1
       103: 4q^2+6q+1
       104: 3q^2+4q+1
       105: q^2+4q+1
       106: q^2+4q+1
       107: q^2+4q+1
       108: 4q^2+6q+1
       109: 4q^2+6q+1
       110: 4q^2+6q+1
       111: 3q+1
       112: 3q^2+4q+1
       113: 3q^2+4q+1
       114: q^2+4q+1
       115: 4q^2+6q+1
       116: 4q^2+6q+1
       117: 4q^2+6q+1
       118: 2q^3+7q^2+6q+1
       119: q^2+4q+1
       120: q^3+8q^2+6q+1
       121: 2q^2+6q+1
       122: q^3+4q^2+6q+1
       123: q^3+4q^2+6q+1
       124: q^2+4q+1
       125: q^3+8q^2+6q+1
       126: 2q^2+6q+1
       127: q^3+4q^2+6q+1
       128: q^3+4q^2+6q+1
       129: 2q^3+10q^2+6q+1
       130: q^3+8q^2+6q+1
       131: 2q^2+6q+1
       132: 3q^2+6q+1
       133: 4q^2+6q+1
       134: q^2+4q+1
       135: q^2+4q+1
       136: 4q+1
       137: 2q^2+6q+1
       138: 2q^2+6q+1
       139: 2q^2+6q+1
       140: q^3+4q^2+6q+1
       141: q^2+4q+1
       142: 3q^2+4q+1
       143: q^2+4q+1
       144: q^3+4q^2+6q+1
       145: q^3+4q^2+6q+1
       146: q^3+6q^2+6q+1
       147: 3q^2+4q+1
       148: q^2+3q+1
       149: q^3+6q^2+6q+1
       150: 3q^2+4q+1
       151: q^3+4q^2+6q+1
       152: q^3+6q^2+6q+1
       153: 2q^3+7q^2+6q+1
       154: 4q^2+6q+1
       155: q^2+4q+1
       156: q^2+4q+1
       157: 4q+1
       158: 2q^2+6q+1
       159: 2q^2+6q+1
       160: 2q^2+6q+1
       161: q^3+4q^2+6q+1
       162: q^2+4q+1
       163: 3q^2+4q+1
       164: q^2+4q+1
       165: q^3+4q^2+6q+1
       166: q^3+4q^2+6q+1
       167: q^3+6q^2+6q+1
       168: 3q^2+4q+1
       169: q^3+4q^2+6q+1
       170: q^3+6q^2+6q+1
       171: 3q^2+4q+1
       172: q^2+3q+1
       173: q^3+6q^2+6q+1
       174: 2q^3+7q^2+6q+1
       175: 4q^2+6q+1
       176: 4q+1
       177: q^3+8q^2+6q+1
       178: q^2+6q+1
       179: 2q^2+6q+1
       180: 2q^2+6q+1
       181: 3q^2+6q+1
       182: 3q+1
       183: 2q^2+6q+1
       184: 3q^2+6q+1
       185: 4q^2+6q+1
       186: 3q^2+6q+1
       187: 4q^2+6q+1
       188: 4q^2+6q+1
       190: q^2+4q+1
       191: q^2+4q+1
       192: q^2+4q+1
       193: 2q+1
       194: 2q+1
       195: 4q^2+6q+1
       196: 3q+1
       197: 3q+1
       198: 3q^2+4q+1
       199: q^2+4q+1
       200: q^2+4q+1
       201: q^2+4q+1
       202: 4q^2+6q+1
       203: 4q^2+6q+1
       204: 4q^2+6q+1
       205: 3q+1
       206: q^2+4q+1
       207: q^2+4q+1
       208: 4q+1
       209: 2q^2+6q+1
       210: 2q^2+6q+1
       211: 2q^2+6q+1
       212: q^3+4q^2+6q+1
       213: q^2+4q+1
       214: q^2+4q+1
       215: 4q+1
       216: 2q^2+6q+1
       217: 2q^2+6q+1
       218: 2q^2+6q+1
       219: q^3+4q^2+6q+1
       220: 4q+1
       221: q^3+8q^2+6q+1
       222: q^2+6q+1
       223: 2q^2+6q+1
       224: 2q^2+6q+1
       225: 3q^2+6q+1
       226: 3q+1
       227: 2q^2+6q+1
       228: q^2+4q+1
       229: 4q+1
       230: 4q+1
       231: 4q+1
       232: 2q^2+6q+1
       233: 2q^2+6q+1
       234: 2q^2+6q+1
       235: 3q+1
       236: q^2+4q+1
       237: q^2+4q+1
       238: 2q+1
       239: q^2+4q+1
       240: q^2+4q+1
       241: q^2+4q+1
       242: q^3+4q^2+6q+1
       243: 2q+1
       244: 3q^2+4q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+4q+1
       249: 3q^2+4q+1
       250: q^2+4q+1
       251: q^3+4q^2+6q+1
       252: q^3+4q^2+6q+1
       253: q^3+6q^2+6q+1
       254: 3q^2+4q+1
       255: q^2+3q+1
       256: 3q^2+6q+1
       257: 4q^2+6q+1
       258: q^2+4q+1
       259: 4q+1
       260: 4q+1
       261: 4q+1
       262: 2q^2+6q+1
       263: 2q^2+6q+1
       264: 2q^2+6q+1
       265: 3q+1
       266: q^2+4q+1
       267: q^2+4q+1
       268: 2q+1
       269: q^2+4q+1
       270: q^2+4q+1
       271: q^2+4q+1
       272: q^3+4q^2+6q+1
       273: q^2+4q+1
       274: 3q^2+4q+1
       275: q^2+4q+1
       276: q^3+4q^2+6q+1
       277: q^3+4q^2+6q+1
       278: 2q+1
       279: 3q^2+4q+1
       280: 2q+1
       281: q^2+3q+1
       282: q^2+3q+1
       283: q^3+6q^2+6q+1
       284: 3q^2+4q+1
       285: q^2+3q+1
       286: 3q^2+6q+1
       287: 4q^2+6q+1
       288: 4q+1
       289: 4q+1
       290: 4q+1
       291: q^2+6q+1
       292: q^2+6q+1
       293: q^2+6q+1
       294: 2q^2+6q+1
       295: 4q+1
       296: 3q+1
       297: 3q+1
       298: 2q^2+6q+1
       299: 2q^2+6q+1
       300: 3q^2+6q+1
       301: 3q+1
       302: q^2+3q+1
       303: 3q^2+6q+1
       304: 3q+1
       305: q^2+3q+1
       306: 3q^2+6q+1
       307: 4q^2+6q+1
       308: 4q^2+6q+1
       311: q^2+4q+1
       312: 2q+1
       313: 2q+1
       314: 2q+1
       315: 2q+1
       316: q+1
       317: 3q+1
       320: q^2+4q+1
       321: q^2+4q+1
       322: q^2+4q+1
       323: 2q+1
       324: 2q+1
       325: 4q^2+6q+1
       326: 3q+1
       327: 3q+1
       328: q^2+4q+1
       329: 4q+1
       330: 4q+1
       331: 4q+1
       332: 2q^2+6q+1
       333: 2q^2+6q+1
       334: 2q^2+6q+1
       335: 3q+1
       336: q^2+4q+1
       337: 4q+1
       338: 4q+1
       339: 4q+1
       340: 2q^2+6q+1
       341: 2q^2+6q+1
       342: 2q^2+6q+1
       343: 3q+1
       344: 4q+1
       345: 4q+1
       346: 4q+1
       347: q^2+6q+1
       348: q^2+6q+1
       349: q^2+6q+1
       350: 2q^2+6q+1
       351: 4q+1
       352: 3q+1
       353: 3q+1
       354: 2q^2+6q+1
       355: 2q^2+6q+1
       357: 4q+1
       358: 4q+1
       359: 4q+1
       360: q+1
       361: 2q+1
       362: 2q^2+6q+1
       363: 3q+1
       364: 3q+1
       365: q^2+4q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: q^2+4q+1
       370: q^2+4q+1
       371: q^2+4q+1
       372: q+1
       373: 2q+1
       374: 2q+1
       375: q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: q^2+3q+1
       380: q^2+4q+1
       381: q^2+4q+1
       382: 2q+1
       383: q^2+4q+1
       384: q^2+4q+1
       385: q^2+4q+1
       386: q^3+4q^2+6q+1
       387: 2q+1
       388: 3q^2+4q+1
       389: 2q+1
       390: q^2+3q+1
       391: q^2+3q+1
       392: 3q^2+6q+1
       393: 3q+1
       394: q^2+3q+1
       396: 4q+1
       397: 4q+1
       398: 4q+1
       399: 2q+1
       400: q+1
       401: 2q^2+6q+1
       402: 3q+1
       403: 3q+1
       404: q^2+4q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: q^2+4q+1
       409: q^2+4q+1
       410: q^2+4q+1
       411: q+1
       412: q^2+4q+1
       413: q^2+4q+1
       414: 2q+1
       415: q^2+4q+1
       416: q^2+4q+1
       417: q^2+4q+1
       418: q^3+4q^2+6q+1
       419: 2q+1
       420: 2q+1
       421: q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: q^2+3q+1
       426: 2q+1
       427: 3q^2+4q+1
       428: 2q+1
       429: q^2+3q+1
       430: q^2+3q+1
       431: 3q^2+6q+1
       432: 3q+1
       433: q^2+3q+1
       434: 4q+1
       435: 4q+1
       436: 4q+1
       437: 4q+1
       438: q^2+6q+1
       439: q^2+6q+1
       440: q^2+6q+1
       441: 3q+1
       442: 4q+1
       443: 4q+1
       444: q+1
       445: 3q+1
       446: 3q+1
       447: 3q+1
       448: 2q^2+6q+1
       449: 2q+1
       450: 3q+1
       451: q+1
       452: q^2+3q+1
       453: q^2+3q+1
       454: 2q+1
       455: 3q+1
       456: q+1
       457: q^2+3q+1
       458: q^2+3q+1
       459: 3q^2+6q+1
       460: 3q+1
       461: q+1
       462: 3q^2+6q+1
       463: 4q^2+6q+1
       467: 2q+1
       468: 2q+1
       469: q+1
       470: q+1
       471: q+1
       475: q^2+4q+1
       476: 2q+1
       477: 2q+1
       478: 2q+1
       479: 2q+1
       480: q+1
       481: 3q+1
       484: 4q+1
       485: 4q+1
       486: 4q+1
       487: 2q+1
       488: q+1
       489: 2q^2+6q+1
       490: 3q+1
       491: 3q+1
       493: 4q+1
       494: 4q+1
       495: 4q+1
       496: q+1
       497: 2q+1
       498: 2q^2+6q+1
       499: 3q+1
       500: 3q+1
       501: 4q+1
       502: 4q+1
       503: 4q+1
       504: 4q+1
       505: q^2+6q+1
       506: q^2+6q+1
       507: q^2+6q+1
       508: 3q+1
       509: 4q+1
       510: 4q+1
       511: q+1
       512: 3q+1
       513: 3q+1
       514: 3q+1
       515: 2q^2+6q+1
       518: 4q+1
       519: q+1
       520: q+1
       521: 2q+1
       522: 2q+1
       523: 1
       524: 3q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q^2+4q+1
       533: q+1
       534: q+1
       535: 2q+1
       536: q+1
       537: q+1
       538: q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       543: q^2+4q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: q^2+4q+1
       548: q^2+4q+1
       549: q^2+4q+1
       550: q+1
       551: 2q+1
       552: 2q+1
       553: q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: q^2+3q+1
       558: 2q+1
       559: 3q+1
       560: q+1
       561: q^2+3q+1
       562: q^2+3q+1
       565: 4q+1
       566: 2q+1
       567: 2q+1
       568: q+1
       569: q+1
       570: 1
       571: 3q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: 1
       579: q^2+4q+1
       580: q+1
       581: q+1
       582: q^2+4q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: q^2+4q+1
       587: q^2+4q+1
       588: q^2+4q+1
       589: q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q+1
       598: 2q+1
       599: 2q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: q^2+3q+1
       605: 2q+1
       606: 3q+1
       607: q+1
       608: q^2+3q+1
       609: q^2+3q+1
       611: 4q+1
       612: 4q+1
       613: 4q+1
       614: q+1
       615: q+1
       616: q^2+6q+1
       617: 3q+1
       618: 3q+1
       619: 4q+1
       620: q+1
       621: q+1
       622: q+1
       623: 3q+1
       624: 3q+1
       625: 3q+1
       626: 1
       627: 2q+1
       628: 2q+1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q^2+3q+1
       634: 2q+1
       635: 2q+1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q^2+3q+1
       641: q+1
       642: 3q+1
       643: 1
       644: q+1
       645: q+1
       646: 3q^2+6q+1
       647: 3q+1
       648: q+1
       653: q+1
       654: q+1
       655: q+1
       660: 2q+1
       661: 2q+1
       662: q+1
       663: q+1
       664: q+1
       668: 4q+1
       669: 2q+1
       670: 2q+1
       671: q+1
       672: q+1
       673: 1
       674: 3q+1
       678: 4q+1
       679: q+1
       680: q+1
       681: 2q+1
       682: 2q+1
       683: 1
       684: 3q+1
       687: 4q+1
       688: 4q+1
       689: 4q+1
       690: q+1
       691: q+1
       692: q^2+6q+1
       693: 3q+1
       694: 3q+1
       695: 4q+1
       696: q+1
       697: q+1
       698: q+1
       699: 3q+1
       700: 3q+1
       701: 3q+1
       702: 1
       706: q+1
       707: 2q+1
       708: 1
       709: 1
       710: 1
       714: 2q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       723: q+1
       724: q+1
       725: q+1
       726: 1
       728: 2q+1
       729: q+1
       730: q+1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q^2+4q+1
       738: q+1
       739: q+1
       740: 2q+1
       741: q+1
       742: q+1
       743: q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: 2q+1
       749: 2q+1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: q^2+3q+1
       758: 2q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       766: 2q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: q+1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: 1
       780: q^2+4q+1
       781: q+1
       782: q+1
       784: q+1
       785: q+1
       786: q+1
       788: 1
       789: 2q+1
       790: q+1
       791: q+1
       792: 2q+1
       793: q+1
       794: q+1
       795: q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: q+1
       800: 2q+1
       801: 2q+1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: q^2+3q+1
       809: 4q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: 3q+1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: 3q+1
       824: 1
       825: 1
       826: 2q+1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 2q+1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: 3q+1
       851: 1
       852: q+1
       853: q+1
       858: q+1
       865: q+1
       866: q+1
       867: q+1
       872: 2q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       881: q+1
       882: 2q+1
       883: 1
       884: 1
       885: 1
       889: 4q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: 3q+1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: 3q+1
       904: 1
       905: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       925: q+1
       926: 1
       927: 1
       931: q+1
       935: 2q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       944: q+1
       945: q+1
       946: q+1
       947: 1
       949: 2q+1
       950: q+1
       951: q+1
       952: 2q+1
       953: 1
       954: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       964: 1
       965: 1
       966: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 2q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: q+1
       989: q+1
       992: 1
       993: 1
       995: q+1
       998: q+1
       999: q+1
      1000: q+1
      1002: 1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1006: 2q+1
      1007: 1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1075: q+1
      1082: 1
      1083: 1
      1084: 1
      1090: 1
      1091: 1
      1092: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1105: q+1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1148: q+1
      1149: 1
      1150: 1
      1154: q+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: q+1
      1163: 1
      1164: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1193: 1
      1200: q+1
      1203: 1
      1204: 1
      1206: q+1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: q+1
      1215: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1283: 1
      1290: 1
      1297: 1
      1298: 1
      1299: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1319: 1
      1334: 1
      1335: 1
      1336: 1
      1341: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1366: 1
      1373: 1
      1374: 1
      1375: 1
      1389: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1408: 1
      1415: 1
      1416: 1
      1417: 1
      1422: 1
      1432: 1
      1439: 1
      1445: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1454: 1
      1455: 1
      1475: 1
      1482: 1
      1483: 1
      1484: 1
      1505: 1
      1519: 1
      1537: 1
      1559: 1
      1573: 1
      1603: 1
      1609: 1
      1629: 1

1630:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q^2+q+1
        52: q^2+q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+q+1
        58: 2q^2+2q+1
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: 2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: 2q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: q+1
       105: q^2+q+1
       107: q^2+q+1
       108: 2q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: 2q+1
       112: q^2+q+1
       114: q^2+q+1
       115: 2q^2+2q+1
       116: 2q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: q+1
       120: 2q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       157: q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: q+1
       187: q+1
       188: q+1
       191: q^2+q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: 2q+1
       197: 2q+1
       199: q^2+q+1
       201: q^2+q+1
       202: 2q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: 2q+1
       206: q+1
       208: q+1
       209: q^2+2q+1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: q+1
       215: q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       229: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: 1
       244: 2q+1
       245: q+1
       246: q+1
       248: q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: 2q+1
       255: q+1
       256: 2q+1
       257: 2q+1
       259: q+1
       261: q+1
       262: q^2+2q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       268: q+1
       269: q^2+2q+1
       270: q^2+2q+1
       271: q+1
       272: q+1
       273: q+1
       274: q^2+2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: q+1
       294: q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       312: q+1
       314: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       321: q^2+q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: 2q+1
       327: 2q+1
       329: q+1
       331: q+1
       332: q^2+2q+1
       333: q+1
       334: q+1
       335: q+1
       337: q+1
       339: q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: q+1
       350: q+1
       351: q+1
       352: 2q+1
       353: 2q+1
       354: 2q+1
       355: q+1
       358: q+1
       360: 1
       361: q+1
       362: 2q+1
       363: 2q+1
       364: 2q+1
       366: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: 1
       375: 1
       376: q+1
       377: q+1
       380: q+1
       382: q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: 1
       388: 2q+1
       389: q+1
       390: q+1
       392: 2q+1
       393: 2q+1
       394: q+1
       397: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       405: q+1
       407: q+1
       408: q^2+2q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: q+1
       415: q^2+2q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       435: q+1
       437: q+1
       438: 2q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: q+1
       448: q+1
       449: 1
       450: 2q+1
       451: q+1
       452: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       469: q+1
       471: q+1
       472: 2q+1
       476: q+1
       478: q+1
       480: q+1
       481: 2q+1
       482: 2q+1
       485: q+1
       487: q+1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       494: q+1
       496: 1
       497: q+1
       498: 2q+1
       499: 2q+1
       500: 2q+1
       502: q+1
       504: q+1
       505: 2q+1
       506: q+1
       507: q+1
       508: q+1
       509: q+1
       511: q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       515: q+1
       519: 1
       521: q+1
       523: 1
       524: 2q+1
       525: 2q+1
       528: q+1
       530: 1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       536: 1
       538: 1
       539: q+1
       544: q+1
       546: q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: 1
       553: 1
       554: q+1
       555: q+1
       558: 1
       559: 2q+1
       560: q+1
       561: q+1
       566: q+1
       568: 1
       570: 1
       571: q+1
       572: q+1
       575: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: q+1
       585: q+1
       586: q^2+2q+1
       587: q+1
       588: q+1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       612: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       620: q+1
       622: q+1
       623: 2q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       629: 1
       630: q+1
       631: q+1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       647: q+1
       648: 1
       654: q+1
       656: q+1
       662: q+1
       664: q+1
       665: 2q+1
       669: q+1
       671: 1
       673: 1
       674: q+1
       675: q+1
       679: 1
       681: q+1
       683: 1
       684: 2q+1
       685: 2q+1
       688: q+1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       696: q+1
       698: q+1
       699: 2q+1
       700: q+1
       701: q+1
       702: 1
       708: 1
       710: 1
       711: 2q+1
       715: 1
       717: q+1
       719: 1
       720: q+1
       721: q+1
       724: 1
       726: 1
       733: q+1
       735: 1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       741: 1
       743: 1
       744: q+1
       748: 1
       750: 1
       751: q+1
       752: q+1
       760: 1
       762: 1
       763: q+1
       767: q+1
       769: 1
       771: 1
       772: 1
       773: 1
       776: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: q+1
       816: q+1
       819: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: q+1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       859: q+1
       866: q+1
       868: q+1
       874: 1
       876: 1
       877: q+1
       883: 1
       885: 1
       886: 2q+1
       890: 1
       892: 1
       894: 1
       895: q+1
       896: q+1
       899: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       911: 1
       913: 1
       919: 1
       921: 1
       922: q+1
       926: 1
       936: 1
       938: q+1
       940: 1
       941: q+1
       942: q+1
       945: 1
       947: 1
       953: 1
       955: 1
       956: q+1
       965: 1
       967: 1
       973: 1
       975: 1
       976: 1
       980: q+1
       982: 1
       984: 1
       985: 1
       986: 1
       992: 1
       995: 1
       996: 1
       999: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1022: q+1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1044: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1076: q+1
      1083: 1
      1085: 1
      1091: 1
      1093: 1
      1099: 1
      1101: 1
      1102: q+1
      1106: 1
      1108: 1
      1110: 1
      1111: 1
      1112: 1
      1118: 1
      1125: 1
      1127: 1
      1142: 1
      1144: 1
      1145: q+1
      1149: 1
      1158: 1
      1160: 1
      1170: 1
      1177: 1
      1179: 1
      1185: 1
      1187: 1
      1188: 1
      1197: 1
      1203: 1
      1206: 1
      1207: 1
      1210: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1222: 1
      1224: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1249: 1
      1252: 1
      1253: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1284: 1
      1291: 1
      1298: 1
      1300: 1
      1306: 1
      1308: 1
      1309: 1
      1320: 1
      1335: 1
      1337: 1
      1350: 1
      1367: 1
      1374: 1
      1376: 1
      1393: 1
      1399: 1
      1402: 1
      1403: 1
      1409: 1
      1416: 1
      1418: 1
      1436: 1
      1449: 1
      1476: 1
      1483: 1
      1485: 1
      1506: 1
      1538: 1
      1563: 1
      1574: 1
      1630: 1

1631:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q^2+q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: q^2+2q+1
        24: 2q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: 2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        51: q^2+q+1
        52: q^2+q+1
        53: 2q^2+2q+1
        54: q^2+2q+1
        55: 2q^2+2q+1
        56: q^2+2q+1
        57: q^2+q+1
        58: 2q^2+2q+1
        59: 2q^2+2q+1
        60: q^2+2q+1
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: 2q+1
        71: q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q^2+2q+1
       109: 2q^2+2q+1
       110: q^2+2q+1
       111: 2q+1
       113: q^2+q+1
       114: q^2+q+1
       115: 2q^2+2q+1
       116: q^2+2q+1
       117: 2q^2+2q+1
       118: q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: 2q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       135: q+1
       136: q+1
       137: q^2+2q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q+1
       148: 1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q+1
       185: q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       192: q^2+q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: 2q+1
       197: 2q+1
       200: q^2+q+1
       201: q^2+q+1
       202: q^2+2q+1
       203: 2q^2+2q+1
       204: q^2+2q+1
       205: 2q+1
       207: q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       214: q+1
       215: q+1
       216: q^2+2q+1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       230: q+1
       231: q+1
       232: q+1
       233: q^2+2q+1
       234: q+1
       235: q+1
       237: q+1
       238: q+1
       239: q^2+2q+1
       240: q+1
       241: q^2+2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: 2q+1
       267: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: 1
       279: 2q+1
       280: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: q+1
       286: 2q+1
       287: 2q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: q+1
       293: 2q+1
       294: q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: q+1
       299: 2q+1
       300: q+1
       301: q+1
       302: 1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       313: q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       322: q^2+q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: 2q+1
       327: 2q+1
       330: q+1
       331: q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       338: q+1
       339: q+1
       340: q+1
       341: q^2+2q+1
       342: q+1
       343: q+1
       345: q+1
       346: q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: q+1
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q^2+2q+1
       371: q+1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       383: q^2+2q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       398: q+1
       399: q+1
       400: 1
       401: 2q+1
       402: 2q+1
       403: 2q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q+1
       413: q+1
       414: q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       420: 1
       421: 1
       422: q+1
       424: q+1
       426: 1
       427: 2q+1
       428: q+1
       430: q+1
       431: 2q+1
       432: 2q+1
       433: q+1
       436: q+1
       437: q+1
       438: q+1
       439: 2q+1
       440: q+1
       441: q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: q+1
       447: 2q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 2q+1
       456: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       470: q+1
       471: q+1
       472: 2q+1
       477: q+1
       479: q+1
       480: q+1
       481: 2q+1
       482: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: 2q+1
       490: 2q+1
       491: 2q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       503: q+1
       504: q+1
       505: q+1
       506: 2q+1
       507: q+1
       508: q+1
       510: q+1
       511: q+1
       512: 2q+1
       513: q+1
       514: 2q+1
       515: q+1
       520: 1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       547: q+1
       548: q^2+2q+1
       549: q+1
       550: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       567: q+1
       569: 1
       570: 1
       571: 2q+1
       572: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: 2q+1
       580: q+1
       581: q+1
       584: q+1
       585: q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q+1
       592: 1
       593: 1
       595: q+1
       599: 1
       600: 1
       601: q+1
       603: q+1
       605: 1
       606: 2q+1
       607: q+1
       609: q+1
       613: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       621: q+1
       622: q+1
       623: q+1
       624: 2q+1
       625: q+1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: q+1
       639: q+1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       655: q+1
       656: q+1
       663: q+1
       664: q+1
       665: 2q+1
       670: q+1
       672: 1
       673: 1
       674: 2q+1
       675: 2q+1
       680: 1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       689: q+1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       697: q+1
       698: q+1
       699: q+1
       700: 2q+1
       701: q+1
       702: 1
       709: 1
       710: 1
       711: q+1
       716: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       761: 1
       762: 1
       763: 2q+1
       768: q+1
       770: 1
       771: 1
       772: q+1
       773: q+1
       777: q+1
       778: q+1
       779: 1
       780: 2q+1
       781: q+1
       782: q+1
       786: 1
       788: 1
       794: 1
       795: 1
       797: q+1
       801: 1
       802: 1
       803: q+1
       805: q+1
       811: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: q+1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: q+1
       851: 1
       853: 1
       860: q+1
       867: q+1
       868: q+1
       875: 1
       876: 1
       877: 2q+1
       884: 1
       885: 1
       886: q+1
       891: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       912: 1
       913: 1
       920: 1
       921: 1
       922: 1
       927: 1
       931: 1
       932: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       942: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: q+1
       981: q+1
       983: 1
       984: 1
       985: q+1
       986: q+1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: q+1
      1020: 1
      1021: 1
      1022: q+1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1077: q+1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1100: 1
      1101: 1
      1102: q+1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1119: 1
      1126: 1
      1127: 1
      1136: 1
      1143: 1
      1144: 1
      1145: 1
      1150: 1
      1154: 1
      1155: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1171: 1
      1178: 1
      1179: 1
      1186: 1
      1187: 1
      1188: q+1
      1204: 1
      1211: 1
      1213: 1
      1223: 1
      1224: 1
      1231: 1
      1232: 1
      1233: 1
      1238: 1
      1242: 1
      1243: 1
      1250: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1285: 1
      1292: 1
      1299: 1
      1300: 1
      1307: 1
      1308: 1
      1309: 1
      1321: 1
      1336: 1
      1337: 1
      1346: 1
      1351: 1
      1355: 1
      1356: 1
      1368: 1
      1375: 1
      1376: 1
      1400: 1
      1410: 1
      1417: 1
      1418: 1
      1427: 1
      1450: 1
      1477: 1
      1484: 1
      1485: 1
      1507: 1
      1524: 1
      1539: 1
      1575: 1
      1631: 1

1632:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^2+1
        11: q+1
        12: q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^3+q^2+q+1
        21: q^3+q^2+q+1
        22: q^3+q^2+q+1
        23: q+1
        24: q^3+q^2+q+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q+1
        29: 1
        30: q^3+q^2+q+1
        31: q^2+1
        32: q+1
        33: q^3+q^2+q+1
        34: q^3+q^2+q+1
        35: q^3+q^2+q+1
        36: q^3+q^2+q+1
        37: q^2+1
        38: q+1
        39: q^3+q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q^3+q^2+q+1
        52: q^3+q^2+q+1
        53: q^2+1
        54: q+1
        55: q^3+q^2+q+1
        56: q+1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: q+1
        69: 1
        70: q+1
        71: q^3+q^2+q+1
        72: q^3+q^2+q+1
        73: q^3+q^2+q+1
        74: q+1
        75: q^3+q^2+q+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: q+1
        80: 1
        81: q^3+q^2+q+1
        82: q^2+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q^3+q^2+q+1
       107: q^2+1
       108: 1
       109: q^2+1
       110: q+1
       111: q+1
       112: 1
       113: q^2+1
       114: q^2+1
       115: q^2+1
       116: 1
       117: q^2+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q^2+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q^3+q^2+q+1
       136: q^3+q^2+q+1
       137: q^2+1
       138: q+1
       139: q^3+q^2+q+1
       140: q+1
       141: q^2+1
       142: q^2+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: q^2+1
       193: 1
       194: q^2+1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: q^2+1
       201: q^2+1
       202: 1
       203: q^2+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: q^2+1
       215: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q^3+q^2+q+1
       231: q^2+1
       232: 1
       233: q^2+1
       234: q+1
       235: q+1
       236: 1
       237: q^2+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q^2+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q^2+1
       323: 1
       324: q^2+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: q^2+1
       360: 1
       361: q^2+1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: q^2+1
       382: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: q^2+1
       480: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: q^2+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: q^2+1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1074: 1
      1094: 1
      1103: 1
      1104: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1265: 1
      1271: 1
      1272: 1
      1273: 1
      1301: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1318: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1357: 1
      1404: 1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1456: 1
      1486: 1
      1487: 1
      1488: 1
      1516: 1
      1564: 1
      1632: 1

1633:    0: q^4+4q^3+6q^2+4q+1
         1: 2q^3+5q^2+4q+1
         2: q^4+4q^3+6q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: q^4+4q^3+6q^2+4q+1
         5: 2q^3+5q^2+4q+1
         6: 2q^3+5q^2+4q+1
         7: 2q^3+5q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+4q^2+4q+1
        10: 2q^3+5q^2+4q+1
        11: 3q^2+4q+1
        12: 2q^3+5q^2+4q+1
        13: 2q^3+5q^2+4q+1
        14: q^4+4q^3+6q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: q^3+4q^2+4q+1
        17: 2q^3+5q^2+4q+1
        18: 3q^2+4q+1
        19: 2q^3+5q^2+4q+1
        20: 2q^2+3q+1
        21: 2q^3+5q^2+4q+1
        22: q^3+4q^2+4q+1
        23: 3q^2+4q+1
        24: 2q^3+5q^2+4q+1
        25: q^3+4q^2+4q+1
        26: 2q^2+3q+1
        27: 2q^3+5q^2+4q+1
        28: 2q^2+4q+1
        29: 3q^2+4q+1
        30: q^3+4q^2+4q+1
        31: 2q^3+5q^2+4q+1
        32: 3q^2+4q+1
        33: 2q^3+5q^2+4q+1
        34: 2q^3+5q^2+4q+1
        35: 2q^3+5q^2+4q+1
        36: q^3+4q^2+4q+1
        37: 2q^3+5q^2+4q+1
        38: 3q^2+4q+1
        39: 2q^3+5q^2+4q+1
        40: q^3+4q^2+4q+1
        41: q^3+4q^2+4q+1
        42: 3q^2+4q+1
        43: 2q^2+4q+1
        44: 3q^2+4q+1
        45: 2q^2+4q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^3+5q^2+4q+1
        49: 3q^2+4q+1
        50: 2q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: q^3+4q^2+4q+1
        54: 2q^2+4q+1
        55: q^3+4q^2+4q+1
        56: 3q^2+4q+1
        57: 2q^2+3q+1
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 3q^2+4q+1
        61: 2q^3+5q^2+4q+1
        62: 2q^2+4q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^3+4q^2+4q+1
        66: 2q^2+3q+1
        67: q^3+3q^2+3q+1
        68: 2q^2+4q+1
        69: 3q^2+4q+1
        70: q^2+4q+1
        71: 2q^2+3q+1
        72: 2q^3+5q^2+4q+1
        73: q^3+4q^2+4q+1
        74: 3q^2+4q+1
        75: 2q^3+5q^2+4q+1
        76: q^3+4q^2+4q+1
        77: 2q^2+3q+1
        78: 2q^3+5q^2+4q+1
        79: 2q^2+4q+1
        80: 3q^2+4q+1
        81: q^3+4q^2+4q+1
        82: 2q^3+5q^2+4q+1
        83: 3q^2+4q+1
        84: q^2+3q+1
        85: q^3+4q^2+4q+1
        86: 2q^2+4q+1
        87: 2q^2+4q+1
        88: 3q^2+4q+1
        89: 2q^2+4q+1
        90: 2q+1
        91: 3q^2+4q+1
        92: q^2+4q+1
        93: 2q^2+4q+1
        94: 2q^2+4q+1
        95: 3q^2+4q+1
        96: 2q^2+4q+1
        97: q^3+4q^2+4q+1
        98: q^3+4q^2+4q+1
        99: 3q^2+4q+1
       100: 2q^2+4q+1
       101: 3q^2+4q+1
       102: 2q^2+4q+1
       103: 3q^2+4q+1
       104: 2q+1
       105: 2q+1
       106: 2q^2+3q+1
       107: 2q^2+3q+1
       108: 2q^2+4q+1
       109: q^3+4q^2+4q+1
       110: 2q^2+4q+1
       111: q^2+4q+1
       112: 2q+1
       113: 2q^2+3q+1
       114: q^2+2q+1
       115: 2q^2+3q+1
       116: q^2+3q+1
       117: 2q^2+3q+1
       118: 3q^2+4q+1
       119: 2q+1
       120: q^2+3q+1
       121: 2q+1
       122: q^2+3q+1
       123: q^2+3q+1
       124: q^2+2q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^3+3q^2+3q+1
       129: 2q^2+4q+1
       130: q^2+3q+1
       131: 3q+1
       132: q^2+4q+1
       133: q^2+4q+1
       134: 2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: q^3+4q^2+4q+1
       138: 2q^2+4q+1
       139: q^3+4q^2+4q+1
       140: 3q^2+4q+1
       141: 2q^2+3q+1
       142: 2q^2+3q+1
       143: 2q^2+3q+1
       144: 3q^2+4q+1
       145: 2q^3+5q^2+4q+1
       146: 2q^2+4q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: q^3+4q^2+4q+1
       150: 2q^2+3q+1
       151: q^3+3q^2+3q+1
       152: 2q^2+4q+1
       153: 3q^2+4q+1
       154: q^2+4q+1
       155: 2q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: 2q^2+4q+1
       159: q^2+4q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: q^2+3q+1
       163: 2q+1
       164: 2q+1
       165: 2q^2+4q+1
       166: 3q^2+4q+1
       167: q^2+4q+1
       168: 2q+1
       169: q^2+3q+1
       170: 2q^2+4q+1
       171: 2q+1
       172: q^2+2q+1
       173: q^2+4q+1
       174: 2q^2+4q+1
       175: q^2+4q+1
       176: q^2+3q+1
       177: q^3+4q^2+4q+1
       178: 2q^2+4q+1
       179: 2q^2+4q+1
       180: 3q^2+4q+1
       181: 2q^2+4q+1
       182: 2q+1
       183: 3q^2+4q+1
       184: q^2+4q+1
       185: 2q^2+4q+1
       186: 2q^2+4q+1
       187: 3q^2+4q+1
       188: 2q^2+4q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q^2+3q+1
       193: 2q+1
       194: q^2+2q+1
       195: 2q^2+4q+1
       196: q^2+4q+1
       197: q^2+4q+1
       198: 2q+1
       199: q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q^2+3q+1
       203: 2q^2+3q+1
       204: q^2+3q+1
       205: 3q+1
       206: q+1
       207: 2q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: q^2+3q+1
       213: q+1
       214: q^2+2q+1
       215: q+1
       216: q^2+2q+1
       217: q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q+1
       221: q^2+3q+1
       222: 2q+1
       223: 2q+1
       224: 3q+1
       225: q^2+4q+1
       226: q+1
       227: 3q+1
       228: 2q+1
       229: 2q+1
       230: 2q^2+3q+1
       231: 2q^2+3q+1
       232: 2q^2+4q+1
       233: q^3+4q^2+4q+1
       234: 2q^2+4q+1
       235: q^2+4q+1
       236: 2q+1
       237: 2q^2+3q+1
       238: q^2+2q+1
       239: 2q^2+3q+1
       240: q^2+3q+1
       241: 2q^2+3q+1
       242: 3q^2+4q+1
       243: 2q+1
       244: q^2+3q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: q^2+2q+1
       249: 2q^2+3q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^3+3q^2+3q+1
       253: 2q^2+4q+1
       254: q^2+3q+1
       255: 3q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q^2+3q+1
       262: q^2+4q+1
       263: 2q^2+4q+1
       264: q^2+4q+1
       265: q^2+4q+1
       266: 2q+1
       267: q^2+3q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q^2+4q+1
       273: 2q+1
       274: 2q+1
       275: q+1
       276: q^2+3q+1
       277: q^2+3q+1
       278: q+1
       279: 2q+1
       280: q+1
       282: q^2+2q+1
       283: q^2+4q+1
       284: 2q+1
       285: 2q+1
       286: q^2+4q+1
       287: q^2+4q+1
       288: 2q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: 2q^2+4q+1
       292: q^2+4q+1
       293: 2q^2+4q+1
       294: 2q^2+4q+1
       295: q^2+3q+1
       296: 2q+1
       297: 2q+1
       298: 2q^2+4q+1
       299: 3q^2+4q+1
       300: q^2+4q+1
       301: 2q+1
       302: q^2+3q+1
       303: 2q^2+4q+1
       304: 2q+1
       305: q^2+2q+1
       306: q^2+4q+1
       307: 2q^2+4q+1
       308: q^2+4q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: 2q+1
       314: q+1
       315: q^2+2q+1
       316: 2q+1
       317: q^2+4q+1
       318: q+1
       319: 1
       320: q+1
       321: q+1
       322: q^2+2q+1
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: 2q+1
       327: 3q+1
       328: q+1
       329: 1
       330: q+1
       331: q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: 3q+1
       336: q+1
       337: 1
       338: q+1
       339: q+1
       340: q+1
       341: q^2+2q+1
       342: q+1
       343: 2q+1
       344: q+1
       345: 2q+1
       346: q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: 2q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 2q+1
       355: 3q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q^2+3q+1
       360: 2q+1
       361: q^2+2q+1
       362: 2q^2+4q+1
       363: q^2+4q+1
       364: q^2+4q+1
       365: 2q+1
       366: q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q^2+3q+1
       370: 2q^2+3q+1
       371: q^2+3q+1
       372: 3q+1
       373: q+1
       374: 2q+1
       375: q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: q^2+3q+1
       380: q+1
       381: q^2+2q+1
       382: q+1
       383: q^2+2q+1
       384: q+1
       385: q^2+2q+1
       386: q^2+2q+1
       387: 2q+1
       388: q^2+3q+1
       389: 2q+1
       390: 2q+1
       391: 3q+1
       392: q^2+4q+1
       393: q+1
       394: 3q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: q^2+3q+1
       399: 2q+1
       400: q+1
       401: q^2+4q+1
       402: q^2+4q+1
       403: q^2+4q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: q+1
       413: 2q+1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q^2+3q+1
       420: q+1
       421: 1
       422: q+1
       424: q+1
       426: q+1
       427: 2q+1
       428: q+1
       430: 2q+1
       431: q^2+4q+1
       432: q+1
       433: 2q+1
       434: 2q+1
       435: 2q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: q^2+4q+1
       439: 2q^2+4q+1
       440: q^2+4q+1
       441: q^2+4q+1
       442: 2q+1
       443: q^2+3q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q^2+4q+1
       449: 2q+1
       450: 2q+1
       451: q+1
       452: q^2+3q+1
       453: q^2+3q+1
       454: q+1
       455: 2q+1
       456: q+1
       458: q^2+2q+1
       459: q^2+4q+1
       460: 2q+1
       461: 2q+1
       462: q^2+4q+1
       463: q^2+4q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: q+1
       470: 2q+1
       471: 2q+1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: q+1
       478: 1
       479: q+1
       480: q+1
       481: 2q+1
       482: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: q+1
       489: 2q+1
       490: 2q+1
       491: 3q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       502: 1
       503: q+1
       504: q+1
       505: q+1
       506: 2q+1
       507: q+1
       508: 2q+1
       509: q+1
       510: 2q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: 2q+1
       521: q+1
       522: q^2+2q+1
       523: 2q+1
       524: q^2+4q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q^2+2q+1
       530: q+1
       531: q+1
       532: q^2+3q+1
       533: 2q+1
       534: 3q+1
       535: q+1
       536: 1
       537: q+1
       538: q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: 3q+1
       543: q+1
       544: 1
       545: q+1
       546: q+1
       547: q+1
       548: q^2+2q+1
       549: q+1
       550: 2q+1
       551: q+1
       552: 2q+1
       553: q+1
       554: 2q+1
       555: q+1
       556: 2q+1
       557: 2q+1
       558: 2q+1
       559: q+1
       560: 1
       561: 2q+1
       562: 3q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: 2q+1
       569: q+1
       570: q+1
       571: q^2+4q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: 2q+1
       580: q+1
       581: 2q+1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 2q+1
       592: 1
       593: 1
       595: q+1
       599: q+1
       600: 1
       601: q+1
       603: q+1
       605: q+1
       606: q+1
       607: 1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: q^2+3q+1
       614: 2q+1
       615: q+1
       616: q^2+4q+1
       617: q^2+4q+1
       618: q^2+4q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: q+1
       628: 2q+1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q^2+3q+1
       635: q+1
       636: 1
       637: q+1
       639: q+1
       641: q+1
       642: 2q+1
       643: q+1
       645: 2q+1
       646: q^2+4q+1
       647: q+1
       648: 2q+1
       650: 1
       651: 1
       652: 1
       653: q+1
       654: q+1
       655: 2q+1
       656: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: q+1
       664: q+1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: q+1
       674: 2q+1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: q+1
       684: q+1
       685: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       692: q+1
       693: q+1
       694: 2q+1
       695: q+1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: q+1
       709: 2q+1
       710: 2q+1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: q+1
       717: 1
       718: q+1
       719: q+1
       720: 2q+1
       721: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: q+1
       728: 2q+1
       729: 2q+1
       730: 3q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 2q+1
       740: q+1
       741: 1
       742: q+1
       743: q+1
       744: q+1
       745: 2q+1
       746: q+1
       747: 2q+1
       748: q+1
       749: 2q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 2q+1
       756: q+1
       757: 1
       758: q+1
       761: q+1
       762: q+1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       770: 1
       771: 1
       772: q+1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: q+1
       781: q+1
       782: 2q+1
       786: 1
       788: 1
       794: 1
       795: 1
       797: q+1
       801: q+1
       802: 1
       803: 1
       805: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: 2q+1
       813: q+1
       814: q+1
       815: q^2+4q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: 2q+1
       824: q+1
       825: 2q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 2q+1
       836: 1
       837: 1
       839: q+1
       843: q+1
       844: 1
       845: q+1
       847: q+1
       849: q+1
       850: q+1
       851: 1
       853: 2q+1
       855: 1
       856: 1
       857: 1
       858: q+1
       859: 1
       860: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       870: 1
       872: 1
       877: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: q+1
       907: 1
       908: 1
       909: 1
       910: q+1
       911: q+1
       912: 2q+1
       913: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       921: q+1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: q+1
       931: 2q+1
       932: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: q+1
       941: q+1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       949: q+1
       950: q+1
       951: 2q+1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q+1
       961: 1
       962: 1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: q+1
       986: 1
       993: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1015: q+1
      1016: 1
      1017: q+1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: q+1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: q+1
      1040: q+1
      1041: 2q+1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: q+1
      1060: q+1
      1061: 1
      1062: 1
      1064: 1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: q+1
      1118: 1
      1119: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: q+1
      1127: 1
      1129: 1
      1131: 1
      1136: 1
      1138: 1
      1141: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: q+1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 1
      1171: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1181: 1
      1183: 1
      1188: 1
      1211: 1
      1218: 1
      1219: 1
      1223: q+1
      1224: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: q+1
      1243: 1
      1250: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1272: 1
      1273: 1
      1276: 1
      1278: 1
      1302: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1339: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1355: 1
      1356: 1
      1363: 1
      1368: 1
      1405: 1
      1410: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1420: 1
      1422: 1
      1427: 1
      1450: 1
      1457: 1
      1487: 1
      1488: 1
      1491: 1
      1493: 1
      1517: 1
      1524: 1
      1570: 1
      1575: 1
      1633: 1

1634:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q+1
        19: q^3+2q^2+2q+1
        20: q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q^3+2q^2+2q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: 1
       120: q^2+2q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^3+2q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: 1
       194: q+1
       195: q^2+2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q^2+2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+2q+1
       237: q^2+2q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: q^2+2q+1
       241: q^2+2q+1
       242: q^2+2q+1
       243: 1
       244: q^2+2q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q^2+2q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       279: q+1
       283: q+1
       284: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q^2+2q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: 1
       324: q+1
       325: q^2+2q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: q^2+2q+1
       360: 1
       361: q+1
       362: q^2+2q+1
       363: q+1
       364: q+1
       365: q^2+2q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q^2+2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: q+1
       431: q+1
       432: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       455: q+1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: q^2+2q+1
       476: 1
       477: 1
       478: q+1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q^2+2q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q^2+2q+1
       528: q^2+2q+1
       529: q^2+2q+1
       530: 1
       531: q+1
       532: q^2+2q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: 1
       567: 1
       571: q+1
       572: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       579: q+1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: q+1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: q+1
       646: q+1
       647: q+1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       661: q+1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: q+1
       681: q+1
       682: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: q+1
       704: q+1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q^2+2q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       758: 1
       763: q+1
       766: q+1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       815: q+1
       816: q+1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       823: q+1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: q+1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       882: q+1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       938: q+1
       939: q+1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       960: q+1
       971: 1
       979: 1
       980: 1
       981: 1
      1014: q+1
      1015: q+1
      1017: 1
      1022: q+1
      1025: q+1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1105: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1141: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1183: 1
      1217: q+1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1293: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1338: 1
      1339: 1
      1346: 1
      1349: 1
      1422: 1
      1458: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1508: 1
      1634: 1

1635:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 2q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: 2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+q+1
        27: 2q^2+2q+1
        28: 2q+1
        29: 2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: 2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: 2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: 2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 2q+1
        51: q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: 2q+1
        55: q^2+2q+1
        56: 2q+1
        57: 2q^2+2q+1
        58: q^2+q+1
        59: q^2+q+1
        60: 2q+1
        61: q^2+2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: q^2+2q+1
        66: q+1
        67: q^2+2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: 2q^2+2q+1
        74: 2q+1
        75: q^2+2q+1
        76: 2q^2+2q+1
        77: q^2+q+1
        78: 2q^2+2q+1
        79: 2q+1
        80: 2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: 2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: 2q+1
        88: q+1
        89: q^2+2q+1
        91: q^2+2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: 2q+1
       103: q+1
       104: 2q+1
       105: 2q+1
       106: q^2+2q+1
       107: 2q^2+2q+1
       108: 2q+1
       109: q^2+2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: q^2+2q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: q^2+2q+1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: 2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: 2q+1
       139: q^2+2q+1
       140: 2q+1
       141: 2q^2+2q+1
       142: q^2+q+1
       143: q^2+q+1
       144: 2q+1
       145: q^2+2q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: q^2+2q+1
       150: q+1
       151: q^2+2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: 2q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: q^2+2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: 2q+1
       180: q+1
       181: q^2+2q+1
       183: q^2+2q+1
       184: 2q+1
       185: 2q+1
       186: q+1
       187: q+1
       188: q+1
       189: 2q+1
       190: 2q+1
       191: 2q+1
       192: q^2+2q+1
       193: 2q+1
       194: q^2+2q+1
       195: 2q+1
       196: 2q+1
       197: 2q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q^2+q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q+1
       206: 2q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: q^2+2q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 2q+1
       227: 2q+1
       228: 2q+1
       229: 2q+1
       230: q^2+2q+1
       231: 2q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q^2+2q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 1
       248: q^2+2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: q^2+2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q+1
       267: q+1
       272: q+1
       273: 2q+1
       276: 2q+1
       277: 1
       278: q+1
       282: q+1
       283: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 2q+1
       289: q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: 2q+1
       293: q+1
       294: q+1
       295: q^2+2q+1
       298: 2q+1
       299: q+1
       300: 2q+1
       302: 2q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 2q+1
       310: 2q+1
       311: 2q+1
       312: 2q+1
       313: 1
       314: q+1
       315: q^2+2q+1
       316: 2q+1
       317: 2q+1
       319: 2q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 2q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: q+1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: 2q+1
       354: q+1
       355: 1
       356: 2q+1
       357: 2q+1
       358: 2q+1
       359: q^2+2q+1
       360: 2q+1
       361: q^2+2q+1
       362: 2q+1
       363: 2q+1
       364: 2q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q^2+q+1
       369: q+1
       370: q+1
       371: q+1
       372: 2q+1
       373: 2q+1
       374: 1
       375: q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       380: q+1
       381: q^2+2q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: q+1
       391: 1
       392: 2q+1
       394: 2q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       411: q+1
       412: 2q+1
       413: 1
       418: 1
       420: q+1
       426: q+1
       430: 1
       431: q+1
       433: q+1
       434: q+1
       435: 2q+1
       436: q+1
       437: q^2+2q+1
       438: 2q+1
       439: q+1
       440: q+1
       441: q+1
       442: 2q+1
       443: q+1
       448: q+1
       449: 2q+1
       452: 2q+1
       453: 1
       454: q+1
       458: q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 2q+1
       466: 2q+1
       467: 1
       468: q+1
       469: q+1
       470: 1
       471: 2q+1
       473: 2q+1
       474: q+1
       475: q+1
       476: q+1
       477: 1
       478: 1
       479: q+1
       480: q+1
       481: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       516: 2q+1
       517: 2q+1
       518: 2q+1
       519: 2q+1
       520: 1
       521: q+1
       522: q^2+2q+1
       523: 2q+1
       524: 2q+1
       526: 2q+1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: 2q+1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: q+1
       551: q+1
       552: 1
       553: q+1
       554: q+1
       555: 1
       556: 1
       557: 1
       558: 2q+1
       561: q+1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: 2q+1
       567: 1
       569: q+1
       570: q+1
       571: q+1
       573: q+1
       581: q+1
       582: 1
       589: 1
       599: 1
       605: q+1
       609: 1
       610: q+1
       611: q+1
       612: 2q+1
       613: q+1
       614: 2q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       626: q+1
       627: 2q+1
       628: 1
       633: 1
       635: q+1
       641: q+1
       645: 1
       646: q+1
       648: q+1
       650: 2q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: q+1
       666: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 2q+1
       705: 2q+1
       706: 1
       707: q+1
       708: q+1
       709: 1
       710: 2q+1
       712: 2q+1
       713: q+1
       714: q+1
       715: q+1
       716: 1
       717: 1
       718: q+1
       719: q+1
       720: q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: q+1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       754: 1
       756: q+1
       757: q+1
       758: 1
       761: 1
       762: q+1
       764: q+1
       774: 1
       782: 1
       801: 1
       807: q+1
       808: q+1
       809: q+1
       810: 2q+1
       811: 1
       813: q+1
       814: q+1
       815: q+1
       817: q+1
       825: q+1
       826: 1
       833: 1
       843: 1
       849: q+1
       853: 1
       855: 1
       856: q+1
       857: 1
       858: 1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 2q+1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       915: q+1
       916: q+1
       917: 1
       918: 1
       919: 1
       920: 1
       921: q+1
       923: 1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: q+1
       962: 1
       966: 1
       977: 1
      1015: q+1
      1016: q+1
      1017: 1
      1020: 1
      1021: q+1
      1023: q+1
      1033: 1
      1041: 1
      1060: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1114: 1
      1115: q+1
      1116: 1
      1117: 1
      1121: q+1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1166: 1
      1218: q+1
      1219: 1
      1223: 1
      1234: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1288: 1
      1294: 1
      1312: 1
      1313: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1328: 1
      1331: 1
      1333: 1
      1335: 1
      1339: 1
      1340: 1
      1345: 1
      1347: 1
      1405: 1
      1459: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1503: 1
      1509: 1
      1635: 1

1636:    0: 2q^3+6q^2+4q+1
         1: 2q^3+6q^2+4q+1
         2: 2q^3+6q^2+4q+1
         3: 2q^3+6q^2+4q+1
         4: 2q^3+6q^2+4q+1
         5: q^3+5q^2+4q+1
         6: q^3+4q^2+4q+1
         7: 2q^3+6q^2+4q+1
         8: 2q^3+6q^2+4q+1
         9: 2q^3+6q^2+4q+1
        10: q^3+4q^2+4q+1
        11: 3q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 2q^3+6q^2+4q+1
        14: 2q^3+6q^2+4q+1
        15: 2q^3+6q^2+4q+1
        16: q^3+5q^2+4q+1
        17: q^3+5q^2+4q+1
        18: q^3+5q^2+4q+1
        19: q^3+5q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+4q^2+4q+1
        22: 2q^3+6q^2+4q+1
        23: 3q^2+4q+1
        24: q^3+4q^2+4q+1
        25: 2q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: 3q^2+4q+1
        29: 2q^2+4q+1
        30: q^3+4q^2+4q+1
        31: 2q^2+4q+1
        32: 2q^2+4q+1
        33: q^3+4q^2+4q+1
        34: 2q^3+6q^2+4q+1
        35: 2q^3+6q^2+4q+1
        36: 2q^3+6q^2+4q+1
        37: q^3+4q^2+4q+1
        38: 3q^2+4q+1
        39: q^3+4q^2+4q+1
        40: q^3+4q^2+4q+1
        41: q^3+5q^2+4q+1
        42: q^3+5q^2+4q+1
        43: q^3+5q^2+4q+1
        44: 2q^2+3q+1
        45: 3q^2+4q+1
        46: 2q^2+3q+1
        47: q^3+5q^2+4q+1
        48: q^3+5q^2+4q+1
        49: q^3+5q^2+4q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^3+4q^2+4q+1
        53: 2q^2+4q+1
        54: 3q^2+4q+1
        55: q^3+4q^2+4q+1
        56: 2q^2+4q+1
        57: 2q^2+4q+1
        58: 2q^2+4q+1
        59: q^3+4q^2+4q+1
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: q^2+4q+1
        63: 2q^2+4q+1
        64: 2q^2+4q+1
        65: q^2+4q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: 2q^2+4q+1
        69: q^2+4q+1
        70: 2q^2+4q+1
        71: q^3+4q^2+4q+1
        72: q^3+4q^2+4q+1
        73: 2q^3+6q^2+4q+1
        74: 3q^2+4q+1
        75: q^3+4q^2+4q+1
        76: 2q^2+4q+1
        77: q^3+4q^2+4q+1
        78: q^3+4q^2+4q+1
        79: 3q^2+4q+1
        80: 2q^2+4q+1
        81: q^3+4q^2+4q+1
        82: 2q^2+4q+1
        83: 2q^2+4q+1
        84: q^3+4q^2+4q+1
        85: q^3+4q^2+4q+1
        86: q^3+5q^2+4q+1
        87: 3q^2+4q+1
        88: 2q^2+3q+1
        89: q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: 3q^2+4q+1
        93: q^2+3q+1
        94: 2q^2+3q+1
        95: 2q+1
        96: q^2+3q+1
        97: q^3+4q^2+4q+1
        98: q^3+5q^2+4q+1
        99: q^3+5q^2+4q+1
       100: q^3+5q^2+4q+1
       101: 2q^2+3q+1
       102: 3q^2+4q+1
       103: 2q^2+3q+1
       104: q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: 2q^2+4q+1
       108: q^2+4q+1
       109: q^2+4q+1
       110: 2q^2+4q+1
       111: 2q^2+4q+1
       112: 2q+1
       113: 2q+1
       114: 2q^2+4q+1
       115: 2q^2+4q+1
       116: 2q^2+4q+1
       117: 2q^2+4q+1
       118: q^2+4q+1
       119: q^2+4q+1
       120: q^2+4q+1
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: 2q+1
       124: q^2+4q+1
       125: q^2+4q+1
       126: 2q^2+4q+1
       127: 2q+1
       128: 2q^2+4q+1
       129: q^2+4q+1
       130: q^2+4q+1
       131: q^2+4q+1
       132: 2q^2+4q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^3+4q^2+4q+1
       137: 2q^2+4q+1
       138: 3q^2+4q+1
       139: q^3+4q^2+4q+1
       140: 2q^2+4q+1
       141: 2q^2+4q+1
       142: 2q^2+4q+1
       143: q^3+4q^2+4q+1
       144: 2q^2+4q+1
       145: 2q^2+4q+1
       146: q^2+4q+1
       147: 2q^2+4q+1
       148: 2q^2+4q+1
       149: q^2+4q+1
       150: 2q^2+4q+1
       151: 2q^2+4q+1
       152: 2q^2+4q+1
       153: q^2+4q+1
       154: 2q^2+4q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^3+4q^2+4q+1
       158: q^2+3q+1
       159: 3q^2+4q+1
       160: 2q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: 2q+1
       167: 3q+1
       168: q^2+3q+1
       169: q^2+3q+1
       170: 2q+1
       171: 2q+1
       172: 2q+1
       173: q^2+3q+1
       174: 2q+1
       175: q^2+3q+1
       176: q^3+4q^2+4q+1
       177: q^3+4q^2+4q+1
       178: q^3+5q^2+4q+1
       179: 3q^2+4q+1
       180: 2q^2+3q+1
       181: q^2+3q+1
       182: 2q^2+3q+1
       183: 2q^2+3q+1
       184: 3q^2+4q+1
       185: q^2+3q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: q^2+3q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: 2q+1
       193: q^2+4q+1
       194: q^2+4q+1
       195: q^2+4q+1
       196: 2q^2+4q+1
       197: 2q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       201: 2q^2+4q+1
       202: q^2+4q+1
       203: q^2+4q+1
       204: q^2+4q+1
       205: q^2+4q+1
       206: 2q+1
       207: q+1
       208: q^2+4q+1
       209: 2q+1
       210: 2q^2+4q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: 2q+1
       215: q^2+4q+1
       216: 2q+1
       217: 2q+1
       218: 2q^2+4q+1
       219: 2q+1
       220: q^2+4q+1
       221: q^2+4q+1
       222: q^2+4q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 2q^2+4q+1
       232: q^2+4q+1
       233: q^2+4q+1
       234: 2q^2+4q+1
       235: 2q^2+4q+1
       236: 2q+1
       237: 2q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+4q+1
       242: q^2+4q+1
       243: q^2+4q+1
       244: q^2+4q+1
       245: 2q^2+4q+1
       246: 2q^2+4q+1
       247: 2q+1
       248: q^2+4q+1
       249: q^2+4q+1
       250: 2q^2+4q+1
       251: 2q+1
       252: 2q^2+4q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^2+4q+1
       256: 2q^2+4q+1
       257: 2q+1
       258: q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q^2+3q+1
       262: 3q+1
       263: 2q+1
       264: q^2+3q+1
       265: q^2+3q+1
       266: 2q+1
       267: q+1
       268: q^2+3q+1
       269: q^2+3q+1
       270: q^2+3q+1
       271: 2q+1
       272: 2q+1
       273: 3q+1
       274: 3q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: q+1
       278: 2q+1
       279: 2q+1
       280: 2q+1
       282: 2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^2+3q+1
       287: q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^3+4q^2+4q+1
       291: q^2+3q+1
       292: 3q^2+4q+1
       293: 2q^2+3q+1
       294: q^2+3q+1
       295: q^2+3q+1
       296: q^2+3q+1
       297: 2q^2+3q+1
       298: q^2+3q+1
       299: 2q+1
       300: 3q+1
       301: q^2+3q+1
       302: q^2+3q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+3q+1
       307: 2q+1
       308: q^2+3q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: q^2+4q+1
       317: 2q+1
       318: 2q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: q^2+4q+1
       324: q^2+4q+1
       325: q^2+4q+1
       326: q^2+4q+1
       327: 2q+1
       328: 1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: q+1
       346: q^2+4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: 2q+1
       359: 2q+1
       360: q^2+4q+1
       361: q^2+4q+1
       362: q^2+4q+1
       363: 2q^2+4q+1
       364: 2q+1
       365: q+1
       366: 2q+1
       367: 2q+1
       368: 2q^2+4q+1
       369: q^2+4q+1
       370: q^2+4q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q+1
       374: q+1
       375: q^2+4q+1
       376: 2q+1
       377: 2q^2+4q+1
       378: 2q+1
       379: 2q+1
       380: q+1
       381: 2q+1
       382: q^2+4q+1
       383: 2q+1
       384: 2q+1
       385: 2q^2+4q+1
       386: 2q+1
       387: q^2+4q+1
       388: q^2+4q+1
       389: q^2+4q+1
       390: 2q+1
       391: 2q+1
       392: 2q+1
       393: 2q+1
       394: 2q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: q+1
       399: 3q+1
       400: 2q+1
       401: 2q+1
       402: q^2+3q+1
       403: q+1
       404: q+1
       405: 2q+1
       406: q+1
       407: q^2+3q+1
       408: 3q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       413: 1
       414: 3q+1
       415: 2q+1
       416: q^2+3q+1
       417: q+1
       418: q+1
       420: q+1
       421: 2q+1
       424: 2q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q^2+3q+1
       438: 3q+1
       439: 2q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: 2q+1
       443: q+1
       444: q^2+3q+1
       445: q^2+3q+1
       446: q^2+3q+1
       447: 2q+1
       448: 2q+1
       449: 3q+1
       450: 3q+1
       451: q^2+3q+1
       452: q^2+3q+1
       453: q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       458: 2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^2+3q+1
       463: q+1
       466: q+1
       467: 1
       468: 1
       469: q+1
       470: q+1
       471: 2q+1
       472: 2q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: q^2+4q+1
       481: q+1
       482: 2q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: 2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: 2q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       511: 2q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       517: q+1
       518: q+1
       519: 2q+1
       520: q+1
       521: q+1
       522: 2q+1
       523: q^2+4q+1
       524: 2q+1
       525: 2q+1
       526: q+1
       527: q+1
       528: 2q+1
       529: 2q+1
       530: q^2+4q+1
       531: q^2+4q+1
       532: q^2+4q+1
       533: q^2+4q+1
       534: 2q+1
       535: 1
       536: 2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: 1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: 2q+1
       550: 2q+1
       551: q+1
       552: q+1
       553: q^2+4q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: q+1
       558: 2q+1
       559: 2q+1
       560: 2q+1
       561: q+1
       562: 1
       564: q+1
       565: q+1
       566: 2q+1
       567: 1
       569: q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: 2q+1
       576: q+1
       577: 3q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: 1
       583: 2q+1
       584: 1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: q+1
       592: q+1
       599: 1
       600: 2q+1
       603: q+1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: q+1
       611: q+1
       612: 2q+1
       613: q+1
       614: 3q+1
       615: 2q+1
       616: 2q+1
       617: q^2+3q+1
       618: q+1
       619: q+1
       620: 2q+1
       621: q+1
       622: q^2+3q+1
       623: 3q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: 2q+1
       628: 1
       629: 3q+1
       630: 2q+1
       631: q^2+3q+1
       632: q+1
       633: q+1
       635: q+1
       636: 2q+1
       639: 2q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       651: 1
       652: 1
       653: 1
       654: q+1
       655: 1
       656: 2q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: q+1
       674: 1
       675: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       705: q+1
       706: 1
       707: 1
       708: q+1
       709: q+1
       710: 2q+1
       711: 2q+1
       713: q+1
       714: q+1
       715: 2q+1
       716: q+1
       717: q+1
       718: 2q+1
       719: q^2+4q+1
       720: q+1
       721: 2q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: 2q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: 2q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: 1
       741: q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       750: 2q+1
       751: q+1
       752: q+1
       753: 1
       754: 1
       757: q+1
       758: 1
       761: 1
       762: q+1
       763: q+1
       765: q+1
       766: q+1
       767: 2q+1
       768: 1
       770: q+1
       771: 2q+1
       773: q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       794: 1
       801: 1
       802: q+1
       805: 1
       808: q+1
       809: q+1
       810: 2q+1
       811: 1
       813: q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: 2q+1
       820: q+1
       821: 3q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: 1
       827: 2q+1
       828: 1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: q+1
       833: q+1
       836: q+1
       843: 1
       844: 2q+1
       847: q+1
       849: q+1
       850: q+1
       851: q+1
       853: 1
       857: 1
       858: 1
       859: q+1
       860: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: q+1
       912: 1
       913: 2q+1
       916: q+1
       917: 1
       918: 1
       919: q+1
       920: q+1
       921: q+1
       922: q+1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: q+1
       931: 1
       932: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       962: 1
       966: 1
       967: q+1
       970: q+1
       971: 1
       974: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: q+1
       986: 1
      1008: 1
      1016: q+1
      1017: 1
      1020: 1
      1021: q+1
      1022: q+1
      1024: q+1
      1025: q+1
      1026: 2q+1
      1027: 1
      1029: q+1
      1030: 2q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: 2q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: 1
      1053: 1
      1060: 1
      1061: q+1
      1064: 1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1093: 1
      1096: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1116: 1
      1117: 1
      1118: q+1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: q+1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1171: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1219: 1
      1223: 1
      1224: q+1
      1227: q+1
      1228: 1
      1231: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: q+1
      1243: 1
      1265: 1
      1273: 1
      1277: 1
      1278: 1
      1285: 1
      1291: 1
      1300: 1
      1303: 1
      1313: 1
      1314: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1324: 1
      1328: 1
      1329: 1
      1333: 1
      1335: 1
      1337: 1
      1340: 1
      1345: 1
      1346: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1356: 1
      1371: 1
      1410: 1
      1413: 1
      1421: 1
      1422: 1
      1425: 1
      1460: 1
      1488: 1
      1492: 1
      1493: 1
      1500: 1
      1506: 1
      1515: 1
      1518: 1
      1578: 1
      1636: 1

1637:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: 2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: 2q+1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q+1
        55: q^2+2q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: 2q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: 1
        94: q^2+2q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: q+1
       112: q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 2q+1
       125: 2q+1
       126: 2q+1
       128: 2q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: 1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: q^2+2q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: 2q+1
       193: q+1
       194: 2q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       214: 2q+1
       215: 2q+1
       216: q+1
       218: 2q+1
       220: q+1
       221: q+1
       222: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       252: 2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: q+1
       262: 1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       315: 2q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: 2q+1
       323: q+1
       324: 2q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       338: 2q+1
       339: q+1
       341: q+1
       345: q+1
       346: q+1
       347: 1
       349: q+1
       351: 1
       352: 1
       353: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: q+1
       363: q+1
       364: 1
       365: q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       381: 2q+1
       382: 2q+1
       383: q+1
       385: 2q+1
       387: q+1
       388: q+1
       389: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       479: 2q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       495: q+1
       497: q+1
       503: q+1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       516: 1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: 2q+1
       523: q+1
       524: 1
       525: 1
       526: q+1
       527: q+1
       528: q+1
       529: 2q+1
       530: q+1
       531: 2q+1
       532: q+1
       533: q+1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       545: 2q+1
       546: q+1
       548: q+1
       552: q+1
       553: q+1
       554: 1
       556: q+1
       558: 1
       559: 1
       560: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: q+1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: q+1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       703: 1
       704: 1
       705: q+1
       706: q+1
       709: q+1
       710: 1
       711: 1
       712: 1
       713: q+1
       714: q+1
       715: q+1
       716: q+1
       718: 2q+1
       719: q+1
       720: 1
       721: 1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       734: q+1
       736: q+1
       742: q+1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: q+1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: q+1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       906: 1
       907: 1
       908: q+1
       912: 1
       913: 1
       914: 1
       915: 1
       916: q+1
       917: q+1
       920: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       939: q+1
       946: 1
       948: 1
       954: 1
       955: 1
       957: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1109: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: q+1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1152: 1
      1159: 1
      1161: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1182: 1
      1183: 1
      1186: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1243: 1
      1265: 1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1353: 1
      1357: 1
      1371: 1
      1404: 1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1421: 1
      1422: 1
      1425: 1
      1461: 1
      1489: 1
      1494: 1
      1495: 1
      1500: 1
      1564: 1
      1578: 1
      1637: 1

1638:    0: 2q^4+8q^3+10q^2+5q+1
         1: 2q^4+8q^3+10q^2+5q+1
         2: q^4+5q^3+9q^2+5q+1
         3: 5q^3+9q^2+5q+1
         4: 2q^4+8q^3+10q^2+5q+1
         5: 2q^4+8q^3+10q^2+5q+1
         6: q^4+5q^3+9q^2+5q+1
         7: q^4+5q^3+9q^2+5q+1
         8: q^3+7q^2+5q+1
         9: 5q^3+9q^2+5q+1
        10: q^3+7q^2+5q+1
        11: 5q^3+9q^2+5q+1
        12: 4q^3+8q^2+5q+1
        13: 2q^4+8q^3+10q^2+5q+1
        14: q^4+5q^3+9q^2+5q+1
        15: 5q^3+9q^2+5q+1
        16: 2q^4+8q^3+10q^2+5q+1
        17: q^4+5q^3+9q^2+5q+1
        18: 4q^3+8q^2+5q+1
        19: 2q^4+8q^3+10q^2+5q+1
        20: q^3+7q^2+5q+1
        21: q^4+5q^3+9q^2+5q+1
        22: q^3+7q^2+5q+1
        23: q^3+7q^2+5q+1
        24: 4q^2+4q+1
        25: q^3+7q^2+5q+1
        26: q^3+7q^2+5q+1
        27: 6q^2+5q+1
        28: 5q^3+9q^2+5q+1
        29: q^3+7q^2+5q+1
        30: 4q^3+8q^2+5q+1
        31: q^3+6q^2+5q+1
        32: 4q^3+8q^2+5q+1
        33: q^4+5q^3+9q^2+5q+1
        34: q^4+5q^3+9q^2+5q+1
        35: q^3+7q^2+5q+1
        36: 5q^3+9q^2+5q+1
        37: q^3+7q^2+5q+1
        38: 5q^3+9q^2+5q+1
        39: 4q^3+8q^2+5q+1
        40: q^4+5q^3+9q^2+5q+1
        41: q^4+5q^3+9q^2+5q+1
        42: q^3+6q^2+5q+1
        43: 4q^3+8q^2+5q+1
        44: 4q^2+4q+1
        45: 4q^3+8q^2+5q+1
        46: 2q^3+5q^2+4q+1
        47: 2q^4+8q^3+10q^2+5q+1
        48: q^4+5q^3+9q^2+5q+1
        49: 4q^3+8q^2+5q+1
        50: q^3+7q^2+5q+1
        51: 4q^2+4q+1
        52: q^3+7q^2+5q+1
        53: 3q^2+4q+1
        54: q^3+7q^2+5q+1
        55: 4q^2+4q+1
        56: 4q^2+4q+1
        57: 6q^2+5q+1
        58: q^3+7q^2+5q+1
        59: 6q^2+5q+1
        60: 6q^2+5q+1
        61: 3q^2+4q+1
        62: q^3+7q^2+5q+1
        63: q^3+7q^2+5q+1
        64: 3q^2+4q+1
        65: q^3+6q^2+5q+1
        66: q^3+6q^2+5q+1
        67: 3q^2+4q+1
        68: 4q^3+8q^2+5q+1
        69: q^3+6q^2+5q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+7q^2+5q+1
        72: q^4+5q^3+9q^2+5q+1
        73: q^3+7q^2+5q+1
        74: q^3+7q^2+5q+1
        75: 4q^2+4q+1
        76: q^3+7q^2+5q+1
        77: q^3+7q^2+5q+1
        78: 6q^2+5q+1
        79: 5q^3+9q^2+5q+1
        80: q^3+7q^2+5q+1
        81: 4q^3+8q^2+5q+1
        82: q^3+6q^2+5q+1
        83: 4q^3+8q^2+5q+1
        84: q^3+6q^2+5q+1
        85: q^4+5q^3+9q^2+5q+1
        86: q^3+6q^2+5q+1
        87: q^3+6q^2+5q+1
        88: 2q^2+3q+1
        89: 4q^2+4q+1
        90: 4q^2+4q+1
        91: 3q^2+4q+1
        92: 4q^3+8q^2+5q+1
        93: 4q^2+4q+1
        94: 2q^3+5q^2+4q+1
        95: 2q^2+3q+1
        96: 2q^3+5q^2+4q+1
        97: q^4+5q^3+9q^2+5q+1
        98: q^4+5q^3+9q^2+5q+1
        99: q^3+6q^2+5q+1
       100: 4q^3+8q^2+5q+1
       101: 4q^2+4q+1
       102: 4q^3+8q^2+5q+1
       103: 2q^3+5q^2+4q+1
       104: 4q^2+4q+1
       105: q^3+7q^2+5q+1
       106: 4q^2+4q+1
       107: 3q^2+4q+1
       108: 3q^2+4q+1
       109: q^2+3q+1
       110: 4q^2+4q+1
       111: 2q^2+3q+1
       112: 6q^2+5q+1
       113: 3q^2+4q+1
       114: 6q^2+5q+1
       115: 3q^2+4q+1
       116: 6q^2+5q+1
       117: 3q^2+4q+1
       118: 3q^2+4q+1
       119: 3q^2+4q+1
       120: q^3+7q^2+5q+1
       121: 3q^2+4q+1
       122: 3q^2+4q+1
       123: q^2+2q+1
       124: 3q^2+4q+1
       125: q^3+6q^2+5q+1
       126: 3q^2+4q+1
       127: 3q^2+4q+1
       128: q^2+3q+1
       129: q^3+6q^2+5q+1
       130: q^3+6q^2+5q+1
       131: q^2+3q+1
       132: 2q^3+5q^2+4q+1
       133: 2q^2+3q+1
       134: q^3+7q^2+5q+1
       135: 4q^2+4q+1
       136: q^3+7q^2+5q+1
       137: 3q^2+4q+1
       138: q^3+7q^2+5q+1
       139: 4q^2+4q+1
       140: 4q^2+4q+1
       141: 6q^2+5q+1
       142: q^3+7q^2+5q+1
       143: 6q^2+5q+1
       144: 6q^2+5q+1
       145: 3q^2+4q+1
       146: q^3+7q^2+5q+1
       147: q^3+7q^2+5q+1
       148: 3q^2+4q+1
       149: q^3+6q^2+5q+1
       150: q^3+6q^2+5q+1
       151: 3q^2+4q+1
       152: 4q^3+8q^2+5q+1
       153: q^3+6q^2+5q+1
       154: 2q^3+5q^2+4q+1
       155: q^3+6q^2+5q+1
       156: 2q^2+3q+1
       157: q^3+6q^2+5q+1
       158: q^2+3q+1
       159: q^3+6q^2+5q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 3q^2+4q+1
       163: 4q^2+4q+1
       164: 3q^2+4q+1
       165: 3q^2+4q+1
       166: 2q+1
       167: 4q^2+4q+1
       168: 4q^2+4q+1
       169: q^2+3q+1
       170: 2q^2+3q+1
       171: 2q^2+3q+1
       172: q^2+2q+1
       173: 2q^3+5q^2+4q+1
       174: 2q^2+3q+1
       175: q^3+3q^2+3q+1
       176: q^3+6q^2+5q+1
       177: q^4+5q^3+9q^2+5q+1
       178: q^3+6q^2+5q+1
       179: q^3+6q^2+5q+1
       180: 2q^2+3q+1
       181: 4q^2+4q+1
       182: 4q^2+4q+1
       183: 3q^2+4q+1
       184: 4q^3+8q^2+5q+1
       185: 4q^2+4q+1
       186: 2q^3+5q^2+4q+1
       187: 2q^2+3q+1
       188: 2q^3+5q^2+4q+1
       189: 2q^2+3q+1
       190: 4q^2+4q+1
       191: 3q^2+4q+1
       192: q^2+3q+1
       193: q^2+2q+1
       194: 2q+1
       195: q^2+3q+1
       196: 2q^2+3q+1
       197: q^2+2q+1
       198: 3q^2+4q+1
       199: 6q^2+5q+1
       200: 3q^2+4q+1
       201: 3q^2+4q+1
       202: 3q^2+4q+1
       203: q^2+3q+1
       204: 3q^2+4q+1
       205: 2q+1
       206: 3q^2+4q+1
       207: q^2+2q+1
       208: 3q^2+4q+1
       209: 2q+1
       210: 3q^2+4q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: 3q^2+4q+1
       214: q^2+3q+1
       215: 3q^2+4q+1
       216: q^2+2q+1
       217: 3q^2+4q+1
       218: q^2+3q+1
       219: q^2+3q+1
       220: q^2+3q+1
       221: q^3+6q^2+5q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 2q+1
       228: 4q^2+4q+1
       229: q^3+7q^2+5q+1
       230: 4q^2+4q+1
       231: 3q^2+4q+1
       232: 3q^2+4q+1
       233: q^2+3q+1
       234: 4q^2+4q+1
       235: 2q^2+3q+1
       236: 6q^2+5q+1
       237: 3q^2+4q+1
       238: 6q^2+5q+1
       239: 3q^2+4q+1
       240: 6q^2+5q+1
       241: 3q^2+4q+1
       242: 3q^2+4q+1
       243: 3q^2+4q+1
       244: q^3+7q^2+5q+1
       245: 3q^2+4q+1
       246: 3q^2+4q+1
       247: q^2+2q+1
       248: 3q^2+4q+1
       249: q^3+6q^2+5q+1
       250: 3q^2+4q+1
       251: 3q^2+4q+1
       252: q^2+3q+1
       253: q^3+6q^2+5q+1
       254: q^3+6q^2+5q+1
       255: q^2+3q+1
       256: 2q^3+5q^2+4q+1
       257: 2q^2+3q+1
       258: 2q^2+3q+1
       259: q^3+6q^2+5q+1
       260: 2q^2+3q+1
       261: q^2+3q+1
       262: q^2+3q+1
       263: 2q+1
       264: 2q^2+3q+1
       265: q^2+2q+1
       266: 3q^2+4q+1
       267: 2q+1
       268: 3q^2+4q+1
       269: q^2+3q+1
       270: 3q^2+4q+1
       271: 2q+1
       272: 2q+1
       273: q^2+3q+1
       274: 4q^2+4q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: q+1
       278: q^2+2q+1
       279: 2q^2+3q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: q+1
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: q+1
       286: q^3+3q^2+3q+1
       287: q^2+2q+1
       288: q^3+6q^2+5q+1
       289: 2q^2+3q+1
       290: q^3+6q^2+5q+1
       291: q^2+3q+1
       292: q^3+6q^2+5q+1
       293: 2q^2+3q+1
       294: 2q^2+3q+1
       295: 3q^2+4q+1
       296: 4q^2+4q+1
       297: 3q^2+4q+1
       298: 3q^2+4q+1
       299: 2q+1
       300: 4q^2+4q+1
       301: 4q^2+4q+1
       302: q^2+3q+1
       303: 2q^2+3q+1
       304: 2q^2+3q+1
       305: q^2+2q+1
       306: 2q^3+5q^2+4q+1
       307: 2q^2+3q+1
       308: q^3+3q^2+3q+1
       309: q^2+2q+1
       310: 2q^2+3q+1
       311: q^2+3q+1
       312: q^2+2q+1
       314: 2q+1
       315: 2q+1
       316: q+1
       317: q+1
       318: q^2+2q+1
       319: 2q+1
       320: 3q^2+4q+1
       321: 3q^2+4q+1
       322: q^2+3q+1
       323: q^2+2q+1
       324: 2q+1
       325: q^2+3q+1
       326: 2q+1
       327: q+1
       328: q^2+2q+1
       329: 3q^2+4q+1
       330: q^2+2q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q^2+2q+1
       335: q+1
       336: q^2+3q+1
       337: 3q^2+4q+1
       338: q^2+3q+1
       339: q^2+2q+1
       340: q^2+2q+1
       341: q+1
       342: q^2+3q+1
       343: 2q+1
       344: q^2+3q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       348: q^2+3q+1
       349: q+1
       350: q+1
       351: 2q+1
       352: 2q^2+3q+1
       353: 2q+1
       354: 2q+1
       355: 1
       356: 2q^2+3q+1
       357: 4q^2+4q+1
       358: 3q^2+4q+1
       359: q^2+3q+1
       360: q^2+2q+1
       361: 2q+1
       362: q^2+3q+1
       363: 2q^2+3q+1
       364: q^2+2q+1
       365: 3q^2+4q+1
       366: 6q^2+5q+1
       367: 3q^2+4q+1
       368: 3q^2+4q+1
       369: 3q^2+4q+1
       370: q^2+3q+1
       371: 3q^2+4q+1
       372: 2q+1
       373: 3q^2+4q+1
       374: q^2+2q+1
       375: 3q^2+4q+1
       376: 2q+1
       377: 3q^2+4q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: 3q^2+4q+1
       381: q^2+3q+1
       382: 3q^2+4q+1
       383: q^2+2q+1
       384: 3q^2+4q+1
       385: q^2+3q+1
       386: q^2+3q+1
       387: q^2+3q+1
       388: q^3+6q^2+5q+1
       389: q^2+3q+1
       390: q^2+3q+1
       391: q+1
       392: 2q^2+3q+1
       393: 2q^2+3q+1
       394: 2q+1
       395: q^2+2q+1
       396: 2q^2+3q+1
       397: q^2+3q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 3q^2+4q+1
       406: 2q+1
       407: q^2+3q+1
       408: q^2+3q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: q^2+3q+1
       413: q+1
       414: q^2+3q+1
       415: 2q+1
       416: q^2+3q+1
       417: q+1
       418: q+1
       419: q^2+2q+1
       420: q+1
       421: q^2+2q+1
       423: q^2+2q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q^2+3q+1
       428: q+1
       429: q+1
       430: 1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q+1
       434: 2q^2+3q+1
       435: q^3+6q^2+5q+1
       436: 2q^2+3q+1
       437: q^2+3q+1
       438: q^2+3q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: 3q^2+4q+1
       443: 2q+1
       444: 3q^2+4q+1
       445: q^2+3q+1
       446: 3q^2+4q+1
       447: 2q+1
       448: 2q+1
       449: q^2+3q+1
       450: 4q^2+4q+1
       451: q^2+3q+1
       452: q^2+3q+1
       453: q+1
       454: q^2+2q+1
       455: 2q^2+3q+1
       456: q^2+2q+1
       457: q^2+2q+1
       458: q+1
       459: 2q^2+3q+1
       460: 2q^2+3q+1
       461: q+1
       462: q^3+3q^2+3q+1
       463: q^2+2q+1
       464: q^2+2q+1
       465: q+1
       466: q+1
       468: 2q+1
       469: q+1
       471: 1
       472: q+1
       473: q+1
       474: 2q+1
       475: q^2+3q+1
       476: q^2+2q+1
       478: 2q+1
       479: 2q+1
       480: q+1
       481: 1
       482: q+1
       483: q+1
       484: q^2+2q+1
       485: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: q+1
       491: 1
       492: 2q+1
       493: q^2+3q+1
       494: q^2+2q+1
       495: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: q^2+3q+1
       503: q+1
       504: q+1
       505: q+1
       506: 1
       507: q+1
       508: q+1
       509: 2q+1
       510: 1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: 1
       515: 1
       516: q^2+2q+1
       517: 2q^2+3q+1
       518: q^2+3q+1
       519: q^2+2q+1
       521: 2q+1
       522: 2q+1
       523: q+1
       524: q+1
       525: q^2+2q+1
       526: 2q+1
       527: 3q^2+4q+1
       528: 3q^2+4q+1
       529: q^2+3q+1
       530: q^2+2q+1
       531: 2q+1
       532: q^2+3q+1
       533: 2q+1
       534: q+1
       535: q^2+2q+1
       536: 3q^2+4q+1
       537: q^2+2q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: q^2+2q+1
       542: q+1
       543: q^2+3q+1
       544: 3q^2+4q+1
       545: q^2+3q+1
       546: q^2+2q+1
       547: q^2+2q+1
       548: q+1
       549: q^2+3q+1
       550: 2q+1
       551: q^2+3q+1
       552: q+1
       553: q^2+3q+1
       554: q+1
       555: q^2+3q+1
       556: q+1
       557: q+1
       558: 2q+1
       559: 2q^2+3q+1
       560: 2q+1
       561: 2q+1
       562: 1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: q^2+3q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: q+1
       583: q^2+3q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q^2+2q+1
       592: q+1
       596: q+1
       597: 1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q^2+2q+1
       607: q+1
       608: q+1
       609: 1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: q^2+3q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 3q^2+4q+1
       621: 2q+1
       622: q^2+3q+1
       623: q^2+3q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q^2+3q+1
       628: q+1
       629: q^2+3q+1
       630: 2q+1
       631: q^2+3q+1
       632: q+1
       633: q+1
       634: q^2+2q+1
       635: q+1
       636: q^2+2q+1
       638: q^2+2q+1
       639: q+1
       640: q+1
       641: q+1
       642: 2q^2+3q+1
       643: q+1
       644: q+1
       645: 1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       652: q+1
       654: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       661: 2q+1
       662: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       681: q+1
       682: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 2q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       703: q^2+2q+1
       704: q+1
       705: q+1
       707: 2q+1
       708: q+1
       710: 1
       711: q+1
       712: q+1
       713: 2q+1
       714: q^2+3q+1
       715: q^2+2q+1
       717: 2q+1
       718: 2q+1
       719: q+1
       720: 1
       721: q+1
       722: q+1
       723: q^2+2q+1
       724: 2q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: q+1
       730: 1
       731: 2q+1
       732: q^2+3q+1
       733: q^2+2q+1
       734: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: q+1
       741: q^2+3q+1
       742: q+1
       743: q+1
       744: q+1
       745: 1
       746: q+1
       747: q+1
       748: 2q+1
       749: 1
       750: 2q+1
       751: q+1
       752: 2q+1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 1
       759: q+1
       760: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       767: q+1
       769: q+1
       770: q+1
       771: 1
       773: 1
       774: 1
       775: q+1
       776: 2q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       804: q+1
       805: 1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: q^2+3q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q^2+3q+1
       828: q+1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q^2+2q+1
       836: q+1
       840: q+1
       841: 1
       842: q+1
       843: 1
       844: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       853: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: q+1
       866: 1
       868: 1
       869: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       877: 1
       878: q+1
       879: 1
       882: q+1
       886: 1
       887: 1
       888: q+1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: q+1
       900: 1
       902: 1
       903: 1
       906: q+1
       907: 1
       909: q+1
       911: 1
       913: 1
       914: q+1
       915: 1
       916: q+1
       918: 2q+1
       919: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: q+1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: q+1
       934: 2q+1
       935: q+1
       938: q+1
       939: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: q+1
       946: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 2q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       960: q+1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       970: 1
       972: q+1
       973: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       982: 1
       983: 1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1012: 1
      1014: q+1
      1015: q+1
      1016: 1
      1018: q+1
      1019: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: 2q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: q+1
      1053: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1063: q+1
      1064: 1
      1065: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: 1
      1094: 1
      1095: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: q+1
      1125: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1141: q+1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1155: 1
      1157: 1
      1158: q+1
      1159: 1
      1161: 1
      1162: 1
      1165: 1
      1167: 1
      1170: 1
      1175: 1
      1180: 1
      1182: 1
      1184: 1
      1185: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1209: 1
      1217: q+1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1227: 1
      1229: q+1
      1230: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1239: 1
      1240: 1
      1241: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1269: 1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1293: 1
      1305: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1322: 1
      1323: 1
      1325: 1
      1327: 1
      1329: 1
      1330: 1
      1338: 1
      1339: 1
      1342: 1
      1346: 1
      1349: 1
      1352: 1
      1353: 1
      1358: 1
      1372: 1
      1385: 1
      1404: 1
      1406: 1
      1409: 1
      1414: 1
      1419: 1
      1421: 1
      1423: 1
      1424: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1448: 1
      1462: 1
      1490: 1
      1494: 1
      1496: 1
      1499: 1
      1508: 1
      1520: 1
      1565: 1
      1579: 1
      1592: 1
      1638: 1

1639:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       169: q+1
       170: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       272: 2q+1
       273: q+1
       276: q+1
       277: q+1
       278: q+1
       281: q+1
       282: q+1
       283: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       411: 1
       412: q+1
       413: q+1
       418: q+1
       419: q+1
       420: q+1
       425: q+1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       448: 2q+1
       449: q+1
       452: q+1
       453: q+1
       454: q+1
       457: q+1
       458: q+1
       459: 2q+1
       461: 1
       462: q+1
       463: q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       581: 1
       582: q+1
       589: 1
       590: q+1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       626: 1
       627: q+1
       628: q+1
       633: q+1
       634: q+1
       635: q+1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: q+1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: q+1
       716: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       825: 1
       826: q+1
       833: 1
       834: q+1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: q+1
       918: 1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       927: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1095: 1
      1098: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: q+1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 1
      1141: 1
      1146: 1
      1147: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1339: 1
      1342: 1
      1359: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1463: 1
      1491: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1566: 1
      1639: 1

1640:    0: 3q^2+2q+1
         1: 2q^2+2q+1
         2: 3q^2+2q+1
         3: 3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 3q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 3q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 3q^2+2q+1
        18: 3q^2+2q+1
        19: 3q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 3q^2+2q+1
        24: 2q^2+2q+1
        25: 2q+1
        26: q^2+q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 3q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: 3q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 3q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: 3q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 3q^2+2q+1
        49: 3q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: 2q+1
        54: 2q^2+2q+1
        55: q^2+2q+1
        56: 2q^2+2q+1
        57: 2q+1
        58: q+1
        59: q^2+q+1
        60: 2q^2+2q+1
        61: q^2+2q+1
        62: 2q+1
        63: q^2+q+1
        64: 2q^2+2q+1
        65: 2q+1
        66: q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: 3q^2+2q+1
        75: 2q^2+2q+1
        76: 2q+1
        77: q^2+q+1
        78: 2q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: 2q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 3q^2+2q+1
        88: q^2+2q+1
        89: 2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 3q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: 3q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: 2q^2+2q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q^2+q+1
       117: q+1
       118: q^2+2q+1
       119: 2q+1
       120: q+1
       121: q^2+q+1
       122: 2q^2+2q+1
       123: q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q+1
       130: q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: 2q+1
       138: 2q^2+2q+1
       139: q^2+2q+1
       140: 2q^2+2q+1
       141: 2q+1
       142: q+1
       143: q^2+q+1
       144: 2q^2+2q+1
       145: q^2+2q+1
       146: 2q+1
       147: q^2+q+1
       148: 2q^2+2q+1
       149: 2q+1
       150: q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: 2q^2+2q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: 2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       169: q^2+2q+1
       170: 2q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: 3q^2+2q+1
       180: q^2+2q+1
       181: 2q+1
       183: q^2+2q+1
       184: 2q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: q+1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q^2+2q+1
       206: 2q+1
       207: 1
       208: q+1
       209: q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q^2+2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: q+1
       225: q+1
       227: q+1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: 2q^2+2q+1
       236: 2q+1
       237: q+1
       238: q+1
       239: q+1
       240: q^2+q+1
       241: q+1
       242: q^2+2q+1
       243: 2q+1
       244: q+1
       245: q^2+q+1
       246: 2q^2+2q+1
       247: q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 2q+1
       254: q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: q+1
       272: 2q+1
       273: 2q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: 2q+1
       292: 2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       298: q^2+2q+1
       299: 2q+1
       300: 2q+1
       302: q^2+2q+1
       303: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: 1
       314: 2q+1
       315: q+1
       316: 2q+1
       317: q+1
       319: q+1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q^2+2q+1
       344: 2q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: 2q+1
       359: q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q^2+2q+1
       373: 2q+1
       374: 1
       375: q+1
       376: q+1
       377: q^2+q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q^2+2q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: q^2+2q+1
       391: q+1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       411: 2q+1
       412: 2q+1
       413: 1
       418: q+1
       419: 2q+1
       420: q+1
       425: 2q+1
       426: 2q+1
       429: 2q+1
       430: q+1
       431: q+1
       433: q+1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: q+1
       448: 2q+1
       449: 2q+1
       452: q^2+2q+1
       453: q+1
       454: 2q+1
       457: 2q+1
       458: 2q+1
       459: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       466: q+1
       467: 1
       468: q+1
       469: 2q+1
       470: 1
       471: q+1
       474: 1
       475: 1
       476: q+1
       477: 1
       478: q+1
       479: 1
       480: q+1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: q+1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       515: 1
       517: q+1
       518: q+1
       519: 2q+1
       520: 1
       521: 2q+1
       522: q+1
       523: 2q+1
       524: q+1
       526: q+1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: 1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q^2+2q+1
       551: 2q+1
       552: 1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: q+1
       561: q+1
       562: 1
       564: q+1
       565: q+1
       566: 2q+1
       567: 1
       568: 2q+1
       569: q+1
       570: 2q+1
       571: q+1
       573: q+1
       581: q+1
       582: 1
       589: q+1
       590: q+1
       597: 2q+1
       598: 2q+1
       599: 1
       604: q+1
       605: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: 2q+1
       613: q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       626: 2q+1
       627: 2q+1
       628: 1
       633: q+1
       634: 2q+1
       635: q+1
       640: 2q+1
       641: 2q+1
       644: 2q+1
       645: q+1
       646: q+1
       648: q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       659: 1
       660: 1
       661: 1
       662: q+1
       663: 1
       664: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: q+1
       706: 1
       707: q+1
       708: 2q+1
       709: 1
       710: q+1
       713: 1
       714: 1
       715: q+1
       716: 1
       717: q+1
       718: 1
       719: q+1
       720: 1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: q+1
       728: q+1
       729: q+1
       730: 1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       739: q+1
       740: 1
       741: q+1
       742: 1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       754: 1
       757: q+1
       758: 1
       759: q+1
       760: 2q+1
       761: 1
       762: q+1
       774: 1
       782: 1
       783: q+1
       791: q+1
       792: 1
       799: q+1
       800: q+1
       801: 1
       806: 1
       808: q+1
       809: q+1
       810: 2q+1
       811: 1
       812: 2q+1
       813: q+1
       814: 2q+1
       815: q+1
       817: q+1
       825: q+1
       826: 1
       833: q+1
       834: q+1
       841: 2q+1
       842: 2q+1
       843: 1
       848: q+1
       849: q+1
       852: q+1
       853: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       880: 1
       882: 1
       883: 1
       885: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       916: 1
       917: 1
       918: 1
       919: q+1
       920: 1
       921: 1
       924: 1
       925: 1
       926: q+1
       927: 1
       928: q+1
       929: 1
       930: q+1
       931: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       959: 1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1016: q+1
      1017: 1
      1018: q+1
      1019: 2q+1
      1020: 1
      1021: q+1
      1033: 1
      1041: 1
      1042: q+1
      1050: q+1
      1051: 1
      1058: q+1
      1059: q+1
      1060: 1
      1065: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1089: 1
      1091: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1132: 1
      1133: q+1
      1134: 1
      1135: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1168: 1
      1169: 1
      1208: 1
      1216: 1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1277: 1
      1282: 1
      1283: 1
      1296: 1
      1298: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1333: 1
      1335: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1360: 1
      1407: 1
      1408: 1
      1447: 1
      1455: 1
      1464: 1
      1492: 1
      1497: 1
      1498: 1
      1511: 1
      1513: 1
      1567: 1
      1640: 1

1641:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: 3q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+4q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 2q^2+3q+1
        11: 3q^2+3q+1
        12: 3q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 3q^2+3q+1
        16: q^3+4q^2+3q+1
        17: q^3+4q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+4q^2+3q+1
        20: q^2+2q+1
        21: q^3+3q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+3q+1
        31: 2q^2+3q+1
        32: 3q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+4q^2+3q+1
        35: 3q^2+3q+1
        36: 3q^2+3q+1
        37: 2q^2+3q+1
        38: 3q^2+3q+1
        39: 3q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+4q^2+3q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+4q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+3q+1
        54: 3q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 2q+1
        58: q^2+3q+1
        59: 2q^2+3q+1
        60: 2q^2+3q+1
        61: 2q^2+3q+1
        62: q^2+3q+1
        63: 2q^2+3q+1
        64: q^2+2q+1
        65: q^2+3q+1
        66: 2q^2+3q+1
        67: q^2+2q+1
        68: 3q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: 3q^2+3q+1
        74: 3q^2+3q+1
        75: 3q^2+3q+1
        76: q^2+3q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 3q^2+3q+1
        80: 2q^2+3q+1
        81: 3q^2+3q+1
        82: 2q^2+3q+1
        83: 3q^2+3q+1
        84: q^2+2q+1
        85: q^3+3q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: 2q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: 3q^2+3q+1
       111: q^2+2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: q^2+3q+1
       116: 2q^2+3q+1
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: q+1
       120: q^2+3q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 2q+1
       125: q^2+3q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+3q+1
       130: 2q^2+3q+1
       131: q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+3q+1
       138: 3q^2+3q+1
       139: 3q^2+3q+1
       140: 3q^2+3q+1
       141: 2q+1
       142: q^2+3q+1
       143: 2q^2+3q+1
       144: 2q^2+3q+1
       145: 2q^2+3q+1
       146: q^2+3q+1
       147: 2q^2+3q+1
       148: q^2+2q+1
       149: q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       152: 3q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q^2+3q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^3+3q^2+3q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: 2q^2+3q+1
       190: q^2+2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: 2q+1
       195: q^2+3q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: 2q^2+3q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+3q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+3q+1
       234: 3q^2+3q+1
       235: q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: q^2+3q+1
       240: 2q^2+3q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: q+1
       244: q^2+3q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: 2q+1
       249: q^2+3q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+3q+1
       254: 2q^2+3q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q^2+3q+1
       265: q^2+2q+1
       266: q+1
       267: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: 2q^2+3q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q^2+3q+1
       307: 2q+1
       308: q^2+2q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: 2q+1
       315: 2q+1
       316: q+1
       317: q+1
       318: q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: 2q+1
       325: q^2+3q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: q^2+2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: q^2+3q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: 2q^2+3q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q^2+2q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: q^2+2q+1
       385: q^2+2q+1
       386: q^2+2q+1
       387: q+1
       388: q^2+3q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: q+1
       394: 1
       396: q^2+2q+1
       397: q+1
       398: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: q+1
       468: 2q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       475: 2q+1
       476: q+1
       477: q+1
       478: 2q+1
       479: 2q+1
       480: q+1
       481: 1
       482: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: 1
       493: 2q+1
       494: q+1
       495: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 2q+1
       519: q+1
       520: q+1
       521: 2q+1
       522: 2q+1
       523: q+1
       524: q+1
       525: q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: 2q+1
       532: q^2+3q+1
       533: q+1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: q+1
       540: q+1
       541: q^2+2q+1
       542: q+1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: q^2+2q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: q+1
       566: 1
       567: 1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q^2+2q+1
       612: q+1
       613: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: q+1
       654: 1
       655: 1
       656: 1
       660: q+1
       661: 2q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       678: q+1
       681: q+1
       682: q+1
       684: 1
       685: 1
       687: q+1
       688: 1
       689: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: q+1
       707: 2q+1
       708: q+1
       709: q+1
       710: 1
       711: q+1
       714: 2q+1
       715: q+1
       716: q+1
       717: 2q+1
       718: 2q+1
       719: q+1
       720: 1
       721: 1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       730: 1
       732: 2q+1
       733: q+1
       734: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       758: 1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: q+1
       767: 1
       768: 1
       769: q+1
       770: q+1
       771: 1
       773: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       784: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       809: q+1
       810: 1
       811: 1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: q+1
       866: 1
       867: 1
       868: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       882: q+1
       886: 1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       910: q+1
       911: 1
       912: 1
       913: 1
       917: q+1
       918: 2q+1
       919: q+1
       920: q+1
       921: 1
       922: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       935: q+1
       938: q+1
       939: q+1
       941: 1
       942: 1
       944: q+1
       945: 1
       946: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: q+1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       986: 1
       996: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1017: 1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: q+1
      1026: 1
      1027: 1
      1028: q+1
      1029: q+1
      1030: 1
      1032: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1117: 1
      1118: 1
      1119: 1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1141: q+1
      1145: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1161: 1
      1162: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1207: 1
      1209: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: q+1
      1230: 1
      1231: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1243: 1
      1253: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1305: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1342: 1
      1346: 1
      1349: 1
      1352: 1
      1353: 1
      1361: 1
      1373: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1446: 1
      1448: 1
      1465: 1
      1493: 1
      1498: 1
      1499: 1
      1500: 1
      1520: 1
      1568: 1
      1580: 1
      1641: 1

1642:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q+1
        24: 2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: 2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: q+1
        55: 2q+1
        56: q+1
        57: 2q+1
        58: q^2+2q+1
        59: 2q+1
        60: q+1
        61: 2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: 2q+1
       107: 2q+1
       108: q+1
       109: 2q+1
       110: q+1
       111: 1
       112: q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: 1
       123: q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: q+1
       191: q+1
       192: 2q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: 1
       213: q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: 1
       236: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: 1
       247: q+1
       248: 2q+1
       249: q^2+2q+1
       250: 2q+1
       251: q+1
       252: 2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: q+1
       279: q+1
       283: q+1
       284: q+1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: 2q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q+1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: 1
       357: q+1
       358: q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       380: q+1
       381: 2q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       412: 1
       413: q+1
       414: q+1
       415: q+1
       416: 1
       417: q+1
       418: 1
       427: q+1
       431: q+1
       432: q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       455: q+1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       579: 1
       582: 1
       583: 1
       584: q+1
       585: q+1
       586: 1
       587: q+1
       588: 1
       606: q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       627: 1
       628: q+1
       629: q+1
       630: q+1
       631: 1
       632: q+1
       633: 1
       642: q+1
       646: q+1
       647: q+1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       703: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: q+1
       778: 1
       780: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       823: 1
       826: 1
       827: 1
       828: q+1
       829: q+1
       830: 1
       831: q+1
       832: 1
       850: q+1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       903: 1
       906: 1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       960: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1014: 1
      1015: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: q+1
      1037: 1
      1039: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1086: 1
      1087: 1
      1088: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1162: 1
      1183: 1
      1217: 1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1274: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1304: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1349: 1
      1350: 1
      1351: 1
      1422: 1
      1466: 1
      1489: 1
      1501: 1
      1502: 1
      1507: 1
      1508: 1
      1519: 1
      1642: 1

1643:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       157: 1
       158: 1
       159: 1
       162: 1
       163: 1
       164: 1
       165: 1
       167: 1
       168: 1
       169: 1
       176: 1
       177: 1
       178: 1
       179: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: 1
       261: 1
       262: 1
       266: 1
       268: 1
       269: 1
       270: 1
       273: 1
       274: 1
       275: 1
       276: 1
       288: 1
       290: 1
       291: 1
       292: 1
       295: 1
       296: 1
       297: 1
       298: 1
       300: 1
       301: 1
       302: 1
       309: 1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: 1
       399: 1
       405: 1
       407: 1
       408: 1
       412: 1
       414: 1
       415: 1
       416: 1
       435: 1
       437: 1
       438: 1
       442: 1
       444: 1
       445: 1
       446: 1
       449: 1
       450: 1
       451: 1
       452: 1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: 1
       575: 1
       577: 1
       583: 1
       585: 1
       586: 1
       612: 1
       614: 1
       620: 1
       622: 1
       623: 1
       627: 1
       629: 1
       630: 1
       631: 1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       665: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       767: 1
       776: 1
       778: 1
       810: 1
       819: 1
       821: 1
       827: 1
       829: 1
       830: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       980: 1
      1026: 1
      1035: 1
      1037: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1106: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1237: 1
      1275: 1
      1286: 1
      1288: 1
      1291: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1467: 1
      1490: 1
      1501: 1
      1503: 1
      1506: 1
      1643: 1

1644:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       283: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       412: 1
       413: 1
       418: 1
       431: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: q+1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       582: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       627: 1
       628: 1
       633: 1
       646: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       758: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       826: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       872: 1
       879: 1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
      1015: 1
      1017: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1097: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1131: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1276: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: 1
      1341: 1
      1468: 1
      1491: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1644: 1

1645:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q+1
        24: q^2+q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q^2+q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q^2+q+1
       127: q+1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: 1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       313: q+1
       314: 1
       315: q+1
       316: q+1
       317: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: 1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: q+1
       471: 1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: 1
       479: q+1
       480: q+1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: q+1
       521: 1
       522: q+1
       523: q+1
       524: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: 1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: q+1
       664: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q+1
       683: q+1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: q+1
       710: 1
       713: 1
       714: 1
       715: 1
       716: q+1
       717: 1
       718: q+1
       719: q+1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       761: 1
       762: 1
       774: 1
       782: 1
       801: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       875: 1
       876: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       921: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q+1
       940: q+1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       959: 1
       962: 1
       966: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1033: 1
      1041: 1
      1060: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1084: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1219: 1
      1223: 1
      1277: 1
      1289: 1
      1290: 1
      1295: 1
      1299: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1328: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1469: 1
      1492: 1
      1504: 1
      1505: 1
      1510: 1
      1514: 1
      1645: 1

1646:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: 1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: 1
       877: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1136: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1183: 1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1278: 1
      1290: 1
      1291: 1
      1292: 1
      1304: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1341: 1
      1346: 1
      1349: 1
      1350: 1
      1351: 1
      1422: 1
      1470: 1
      1493: 1
      1505: 1
      1506: 1
      1507: 1
      1519: 1
      1646: 1

1647:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: q^3+3q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: 2q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 2q^2+3q+1
        23: 2q+1
        24: q^2+2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^3+3q^2+3q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: q^3+3q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: q^2+2q+1
        52: 2q^2+3q+1
        53: q^2+2q+1
        54: 2q+1
        55: q^2+2q+1
        56: 2q+1
        57: 2q^2+3q+1
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 2q+1
        61: q^2+2q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: 2q^2+3q+1
        72: 2q^2+3q+1
        73: 2q^2+3q+1
        74: 2q+1
        75: q^2+2q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: q^2+3q+1
        81: q^3+3q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       104: 2q+1
       105: 2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: q^2+2q+1
       114: 2q^2+3q+1
       115: q^2+2q+1
       116: 2q+1
       117: q^2+2q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: 2q+1
       123: q+1
       124: 2q^2+3q+1
       125: 2q^2+3q+1
       126: 2q^2+3q+1
       127: 2q+1
       128: q^2+2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: 2q+1
       135: q^2+2q+1
       136: 2q^2+3q+1
       137: q^2+2q+1
       138: 2q+1
       139: q^2+2q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: 2q^2+3q+1
       143: 2q^2+3q+1
       144: 2q+1
       145: q^2+2q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 2q^2+3q+1
       152: 2q^2+3q+1
       153: q^2+3q+1
       154: 2q^2+3q+1
       155: 2q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: q+1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: 2q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: q+1
       208: q^2+3q+1
       209: q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: q^2+2q+1
       215: 2q^2+3q+1
       216: q^2+2q+1
       217: 2q+1
       218: q^2+2q+1
       219: 2q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: 2q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: 2q+1
       229: 2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: 2q+1
       236: 2q+1
       237: q^2+2q+1
       238: 2q^2+3q+1
       239: q^2+2q+1
       240: 2q+1
       241: q^2+2q+1
       242: 2q+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: 2q+1
       247: q+1
       248: 2q^2+3q+1
       249: 2q^2+3q+1
       250: 2q^2+3q+1
       251: 2q+1
       252: q^2+2q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 2q^2+3q+1
       257: 2q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: 2q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: 2q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: 2q+1
       293: q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: q+1
       299: 1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q^2+2q+1
       339: q^2+2q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       348: 2q+1
       349: q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 1
       356: 2q+1
       357: 2q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: 2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: 2q+1
       374: q+1
       375: q^2+3q+1
       376: q+1
       377: 2q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: q^2+2q+1
       382: 2q^2+3q+1
       383: q^2+2q+1
       384: 2q+1
       385: q^2+2q+1
       386: 2q+1
       387: q^2+3q+1
       388: q^2+3q+1
       389: q^2+3q+1
       390: 2q+1
       391: q+1
       392: 2q+1
       393: 2q+1
       394: 2q+1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: 2q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: 1
       444: 2q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: 2q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       511: 2q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: 2q+1
       518: q+1
       519: q+1
       522: q+1
       523: q+1
       524: 1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: 2q+1
       534: q+1
       535: q+1
       536: 2q+1
       537: q+1
       538: q+1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: 2q+1
       544: 2q+1
       545: q^2+2q+1
       546: q^2+2q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: q+1
       553: q^2+3q+1
       554: q+1
       555: 2q+1
       556: q+1
       557: q+1
       558: 2q+1
       559: 2q+1
       560: 2q+1
       561: q+1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: 1
       629: 2q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       635: 1
       636: q+1
       639: 1
       641: q+1
       642: q+1
       643: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: 1
       705: q+1
       710: 1
       711: 1
       712: q+1
       713: 2q+1
       714: q+1
       715: q+1
       718: q+1
       719: q+1
       720: 1
       721: q+1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       731: 2q+1
       732: 2q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: q+1
       741: 2q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       750: 2q+1
       751: q+1
       752: q+1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: q+1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: q+1
       847: 1
       849: q+1
       850: q+1
       851: q+1
       853: 1
       854: 1
       861: 1
       862: 1
       868: 1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       913: 1
       914: q+1
       915: 1
       916: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: q+1
       934: 2q+1
       935: q+1
       936: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       960: 1
       961: 1
       967: 1
       968: 1
       970: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: q+1
      1064: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1086: 1
      1087: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1180: 1
      1182: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1227: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1243: 1
      1265: 1
      1279: 1
      1286: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1303: 1
      1315: 1
      1322: 1
      1323: 1
      1329: 1
      1330: 1
      1331: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1356: 1
      1404: 1
      1419: 1
      1421: 1
      1471: 1
      1494: 1
      1501: 1
      1508: 1
      1509: 1
      1515: 1
      1516: 1
      1518: 1
      1647: 1

1648:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: 1
        24: q^2+q+1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: 1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q+1
        73: q+1
        74: 1
        75: q^2+q+1
        76: q^2+q+1
        77: q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q^2+q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q^2+q+1
       125: q+1
       126: q+1
       127: 1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q^2+q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q^2+q+1
       142: q+1
       143: q+1
       144: 1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       165: 1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q^2+q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q^2+q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q^2+q+1
       249: q+1
       250: q+1
       251: 1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       272: 1
       273: q+1
       276: 1
       277: q+1
       278: q+1
       282: q+1
       283: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       298: 1
       299: q+1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       354: 1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q^2+q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: q+1
       418: 1
       420: q+1
       426: q+1
       430: q+1
       431: q+1
       433: q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       448: 1
       449: q+1
       452: 1
       453: q+1
       454: q+1
       458: q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: q+1
       605: q+1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: q+1
       633: 1
       635: q+1
       641: q+1
       645: q+1
       646: q+1
       648: q+1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       727: q+1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: q+1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: q+1
       849: q+1
       853: q+1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: q+1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1060: q+1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: q+1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1166: 1
      1218: 1
      1219: 1
      1223: 1
      1234: 1
      1280: 1
      1287: 1
      1294: 1
      1295: 1
      1299: 1
      1316: 1
      1323: 1
      1324: 1
      1328: 1
      1331: 1
      1332: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1347: 1
      1405: 1
      1472: 1
      1495: 1
      1502: 1
      1509: 1
      1510: 1
      1514: 1
      1648: 1

1649:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: 2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: 2q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 2q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: 2q+1
        88: 1
        89: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: q+1
       104: q+1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: 2q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: 2q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: 2q+1
       165: 2q+1
       166: 1
       167: 2q+1
       169: 2q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 2q+1
       180: 1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: 2q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: q+1
       236: 2q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 1
       248: 2q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: 2q+1
       257: 2q+1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: 2q+1
       267: 1
       272: 1
       273: 2q+1
       276: 2q+1
       277: 1
       278: q+1
       281: q+1
       282: 1
       283: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 2q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: 2q+1
       298: 2q+1
       299: 1
       300: 2q+1
       302: 2q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: 2q+1
       354: 2q+1
       355: 1
       356: q+1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: q+1
       365: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: q+1
       373: 2q+1
       374: 1
       375: q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       380: 2q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: 1
       386: q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: 1
       392: 2q+1
       394: 2q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 2q+1
       413: 1
       418: 1
       419: q+1
       420: 1
       425: 1
       426: q+1
       429: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: 2q+1
       443: 1
       448: 1
       449: 2q+1
       452: 2q+1
       453: 1
       454: q+1
       457: q+1
       458: 1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: 2q+1
       510: 1
       515: 1
       516: q+1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       526: q+1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: q+1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 1
       546: q+1
       547: q+1
       548: 1
       549: 1
       550: q+1
       551: 2q+1
       552: 1
       553: q+1
       554: q+1
       555: q+1
       556: 1
       557: 1
       558: 2q+1
       561: 2q+1
       562: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: q+1
       599: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 2q+1
       628: 1
       633: 1
       634: q+1
       635: 1
       640: 1
       641: q+1
       644: q+1
       645: 1
       646: q+1
       648: q+1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: q+1
       713: 1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: q+1
       732: 1
       733: q+1
       734: 1
       735: q+1
       736: 1
       737: 1
       738: 1
       739: q+1
       740: 1
       741: q+1
       742: 1
       743: q+1
       744: q+1
       745: 1
       746: 1
       747: 1
       748: 2q+1
       749: 1
       754: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: q+1
       843: 1
       848: 1
       849: q+1
       852: q+1
       853: 1
       856: 1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       909: 1
       911: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: q+1
       938: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: q+1
       946: 1
       947: q+1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: 1
       963: 1
       965: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: q+1
      1060: 1
      1065: 1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1129: 1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1167: 1
      1198: 1
      1208: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1281: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1317: 1
      1323: 1
      1325: 1
      1327: 1
      1331: 1
      1333: 1
      1335: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1347: 1
      1394: 1
      1406: 1
      1437: 1
      1447: 1
      1455: 1
      1473: 1
      1496: 1
      1503: 1
      1509: 1
      1511: 1
      1513: 1
      1601: 1
      1649: 1

1650:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: 1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q+1
        49: q^2+q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+q+1
        69: q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        91: 1
        92: q^2+q+1
        93: 1
        94: q^2+q+1
        95: 1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: 1
       102: q^2+q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+q+1
       153: q+1
       154: q^2+q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q^2+q+1
       174: 1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       183: 1
       184: q^2+q+1
       185: 1
       186: q^2+q+1
       187: 1
       188: q^2+q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: q^2+q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q^2+q+1
       307: 1
       308: q^2+q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q^2+q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       731: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       774: 1
       783: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       897: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: q+1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       934: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       952: 1
       959: 1
       962: 1
       963: 1
       964: 1
       997: 1
      1006: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1088: 1
      1089: 1
      1090: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1156: 1
      1168: 1
      1208: 1
      1219: 1
      1220: 1
      1221: 1
      1254: 1
      1263: 1
      1270: 1
      1282: 1
      1289: 1
      1295: 1
      1296: 1
      1297: 1
      1318: 1
      1324: 1
      1325: 1
      1326: 1
      1332: 1
      1333: 1
      1334: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1407: 1
      1447: 1
      1474: 1
      1497: 1
      1504: 1
      1510: 1
      1511: 1
      1512: 1
      1650: 1

1651:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: 1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q^2+q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q^2+q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: 1
        72: q+1
        73: q+1
        74: q^2+q+1
        75: q^2+q+1
        76: q+1
        77: q+1
        78: q^2+q+1
        79: q+1
        80: q^2+q+1
        81: q+1
        82: q^2+q+1
        83: q^2+q+1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q^2+q+1
       141: 1
       142: q+1
       143: q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q^2+q+1
       152: q+1
       153: q^2+q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       165: q+1
       166: q+1
       167: q+1
       169: q+1
       170: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+q+1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       227: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q^2+q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: 1
       272: q+1
       273: 1
       276: q+1
       277: q+1
       278: 1
       281: 1
       282: 1
       283: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: q+1
       299: q+1
       300: q+1
       302: q+1
       303: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       354: q+1
       355: q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q^2+q+1
       387: 1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       394: q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: 1
       411: 1
       412: 1
       413: 1
       418: q+1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: q+1
       453: q+1
       454: 1
       457: 1
       458: 1
       459: q+1
       461: 1
       462: q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: 1
       515: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: 1
       552: 1
       553: 1
       554: q+1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: q+1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       730: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: 1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: 1
       749: 1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       782: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       905: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       951: q+1
       952: 1
       959: 1
       964: 1
       965: 1
       966: 1
      1005: 1
      1006: 1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1041: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1164: 1
      1169: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1262: 1
      1263: 1
      1270: 1
      1283: 1
      1290: 1
      1297: 1
      1298: 1
      1299: 1
      1319: 1
      1326: 1
      1327: 1
      1328: 1
      1334: 1
      1335: 1
      1336: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1408: 1
      1455: 1
      1475: 1
      1498: 1
      1505: 1
      1512: 1
      1513: 1
      1514: 1
      1651: 1

1652:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: q+1
        45: 2q+1
        46: q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: 1
        90: q+1
        91: q+1
        92: 2q+1
        93: q+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: 2q+1
       103: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       134: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q+1
       147: 2q+1
       148: 2q+1
       149: q+1
       150: 2q+1
       151: 2q+1
       152: 2q+1
       153: 2q+1
       154: 2q+1
       155: q+1
       157: q+1
       158: 1
       159: 2q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: 1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: 1
       182: q+1
       183: q+1
       184: 2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       191: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       199: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: q+1
       208: q+1
       209: 1
       210: 2q+1
       211: q+1
       212: q+1
       213: q+1
       215: q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: 1
       226: q+1
       227: q+1
       229: q+1
       231: q+1
       232: q+1
       233: q+1
       234: 2q+1
       235: 2q+1
       236: q+1
       238: q+1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 2q+1
       246: 2q+1
       247: q+1
       248: q+1
       249: q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: q+1
       254: 2q+1
       255: 2q+1
       256: 2q+1
       257: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       268: 1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: 2q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: 1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: q+1
       314: q+1
       316: q+1
       317: 1
       318: q+1
       321: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       337: q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       346: q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: q+1
       355: 1
       358: q+1
       360: q+1
       361: q+1
       362: q+1
       363: 2q+1
       364: q+1
       366: q+1
       368: q+1
       369: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       375: q+1
       376: 1
       377: 2q+1
       378: q+1
       379: q+1
       380: q+1
       382: q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: q+1
       388: q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: 1
       393: q+1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       414: 1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       469: q+1
       471: 1
       472: 1
       476: q+1
       478: q+1
       480: q+1
       481: 1
       482: q+1
       485: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       494: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       511: 1
       512: 1
       513: q+1
       514: 1
       515: 1
       519: q+1
       521: q+1
       523: q+1
       524: 1
       525: q+1
       528: q+1
       530: q+1
       531: q+1
       532: q+1
       533: 2q+1
       534: q+1
       536: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       544: q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: q+1
       553: q+1
       554: 1
       555: 2q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: q+1
       561: q+1
       562: 1
       566: 1
       568: 1
       570: 1
       571: 1
       572: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: 1
       596: 1
       597: 1
       598: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       654: 1
       656: 1
       662: q+1
       664: 1
       665: 1
       669: 1
       671: 1
       673: 1
       674: 1
       675: 1
       679: q+1
       681: q+1
       683: q+1
       684: 1
       685: q+1
       688: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: q+1
       710: 1
       711: 1
       715: q+1
       717: q+1
       719: q+1
       720: 1
       721: q+1
       724: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       733: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       741: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       750: 1
       751: 1
       752: q+1
       753: 1
       754: 1
       760: 1
       762: 1
       763: 1
       767: 1
       769: 1
       771: 1
       773: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       790: 1
       791: 1
       793: 1
       798: 1
       799: 1
       800: 1
       802: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: 1
       816: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       835: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       859: 1
       866: 1
       868: 1
       874: 1
       876: 1
       877: 1
       883: q+1
       885: 1
       886: 1
       890: 1
       892: 1
       894: 1
       895: 1
       896: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       911: 1
       913: 1
       919: q+1
       921: 1
       922: 1
       926: 1
       928: 1
       930: 1
       931: 1
       932: 1
       936: q+1
       938: q+1
       940: q+1
       941: 1
       942: q+1
       945: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       953: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       965: 1
       967: 1
       973: 1
       980: 1
       982: 1
       984: 1
       986: 1
       996: 1
      1004: 1
      1005: 1
      1007: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1022: 1
      1026: 1
      1028: 1
      1030: 1
      1032: 1
      1035: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1049: 1
      1050: 1
      1052: 1
      1057: 1
      1058: 1
      1059: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1076: 1
      1083: 1
      1085: 1
      1091: 1
      1093: 1
      1099: 1
      1101: 1
      1102: 1
      1106: 1
      1108: 1
      1110: 1
      1112: 1
      1118: 1
      1125: 1
      1127: 1
      1133: 1
      1135: 1
      1136: 1
      1142: q+1
      1144: 1
      1145: 1
      1149: 1
      1151: 1
      1153: 1
      1154: 1
      1155: 1
      1158: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1170: 1
      1185: 1
      1207: 1
      1215: 1
      1216: 1
      1222: 1
      1224: 1
      1230: 1
      1237: 1
      1239: 1
      1241: 1
      1243: 1
      1253: 1
      1261: 1
      1262: 1
      1264: 1
      1269: 1
      1270: 1
      1284: 1
      1291: 1
      1298: 1
      1300: 1
      1306: 1
      1320: 1
      1327: 1
      1329: 1
      1335: 1
      1337: 1
      1343: 1
      1345: 1
      1346: 1
      1350: 1
      1352: 1
      1354: 1
      1356: 1
      1403: 1
      1409: 1
      1424: 1
      1446: 1
      1454: 1
      1455: 1
      1476: 1
      1499: 1
      1506: 1
      1513: 1
      1515: 1
      1521: 1
      1610: 1
      1652: 1

1653:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q+1
        24: q^2+q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q^2+q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q^2+q+1
       127: q+1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       313: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       470: q+1
       471: 1
       472: 1
       477: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       520: q+1
       522: q+1
       523: q+1
       524: 1
       525: 1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       655: 1
       656: 1
       663: q+1
       664: 1
       665: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       680: q+1
       682: q+1
       683: q+1
       684: 1
       685: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: q+1
       710: 1
       711: 1
       716: q+1
       718: q+1
       719: q+1
       720: 1
       721: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       761: 1
       762: 1
       763: 1
       768: 1
       770: 1
       771: 1
       773: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       860: 1
       867: 1
       868: 1
       875: 1
       876: 1
       877: 1
       884: q+1
       885: 1
       886: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       912: 1
       913: 1
       920: q+1
       921: 1
       922: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       937: q+1
       939: q+1
       940: q+1
       941: 1
       942: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: 1
       967: 1
       974: 1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1077: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1100: 1
      1101: 1
      1102: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1119: 1
      1126: 1
      1127: 1
      1134: 1
      1135: 1
      1136: 1
      1143: q+1
      1144: 1
      1145: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1171: 1
      1186: 1
      1223: 1
      1224: 1
      1231: 1
      1238: 1
      1240: 1
      1241: 1
      1243: 1
      1265: 1
      1285: 1
      1292: 1
      1299: 1
      1300: 1
      1307: 1
      1321: 1
      1328: 1
      1329: 1
      1336: 1
      1337: 1
      1344: 1
      1345: 1
      1346: 1
      1351: 1
      1353: 1
      1354: 1
      1356: 1
      1410: 1
      1425: 1
      1477: 1
      1500: 1
      1507: 1
      1514: 1
      1515: 1
      1522: 1
      1653: 1

1654:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^2+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q+1
        12: q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+1
        21: q^3+q^2+q+1
        22: q^2+1
        23: 1
        24: q^2+1
        25: q^3+q^2+q+1
        26: q^3+q^2+q+1
        27: q^2+1
        28: q+1
        29: q+1
        30: q^3+q^2+q+1
        31: q^3+q^2+q+1
        32: q+1
        33: q^3+q^2+q+1
        34: q^3+q^2+q+1
        35: q^2+1
        36: q^3+q^2+q+1
        37: q^3+q^2+q+1
        38: q+1
        39: q^3+q^2+q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: 1
        55: q^2+1
        56: 1
        57: q^2+1
        58: q^3+q^2+q+1
        59: q^2+1
        60: 1
        61: q^2+1
        62: q+1
        63: q+1
        64: 1
        65: q^3+q^2+q+1
        66: q^3+q^2+q+1
        67: q^2+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+1
        72: q^3+q^2+q+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^3+q^2+q+1
        77: q^3+q^2+q+1
        78: q^2+1
        79: q+1
        80: q+1
        81: q^3+q^2+q+1
        82: q^3+q^2+q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q^2+1
       107: q^2+1
       108: 1
       109: q^2+1
       110: 1
       111: 1
       112: 1
       113: q^2+1
       114: q^2+1
       115: q^2+1
       116: 1
       117: q^2+1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q^2+1
       125: q^3+q^2+q+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: q^2+1
       136: q^2+1
       137: q^2+1
       138: 1
       139: q^2+1
       140: 1
       141: q^2+1
       142: q^3+q^2+q+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: q+1
       147: q+1
       148: 1
       149: q^3+q^2+q+1
       150: q^3+q^2+q+1
       151: q^2+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q^2+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q^2+1
       201: q^2+1
       202: 1
       203: q^2+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: q^2+1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: q^2+1
       231: q^2+1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       236: 1
       237: q^2+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^3+q^2+q+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q^2+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q^2+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: q^2+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q^2+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       786: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: q+1
       851: 1
       853: 1
       861: 1
       869: 1
       870: 1
       877: 1
       878: 1
       879: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       906: 1
       914: 1
       915: 1
       922: 1
       923: 1
       924: 1
       925: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: 1
       968: 1
       969: 1
       976: 1
       977: 1
       978: 1
       979: 1
       985: 1
       986: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1014: 1
      1015: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1120: 1
      1128: 1
      1129: 1
      1136: 1
      1137: 1
      1138: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1163: 1
      1164: 1
      1172: 1
      1180: 1
      1181: 1
      1188: 1
      1211: 1
      1217: 1
      1225: 1
      1226: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1242: 1
      1243: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1293: 1
      1301: 1
      1302: 1
      1309: 1
      1322: 1
      1330: 1
      1338: 1
      1339: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1355: 1
      1356: 1
      1369: 1
      1411: 1
      1419: 1
      1420: 1
      1427: 1
      1450: 1
      1478: 1
      1508: 1
      1516: 1
      1517: 1
      1524: 1
      1576: 1
      1654: 1

1655:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: q^3+3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: q^3+3q^2+2q+1
         5: 2q^2+2q+1
         6: q^3+3q^2+2q+1
         7: q^2+2q+1
         8: q^3+3q^2+2q+1
         9: q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: 2q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^3+3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+1
        24: q^2+q+1
        25: q^3+3q^2+2q+1
        26: q^2+2q+1
        27: q^3+3q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^3+3q^2+2q+1
        32: 2q^2+2q+1
        33: q^3+3q^2+2q+1
        34: q^2+2q+1
        35: q^3+3q^2+2q+1
        36: q^3+3q^2+2q+1
        37: q^3+3q^2+2q+1
        38: 2q^2+2q+1
        39: q^3+3q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+1
        51: q^2+q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: 1
        55: q+1
        56: 1
        57: q^3+3q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+1
        61: q^2+q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: 2q^2+2q+1
        65: q^3+3q^2+2q+1
        66: q^2+2q+1
        67: q^3+3q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: 2q^2+2q+1
        71: q^3+3q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+1
        75: q^2+q+1
        76: q^3+3q^2+2q+1
        77: q^2+2q+1
        78: q^3+3q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: q^3+3q^2+2q+1
        82: q^3+3q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+1
        88: q+1
        89: 2q^2+2q+1
        90: q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: q+1
       107: q^2+2q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: q^2+1
       113: q^2+q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: 1
       117: q+1
       118: 1
       119: 2q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^2+1
       123: q+1
       124: q^3+3q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+1
       128: q^2+q+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: 2q^2+2q+1
       132: 2q^2+2q+1
       133: 2q^2+2q+1
       134: q^2+1
       135: q^2+q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 1
       139: q+1
       140: 1
       141: q^3+3q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+1
       145: q^2+q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: 2q^2+2q+1
       149: q^3+3q^2+2q+1
       150: q^2+2q+1
       151: q^3+3q^2+2q+1
       152: 2q^2+2q+1
       153: 2q^2+2q+1
       154: 2q^2+2q+1
       155: q^2+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: 1
       160: q+1
       161: 1
       162: 2q^2+2q+1
       163: q+1
       164: q+1
       165: q^2+1
       166: q+1
       167: 2q^2+2q+1
       168: q+1
       169: 2q^2+2q+1
       170: q^2+2q+1
       171: q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+1
       180: q+1
       181: 2q^2+2q+1
       182: q+1
       183: 2q^2+2q+1
       184: 2q^2+2q+1
       185: 2q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q^2+2q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       206: q^2+1
       207: q+1
       208: q^2+2q+1
       209: q^2+2q+1
       210: 1
       211: q+1
       212: 1
       213: q^2+1
       214: q^2+q+1
       215: q^2+2q+1
       216: q^2+2q+1
       217: 1
       218: q+1
       219: 1
       220: 2q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+1
       224: q+1
       225: 2q^2+2q+1
       226: q+1
       227: 2q^2+2q+1
       228: 1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: q^2+1
       237: q^2+q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: 1
       241: q+1
       242: 1
       243: 2q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q^2+1
       247: q+1
       248: q^3+3q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+1
       252: q^2+q+1
       253: 2q^2+2q+1
       254: q^2+2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 1
       259: 1
       260: q+1
       261: q^2+2q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: q^2+1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 2q^2+2q+1
       274: q+1
       275: q+1
       276: q^2+1
       277: q+1
       278: q^2+2q+1
       279: q+1
       280: q+1
       282: q+1
       283: q^2+2q+1
       284: q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q^2+1
       289: q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: 1
       293: q+1
       294: 1
       295: 2q^2+2q+1
       296: q+1
       297: q+1
       298: q^2+1
       299: q+1
       300: 2q^2+2q+1
       301: q+1
       302: 2q^2+2q+1
       303: q^2+2q+1
       304: q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: q^2+2q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q^2+2q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: q^2+1
       345: q+1
       346: q^2+2q+1
       347: q^2+2q+1
       348: 1
       349: q+1
       350: 1
       351: 2q^2+2q+1
       352: q+1
       353: q+1
       354: q^2+1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q^2+2q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: q^2+1
       374: q+1
       375: q^2+2q+1
       376: q^2+2q+1
       377: 1
       378: q+1
       379: 1
       380: q^2+1
       381: q^2+q+1
       382: q^2+2q+1
       383: q^2+2q+1
       384: 1
       385: q+1
       386: 1
       387: 2q^2+2q+1
       388: q^2+2q+1
       389: q^2+2q+1
       390: q^2+1
       391: q+1
       392: 2q^2+2q+1
       393: q+1
       394: 2q^2+2q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: q+1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       422: q+1
       424: 1
       426: q^2+2q+1
       427: q+1
       428: q+1
       430: q+1
       431: q^2+2q+1
       432: q+1
       433: q^2+2q+1
       434: 1
       435: 1
       436: q+1
       437: q^2+2q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: q^2+1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 2q^2+2q+1
       450: q+1
       451: q+1
       452: q^2+1
       453: q+1
       454: q^2+2q+1
       455: q+1
       456: q+1
       458: q+1
       459: q^2+2q+1
       460: q+1
       461: q^2+2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q^2+2q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: q^2+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: q^2+2q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: q^2+2q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: q^2+1
       552: q+1
       553: q^2+2q+1
       554: q^2+2q+1
       555: 1
       556: q+1
       557: 1
       558: 2q^2+2q+1
       559: q+1
       560: q+1
       561: q^2+1
       562: q+1
       563: 1
       564: 1
       565: 1
       566: 1
       569: q+1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: q+1
       595: 1
       599: q+1
       600: q+1
       601: q+1
       603: 1
       605: q^2+2q+1
       606: q+1
       607: q+1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q^2+1
       628: q+1
       629: q+1
       630: q+1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       637: q+1
       639: 1
       641: q^2+2q+1
       642: q+1
       643: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q^2+2q+1
       650: 1
       658: 1
       659: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: q+1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       705: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       727: q+1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q^2+2q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: q^2+1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: 1
       754: 1
       756: 1
       757: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: q+1
       797: 1
       801: q+1
       802: q+1
       803: q+1
       805: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: q+1
       839: 1
       843: q+1
       844: q+1
       845: q+1
       847: 1
       849: q^2+2q+1
       850: q+1
       851: q+1
       853: q+1
       862: 1
       870: 1
       871: 1
       876: 1
       879: 1
       880: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: q+1
       894: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       907: 1
       915: 1
       916: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       929: q+1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       961: 1
       969: 1
       970: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: q+1
      1011: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: q+1
      1056: 1
      1060: q+1
      1061: q+1
      1062: q+1
      1064: 1
      1079: 1
      1087: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1121: 1
      1129: 1
      1130: 1
      1135: 1
      1138: 1
      1139: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: q+1
      1153: 1
      1154: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1173: 1
      1181: 1
      1182: 1
      1187: 1
      1204: 1
      1211: 1
      1213: 1
      1218: 1
      1226: 1
      1227: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1242: 1
      1250: 1
      1257: 1
      1259: 1
      1265: 1
      1266: q+1
      1268: 1
      1294: 1
      1302: 1
      1303: 1
      1308: 1
      1323: 1
      1331: 1
      1339: 1
      1340: 1
      1345: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1355: 1
      1370: 1
      1400: 1
      1412: 1
      1420: 1
      1421: 1
      1426: 1
      1443: 1
      1450: 1
      1452: 1
      1479: 1
      1509: 1
      1517: 1
      1518: 1
      1523: 1
      1577: 1
      1607: 1
      1655: 1

1656:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: 1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: 1
       555: 1
       556: q+1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       794: 1
       801: 1
       802: 1
       805: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       863: 1
       871: 1
       872: 1
       875: 1
       880: 1
       881: 1
       884: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
      1008: 1
      1016: 1
      1017: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1080: 1
      1088: 1
      1096: 1
      1097: 1
      1100: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1122: 1
      1130: 1
      1131: 1
      1134: 1
      1139: 1
      1140: 1
      1143: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1219: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1265: 1
      1295: 1
      1303: 1
      1304: 1
      1307: 1
      1324: 1
      1332: 1
      1340: 1
      1341: 1
      1344: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1371: 1
      1413: 1
      1421: 1
      1422: 1
      1425: 1
      1480: 1
      1510: 1
      1518: 1
      1519: 1
      1522: 1
      1578: 1
      1656: 1

1657:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: q^2+2q+1
         3: q^3+3q^2+2q+1
         4: q^3+3q^2+2q+1
         5: q^3+3q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+3q^2+2q+1
        10: q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^2+2q+1
        15: q^3+3q^2+2q+1
        16: q^3+3q^2+2q+1
        17: q^2+2q+1
        18: q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^2+2q+1
        32: q^3+3q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^3+3q^2+2q+1
        37: q^2+2q+1
        38: q^3+3q^2+2q+1
        39: q^3+3q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^3+3q^2+2q+1
        44: q+1
        45: q^3+3q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: 1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^3+3q^2+2q+1
        69: q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^3+3q^2+2q+1
        80: q^2+2q+1
        81: q^3+3q^2+2q+1
        82: q^2+2q+1
        83: q^3+3q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^3+3q^2+2q+1
        93: q+1
        94: q^3+2q^2+2q+1
        95: q+1
        96: q^3+2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^3+3q^2+2q+1
       101: q+1
       102: q^3+3q^2+2q+1
       103: q^3+2q^2+2q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: q^2+2q+1
       113: q+1
       114: q^2+2q+1
       115: 1
       116: q^2+2q+1
       117: q+1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^3+3q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: 1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^3+3q^2+2q+1
       153: q^2+2q+1
       154: q^3+3q^2+2q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: 1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^3+2q^2+2q+1
       174: q+1
       175: q^3+2q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^3+3q^2+2q+1
       185: q+1
       186: q^3+2q^2+2q+1
       187: q+1
       188: q^3+2q^2+2q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: q+1
       199: q^2+2q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       206: q^2+2q+1
       207: q+1
       208: q^2+2q+1
       209: 1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: q^2+2q+1
       214: q+1
       215: q^2+2q+1
       216: 1
       217: q^2+2q+1
       218: q+1
       219: q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: q^2+2q+1
       237: q+1
       238: q^2+2q+1
       239: 1
       240: q^2+2q+1
       241: q+1
       242: q+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^3+3q^2+2q+1
       257: q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^3+2q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: 1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^3+2q^2+2q+1
       307: q+1
       308: q^3+2q^2+2q+1
       310: q+1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       328: q+1
       329: q^2+2q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+2q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q^2+2q+1
       345: q+1
       346: q^2+2q+1
       347: 1
       348: q^2+2q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: q+1
       366: q^2+2q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q^2+2q+1
       374: q+1
       375: q^2+2q+1
       376: 1
       377: q^2+2q+1
       378: q+1
       379: q+1
       380: q^2+2q+1
       381: q+1
       382: q^2+2q+1
       383: 1
       384: q^2+2q+1
       385: q+1
       386: q+1
       387: q^2+2q+1
       388: q^2+2q+1
       389: q^2+2q+1
       390: q^2+2q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: 1
       444: q+1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^3+2q^2+2q+1
       463: q+1
       466: 1
       468: 1
       469: 1
       474: q+1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: q+1
       502: q^2+2q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       535: q+1
       536: q^2+2q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: q+1
       544: q^2+2q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q+1
       551: q^2+2q+1
       552: q+1
       553: q^2+2q+1
       554: 1
       555: q^2+2q+1
       556: q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       564: q+1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: 1
       629: q+1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: q+1
       635: 1
       636: q+1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       652: 1
       659: 1
       661: 1
       662: 1
       667: q+1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: 1
       696: q+1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       707: 1
       708: 1
       713: q+1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       731: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       740: q+1
       741: q^2+2q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       750: q+1
       751: 1
       752: q+1
       753: 1
       754: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       804: q+1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: q+1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: q+1
       836: 1
       840: 1
       841: 1
       842: q+1
       843: 1
       844: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       864: 1
       871: 1
       873: 1
       874: 1
       880: 1
       882: 1
       883: 1
       888: q+1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       909: 1
       916: 1
       918: 1
       919: 1
       924: q+1
       925: 1
       926: 1
       928: 1
       929: 1
       930: 1
       934: q+1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       952: 1
       953: q+1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       963: 1
       970: 1
       972: 1
       973: 1
       978: 1
       979: 1
       980: 1
       982: 1
       983: 1
       984: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1006: 1
      1007: q+1
      1008: 1
      1012: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: 1
      1043: 1
      1049: 1
      1051: 1
      1052: q+1
      1053: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1063: q+1
      1064: 1
      1065: 1
      1081: 1
      1089: 1
      1096: 1
      1098: 1
      1099: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1123: 1
      1130: 1
      1132: 1
      1133: 1
      1139: 1
      1141: 1
      1142: 1
      1147: q+1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1175: 1
      1182: 1
      1184: 1
      1185: 1
      1199: 1
      1208: 1
      1209: 1
      1215: 1
      1220: 1
      1227: 1
      1229: 1
      1230: 1
      1235: 1
      1236: 1
      1237: 1
      1239: 1
      1240: 1
      1241: 1
      1245: 1
      1254: 1
      1255: 1
      1261: 1
      1263: 1
      1264: q+1
      1265: 1
      1269: 1
      1270: 1
      1296: 1
      1303: 1
      1305: 1
      1306: 1
      1325: 1
      1333: 1
      1340: 1
      1342: 1
      1343: 1
      1348: 1
      1349: 1
      1350: 1
      1352: 1
      1353: 1
      1354: 1
      1372: 1
      1395: 1
      1414: 1
      1421: 1
      1423: 1
      1424: 1
      1438: 1
      1447: 1
      1448: 1
      1454: 1
      1481: 1
      1511: 1
      1518: 1
      1520: 1
      1521: 1
      1579: 1
      1602: 1
      1657: 1

1658:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: 2q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: 2q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: 2q^2+2q+1
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: q^2+2q+1
        83: 2q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 2q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: 2q+1
       152: 2q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: 2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: q+1
       370: q+1
       371: 2q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: q+1
       388: q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q+1
       393: q+1
       394: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: q+1
       540: q+1
       541: 2q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: q+1
       548: q+1
       549: 2q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: q+1
       745: q+1
       746: 2q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       998: 1
      1004: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1082: 1
      1090: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1124: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1209: 1
      1215: 1
      1221: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1255: 1
      1261: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1297: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1326: 1
      1334: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1373: 1
      1415: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1448: 1
      1454: 1
      1482: 1
      1512: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1580: 1
      1658: 1

1659:    0: 3q^2+2q+1
         1: 2q^2+2q+1
         2: 3q^2+2q+1
         3: 3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 3q^2+2q+1
        11: 3q^2+2q+1
        12: 3q^2+2q+1
        13: 2q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 3q^2+2q+1
        18: 2q^2+2q+1
        19: 3q^2+2q+1
        20: q^2+q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 3q^2+2q+1
        30: 2q^2+2q+1
        31: 3q^2+2q+1
        32: 3q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 3q^2+2q+1
        38: 3q^2+2q+1
        39: 3q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 3q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^2+q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: 2q^2+2q+1
        68: 2q^2+2q+1
        69: 3q^2+2q+1
        70: 2q^2+2q+1
        71: q^2+q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q^2+2q+1
        75: q^2+2q+1
        76: 2q^2+2q+1
        77: q^2+2q+1
        78: 2q^2+2q+1
        79: 2q^2+2q+1
        80: 3q^2+2q+1
        81: 2q^2+2q+1
        82: 3q^2+2q+1
        83: 3q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: 2q+1
        89: q^2+2q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: 2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       105: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+2q+1
       123: 2q+1
       124: q^2+q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q^2+2q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q^2+2q+1
       141: q^2+q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q^2+2q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: q^2+2q+1
       151: 2q^2+2q+1
       152: 2q^2+2q+1
       153: 3q^2+2q+1
       154: 2q^2+2q+1
       155: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: q+1
       165: q^2+2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q+1
       169: q^2+2q+1
       170: q^2+2q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: q^2+2q+1
       180: 2q+1
       181: q^2+2q+1
       182: q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: 2q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       191: q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       199: q+1
       201: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q^2+q+1
       215: q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: q^2+2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q+1
       227: q^2+2q+1
       229: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q^2+q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: q^2+2q+1
       243: q+1
       244: q^2+2q+1
       245: 2q+1
       246: q^2+2q+1
       247: 2q+1
       248: q^2+q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q^2+2q+1
       252: q^2+2q+1
       253: 2q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: 2q^2+2q+1
       259: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: q+1
       276: q^2+2q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: q^2+2q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: q+1
       298: q^2+2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q+1
       302: q^2+2q+1
       303: q^2+2q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       312: 1
       314: q+1
       316: 1
       317: q+1
       321: q+1
       323: 1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       329: q+1
       331: q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       337: q+1
       339: q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: 2q+1
       358: q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       366: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: q+1
       375: q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q^2+q+1
       382: q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: q^2+2q+1
       387: q+1
       388: q^2+2q+1
       389: 2q+1
       390: q^2+2q+1
       391: 2q+1
       392: q^2+2q+1
       393: q+1
       394: q^2+2q+1
       397: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       405: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: 2q+1
       419: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q+1
       427: q+1
       428: 1
       429: q+1
       430: q+1
       431: q^2+2q+1
       432: q+1
       433: q+1
       435: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: q+1
       452: q^2+2q+1
       453: 2q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: q^2+2q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       469: 1
       471: 1
       476: 1
       478: q+1
       480: 1
       481: q+1
       485: q+1
       487: 1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       494: q+1
       496: 1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       502: q+1
       504: q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: q+1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: 2q+1
       519: 1
       521: q+1
       523: 1
       524: q+1
       528: q+1
       530: 1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       536: q+1
       538: q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       544: q+1
       546: q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: q+1
       553: q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: q+1
       559: q+1
       560: q+1
       561: q^2+2q+1
       562: 2q+1
       566: 1
       568: q+1
       570: 1
       571: q+1
       575: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q+1
       605: q+1
       606: q+1
       607: 1
       608: q+1
       609: q+1
       612: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       620: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: 2q+1
       634: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q+1
       654: 1
       662: 1
       664: 1
       669: 1
       671: q+1
       673: 1
       674: q+1
       679: 1
       681: q+1
       683: 1
       684: q+1
       688: q+1
       690: 1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       696: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       708: 1
       710: 1
       715: 1
       717: q+1
       719: 1
       720: q+1
       724: q+1
       726: 1
       727: q+1
       728: 2q+1
       729: q+1
       730: q+1
       733: q+1
       735: 1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       741: q+1
       743: q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: q+1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: 2q+1
       760: 1
       762: 1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       810: 1
       812: q+1
       814: 1
       815: q+1
       819: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       866: 1
       874: 1
       876: 1
       883: 1
       885: 1
       890: 1
       892: q+1
       894: 1
       895: q+1
       899: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       911: 1
       919: 1
       921: 1
       926: 1
       928: q+1
       930: 1
       931: q+1
       936: 1
       938: q+1
       940: 1
       941: q+1
       945: q+1
       947: 1
       948: q+1
       949: 2q+1
       950: q+1
       951: q+1
       953: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       965: 1
       973: 1
       975: 1
       980: 1
       982: 1
       984: 1
       985: 1
       992: 1
       995: 1
       999: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1044: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1083: 1
      1091: 1
      1099: 1
      1101: 1
      1106: 1
      1108: 1
      1110: 1
      1111: 1
      1125: 1
      1133: 1
      1135: 1
      1142: 1
      1144: 1
      1149: 1
      1151: q+1
      1153: 1
      1154: q+1
      1158: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1177: 1
      1185: 1
      1187: 1
      1203: 1
      1206: 1
      1210: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1222: 1
      1230: 1
      1232: 1
      1237: 1
      1239: 1
      1241: 1
      1242: 1
      1249: 1
      1252: 1
      1256: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1264: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1298: 1
      1306: 1
      1308: 1
      1327: 1
      1335: 1
      1343: 1
      1345: 1
      1350: 1
      1352: 1
      1354: 1
      1355: 1
      1374: 1
      1399: 1
      1402: 1
      1416: 1
      1424: 1
      1426: 1
      1442: 1
      1445: 1
      1449: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1483: 1
      1513: 1
      1521: 1
      1523: 1
      1581: 1
      1606: 1
      1609: 1
      1659: 1

1660:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: 1
        24: q^2+q+1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: 1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q+1
        73: q+1
        74: 1
        75: q^2+q+1
        76: q^2+q+1
        77: q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       113: q^2+q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q^2+q+1
       125: q+1
       126: q+1
       127: 1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       135: q^2+q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q^2+q+1
       142: q+1
       143: q+1
       144: 1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       207: q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: 1
       214: q^2+q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: q+1
       226: 1
       227: q+1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       237: q^2+q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q^2+q+1
       249: q+1
       250: q+1
       251: 1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: 1
       277: q+1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: 1
       299: q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       313: 1
       315: q+1
       316: 1
       317: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: q+1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       381: q^2+q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: 1
       394: q+1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: q+1
       427: 1
       428: 1
       430: q+1
       431: q+1
       432: 1
       433: q+1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: 1
       453: q+1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       470: 1
       471: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: 1
       560: 1
       561: 1
       562: q+1
       567: 1
       569: q+1
       570: 1
       571: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: q+1
       600: 1
       601: 1
       603: 1
       605: q+1
       606: 1
       607: 1
       609: q+1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: 1
       643: 1
       645: q+1
       646: q+1
       647: 1
       648: q+1
       655: 1
       663: 1
       664: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 1
       710: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       725: q+1
       726: 1
       727: q+1
       728: 1
       729: 1
       730: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       761: 1
       762: 1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: q+1
       802: 1
       803: 1
       805: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: q+1
       844: 1
       845: 1
       847: 1
       849: q+1
       850: 1
       851: 1
       853: q+1
       867: 1
       875: 1
       876: 1
       884: 1
       885: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       912: 1
       920: 1
       921: 1
       927: 1
       929: q+1
       930: 1
       931: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: 1
       974: 1
       975: 1
       981: 1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1020: 1
      1021: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: q+1
      1061: 1
      1062: 1
      1064: 1
      1084: 1
      1092: 1
      1100: 1
      1101: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1126: 1
      1134: 1
      1135: 1
      1143: 1
      1144: 1
      1150: 1
      1152: q+1
      1153: 1
      1154: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1178: 1
      1186: 1
      1187: 1
      1204: 1
      1211: 1
      1213: 1
      1223: 1
      1231: 1
      1232: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1250: 1
      1257: 1
      1259: 1
      1265: 1
      1266: 1
      1268: 1
      1299: 1
      1307: 1
      1308: 1
      1328: 1
      1336: 1
      1344: 1
      1345: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1375: 1
      1400: 1
      1417: 1
      1425: 1
      1426: 1
      1443: 1
      1450: 1
      1452: 1
      1484: 1
      1514: 1
      1522: 1
      1523: 1
      1582: 1
      1607: 1
      1660: 1

1661:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: 1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: q^2+1
        32: 1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: q^2+1
        53: q^2+1
        54: 1
        55: q^2+1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q^2+1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: q^2+1
       108: 1
       109: q^2+1
       110: 1
       111: 1
       114: q^2+1
       115: q^2+1
       116: 1
       117: q^2+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q^2+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: q^2+1
       137: q^2+1
       138: 1
       139: q^2+1
       140: 1
       141: q^2+1
       142: q^2+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       193: 1
       194: q^2+1
       195: 1
       196: 1
       197: 1
       201: q^2+1
       202: 1
       203: q^2+1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       231: q^2+1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: q^2+1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       360: 1
       361: q^2+1
       362: 1
       363: 1
       364: 1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       496: 1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: 1
       595: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       673: 1
       674: 1
       675: 1
       683: 1
       684: 1
       685: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       711: 1
       719: 1
       720: 1
       721: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       762: 1
       763: 1
       771: 1
       772: 1
       773: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       788: 1
       795: 1
       797: 1
       802: 1
       803: 1
       805: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       837: 1
       839: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       868: 1
       876: 1
       877: 1
       885: 1
       886: 1
       894: 1
       895: 1
       896: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       913: 1
       921: 1
       922: 1
       930: 1
       931: 1
       932: 1
       940: 1
       941: 1
       942: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       967: 1
       975: 1
       976: 1
       984: 1
       985: 1
       986: 1
      1002: 1
      1009: 1
      1011: 1
      1021: 1
      1022: 1
      1030: 1
      1031: 1
      1032: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1047: 1
      1054: 1
      1056: 1
      1061: 1
      1062: 1
      1064: 1
      1085: 1
      1093: 1
      1101: 1
      1102: 1
      1110: 1
      1111: 1
      1112: 1
      1127: 1
      1135: 1
      1136: 1
      1144: 1
      1145: 1
      1153: 1
      1154: 1
      1155: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1179: 1
      1187: 1
      1188: 1
      1213: 1
      1224: 1
      1232: 1
      1233: 1
      1241: 1
      1242: 1
      1243: 1
      1259: 1
      1266: 1
      1268: 1
      1300: 1
      1308: 1
      1309: 1
      1329: 1
      1337: 1
      1345: 1
      1346: 1
      1354: 1
      1355: 1
      1356: 1
      1376: 1
      1418: 1
      1426: 1
      1427: 1
      1452: 1
      1485: 1
      1515: 1
      1523: 1
      1524: 1
      1583: 1
      1661: 1

1662:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q+1
         5: q^3+q^2+q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^2+1
        11: q^3+q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^3+q^2+q+1
        17: q^3+q^2+q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q^3+q^2+q+1
        21: q^3+q^2+q+1
        22: q^3+q^2+q+1
        23: q^3+q^2+q+1
        24: q+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^3+q^2+q+1
        29: q^2+1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^3+q^2+q+1
        41: q^3+q^2+q+1
        42: q^3+q^2+q+1
        43: q^3+q^2+q+1
        44: q^2+1
        45: q^3+q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^3+q^2+q+1
        51: q+1
        52: q^3+q^2+q+1
        53: q^2+1
        54: q^3+q^2+q+1
        55: q+1
        56: q+1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q^3+q^2+q+1
        85: q^3+q^2+q+1
        86: q^3+q^2+q+1
        87: q^3+q^2+q+1
        88: q+1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^3+q^2+q+1
        93: q^2+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q^3+q^2+q+1
       106: q+1
       107: q^2+1
       108: q^2+1
       109: 1
       110: q+1
       111: q+1
       112: q^2+1
       113: 1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: 1
       118: 1
       119: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^3+q^2+q+1
       156: q+1
       157: q^3+q^2+q+1
       158: q^2+1
       159: q^3+q^2+q+1
       160: q+1
       161: q+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q^2+1
       192: 1
       193: q^2+1
       194: 1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: q^2+1
       200: 1
       201: q^2+1
       202: q^2+1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       207: 1
       208: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q^3+q^2+q+1
       260: q+1
       261: q^2+1
       262: q^2+1
       263: 1
       264: q+1
       265: q+1
       266: q^2+1
       267: 1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: 1
       273: q^2+1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: 1
       312: q^2+1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q^2+1
       322: 1
       323: q^2+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q^2+1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q^2+1
       398: 1
       399: q^2+1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q^2+1
       406: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: q^2+1
       477: 1
       478: 1
       479: 1
       480: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: q+1
       565: 1
       566: q^2+1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q^2+1
       576: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q^2+1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q^2+1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       942: 1
       953: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       977: 1
       978: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1074: 1
      1094: 1
      1103: 1
      1104: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1227: 1
      1229: 1
      1230: 1
      1244: 1
      1245: 1
      1253: 1
      1264: 1
      1271: 1
      1272: 1
      1273: 1
      1301: 1
      1311: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1365: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1414: 1
      1428: 1
      1456: 1
      1525: 1
      1526: 1
      1527: 1
      1555: 1
      1565: 1
      1662: 1

1663:    0: q^4+4q^3+6q^2+4q+1
         1: 2q^3+5q^2+4q+1
         2: q^4+4q^3+6q^2+4q+1
         3: 2q^3+5q^2+4q+1
         4: 2q^3+5q^2+4q+1
         5: q^4+4q^3+6q^2+4q+1
         6: 2q^3+5q^2+4q+1
         7: 2q^3+5q^2+4q+1
         8: 2q^3+5q^2+4q+1
         9: q^3+4q^2+4q+1
        10: 2q^3+5q^2+4q+1
        11: 2q^3+5q^2+4q+1
        12: 3q^2+4q+1
        13: q^3+4q^2+4q+1
        14: 2q^3+5q^2+4q+1
        15: 3q^2+4q+1
        16: 2q^3+5q^2+4q+1
        17: q^4+4q^3+6q^2+4q+1
        18: 2q^3+5q^2+4q+1
        19: 2q^3+5q^2+4q+1
        20: 2q^2+3q+1
        21: 2q^3+5q^2+4q+1
        22: q^3+4q^2+4q+1
        23: 2q^3+5q^2+4q+1
        24: 3q^2+4q+1
        25: q^3+4q^2+4q+1
        26: 2q^2+3q+1
        27: 2q^3+5q^2+4q+1
        28: q^3+4q^2+4q+1
        29: 2q^3+5q^2+4q+1
        30: 2q^2+4q+1
        31: 3q^2+4q+1
        32: 3q^2+4q+1
        33: q^3+4q^2+4q+1
        34: q^3+4q^2+4q+1
        35: 3q^2+4q+1
        36: 2q^2+4q+1
        37: 3q^2+4q+1
        38: 3q^2+4q+1
        39: 2q^2+4q+1
        40: 2q^3+5q^2+4q+1
        41: 2q^3+5q^2+4q+1
        42: 2q^3+5q^2+4q+1
        43: q^3+4q^2+4q+1
        44: 2q^3+5q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 3q^2+4q+1
        47: q^3+4q^2+4q+1
        48: 2q^3+5q^2+4q+1
        49: 3q^2+4q+1
        50: 2q^2+3q+1
        51: 2q+1
        52: 2q^2+3q+1
        53: q^3+4q^2+4q+1
        54: q^3+4q^2+4q+1
        55: 2q^2+4q+1
        56: 3q^2+4q+1
        57: 2q^2+3q+1
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: 2q^3+5q^2+4q+1
        61: 3q^2+4q+1
        62: q^3+4q^2+4q+1
        63: 2q^2+3q+1
        64: q^3+3q^2+3q+1
        65: 2q^2+4q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+4q+1
        69: 3q^2+4q+1
        70: q^2+4q+1
        71: q^2+3q+1
        72: q^3+4q^2+4q+1
        73: 2q^2+4q+1
        74: 3q^2+4q+1
        75: 2q^2+4q+1
        76: 2q^2+4q+1
        77: 2q+1
        78: 3q^2+4q+1
        79: 2q^2+4q+1
        80: 3q^2+4q+1
        81: q^2+4q+1
        82: 2q^2+4q+1
        83: 2q^2+4q+1
        84: 2q^2+3q+1
        85: 2q^3+5q^2+4q+1
        86: q^3+4q^2+4q+1
        87: 2q^3+5q^2+4q+1
        88: 3q^2+4q+1
        89: q^3+4q^2+4q+1
        90: 2q^2+3q+1
        91: 2q^3+5q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^3+5q^2+4q+1
        94: 2q^2+4q+1
        95: 3q^2+4q+1
        96: 3q^2+4q+1
        97: q^3+4q^2+4q+1
        98: q^3+4q^2+4q+1
        99: 3q^2+4q+1
       100: 2q^2+4q+1
       101: 3q^2+4q+1
       102: 3q^2+4q+1
       103: 2q^2+4q+1
       104: 2q+1
       105: 2q^2+3q+1
       106: 2q+1
       107: 2q^2+3q+1
       108: q^3+4q^2+4q+1
       109: 2q^2+4q+1
       110: 2q^2+4q+1
       111: q^2+4q+1
       112: 2q^2+3q+1
       113: 2q+1
       114: q^2+2q+1
       115: 2q^2+3q+1
       116: 2q^2+3q+1
       117: q^2+3q+1
       118: 3q^2+4q+1
       119: q^2+2q+1
       120: 2q^2+3q+1
       121: q^2+2q+1
       122: q^3+3q^2+3q+1
       123: q^2+2q+1
       124: 2q+1
       125: q^2+3q+1
       126: 2q+1
       127: q^2+3q+1
       128: q^2+3q+1
       129: 2q^2+4q+1
       130: q^2+3q+1
       131: 3q+1
       132: q^2+4q+1
       133: q^2+4q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: 2q^2+4q+1
       138: 2q^2+4q+1
       139: q^2+4q+1
       140: 2q^2+4q+1
       141: q^2+3q+1
       142: 2q+1
       143: 2q+1
       144: 3q^2+4q+1
       145: 2q^2+4q+1
       146: 2q^2+4q+1
       147: 2q+1
       148: q^2+2q+1
       149: q^2+4q+1
       150: 2q+1
       151: q^2+3q+1
       152: q^2+4q+1
       153: 2q^2+4q+1
       154: q^2+4q+1
       155: 2q^2+3q+1
       156: 2q+1
       157: 2q^2+3q+1
       158: q^3+4q^2+4q+1
       159: q^3+4q^2+4q+1
       160: 2q^2+4q+1
       161: 3q^2+4q+1
       162: 2q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^3+5q^2+4q+1
       166: 3q^2+4q+1
       167: q^3+4q^2+4q+1
       168: 2q^2+3q+1
       169: q^3+3q^2+3q+1
       170: 2q^2+4q+1
       171: q^2+3q+1
       172: q^2+3q+1
       173: 2q^2+4q+1
       174: 3q^2+4q+1
       175: q^2+4q+1
       176: q^2+3q+1
       177: q^3+4q^2+4q+1
       178: 2q^2+4q+1
       179: 3q^2+4q+1
       180: 2q^2+4q+1
       181: 2q^2+4q+1
       182: 2q+1
       183: 3q^2+4q+1
       184: 2q^2+4q+1
       185: 3q^2+4q+1
       186: q^2+4q+1
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: q+1
       190: 2q+1
       191: 2q^2+3q+1
       192: 2q+1
       193: q^2+2q+1
       194: 2q+1
       195: 2q^2+4q+1
       196: q^2+4q+1
       197: q^2+4q+1
       198: 2q+1
       199: q^2+2q+1
       200: q+1
       201: q^2+2q+1
       202: 2q^2+3q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: 3q+1
       206: q^2+2q+1
       207: q+1
       208: q+1
       209: q^2+2q+1
       210: q^2+2q+1
       211: q+1
       212: q^2+2q+1
       213: 2q+1
       214: q+1
       215: q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: q^2+3q+1
       220: 2q+1
       221: q^2+3q+1
       222: 2q+1
       223: 3q+1
       224: 2q+1
       225: q^2+4q+1
       226: q+1
       227: 3q+1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q^2+3q+1
       232: 2q^2+4q+1
       233: q^2+4q+1
       234: q^2+4q+1
       235: q^2+4q+1
       236: q^2+3q+1
       237: 2q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q^2+4q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q^2+2q+1
       248: 2q+1
       249: 2q+1
       250: q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+4q+1
       254: 2q+1
       255: 2q+1
       256: q^2+4q+1
       257: q^2+4q+1
       258: 2q+1
       259: 2q^2+3q+1
       260: 2q+1
       261: 2q^2+3q+1
       262: q^3+4q^2+4q+1
       263: 2q^2+4q+1
       264: 2q^2+4q+1
       265: q^2+4q+1
       266: 2q^2+3q+1
       267: 2q+1
       268: q^2+2q+1
       269: 2q^2+3q+1
       270: 2q^2+3q+1
       271: q^2+3q+1
       272: 3q^2+4q+1
       273: q^2+2q+1
       274: 2q^2+3q+1
       275: q^2+2q+1
       276: q^3+3q^2+3q+1
       277: q^2+2q+1
       278: 2q+1
       279: q^2+3q+1
       280: 2q+1
       281: q^2+3q+1
       282: q^2+3q+1
       283: 2q^2+4q+1
       284: q^2+3q+1
       285: 3q+1
       286: q^2+4q+1
       287: q^2+4q+1
       288: q^2+3q+1
       289: 2q+1
       290: q^2+3q+1
       291: 2q^2+4q+1
       292: 2q^2+4q+1
       293: q^2+4q+1
       294: 2q^2+4q+1
       295: q^2+3q+1
       296: 2q+1
       297: 2q+1
       298: 3q^2+4q+1
       299: 2q^2+4q+1
       300: 2q^2+4q+1
       301: 2q+1
       302: q^2+2q+1
       303: q^2+4q+1
       304: 2q+1
       305: q^2+3q+1
       306: q^2+4q+1
       307: 2q^2+4q+1
       308: q^2+4q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q^2+2q+1
       313: q+1
       314: 2q+1
       315: q+1
       316: 2q+1
       317: q^2+4q+1
       318: q+1
       319: 1
       320: q+1
       321: q^2+2q+1
       322: q+1
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: 2q+1
       327: 3q+1
       328: q+1
       329: q+1
       330: 1
       331: q+1
       332: q^2+2q+1
       333: q+1
       334: q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: 1
       339: q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: 3q+1
       344: 2q+1
       345: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: q+1
       350: 2q+1
       351: 2q+1
       352: q+1
       353: 1
       354: 3q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q^2+3q+1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: q^2+4q+1
       363: q^2+4q+1
       364: q^2+4q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       375: 1
       376: q+1
       377: q+1
       380: 2q+1
       381: q+1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q^2+3q+1
       387: q+1
       388: 2q+1
       389: q+1
       390: 2q+1
       392: q^2+4q+1
       393: q+1
       394: 2q+1
       395: q+1
       396: 2q+1
       397: 2q^2+3q+1
       398: 2q+1
       399: q^2+2q+1
       400: 2q+1
       401: 2q^2+4q+1
       402: q^2+4q+1
       403: q^2+4q+1
       404: 2q+1
       405: q^2+2q+1
       406: q+1
       407: q^2+2q+1
       408: 2q^2+3q+1
       409: q^2+3q+1
       410: q^2+3q+1
       411: 3q+1
       412: q^2+2q+1
       413: q+1
       414: q+1
       415: q^2+2q+1
       416: q^2+2q+1
       417: q+1
       418: q^2+2q+1
       419: 2q+1
       420: q+1
       421: q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: q^2+3q+1
       426: 2q+1
       427: q^2+3q+1
       428: 2q+1
       429: 3q+1
       430: 2q+1
       431: q^2+4q+1
       432: q+1
       433: 3q+1
       434: 2q+1
       435: q^2+3q+1
       436: 2q+1
       437: q^2+3q+1
       438: 2q^2+4q+1
       439: q^2+4q+1
       440: q^2+4q+1
       441: q^2+4q+1
       442: q^2+3q+1
       443: 2q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q^2+4q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q^2+2q+1
       454: 2q+1
       455: 2q+1
       456: q+1
       457: q^2+3q+1
       458: q^2+3q+1
       459: q^2+4q+1
       460: 2q+1
       461: 2q+1
       462: q^2+4q+1
       463: q^2+4q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 2q+1
       470: q+1
       471: 2q+1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: q+1
       477: 1
       478: q+1
       479: 1
       480: q+1
       481: 2q+1
       482: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       489: q+1
       490: q+1
       491: 2q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       497: q+1
       498: 2q+1
       499: 2q+1
       500: 3q+1
       501: q+1
       502: q+1
       503: 1
       504: q+1
       505: 2q+1
       506: q+1
       507: q+1
       508: 2q+1
       509: 2q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       521: 2q+1
       522: q+1
       523: q+1
       524: q^2+4q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: 2q+1
       533: q+1
       534: 2q+1
       536: 1
       538: 1
       539: q+1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 2q+1
       551: q+1
       553: 1
       554: q+1
       555: q+1
       558: q+1
       559: q+1
       560: 1
       561: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q^2+2q+1
       567: q+1
       568: 2q+1
       569: q+1
       570: 2q+1
       571: q^2+4q+1
       572: q+1
       573: 1
       574: q+1
       575: q^2+2q+1
       576: q+1
       577: q+1
       578: q+1
       579: q^2+3q+1
       580: 2q+1
       581: 3q+1
       582: q+1
       583: q+1
       584: 1
       585: q+1
       586: q^2+2q+1
       587: q+1
       588: q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: 1
       593: q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: 3q+1
       598: 2q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       603: q+1
       604: 2q+1
       605: 2q+1
       606: q+1
       607: 1
       608: 3q+1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: q^2+3q+1
       613: 2q+1
       614: q+1
       615: 2q+1
       616: q^2+4q+1
       617: q^2+4q+1
       618: q^2+4q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: q+1
       629: 1
       630: q+1
       631: q+1
       634: 2q+1
       635: q+1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q^2+3q+1
       641: q+1
       642: 2q+1
       643: q+1
       644: 2q+1
       646: q^2+4q+1
       647: q+1
       648: 2q+1
       650: 1
       651: 1
       652: 1
       653: q+1
       654: 2q+1
       655: q+1
       656: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: q+1
       663: 1
       664: q+1
       665: 1
       666: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       681: q+1
       682: 1
       684: 2q+1
       685: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       692: q+1
       693: q+1
       694: 2q+1
       695: q+1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: q+1
       705: 1
       707: q+1
       708: q+1
       710: q+1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       717: 1
       718: 1
       719: 1
       720: q+1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: q+1
       738: q+1
       739: 2q+1
       741: 1
       743: 1
       744: q+1
       748: q+1
       750: 1
       751: 1
       752: 1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 2q+1
       761: q+1
       762: 2q+1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: 1
       769: q+1
       770: 1
       771: q+1
       772: 2q+1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       780: q+1
       781: q+1
       782: 2q+1
       783: 1
       784: 1
       785: q+1
       786: 1
       788: q+1
       789: 2q+1
       790: 2q+1
       791: 3q+1
       792: q+1
       793: q+1
       794: 1
       795: q+1
       796: 2q+1
       797: q+1
       798: q+1
       799: 2q+1
       800: 2q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       812: 2q+1
       813: q+1
       814: q+1
       815: q^2+4q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: 2q+1
       824: q+1
       825: 2q+1
       827: 1
       829: 1
       830: q+1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 2q+1
       842: q+1
       844: 1
       845: q+1
       846: q+1
       849: q+1
       850: q+1
       851: 1
       852: 2q+1
       855: 1
       856: 1
       857: 1
       858: q+1
       859: 1
       860: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: q+1
       867: 1
       868: 1
       870: 1
       872: 1
       877: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: q+1
       907: 1
       909: 1
       911: q+1
       913: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: q+1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       961: 1
       962: 1
       963: 1
       964: q+1
       965: 2q+1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: q+1
       974: 1
       975: q+1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       985: q+1
       986: 1
       987: 1
       988: 1
       989: 1
       992: q+1
       993: 1
       995: 2q+1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1003: q+1
      1004: q+1
      1005: 2q+1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q+1
      1015: q+1
      1016: 1
      1018: q+1
      1019: q+1
      1021: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: q+1
      1032: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: q+1
      1049: q+1
      1050: 2q+1
      1052: 1
      1054: 1
      1055: q+1
      1059: q+1
      1061: 1
      1062: 1
      1063: 1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1115: 1
      1118: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1138: 1
      1141: 1
      1145: 1
      1158: 1
      1166: 1
      1167: 1
      1168: 1
      1169: q+1
      1170: 1
      1171: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: q+1
      1178: 1
      1179: 1
      1181: 1
      1183: 1
      1188: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: q+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: 1
      1220: 1
      1222: q+1
      1224: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: q+1
      1253: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1272: 1
      1273: 1
      1276: 1
      1278: 1
      1302: 1
      1309: 1
      1317: 1
      1320: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1386: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1402: 1
      1403: 1
      1406: 1
      1409: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1429: 1
      1432: 1
      1436: 1
      1449: 1
      1457: 1
      1526: 1
      1527: 1
      1530: 1
      1532: 1
      1556: 1
      1563: 1
      1571: 1
      1574: 1
      1663: 1

1664:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^3+2q^2+2q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q^2+2q+1
       126: 1
       127: 1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: 1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q+1
       176: q+1
       177: q^3+2q^2+2q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: q+1
       194: 1
       195: q^2+2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q^2+2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       244: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       256: q+1
       257: q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: q^2+2q+1
       263: q^2+2q+1
       264: q^2+2q+1
       265: q+1
       266: q^2+2q+1
       267: q^2+2q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q^2+2q+1
       271: q^2+2q+1
       272: q^2+2q+1
       273: q+1
       274: q^2+2q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q^2+2q+1
       280: 1
       281: 1
       282: 1
       283: q^2+2q+1
       284: q^2+2q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q^2+2q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: q+1
       324: 1
       325: q^2+2q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: q+1
       392: q+1
       393: q+1
       395: q+1
       396: q^2+2q+1
       397: q^2+2q+1
       398: q^2+2q+1
       399: q+1
       400: 1
       401: q^2+2q+1
       402: q+1
       403: q+1
       404: q^2+2q+1
       405: q^2+2q+1
       406: q^2+2q+1
       407: q^2+2q+1
       408: q^2+2q+1
       409: q^2+2q+1
       410: q^2+2q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q^2+2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       450: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: q^2+2q+1
       476: q+1
       477: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       521: 1
       522: 1
       524: q+1
       525: q+1
       527: q+1
       528: q+1
       529: q+1
       531: 1
       532: q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: q+1
       563: q+1
       564: q+1
       565: q^2+2q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q^2+2q+1
       575: q^2+2q+1
       576: q^2+2q+1
       577: q+1
       578: 1
       579: q^2+2q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: q+1
       646: q+1
       647: q+1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: q+1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: q+1
       704: q+1
       707: 1
       711: q+1
       714: q+1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q^2+2q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       812: 1
       813: 1
       815: q+1
       816: q+1
       818: q+1
       819: q+1
       820: q+1
       822: 1
       823: q+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: q+1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: q+1
       877: 1
       878: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       906: q+1
       918: 1
       935: 1
       938: 1
       939: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1014: q+1
      1015: q+1
      1018: 1
      1022: q+1
      1025: q+1
      1028: 1
      1029: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1105: 1
      1141: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: q+1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1217: q+1
      1229: 1
      1246: 1
      1249: 1
      1250: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1293: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1377: 1
      1385: 1
      1386: 1
      1393: 1
      1396: 1
      1432: 1
      1458: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1547: 1
      1664: 1

1665:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: q^2+2q+1
        20: 2q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q^2+2q+1
        26: q^2+q+1
        27: 2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: 2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: q^2+2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: 2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: 2q^2+2q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+2q+1
        61: 2q+1
        62: q^2+2q+1
        63: q+1
        64: q^2+2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: 2q+1
        76: q^2+2q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q^2+2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: 2q+1
       104: 2q+1
       105: q^2+2q+1
       106: 2q+1
       107: 2q^2+2q+1
       108: q^2+2q+1
       109: 2q+1
       110: 2q+1
       111: 2q+1
       112: q^2+2q+1
       113: 2q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q^2+2q+1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: q+1
       135: 2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: q^2+2q+1
       144: q+1
       145: 2q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+2q+1
       156: 2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^2+2q+1
       160: 2q+1
       161: 2q+1
       162: 2q^2+2q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q+1
       169: q^2+2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: 2q+1
       181: q^2+2q+1
       183: q^2+2q+1
       184: q+1
       185: q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       189: 2q+1
       190: 2q+1
       191: q^2+2q+1
       192: 2q+1
       193: q^2+2q+1
       194: 2q+1
       195: 2q+1
       196: 2q+1
       197: 2q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q^2+q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q+1
       206: q^2+2q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: q+1
       213: 1
       214: 2q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q^2+2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q+1
       242: q+1
       243: q+1
       246: q+1
       248: 2q+1
       251: 1
       252: 2q+1
       253: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 2q+1
       259: q^2+2q+1
       260: 2q+1
       261: 2q^2+2q+1
       262: q^2+2q+1
       263: 2q+1
       264: 2q+1
       265: 2q+1
       266: q^2+2q+1
       267: 2q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q^2+2q+1
       274: q+1
       275: q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       287: 2q+1
       288: q+1
       289: 2q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q+1
       293: 2q+1
       294: q+1
       295: q^2+2q+1
       298: q+1
       299: 2q+1
       300: q+1
       302: q+1
       303: 2q+1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       309: 2q+1
       310: 2q+1
       311: 2q+1
       312: q^2+2q+1
       313: q+1
       314: 1
       315: 2q+1
       316: 2q+1
       317: 2q+1
       319: 2q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 2q+1
       328: q+1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: 2q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       372: q+1
       373: q+1
       380: 1
       381: 2q+1
       386: 1
       387: q+1
       390: 1
       392: q+1
       394: q+1
       395: 2q+1
       396: 2q+1
       397: q^2+2q+1
       398: 2q+1
       399: q^2+2q+1
       400: 2q+1
       401: 2q+1
       402: 2q+1
       403: 2q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q^2+q+1
       408: q+1
       409: q+1
       410: q+1
       411: 2q+1
       412: q^2+2q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: q+1
       419: 1
       420: 2q+1
       421: q+1
       422: q+1
       423: 1
       424: q+1
       425: 1
       426: 2q+1
       427: q+1
       428: q+1
       429: 1
       430: q+1
       431: 2q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: 2q+1
       437: q^2+2q+1
       438: q+1
       439: 2q+1
       440: q+1
       441: q+1
       442: q+1
       443: 2q+1
       448: q+1
       449: q+1
       452: q+1
       454: 2q+1
       457: 1
       458: 2q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 2q+1
       466: 2q+1
       467: q+1
       468: 1
       469: 1
       470: q+1
       471: 2q+1
       473: 2q+1
       474: q+1
       475: q+1
       476: q+1
       477: 1
       478: 1
       479: q+1
       480: q+1
       481: q+1
       483: q+1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       521: 1
       522: 2q+1
       523: q+1
       524: q+1
       526: q+1
       534: q+1
       543: 1
       550: 1
       551: 1
       558: q+1
       561: 1
       563: 2q+1
       564: 2q+1
       565: 2q+1
       566: q^2+2q+1
       567: q+1
       568: 1
       569: 2q+1
       570: 2q+1
       571: 2q+1
       573: 2q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: 2q+1
       582: q+1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: q+1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: q+1
       596: 1
       597: 1
       598: 1
       599: q+1
       600: q+1
       601: q+1
       602: 1
       603: 1
       604: 1
       605: 2q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: 2q+1
       614: q+1
       615: 2q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       626: q+1
       627: q+1
       634: 1
       635: 2q+1
       640: 1
       641: q+1
       644: 1
       646: q+1
       648: q+1
       650: 2q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: q+1
       666: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: q+1
       705: q+1
       707: 1
       708: 1
       710: q+1
       712: q+1
       731: 1
       739: 1
       748: 1
       756: 2q+1
       757: 2q+1
       758: q+1
       759: 1
       760: 1
       761: q+1
       762: 2q+1
       764: 2q+1
       765: q+1
       766: q+1
       767: q+1
       768: 1
       769: 1
       770: q+1
       771: q+1
       772: q+1
       774: q+1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: q+1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       812: 1
       813: 2q+1
       814: q+1
       815: q+1
       817: q+1
       825: q+1
       834: 1
       841: 1
       842: 1
       849: q+1
       852: 1
       855: q+1
       856: 1
       857: 1
       858: 1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: q+1
       909: 1
       911: 1
       933: 1
       961: 2q+1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       969: q+1
       970: q+1
       971: 1
       972: 1
       973: 1
       974: 1
       975: q+1
       977: q+1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: q+1
      1016: q+1
      1018: 1
      1019: 1
      1021: q+1
      1023: q+1
      1042: 1
      1050: 1
      1059: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1115: 1
      1166: q+1
      1167: 1
      1168: 1
      1169: 1
      1173: q+1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: q+1
      1220: 1
      1222: 1
      1244: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1288: 1
      1294: 1
      1359: 1
      1360: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1375: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1387: 1
      1392: 1
      1394: 1
      1406: 1
      1459: 1
      1526: 1
      1530: 1
      1531: 1
      1534: 1
      1542: 1
      1548: 1
      1665: 1

1666:    0: 2q^3+6q^2+4q+1
         1: 2q^3+6q^2+4q+1
         2: 2q^3+6q^2+4q+1
         3: 2q^3+6q^2+4q+1
         4: q^3+5q^2+4q+1
         5: 2q^3+6q^2+4q+1
         6: q^3+4q^2+4q+1
         7: 2q^3+6q^2+4q+1
         8: 2q^3+6q^2+4q+1
         9: 2q^3+6q^2+4q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: 3q^2+4q+1
        13: q^3+5q^2+4q+1
        14: q^3+5q^2+4q+1
        15: q^3+5q^2+4q+1
        16: 2q^3+6q^2+4q+1
        17: 2q^3+6q^2+4q+1
        18: 2q^3+6q^2+4q+1
        19: q^3+5q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+4q^2+4q+1
        22: 2q^3+6q^2+4q+1
        23: q^3+4q^2+4q+1
        24: 3q^2+4q+1
        25: 2q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: q^3+4q^2+4q+1
        29: 2q^2+4q+1
        30: 3q^2+4q+1
        31: 2q^2+4q+1
        32: 2q^2+4q+1
        33: q^3+4q^2+4q+1
        34: q^3+5q^2+4q+1
        35: q^3+5q^2+4q+1
        36: q^3+5q^2+4q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 3q^2+4q+1
        40: q^3+4q^2+4q+1
        41: 2q^3+6q^2+4q+1
        42: 2q^3+6q^2+4q+1
        43: 2q^3+6q^2+4q+1
        44: q^3+4q^2+4q+1
        45: q^3+4q^2+4q+1
        46: 3q^2+4q+1
        47: q^3+5q^2+4q+1
        48: q^3+5q^2+4q+1
        49: q^3+5q^2+4q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^3+4q^2+4q+1
        53: 2q^2+4q+1
        54: q^3+4q^2+4q+1
        55: 3q^2+4q+1
        56: 2q^2+4q+1
        57: 2q^2+4q+1
        58: 2q^2+4q+1
        59: q^3+4q^2+4q+1
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: q^2+4q+1
        63: 2q^2+4q+1
        64: 2q^2+4q+1
        65: q^2+4q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: 2q^2+4q+1
        69: q^2+4q+1
        70: 2q^2+4q+1
        71: q^3+4q^2+4q+1
        72: q^3+4q^2+4q+1
        73: q^3+5q^2+4q+1
        74: 2q^2+3q+1
        75: 3q^2+4q+1
        76: q^2+3q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q+1
        81: 3q^2+4q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: q^3+4q^2+4q+1
        85: q^3+4q^2+4q+1
        86: 2q^3+6q^2+4q+1
        87: q^3+4q^2+4q+1
        88: 3q^2+4q+1
        89: 2q^2+4q+1
        90: q^3+4q^2+4q+1
        91: q^3+4q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+4q+1
        94: 3q^2+4q+1
        95: 2q^2+4q+1
        96: 2q^2+4q+1
        97: q^3+4q^2+4q+1
        98: q^3+5q^2+4q+1
        99: q^3+5q^2+4q+1
       100: q^3+5q^2+4q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: 3q^2+4q+1
       104: q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: 2q^2+4q+1
       108: q^2+4q+1
       109: q^2+4q+1
       110: 2q^2+4q+1
       111: 2q^2+4q+1
       112: 2q+1
       113: 2q+1
       114: 2q^2+4q+1
       115: 2q^2+4q+1
       116: 2q^2+4q+1
       117: 2q^2+4q+1
       118: q^2+4q+1
       119: q^2+4q+1
       120: q^2+4q+1
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: 2q+1
       124: q^2+4q+1
       125: q^2+4q+1
       126: 2q^2+4q+1
       127: 2q+1
       128: 2q^2+4q+1
       129: q^2+4q+1
       130: q^2+4q+1
       131: q^2+4q+1
       132: 2q^2+4q+1
       133: 2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^3+4q^2+4q+1
       137: q^2+3q+1
       138: 2q^2+3q+1
       139: 3q^2+4q+1
       140: q^2+3q+1
       141: q^2+3q+1
       142: q^2+3q+1
       143: 2q^2+3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q+1
       147: 2q+1
       148: 2q+1
       149: 3q+1
       150: q^2+3q+1
       151: q^2+3q+1
       152: q^2+3q+1
       153: 2q+1
       154: q^2+3q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^3+4q^2+4q+1
       158: 2q^2+4q+1
       159: q^3+4q^2+4q+1
       160: 3q^2+4q+1
       161: 2q^2+4q+1
       162: 2q^2+4q+1
       163: 2q^2+4q+1
       164: q^3+4q^2+4q+1
       165: 2q^2+4q+1
       166: 2q^2+4q+1
       167: q^2+4q+1
       168: 2q^2+4q+1
       169: 2q^2+4q+1
       170: q^2+4q+1
       171: 2q^2+4q+1
       172: 2q^2+4q+1
       173: 2q^2+4q+1
       174: q^2+4q+1
       175: 2q^2+4q+1
       176: q^3+4q^2+4q+1
       177: q^3+4q^2+4q+1
       178: q^3+5q^2+4q+1
       179: 2q^2+3q+1
       180: 3q^2+4q+1
       181: q^2+3q+1
       182: 2q^2+3q+1
       183: 2q^2+3q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: 3q^2+4q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: 2q+1
       193: q^2+4q+1
       194: q^2+4q+1
       195: q^2+4q+1
       196: 2q^2+4q+1
       197: 2q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       201: 2q^2+4q+1
       202: q^2+4q+1
       203: q^2+4q+1
       204: q^2+4q+1
       205: q^2+4q+1
       206: 2q+1
       207: q+1
       208: q^2+4q+1
       209: 2q+1
       210: 2q^2+4q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: 2q+1
       215: q^2+4q+1
       216: 2q+1
       217: 2q+1
       218: 2q^2+4q+1
       219: 2q+1
       220: q^2+4q+1
       221: q^2+4q+1
       222: q^2+4q+1
       223: 2q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+3q+1
       232: 2q+1
       233: 3q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: q+1
       237: 2q+1
       238: q^2+3q+1
       239: q^2+3q+1
       240: 2q+1
       241: q^2+3q+1
       242: 2q+1
       243: 2q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       248: 3q+1
       249: 3q+1
       250: q^2+3q+1
       251: q+1
       252: q^2+3q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^2+3q+1
       257: q+1
       258: q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: 2q^2+4q+1
       262: q^2+4q+1
       263: q^2+4q+1
       264: 2q^2+4q+1
       265: 2q^2+4q+1
       266: 2q+1
       267: 2q+1
       268: 2q^2+4q+1
       269: 2q^2+4q+1
       270: 2q^2+4q+1
       271: 2q^2+4q+1
       272: q^2+4q+1
       273: q^2+4q+1
       274: q^2+4q+1
       275: 2q^2+4q+1
       276: 2q^2+4q+1
       277: 2q+1
       278: q^2+4q+1
       279: q^2+4q+1
       280: 2q^2+4q+1
       281: 2q+1
       282: 2q^2+4q+1
       283: q^2+4q+1
       284: q^2+4q+1
       285: q^2+4q+1
       286: 2q^2+4q+1
       287: 2q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^3+4q^2+4q+1
       291: q^2+3q+1
       292: 2q^2+3q+1
       293: 3q^2+4q+1
       294: q^2+3q+1
       295: q^2+3q+1
       296: q^2+3q+1
       297: 2q^2+3q+1
       298: 2q+1
       299: q^2+3q+1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: 3q+1
       304: q^2+3q+1
       305: q^2+3q+1
       306: q^2+3q+1
       307: 2q+1
       308: q^2+3q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: q^2+4q+1
       317: 2q+1
       318: 2q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: q^2+4q+1
       324: q^2+4q+1
       325: q^2+4q+1
       326: q^2+4q+1
       327: 2q+1
       328: 1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: q+1
       346: q^2+4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       361: 3q+1
       362: 2q+1
       363: q^2+3q+1
       364: q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: q^2+3q+1
       369: 2q+1
       370: 3q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       375: 2q+1
       377: 2q+1
       380: 1
       381: 2q+1
       382: 3q+1
       383: 2q+1
       384: q+1
       385: q^2+3q+1
       386: q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: 2q+1
       399: q^2+4q+1
       400: q^2+4q+1
       401: q^2+4q+1
       402: 2q^2+4q+1
       403: 2q+1
       404: q+1
       405: 2q+1
       406: 2q+1
       407: 2q^2+4q+1
       408: q^2+4q+1
       409: q^2+4q+1
       410: q^2+4q+1
       411: q^2+4q+1
       412: 2q+1
       413: q+1
       414: q^2+4q+1
       415: 2q+1
       416: 2q^2+4q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: 2q+1
       421: q^2+4q+1
       422: 2q+1
       423: 2q+1
       424: 2q^2+4q+1
       425: 2q+1
       426: q^2+4q+1
       427: q^2+4q+1
       428: q^2+4q+1
       429: 2q+1
       430: 2q+1
       431: 2q+1
       432: 2q+1
       433: 2q+1
       434: q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q^2+3q+1
       438: 2q+1
       439: 3q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: q+1
       443: 2q+1
       444: q^2+3q+1
       445: q^2+3q+1
       446: 2q+1
       447: q^2+3q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       454: 3q+1
       455: 3q+1
       456: q^2+3q+1
       457: q+1
       458: q^2+3q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^2+3q+1
       463: q+1
       466: q+1
       467: 1
       468: 1
       469: q+1
       470: q+1
       471: 2q+1
       472: 2q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: q^2+4q+1
       481: q+1
       482: 2q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: 2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: 2q+1
       498: q+1
       499: 2q+1
       500: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       511: 2q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       517: q+1
       518: q+1
       519: q+1
       521: 1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: 2q+1
       530: 2q+1
       531: 3q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       536: q+1
       543: 1
       544: 1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: q+1
       551: 1
       553: 2q+1
       555: q+1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       564: q+1
       565: q+1
       566: 2q+1
       567: q+1
       568: q+1
       569: 2q+1
       570: q^2+4q+1
       571: 2q+1
       572: 2q+1
       573: q+1
       574: q+1
       575: 2q+1
       576: 2q+1
       577: q^2+4q+1
       578: q^2+4q+1
       579: q^2+4q+1
       580: q^2+4q+1
       581: 2q+1
       582: 1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: 1
       591: q+1
       592: 2q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       597: 2q+1
       598: q+1
       599: q+1
       600: q^2+4q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: q+1
       605: 2q+1
       606: 2q+1
       607: 2q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: 2q+1
       614: 2q+1
       615: 3q+1
       616: 2q+1
       617: q^2+3q+1
       618: q+1
       619: q+1
       620: q+1
       621: 2q+1
       622: q^2+3q+1
       623: 2q+1
       624: 3q+1
       625: 2q+1
       626: 2q+1
       627: q+1
       629: 2q+1
       631: 2q+1
       634: 1
       635: 2q+1
       636: 3q+1
       637: 2q+1
       638: q+1
       639: q^2+3q+1
       640: q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: q+1
       646: q+1
       647: q+1
       648: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: q+1
       656: 2q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: q+1
       674: 1
       675: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       705: q+1
       707: 1
       708: 1
       710: q+1
       711: q+1
       713: q+1
       714: q+1
       715: q+1
       717: 1
       718: 2q+1
       719: 2q+1
       721: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: 2q+1
       737: q+1
       738: q+1
       739: 1
       741: 1
       748: 1
       750: q+1
       752: 1
       757: q+1
       758: 1
       759: 1
       760: q+1
       761: q+1
       762: 2q+1
       763: 2q+1
       765: q+1
       766: q+1
       767: 2q+1
       768: q+1
       769: q+1
       770: 2q+1
       771: q^2+4q+1
       772: q+1
       773: 2q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: 2q+1
       789: q+1
       790: 2q+1
       791: 1
       792: 1
       793: q+1
       794: q+1
       795: q+1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       802: 2q+1
       803: q+1
       804: 1
       805: q+1
       806: 1
       808: q+1
       809: q+1
       810: q+1
       812: 1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: 2q+1
       821: 2q+1
       822: 3q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       827: q+1
       834: 1
       835: 1
       836: 2q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: q+1
       841: q+1
       842: 1
       844: 2q+1
       846: q+1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       857: 1
       858: 1
       859: 1
       860: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       909: 1
       911: 1
       913: q+1
       916: q+1
       918: 1
       919: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: q+1
       942: 1
       953: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: q+1
       967: 2q+1
       970: q+1
       971: 1
       972: 1
       973: q+1
       974: q+1
       975: q+1
       976: q+1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: q+1
       985: 1
       986: q+1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: q+1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: q+1
      1018: 1
      1019: 1
      1021: q+1
      1022: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1028: 1
      1029: 2q+1
      1030: 2q+1
      1032: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: 2q+1
      1048: q+1
      1049: q+1
      1050: 1
      1052: 1
      1059: 1
      1061: q+1
      1063: 1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1093: 1
      1096: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1118: 1
      1123: 1
      1139: 1
      1141: 1
      1142: 1
      1168: 1
      1169: 1
      1170: 1
      1171: q+1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: q+1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1220: 1
      1222: 1
      1224: q+1
      1227: q+1
      1229: 1
      1230: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: q+1
      1253: 1
      1264: 1
      1273: 1
      1277: 1
      1278: 1
      1285: 1
      1291: 1
      1300: 1
      1303: 1
      1333: 1
      1360: 1
      1361: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1371: 1
      1375: 1
      1376: 1
      1380: 1
      1382: 1
      1384: 1
      1387: 1
      1392: 1
      1393: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1403: 1
      1409: 1
      1414: 1
      1430: 1
      1432: 1
      1433: 1
      1460: 1
      1527: 1
      1531: 1
      1532: 1
      1539: 1
      1545: 1
      1554: 1
      1557: 1
      1587: 1
      1666: 1

1667:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        75: 1
        76: 1
        77: 1
        78: 1
        81: 1
        82: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: 1
       136: 1
       137: 1
       139: 1
       141: 1
       142: 1
       143: 1
       145: 1
       149: 1
       150: 1
       151: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       180: 1
       181: 1
       182: 1
       183: 1
       186: 1
       187: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: 1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: 1
       231: 1
       233: 1
       237: 1
       238: 1
       239: 1
       241: 1
       248: 1
       249: 1
       250: 1
       252: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       293: 1
       295: 1
       296: 1
       297: 1
       299: 1
       303: 1
       304: 1
       305: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: 1
       361: 1
       367: 1
       368: 1
       370: 1
       381: 1
       382: 1
       383: 1
       385: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: 1
       437: 1
       439: 1
       443: 1
       444: 1
       445: 1
       447: 1
       454: 1
       455: 1
       456: 1
       458: 1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       522: 1
       529: 1
       531: 1
       545: 1
       546: 1
       548: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       615: 1
       621: 1
       622: 1
       624: 1
       635: 1
       636: 1
       637: 1
       639: 1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: 1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       718: 1
       734: 1
       736: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       813: 1
       820: 1
       822: 1
       836: 1
       837: 1
       839: 1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       939: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1029: 1
      1045: 1
      1047: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1109: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1250: 1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1461: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1667: 1

1668:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: 2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q+1
        50: 2q+1
        51: q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: 2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: 1
       112: 2q+1
       113: q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 2q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q+1
       125: q^2+2q+1
       126: q+1
       127: q+1
       128: 1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: q+1
       191: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: 2q+1
       207: q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: q+1
       214: 1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       244: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: 1
       253: q+1
       254: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: 1
       266: 2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: 2q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q+1
       277: q+1
       278: q+1
       279: q^2+2q+1
       280: q+1
       281: q+1
       282: 1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: q+1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: 2q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       380: q+1
       381: 1
       382: q+1
       383: q+1
       384: q+1
       385: 1
       386: 1
       388: q+1
       392: q+1
       393: q+1
       395: 1
       396: q+1
       397: 2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: 2q+1
       413: q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       450: q+1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       511: q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: q+1
       529: 1
       531: 1
       532: 1
       543: 1
       544: q+1
       545: 1
       546: q+1
       547: q+1
       548: 1
       549: 1
       559: q+1
       563: 1
       564: 1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       634: q+1
       635: 1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: 1
       642: q+1
       646: q+1
       647: q+1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: q+1
       734: 1
       736: 1
       737: 1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: 2q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: q+1
       820: 1
       822: 1
       823: 1
       834: 1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       850: q+1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       869: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       877: 1
       878: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: q+1
       900: 1
       902: 1
       903: 1
       906: 1
       918: 1
       935: 1
       938: 1
       939: 1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1014: 1
      1015: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1044: q+1
      1045: 1
      1047: 1
      1048: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: 1
      1094: 1
      1095: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1141: 1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: 1
      1177: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1209: 1
      1210: q+1
      1211: 1
      1213: 1
      1214: 1
      1217: 1
      1229: 1
      1246: 1
      1249: 1
      1250: 1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1293: 1
      1305: 1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1369: 1
      1370: 1
      1372: 1
      1374: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1396: 1
      1399: 1
      1400: 1
      1432: 1
      1462: 1
      1529: 1
      1533: 1
      1535: 1
      1538: 1
      1547: 1
      1559: 1
      1668: 1

1669:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       248: 1
       251: 1
       252: 1
       253: 1
       256: 1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       380: 1
       381: 1
       386: 1
       392: 1
       395: 1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       454: 1
       457: 1
       458: 1
       459: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       543: 1
       563: 1
       564: 1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       634: 1
       635: 1
       640: 1
       646: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: q+1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 1
       707: 1
       756: 1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       834: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: 1
      1018: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1095: 1
      1098: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1190: 1
      1193: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1386: 1
      1389: 1
      1463: 1
      1530: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1669: 1

1670:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q+1
        62: q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: 1
       114: q+1
       115: q+1
       116: q^2+q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: q+1
       214: 1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: q+1
       313: 1
       314: q+1
       315: 1
       316: q+1
       317: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: q+1
       470: 1
       471: 1
       474: 1
       475: 1
       476: q+1
       477: 1
       478: q+1
       479: 1
       480: q+1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       568: q+1
       569: 1
       570: q+1
       571: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: 1
       591: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: 1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       659: 1
       660: 1
       661: 1
       662: q+1
       663: 1
       664: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       731: 1
       739: 1
       748: 1
       757: 1
       758: 1
       759: 1
       760: q+1
       761: 1
       762: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       769: q+1
       770: 1
       771: q+1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       880: 1
       882: 1
       883: 1
       885: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       909: 1
       911: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       970: 1
       971: 1
       972: 1
       973: q+1
       974: 1
       975: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       985: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1042: 1
      1050: 1
      1059: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1089: 1
      1091: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1168: 1
      1169: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1187: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1220: 1
      1222: 1
      1277: 1
      1282: 1
      1283: 1
      1296: 1
      1298: 1
      1360: 1
      1365: 1
      1366: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1380: 1
      1382: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1464: 1
      1531: 1
      1536: 1
      1537: 1
      1550: 1
      1552: 1
      1670: 1

1671:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: 1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       882: 1
       886: 1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       918: 1
       935: 1
       938: 1
       939: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1141: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1193: 1
      1197: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1229: 1
      1246: 1
      1249: 1
      1250: 1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1305: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1389: 1
      1393: 1
      1396: 1
      1399: 1
      1400: 1
      1432: 1
      1465: 1
      1532: 1
      1537: 1
      1538: 1
      1539: 1
      1559: 1
      1671: 1

1672:    0: 2q^4+8q^3+10q^2+5q+1
         1: 2q^4+8q^3+10q^2+5q+1
         2: q^4+5q^3+9q^2+5q+1
         3: 5q^3+9q^2+5q+1
         4: 2q^4+8q^3+10q^2+5q+1
         5: 2q^4+8q^3+10q^2+5q+1
         6: q^4+5q^3+9q^2+5q+1
         7: q^4+5q^3+9q^2+5q+1
         8: q^3+7q^2+5q+1
         9: 5q^3+9q^2+5q+1
        10: q^3+7q^2+5q+1
        11: 4q^3+8q^2+5q+1
        12: 5q^3+9q^2+5q+1
        13: 2q^4+8q^3+10q^2+5q+1
        14: q^4+5q^3+9q^2+5q+1
        15: 4q^3+8q^2+5q+1
        16: 2q^4+8q^3+10q^2+5q+1
        17: q^4+5q^3+9q^2+5q+1
        18: 5q^3+9q^2+5q+1
        19: 2q^4+8q^3+10q^2+5q+1
        20: q^3+7q^2+5q+1
        21: q^4+5q^3+9q^2+5q+1
        22: q^3+7q^2+5q+1
        23: 4q^2+4q+1
        24: q^3+7q^2+5q+1
        25: q^3+7q^2+5q+1
        26: q^3+7q^2+5q+1
        27: 6q^2+5q+1
        28: 4q^3+8q^2+5q+1
        29: q^3+6q^2+5q+1
        30: 5q^3+9q^2+5q+1
        31: q^3+7q^2+5q+1
        32: 4q^3+8q^2+5q+1
        33: q^4+5q^3+9q^2+5q+1
        34: q^4+5q^3+9q^2+5q+1
        35: q^3+6q^2+5q+1
        36: 4q^3+8q^2+5q+1
        37: 4q^2+4q+1
        38: 2q^3+5q^2+4q+1
        39: 4q^3+8q^2+5q+1
        40: q^4+5q^3+9q^2+5q+1
        41: q^4+5q^3+9q^2+5q+1
        42: q^3+7q^2+5q+1
        43: 5q^3+9q^2+5q+1
        44: q^3+7q^2+5q+1
        45: 4q^3+8q^2+5q+1
        46: 5q^3+9q^2+5q+1
        47: 2q^4+8q^3+10q^2+5q+1
        48: q^4+5q^3+9q^2+5q+1
        49: 4q^3+8q^2+5q+1
        50: 4q^2+4q+1
        51: q^3+7q^2+5q+1
        52: q^3+7q^2+5q+1
        53: 3q^2+4q+1
        54: 4q^2+4q+1
        55: q^3+7q^2+5q+1
        56: 4q^2+4q+1
        57: 6q^2+5q+1
        58: q^3+7q^2+5q+1
        59: 6q^2+5q+1
        60: 3q^2+4q+1
        61: 6q^2+5q+1
        62: q^3+6q^2+5q+1
        63: q^3+6q^2+5q+1
        64: 3q^2+4q+1
        65: q^3+7q^2+5q+1
        66: q^3+7q^2+5q+1
        67: 3q^2+4q+1
        68: 4q^3+8q^2+5q+1
        69: q^3+6q^2+5q+1
        70: 2q^3+5q^2+4q+1
        71: q^3+6q^2+5q+1
        72: q^4+5q^3+9q^2+5q+1
        73: q^3+6q^2+5q+1
        74: 2q^2+3q+1
        75: q^3+6q^2+5q+1
        76: 4q^2+4q+1
        77: 4q^2+4q+1
        78: 3q^2+4q+1
        79: 2q^3+5q^2+4q+1
        80: 2q^2+3q+1
        81: 4q^3+8q^2+5q+1
        82: 4q^2+4q+1
        83: 2q^3+5q^2+4q+1
        84: q^3+7q^2+5q+1
        85: q^4+5q^3+9q^2+5q+1
        86: q^3+7q^2+5q+1
        87: 4q^2+4q+1
        88: q^3+7q^2+5q+1
        89: q^3+7q^2+5q+1
        90: q^3+7q^2+5q+1
        91: 6q^2+5q+1
        92: 4q^3+8q^2+5q+1
        93: q^3+6q^2+5q+1
        94: 5q^3+9q^2+5q+1
        95: q^3+7q^2+5q+1
        96: 4q^3+8q^2+5q+1
        97: q^4+5q^3+9q^2+5q+1
        98: q^4+5q^3+9q^2+5q+1
        99: q^3+6q^2+5q+1
       100: 4q^3+8q^2+5q+1
       101: 4q^2+4q+1
       102: 2q^3+5q^2+4q+1
       103: 4q^3+8q^2+5q+1
       104: 4q^2+4q+1
       105: 4q^2+4q+1
       106: q^3+7q^2+5q+1
       107: 3q^2+4q+1
       108: q^2+3q+1
       109: 3q^2+4q+1
       110: 4q^2+4q+1
       111: 2q^2+3q+1
       112: 3q^2+4q+1
       113: 6q^2+5q+1
       114: 6q^2+5q+1
       115: 3q^2+4q+1
       116: 3q^2+4q+1
       117: 6q^2+5q+1
       118: 3q^2+4q+1
       119: 3q^2+4q+1
       120: q^3+6q^2+5q+1
       121: 3q^2+4q+1
       122: q^2+3q+1
       123: 3q^2+4q+1
       124: 3q^2+4q+1
       125: q^3+7q^2+5q+1
       126: 3q^2+4q+1
       127: q^2+2q+1
       128: 3q^2+4q+1
       129: q^3+6q^2+5q+1
       130: q^3+6q^2+5q+1
       131: q^2+3q+1
       132: 2q^3+5q^2+4q+1
       133: 2q^2+3q+1
       134: 2q^2+3q+1
       135: q^3+6q^2+5q+1
       136: q^3+6q^2+5q+1
       137: q^2+3q+1
       138: 2q^2+3q+1
       139: q^3+6q^2+5q+1
       140: 2q^2+3q+1
       141: 3q^2+4q+1
       142: 4q^2+4q+1
       143: 3q^2+4q+1
       144: 2q+1
       145: 3q^2+4q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: q^2+2q+1
       149: 4q^2+4q+1
       150: 4q^2+4q+1
       151: q^2+3q+1
       152: 2q^3+5q^2+4q+1
       153: 2q^2+3q+1
       154: q^3+3q^2+3q+1
       155: 4q^2+4q+1
       156: q^3+7q^2+5q+1
       157: q^3+7q^2+5q+1
       158: 3q^2+4q+1
       159: 4q^2+4q+1
       160: q^3+7q^2+5q+1
       161: 4q^2+4q+1
       162: 6q^2+5q+1
       163: q^3+7q^2+5q+1
       164: 6q^2+5q+1
       165: 3q^2+4q+1
       166: 6q^2+5q+1
       167: q^3+6q^2+5q+1
       168: q^3+6q^2+5q+1
       169: 3q^2+4q+1
       170: q^3+7q^2+5q+1
       171: q^3+7q^2+5q+1
       172: 3q^2+4q+1
       173: 4q^3+8q^2+5q+1
       174: q^3+6q^2+5q+1
       175: 2q^3+5q^2+4q+1
       176: q^3+6q^2+5q+1
       177: q^4+5q^3+9q^2+5q+1
       178: q^3+6q^2+5q+1
       179: 2q^2+3q+1
       180: q^3+6q^2+5q+1
       181: 4q^2+4q+1
       182: 4q^2+4q+1
       183: 3q^2+4q+1
       184: 2q^3+5q^2+4q+1
       185: 2q^2+3q+1
       186: 4q^3+8q^2+5q+1
       187: 4q^2+4q+1
       188: 2q^3+5q^2+4q+1
       189: 2q^2+3q+1
       190: 4q^2+4q+1
       191: q^2+3q+1
       192: 3q^2+4q+1
       193: 2q+1
       194: q^2+2q+1
       195: q^2+3q+1
       196: 2q^2+3q+1
       197: q^2+2q+1
       198: 3q^2+4q+1
       199: 3q^2+4q+1
       200: 6q^2+5q+1
       201: 3q^2+4q+1
       202: q^2+3q+1
       203: 3q^2+4q+1
       204: 3q^2+4q+1
       205: 2q+1
       206: q^2+3q+1
       207: 3q^2+4q+1
       208: 3q^2+4q+1
       209: q^2+2q+1
       210: q^2+3q+1
       211: 3q^2+4q+1
       212: q^2+3q+1
       213: q^2+2q+1
       214: 3q^2+4q+1
       215: 3q^2+4q+1
       216: 2q+1
       217: q^2+2q+1
       218: 3q^2+4q+1
       219: q^2+2q+1
       220: q^2+3q+1
       221: q^3+6q^2+5q+1
       222: q^2+3q+1
       223: q+1
       224: q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: 2q^2+3q+1
       230: q^3+6q^2+5q+1
       231: q^2+3q+1
       232: 2q+1
       233: q^2+3q+1
       234: 2q^2+3q+1
       235: q^2+2q+1
       236: 2q+1
       237: 3q^2+4q+1
       238: 3q^2+4q+1
       239: q^2+3q+1
       240: 2q+1
       241: 3q^2+4q+1
       242: 2q+1
       243: q^2+2q+1
       244: 2q^2+3q+1
       245: q^2+2q+1
       246: q+1
       247: q^2+2q+1
       248: q^2+3q+1
       249: 4q^2+4q+1
       250: q^2+3q+1
       251: q+1
       252: q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: q+1
       256: q^3+3q^2+3q+1
       257: q^2+2q+1
       258: 4q^2+4q+1
       259: 4q^2+4q+1
       260: q^3+7q^2+5q+1
       261: 3q^2+4q+1
       262: q^2+3q+1
       263: 3q^2+4q+1
       264: 4q^2+4q+1
       265: 2q^2+3q+1
       266: 3q^2+4q+1
       267: 6q^2+5q+1
       268: 6q^2+5q+1
       269: 3q^2+4q+1
       270: 3q^2+4q+1
       271: 6q^2+5q+1
       272: 3q^2+4q+1
       273: 3q^2+4q+1
       274: q^3+6q^2+5q+1
       275: 3q^2+4q+1
       276: q^2+3q+1
       277: 3q^2+4q+1
       278: 3q^2+4q+1
       279: q^3+7q^2+5q+1
       280: 3q^2+4q+1
       281: q^2+2q+1
       282: 3q^2+4q+1
       283: q^3+6q^2+5q+1
       284: q^3+6q^2+5q+1
       285: q^2+3q+1
       286: 2q^3+5q^2+4q+1
       287: 2q^2+3q+1
       288: 2q^2+3q+1
       289: q^3+6q^2+5q+1
       290: q^3+6q^2+5q+1
       291: q^2+3q+1
       292: 2q^2+3q+1
       293: q^3+6q^2+5q+1
       294: 2q^2+3q+1
       295: 3q^2+4q+1
       296: 4q^2+4q+1
       297: 3q^2+4q+1
       298: 2q+1
       299: 3q^2+4q+1
       300: 2q^2+3q+1
       301: 2q^2+3q+1
       302: q^2+2q+1
       303: 4q^2+4q+1
       304: 4q^2+4q+1
       305: q^2+3q+1
       306: 2q^3+5q^2+4q+1
       307: 2q^2+3q+1
       308: q^3+3q^2+3q+1
       309: q^2+2q+1
       310: 2q^2+3q+1
       311: q^2+3q+1
       312: 2q+1
       313: 2q+1
       315: q^2+2q+1
       316: q+1
       317: q+1
       318: q^2+2q+1
       319: 2q+1
       320: 3q^2+4q+1
       321: q^2+3q+1
       322: 3q^2+4q+1
       323: 2q+1
       324: q^2+2q+1
       325: q^2+3q+1
       326: 2q+1
       327: q+1
       328: q^2+3q+1
       329: q^2+3q+1
       330: 3q^2+4q+1
       331: q^2+2q+1
       332: q+1
       333: q^2+2q+1
       334: q^2+3q+1
       335: 2q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: 3q^2+4q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q^2+2q+1
       343: q+1
       344: q+1
       345: q^2+3q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+3q+1
       350: q+1
       351: 2q+1
       352: 2q^2+3q+1
       353: 2q+1
       354: 1
       355: 2q+1
       356: q^2+2q+1
       357: 2q^2+3q+1
       358: 2q+1
       359: q^2+3q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 3q^2+4q+1
       368: q^2+3q+1
       369: 2q+1
       370: q^2+3q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       377: q+1
       378: q^2+2q+1
       379: q+1
       380: q+1
       381: q^2+3q+1
       382: q^2+3q+1
       383: 2q+1
       384: q+1
       385: q^2+3q+1
       386: q+1
       387: q+1
       388: 2q^2+3q+1
       389: q+1
       390: 1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q+1
       395: 2q^2+3q+1
       396: 4q^2+4q+1
       397: q^2+3q+1
       398: 3q^2+4q+1
       399: 2q+1
       400: q^2+2q+1
       401: q^2+3q+1
       402: 2q^2+3q+1
       403: q^2+2q+1
       404: 3q^2+4q+1
       405: 3q^2+4q+1
       406: 6q^2+5q+1
       407: 3q^2+4q+1
       408: q^2+3q+1
       409: 3q^2+4q+1
       410: 3q^2+4q+1
       411: 2q+1
       412: q^2+3q+1
       413: 3q^2+4q+1
       414: 3q^2+4q+1
       415: q^2+2q+1
       416: q^2+3q+1
       417: 3q^2+4q+1
       418: q^2+3q+1
       419: q^2+2q+1
       420: 3q^2+4q+1
       421: 3q^2+4q+1
       422: 2q+1
       423: q^2+2q+1
       424: 3q^2+4q+1
       425: q^2+2q+1
       426: q^2+3q+1
       427: q^3+6q^2+5q+1
       428: q^2+3q+1
       429: q+1
       430: q^2+3q+1
       431: 2q^2+3q+1
       432: 2q^2+3q+1
       433: 2q+1
       434: 2q^2+3q+1
       435: 2q^2+3q+1
       436: q^3+6q^2+5q+1
       437: q^2+3q+1
       438: 2q+1
       439: q^2+3q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: 2q+1
       443: 3q^2+4q+1
       444: 3q^2+4q+1
       445: q^2+3q+1
       446: 2q+1
       447: 3q^2+4q+1
       448: 2q+1
       449: q^2+2q+1
       450: 2q^2+3q+1
       451: q^2+2q+1
       452: q+1
       453: q^2+2q+1
       454: q^2+3q+1
       455: 4q^2+4q+1
       456: q^2+3q+1
       457: q+1
       458: q^2+3q+1
       459: 2q^2+3q+1
       460: 2q^2+3q+1
       461: q+1
       462: q^3+3q^2+3q+1
       463: q^2+2q+1
       464: q^2+2q+1
       465: q+1
       466: q+1
       467: 2q+1
       470: q+1
       471: 1
       472: q+1
       473: q+1
       474: 2q+1
       475: q^2+3q+1
       476: 2q+1
       477: 2q+1
       479: q^2+2q+1
       480: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: q^2+3q+1
       485: q+1
       486: q^2+2q+1
       487: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: q+1
       493: q^2+2q+1
       494: q+1
       495: 2q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q^2+3q+1
       504: q+1
       505: 1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 1
       514: 2q+1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: q+1
       520: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: 2q+1
       529: q^2+3q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q^2+2q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: q^2+3q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q^2+2q+1
       560: q+1
       561: 1
       562: q+1
       563: q^2+2q+1
       564: 2q^2+3q+1
       565: q^2+3q+1
       566: 2q+1
       567: 2q+1
       569: q^2+2q+1
       570: q+1
       571: q+1
       572: q^2+2q+1
       573: 2q+1
       574: 3q^2+4q+1
       575: q^2+3q+1
       576: 3q^2+4q+1
       577: 2q+1
       578: q^2+2q+1
       579: q^2+3q+1
       580: 2q+1
       581: q+1
       582: q^2+3q+1
       583: q^2+3q+1
       584: 3q^2+4q+1
       585: q^2+2q+1
       586: q+1
       587: q^2+2q+1
       588: q^2+3q+1
       589: 2q+1
       590: q^2+2q+1
       591: q^2+2q+1
       592: 3q^2+4q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: q^2+2q+1
       597: q+1
       598: q+1
       599: q^2+3q+1
       600: q^2+3q+1
       601: q+1
       602: q+1
       603: q^2+3q+1
       604: q+1
       605: 2q+1
       606: 2q^2+3q+1
       607: 2q+1
       608: 1
       609: 2q+1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: 2q+1
       613: q^2+3q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 3q^2+4q+1
       622: q^2+3q+1
       623: 2q+1
       624: q^2+3q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q^2+2q+1
       629: q^2+2q+1
       631: q+1
       632: q^2+2q+1
       633: q+1
       634: q+1
       635: q^2+3q+1
       636: q^2+3q+1
       637: 2q+1
       638: q+1
       639: q^2+3q+1
       640: q+1
       641: q+1
       642: 2q^2+3q+1
       643: q+1
       644: 1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       651: q+1
       655: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       660: 2q+1
       663: q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: q+1
       669: q+1
       670: q+1
       674: 1
       675: q+1
       676: 1
       677: q+1
       678: q+1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 2q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       715: q+1
       716: q+1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       752: 1
       753: q+1
       754: 1
       755: q^2+2q+1
       756: q+1
       757: q+1
       758: 2q+1
       761: q+1
       762: 1
       763: q+1
       764: q+1
       765: 2q+1
       766: q^2+3q+1
       767: 2q+1
       768: 2q+1
       770: q^2+2q+1
       771: q+1
       772: 1
       773: q+1
       774: 2q+1
       775: q^2+3q+1
       776: q+1
       777: q^2+2q+1
       778: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: q+1
       784: q^2+2q+1
       785: q+1
       786: 2q+1
       787: 1
       788: q+1
       789: q+1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: q^2+3q+1
       795: q+1
       796: 1
       797: q+1
       798: q+1
       799: q+1
       800: 1
       801: 2q+1
       802: 2q+1
       803: q+1
       804: 1
       805: 2q+1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: q+1
       811: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: q^2+3q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q^2+2q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q^2+3q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: q+1
       841: 1
       842: 1
       843: q+1
       844: q+1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: 1
       853: q+1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       867: 1
       868: 1
       869: q+1
       870: 1
       872: q+1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       903: 1
       906: q+1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: q+1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q+1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       958: 1
       960: q+1
       961: 1
       962: q+1
       966: 1
       967: 1
       968: q+1
       969: 1
       970: q+1
       971: 2q+1
       974: q+1
       975: 1
       976: 1
       977: q+1
       978: 2q+1
       979: q+1
       980: q+1
       981: q+1
       985: 1
       986: q+1
       987: 1
       988: q+1
       989: q+1
       990: 1
       991: 1
       993: q+1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: q+1
      1001: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 2q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: 2q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1061: q+1
      1063: 1
      1064: q+1
      1065: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1086: 1
      1087: 1
      1088: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1113: 1
      1114: 1
      1119: 1
      1122: 1
      1128: 1
      1137: 1
      1139: 1
      1140: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1157: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: q+1
      1178: 1
      1179: 1
      1180: q+1
      1181: 1
      1183: q+1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1214: 1
      1217: q+1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: q+1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1250: q+1
      1251: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1269: 1
      1274: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1304: 1
      1310: 1
      1332: 1
      1338: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1377: 1
      1378: 1
      1379: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1388: 1
      1393: 1
      1396: 1
      1397: 1
      1398: 1
      1404: 1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1428: 1
      1430: 1
      1431: 1
      1434: 1
      1437: 1
      1438: 1
      1446: 1
      1448: 1
      1466: 1
      1528: 1
      1540: 1
      1541: 1
      1546: 1
      1547: 1
      1558: 1
      1564: 1
      1586: 1
      1592: 1
      1672: 1

1673:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: 2q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: 2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q+1
        82: 1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: q+1
       110: q+1
       111: q+1
       112: 2q+1
       113: q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: q+1
       119: 2q+1
       120: 2q+1
       121: 2q+1
       122: 2q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: 2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: q+1
       193: 2q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: q+1
       206: 2q+1
       208: 2q+1
       209: q+1
       210: 2q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: q+1
       232: q+1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: 2q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: 2q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: 2q+1
       322: q+1
       323: 2q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       329: 2q+1
       331: q+1
       332: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       356: q+1
       357: q+1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       377: q+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       404: q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: q+1
       412: 2q+1
       414: 2q+1
       415: q+1
       416: 2q+1
       419: q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       468: q+1
       469: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: 2q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       485: q+1
       487: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       502: q+1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: q+1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: q+1
       565: q+1
       566: 2q+1
       568: q+1
       569: q+1
       570: q+1
       571: 1
       572: 1
       573: q+1
       574: q+1
       575: 2q+1
       576: q+1
       577: 2q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       583: 2q+1
       585: q+1
       586: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       600: q+1
       601: 1
       602: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       610: q+1
       611: q+1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       631: q+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: q+1
       654: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       661: q+1
       662: q+1
       664: 1
       665: 1
       669: q+1
       676: 1
       677: q+1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       756: 1
       757: q+1
       759: q+1
       760: q+1
       762: 1
       763: 1
       764: 1
       765: q+1
       766: q+1
       767: 2q+1
       769: q+1
       770: q+1
       771: q+1
       772: 1
       773: 1
       776: q+1
       778: q+1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       793: q+1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       807: 1
       808: q+1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: q+1
       866: 1
       868: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       942: 1
       953: 1
       960: 1
       961: 1
       963: q+1
       965: 1
       967: 1
       968: 1
       969: 1
       970: q+1
       972: q+1
       973: q+1
       975: 1
       976: 1
       980: q+1
       987: 1
       988: q+1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       999: 1
      1001: 1
      1007: 1
      1009: 1
      1010: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1106: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1139: 1
      1141: 1
      1142: 1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: q+1
      1177: 1
      1179: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1201: 1
      1210: 1
      1212: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1227: 1
      1229: 1
      1230: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1253: 1
      1264: 1
      1275: 1
      1286: 1
      1288: 1
      1291: 1
      1311: 1
      1333: 1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1397: 1
      1404: 1
      1406: 1
      1409: 1
      1414: 1
      1428: 1
      1430: 1
      1432: 1
      1433: 1
      1467: 1
      1529: 1
      1540: 1
      1542: 1
      1545: 1
      1565: 1
      1587: 1
      1673: 1

1674:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       148: q+1
       149: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       242: 2q+1
       243: q+1
       246: q+1
       247: q+1
       248: q+1
       251: q+1
       252: q+1
       253: 2q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       302: q+1
       303: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       372: 1
       373: q+1
       374: q+1
       379: q+1
       380: q+1
       381: q+1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       448: 2q+1
       449: q+1
       452: q+1
       453: q+1
       454: q+1
       457: q+1
       458: q+1
       459: 2q+1
       461: 1
       462: q+1
       463: q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: q+1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       534: 1
       535: q+1
       542: 1
       543: q+1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: q+1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       626: 1
       627: q+1
       628: q+1
       633: q+1
       634: q+1
       635: q+1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       769: q+1
       770: q+1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: q+1
       785: q+1
       786: q+1
       787: 1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       825: 1
       826: q+1
       833: 1
       834: q+1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       872: 1
       879: 1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: 1
       970: 1
       971: 1
       972: q+1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       987: 1
       988: 1
       989: q+1
       990: 1
       991: 1
       992: q+1
       993: q+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1097: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1183: 1
      1190: 1
      1191: 1
      1192: 1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1276: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1312: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: 1
      1388: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1468: 1
      1530: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1566: 1
      1674: 1

1675:    0: 3q^2+2q+1
         1: 2q^2+2q+1
         2: 3q^2+2q+1
         3: 3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 3q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 3q^2+2q+1
        13: 2q^2+2q+1
        14: 3q^2+2q+1
        15: 3q^2+2q+1
        16: 2q^2+2q+1
        17: 3q^2+2q+1
        18: 3q^2+2q+1
        19: 3q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: 3q^2+2q+1
        25: 2q+1
        26: q^2+q+1
        27: 2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 3q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 3q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 3q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 3q^2+2q+1
        47: 2q^2+2q+1
        48: 3q^2+2q+1
        49: 3q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: 2q+1
        58: q+1
        59: q^2+q+1
        60: q^2+2q+1
        61: 2q^2+2q+1
        62: 2q+1
        63: q+1
        64: q^2+2q+1
        65: 2q+1
        66: q^2+q+1
        67: 2q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: 2q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        75: 3q^2+2q+1
        76: 2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 3q^2+2q+1
        89: 2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 3q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 3q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: 2q^2+2q+1
       112: q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q^2+q+1
       118: q^2+2q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 2q+1
       125: q+1
       126: q^2+q+1
       127: q+1
       128: 2q^2+2q+1
       129: 2q+1
       130: q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       144: 2q+1
       145: q^2+2q+1
       146: 2q+1
       148: 2q+1
       149: 2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q+1
       163: q+1
       164: q^2+q+1
       165: q^2+2q+1
       166: 2q^2+2q+1
       167: 2q+1
       168: q+1
       169: q^2+2q+1
       170: 2q+1
       171: q^2+q+1
       172: 2q^2+2q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: 2q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: q^2+2q+1
       180: 3q^2+2q+1
       181: 2q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: 2q+1
       186: 2q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: q+1
       199: 1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q^2+2q+1
       206: q+1
       207: 2q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q^2+2q+1
       213: 1
       214: 2q+1
       215: q+1
       216: q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: q^2+2q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: 2q+1
       242: 2q+1
       243: 2q+1
       246: 2q+1
       247: 2q+1
       248: 2q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: 2q^2+2q+1
       266: q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q^2+q+1
       272: q^2+2q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 2q+1
       279: q+1
       280: q^2+q+1
       281: q+1
       282: 2q^2+2q+1
       283: 2q+1
       284: q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       298: 2q+1
       299: q^2+2q+1
       300: 2q+1
       302: 2q+1
       303: 2q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: q+1
       313: 2q+1
       314: 1
       315: 2q+1
       316: 2q+1
       317: q+1
       319: q+1
       320: 1
       321: 1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: q+1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q^2+2q+1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: 2q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       379: 2q+1
       380: 1
       381: 2q+1
       386: q+1
       387: 2q+1
       390: q+1
       391: 2q+1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: 1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: q^2+2q+1
       412: q+1
       413: 2q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q^2+2q+1
       419: 1
       420: 2q+1
       421: q+1
       422: q+1
       423: q+1
       424: q^2+q+1
       425: q+1
       426: 2q+1
       427: q+1
       428: q+1
       429: q+1
       430: q^2+2q+1
       431: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q+1
       443: 2q+1
       448: 2q+1
       449: 2q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       457: q+1
       458: q^2+2q+1
       459: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       466: q+1
       467: q+1
       468: 1
       469: 1
       470: 2q+1
       471: q+1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: 1
       479: q+1
       480: q+1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       515: 1
       517: q+1
       518: q+1
       519: q+1
       520: 2q+1
       521: 1
       522: 2q+1
       523: 2q+1
       524: q+1
       526: q+1
       534: q+1
       535: q+1
       542: 2q+1
       543: 1
       550: q+1
       551: 1
       552: 2q+1
       557: q+1
       558: q+1
       561: 1
       562: q+1
       564: q+1
       565: q+1
       566: q+1
       567: 2q+1
       568: 1
       569: 2q+1
       570: 2q+1
       571: q+1
       573: q+1
       574: 1
       575: 1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: q+1
       583: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q^2+2q+1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: 1
       599: 2q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       626: 2q+1
       627: q+1
       628: 2q+1
       633: 2q+1
       634: 1
       635: 2q+1
       640: q+1
       641: 2q+1
       644: q+1
       645: 2q+1
       646: q+1
       648: q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       659: 1
       660: 1
       661: 1
       662: 1
       663: q+1
       664: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q+1
       683: q+1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: 2q+1
       710: q+1
       722: q+1
       730: q+1
       731: 1
       739: 1
       740: 1
       747: q+1
       748: 1
       749: q+1
       754: 1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: 2q+1
       762: q+1
       765: 1
       766: 1
       767: 1
       768: q+1
       769: 1
       770: q+1
       771: q+1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: q+1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       806: 1
       808: q+1
       809: q+1
       810: q+1
       811: 2q+1
       812: 1
       813: 2q+1
       814: 2q+1
       815: q+1
       817: q+1
       825: q+1
       826: q+1
       833: 2q+1
       834: 1
       841: q+1
       842: 1
       843: 2q+1
       848: q+1
       849: q+1
       852: 1
       853: q+1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       875: 1
       876: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       943: 1
       951: 1
       952: 1
       959: 1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       970: 1
       971: 1
       972: 1
       973: 1
       974: q+1
       975: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       988: 1
       989: 1
       990: 1
       991: q+1
       992: 1
       993: q+1
       994: q+1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1013: 1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: 2q+1
      1021: q+1
      1033: q+1
      1041: q+1
      1042: 1
      1050: 1
      1051: 1
      1058: q+1
      1059: 1
      1060: q+1
      1065: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1084: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1116: 1
      1117: 1
      1156: 1
      1164: 1
      1168: 1
      1169: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: q+1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1277: 1
      1289: 1
      1290: 1
      1295: 1
      1299: 1
      1313: 1
      1360: 1
      1365: 1
      1366: 1
      1371: 1
      1375: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1407: 1
      1408: 1
      1447: 1
      1455: 1
      1469: 1
      1531: 1
      1543: 1
      1544: 1
      1549: 1
      1553: 1
      1567: 1
      1675: 1

1676:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: 3q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+4q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 2q^2+3q+1
        11: 3q^2+3q+1
        12: 3q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+4q^2+3q+1
        17: q^3+4q^2+3q+1
        18: 3q^2+3q+1
        19: q^3+4q^2+3q+1
        20: q^2+2q+1
        21: q^3+3q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 3q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+3q+1
        31: 2q^2+3q+1
        32: 3q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+4q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+4q^2+3q+1
        42: 3q^2+3q+1
        43: 3q^2+3q+1
        44: 2q^2+3q+1
        45: 3q^2+3q+1
        46: 3q^2+3q+1
        47: q^3+4q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+3q+1
        54: 3q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 2q+1
        58: q^2+3q+1
        59: 2q^2+3q+1
        60: 2q^2+3q+1
        61: 2q^2+3q+1
        62: q^2+3q+1
        63: 2q^2+3q+1
        64: q^2+2q+1
        65: q^2+3q+1
        66: 2q^2+3q+1
        67: q^2+2q+1
        68: 3q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q^2+3q+1
        80: 2q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: q^2+2q+1
        85: q^3+3q^2+3q+1
        86: 3q^2+3q+1
        87: 3q^2+3q+1
        88: 3q^2+3q+1
        89: q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: 3q^2+3q+1
        93: 2q^2+3q+1
        94: 3q^2+3q+1
        95: 2q^2+3q+1
        96: 3q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: 2q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: 3q^2+3q+1
       111: q^2+2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: q^2+3q+1
       116: 2q^2+3q+1
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: 2q+1
       120: q^2+3q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q+1
       125: q^2+3q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+3q+1
       130: 2q^2+3q+1
       131: q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: 2q^2+3q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q^2+3q+1
       153: 2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+3q+1
       159: 3q^2+3q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: 2q+1
       163: q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: 2q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+3q+1
       169: q^2+2q+1
       170: q^2+3q+1
       171: 2q^2+3q+1
       172: q^2+2q+1
       173: 3q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^3+3q^2+3q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: 2q^2+3q+1
       190: q^2+2q+1
       191: 2q+1
       192: 2q+1
       193: 2q+1
       194: q+1
       195: q^2+3q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: 2q^2+3q+1
       205: q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+3q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q^2+3q+1
       235: q^2+2q+1
       236: q+1
       237: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: 2q+1
       262: q^2+3q+1
       263: q^2+3q+1
       264: 3q^2+3q+1
       265: q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: q^2+3q+1
       270: 2q^2+3q+1
       271: 2q^2+3q+1
       272: 2q^2+3q+1
       273: 2q+1
       274: q^2+3q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q+1
       279: q^2+3q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: q^2+3q+1
       284: 2q^2+3q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: 2q^2+3q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q^2+3q+1
       307: 2q+1
       308: q^2+2q+1
       311: 2q+1
       312: 2q+1
       313: 2q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: 2q+1
       324: q+1
       325: q^2+3q+1
       326: q+1
       327: 1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: q^2+2q+1
       358: q+1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: q^2+2q+1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: q+1
       401: q^2+3q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: q^2+3q+1
       409: q^2+3q+1
       410: 2q^2+3q+1
       411: q+1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: q^2+2q+1
       417: q^2+2q+1
       418: q^2+2q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q^2+2q+1
       424: q^2+2q+1
       425: q^2+2q+1
       426: q+1
       427: q^2+3q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: 1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: 2q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       475: 2q+1
       476: 2q+1
       477: 2q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       489: q+1
       490: q+1
       491: 1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: 1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: 2q+1
       578: q+1
       579: q^2+3q+1
       580: q+1
       581: 1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: q^2+2q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: q+1
       595: q+1
       596: q^2+2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q^2+2q+1
       612: q+1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: q+1
       654: 1
       655: 1
       656: 1
       660: 2q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       668: q+1
       669: q+1
       670: q+1
       674: 1
       675: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: q+1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: q+1
       715: q+1
       716: q+1
       717: 1
       718: 1
       719: 1
       721: 1
       723: q+1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       758: 2q+1
       759: q+1
       760: q+1
       761: q+1
       762: 1
       763: q+1
       766: 2q+1
       767: 2q+1
       768: 2q+1
       769: q+1
       770: q+1
       771: q+1
       772: 1
       773: 1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       780: q+1
       781: q+1
       782: 1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: 1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: q+1
       866: 1
       867: 1
       868: 1
       872: q+1
       877: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: q+1
       918: 1
       919: 1
       920: 1
       932: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       942: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       964: q+1
       965: 1
       966: 1
       967: 1
       971: 2q+1
       972: q+1
       973: q+1
       974: q+1
       975: 1
       976: 1
       979: q+1
       980: q+1
       981: q+1
       985: 1
       986: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1017: q+1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: q+1
      1026: q+1
      1027: q+1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1034: q+1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1155: 1
      1157: 1
      1169: 1
      1170: 1
      1171: 1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1183: q+1
      1188: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1214: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: q+1
      1229: 1
      1230: 1
      1231: 1
      1243: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1253: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1278: 1
      1290: 1
      1291: 1
      1292: 1
      1304: 1
      1314: 1
      1334: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1388: 1
      1393: 1
      1396: 1
      1397: 1
      1398: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1446: 1
      1448: 1
      1470: 1
      1532: 1
      1544: 1
      1545: 1
      1546: 1
      1558: 1
      1568: 1
      1588: 1
      1676: 1

1677:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: 2q^2+3q+1
         3: q^3+3q^2+3q+1
         4: 2q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^3+3q^2+3q+1
        10: 2q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: 2q^2+3q+1
        18: q^3+3q^2+3q+1
        19: 2q^2+3q+1
        20: 2q^2+3q+1
        21: 2q^2+3q+1
        22: 2q^2+3q+1
        23: q^2+2q+1
        24: 2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: q^3+3q^2+3q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: 2q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+2q+1
        51: 2q+1
        52: 2q^2+3q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: 2q+1
        56: 2q+1
        57: 2q^2+3q+1
        58: 2q^2+3q+1
        59: 2q^2+3q+1
        60: q^2+2q+1
        61: 2q+1
        62: 2q^2+3q+1
        63: 2q^2+3q+1
        64: 2q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 2q^2+3q+1
        85: 2q^2+3q+1
        86: 2q^2+3q+1
        87: q^2+2q+1
        88: 2q+1
        89: 2q^2+3q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+3q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: q^2+2q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: q^2+2q+1
       106: 2q+1
       107: q^2+2q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: q^2+2q+1
       113: 2q+1
       114: 2q^2+3q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: 2q+1
       118: 2q+1
       119: 2q^2+3q+1
       120: 2q^2+3q+1
       121: 2q^2+3q+1
       122: q^2+2q+1
       123: 2q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q+1
       135: 2q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: 2q+1
       157: 2q^2+3q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: 2q+1
       161: 2q+1
       162: 2q^2+3q+1
       163: 2q^2+3q+1
       164: 2q^2+3q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: 2q^2+3q+1
       170: q^2+3q+1
       171: q^2+3q+1
       172: q^2+3q+1
       173: 2q^2+3q+1
       174: q^2+3q+1
       175: 2q^2+3q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: q^2+2q+1
       200: 2q+1
       201: q^2+2q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: q^2+2q+1
       207: 2q+1
       208: 2q^2+3q+1
       209: q^2+2q+1
       210: q^2+2q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: 2q+1
       215: q^2+3q+1
       216: q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: q+1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: 2q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: 2q+1
       259: q^2+2q+1
       260: 2q+1
       261: q^2+2q+1
       262: q+1
       263: q+1
       264: 2q+1
       265: 2q+1
       266: q^2+2q+1
       267: 2q+1
       268: 2q^2+3q+1
       269: q^2+2q+1
       270: q^2+2q+1
       271: 2q+1
       272: 2q+1
       273: 2q^2+3q+1
       274: 2q^2+3q+1
       275: 2q^2+3q+1
       276: q^2+2q+1
       277: 2q+1
       278: q^2+3q+1
       279: q^2+3q+1
       280: q^2+3q+1
       281: q+1
       282: 2q+1
       283: q^2+3q+1
       284: q^2+3q+1
       285: q^2+3q+1
       286: 2q^2+3q+1
       287: 2q+1
       288: q+1
       289: 2q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: 2q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       328: 2q+1
       329: q^2+2q+1
       330: 2q+1
       331: q^2+2q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: 2q+1
       339: q+1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: 2q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       377: 1
       380: 1
       381: q+1
       382: 2q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       395: 2q+1
       396: 2q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: 2q+1
       403: q+1
       404: 2q+1
       405: q^2+2q+1
       406: 2q+1
       407: q^2+2q+1
       408: q+1
       409: q+1
       410: 2q+1
       411: 2q+1
       412: q^2+2q+1
       413: 2q+1
       414: 2q^2+3q+1
       415: q^2+2q+1
       416: q^2+2q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: 2q+1
       421: q^2+3q+1
       422: q+1
       423: q+1
       424: 2q+1
       425: q+1
       426: q^2+3q+1
       427: q^2+3q+1
       428: q^2+3q+1
       429: q+1
       430: 2q+1
       431: 2q+1
       432: 2q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: 2q+1
       437: q+1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: q+1
       444: 2q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: 2q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       511: 2q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       563: q+1
       564: 2q+1
       565: q+1
       566: q+1
       569: q+1
       570: q+1
       571: 1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: 2q+1
       581: q+1
       582: 2q+1
       583: q^2+2q+1
       584: 2q+1
       585: q^2+2q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: 2q+1
       593: q+1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: 2q+1
       600: q^2+3q+1
       601: q+1
       602: q+1
       603: 2q+1
       604: q+1
       605: 2q+1
       606: 2q+1
       607: 2q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: q+1
       631: 1
       634: 1
       635: q+1
       636: 2q+1
       637: q+1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: q+1
       669: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       676: 1
       677: q+1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: q+1
       752: 1
       755: q+1
       756: 1
       757: q+1
       762: 1
       763: 1
       764: q+1
       765: 2q+1
       766: q+1
       767: q+1
       770: q+1
       771: q+1
       772: 1
       773: q+1
       774: 2q+1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: 2q+1
       795: q+1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       802: 2q+1
       803: q+1
       804: 1
       805: q+1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: q+1
       846: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       854: 1
       861: 1
       862: 1
       868: 1
       869: q+1
       870: 1
       871: q+1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       913: 1
       914: 1
       916: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       942: 1
       953: 1
       960: 1
       961: 1
       967: 1
       968: q+1
       969: 1
       970: q+1
       975: 1
       976: 1
       977: q+1
       978: 2q+1
       979: q+1
       980: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       987: 1
       988: q+1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: q+1
      1063: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1086: 1
      1087: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1137: 1
      1139: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1180: q+1
      1181: 1
      1182: q+1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1227: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1253: 1
      1264: 1
      1279: 1
      1286: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1303: 1
      1362: 1
      1369: 1
      1370: 1
      1376: 1
      1377: 1
      1378: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1403: 1
      1404: 1
      1428: 1
      1430: 1
      1471: 1
      1533: 1
      1540: 1
      1547: 1
      1548: 1
      1554: 1
      1555: 1
      1557: 1
      1677: 1

1678:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: 2q+1
         7: q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: 2q+1
        21: q+1
        22: q+1
        23: q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: 2q+1
        34: q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: q+1
        39: 2q+1
        40: 2q+1
        41: q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        50: q+1
        51: 2q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: 2q+1
        72: q+1
        73: q+1
        74: 1
        75: 2q+1
        76: 2q+1
        78: 2q+1
        79: q+1
        80: q+1
        81: 2q+1
        82: 2q+1
        83: q+1
        84: 2q+1
        85: q+1
        86: q+1
        87: q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: 2q+1
        98: q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: q+1
       103: 2q+1
       104: q+1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: q+1
       112: q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: 2q+1
       133: 2q+1
       134: 1
       135: 2q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: 2q+1
       144: 1
       145: 2q+1
       146: q+1
       148: q+1
       149: 2q+1
       151: 2q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 2q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: 2q+1
       177: q+1
       178: q+1
       179: 1
       180: 2q+1
       181: 2q+1
       183: 2q+1
       184: q+1
       185: q+1
       186: 2q+1
       187: 2q+1
       188: q+1
       189: q+1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: q+1
       198: q+1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: q+1
       206: q+1
       207: 2q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: q+1
       213: 1
       214: 2q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: 2q+1
       227: 2q+1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: 2q+1
       242: 1
       243: q+1
       246: 1
       247: q+1
       248: 2q+1
       251: 1
       252: 2q+1
       253: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: q+1
       266: q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: q+1
       277: 2q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: 2q+1
       287: 2q+1
       288: 1
       289: 2q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: 2q+1
       298: 1
       299: 2q+1
       300: q+1
       302: q+1
       303: 2q+1
       305: 2q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: q+1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: q+1
       328: q+1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: 2q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: 2q+1
       354: 1
       355: 2q+1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: q+1
       379: 1
       380: 1
       381: 2q+1
       386: 1
       387: q+1
       390: 1
       391: q+1
       392: q+1
       394: q+1
       395: q+1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: q+1
       404: q+1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: q+1
       412: q+1
       413: 2q+1
       414: q+1
       415: q+1
       416: 1
       417: q+1
       418: q+1
       419: 1
       420: 2q+1
       421: q+1
       422: q+1
       423: 1
       424: q+1
       425: 1
       426: 2q+1
       427: q+1
       428: q+1
       429: 1
       430: 2q+1
       431: 2q+1
       433: 2q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: 2q+1
       448: 1
       449: q+1
       452: 1
       453: q+1
       454: 2q+1
       457: 1
       458: 2q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: q+1
       474: 1
       475: 1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: 2q+1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       563: q+1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       573: q+1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: q+1
       582: q+1
       583: 1
       584: q+1
       585: q+1
       586: 1
       587: q+1
       588: 1
       589: q+1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: q+1
       596: 1
       597: 1
       598: 1
       599: 2q+1
       600: q+1
       601: q+1
       602: 1
       603: q+1
       604: 1
       605: 2q+1
       608: 1
       609: 2q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: q+1
       633: 1
       634: 1
       635: 2q+1
       640: 1
       641: q+1
       644: 1
       645: q+1
       646: q+1
       648: q+1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       770: q+1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: q+1
       778: 1
       779: q+1
       780: 1
       781: 1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: q+1
       796: 1
       797: q+1
       798: 1
       799: 1
       800: 1
       801: 2q+1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: q+1
       848: 1
       849: q+1
       852: 1
       853: q+1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       908: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       966: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: q+1
       978: 1
       979: 1
       980: 1
       981: 1
       983: q+1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       991: 1
       993: q+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: 1
      1002: q+1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: q+1
      1065: 1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1146: 1
      1156: 1
      1164: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: q+1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: 1
      1219: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1280: 1
      1287: 1
      1294: 1
      1295: 1
      1299: 1
      1347: 1
      1363: 1
      1370: 1
      1371: 1
      1375: 1
      1378: 1
      1379: 1
      1383: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1394: 1
      1405: 1
      1437: 1
      1447: 1
      1455: 1
      1472: 1
      1534: 1
      1541: 1
      1548: 1
      1549: 1
      1553: 1
      1601: 1
      1678: 1

1679:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: 1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: 1
        62: q^2+q+1
        63: q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: 1
        89: q^2+q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q^2+q+1
       113: 1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q^2+q+1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       144: q+1
       145: 1
       146: q+1
       148: q+1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: 1
       167: q^2+q+1
       168: q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q^2+q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       242: 1
       243: q+1
       246: q+1
       248: q+1
       251: q+1
       252: 1
       253: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q^2+q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q^2+q+1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       298: q+1
       299: 1
       300: q+1
       302: q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: q+1
       380: q+1
       381: 1
       386: 1
       387: q+1
       390: q+1
       392: q+1
       394: q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q^2+q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       448: 1
       449: q+1
       452: q+1
       454: q+1
       457: q+1
       458: 1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: q+1
       558: q+1
       561: q+1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: q+1
       634: q+1
       635: 1
       640: 1
       641: q+1
       644: q+1
       646: q+1
       648: q+1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: q+1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       787: q+1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: q+1
       849: q+1
       852: q+1
       856: 1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       909: 1
       911: 1
       933: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: q+1
       992: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1042: 1
      1050: 1
      1059: q+1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1115: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1244: 1
      1281: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1364: 1
      1370: 1
      1372: 1
      1374: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1394: 1
      1406: 1
      1473: 1
      1535: 1
      1542: 1
      1548: 1
      1550: 1
      1552: 1
      1679: 1

1680:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: 1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q+1
        49: q^2+q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+q+1
        69: q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        78: 1
        79: q^2+q+1
        80: 1
        81: q^2+q+1
        82: 1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q^2+q+1
        95: q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: 1
       102: q^2+q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q^2+q+1
       153: 1
       154: q^2+q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+q+1
       174: q+1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       183: 1
       184: q^2+q+1
       185: 1
       186: q^2+q+1
       187: 1
       188: q^2+q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q^2+q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q^2+q+1
       307: 1
       308: q^2+q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q^2+q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: q+1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       722: 1
       731: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: q+1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       897: 1
       908: 1
       909: 1
       910: 1
       943: 1
       952: 1
       959: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: q+1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       988: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1006: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1033: 1
      1042: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1088: 1
      1089: 1
      1090: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1116: 1
      1156: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1208: 1
      1219: 1
      1220: 1
      1221: 1
      1254: 1
      1263: 1
      1270: 1
      1282: 1
      1289: 1
      1295: 1
      1296: 1
      1297: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1379: 1
      1380: 1
      1381: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1407: 1
      1447: 1
      1474: 1
      1536: 1
      1543: 1
      1549: 1
      1550: 1
      1551: 1
      1680: 1

1681:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: 1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q+1
        48: q^2+q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q^2+q+1
        57: 1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q^2+q+1
        70: q+1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q+1
        90: q+1
        91: q^2+q+1
        92: q+1
        93: q^2+q+1
        94: q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+q+1
       119: 1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: q^2+q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       144: q+1
       145: q+1
       146: q+1
       148: 1
       149: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q^2+q+1
       162: 1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: q^2+q+1
       167: q+1
       168: q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q^2+q+1
       175: q+1
       176: 1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q^2+q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       227: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: 1
       242: q+1
       243: 1
       246: 1
       247: 1
       248: 1
       251: q+1
       252: q+1
       253: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q^2+q+1
       273: 1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: q^2+q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       298: q+1
       299: q+1
       300: q+1
       302: 1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       354: q+1
       355: q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: q+1
       387: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q^2+q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: 1
       448: q+1
       449: 1
       452: 1
       453: 1
       454: 1
       457: q+1
       458: q+1
       459: q+1
       461: 1
       462: q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: 1
       515: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: 1
       599: 1
       600: 1
       601: q+1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       608: q+1
       609: q+1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: q+1
       641: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       730: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       782: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       791: q+1
       792: 1
       793: 1
       794: 1
       795: 1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       800: 1
       801: 1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       905: 1
       910: 1
       911: 1
       912: 1
       951: 1
       952: 1
       959: 1
       964: 1
       965: 1
       966: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: q+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1041: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1117: 1
      1164: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: q+1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1262: 1
      1263: 1
      1270: 1
      1283: 1
      1290: 1
      1297: 1
      1298: 1
      1299: 1
      1366: 1
      1373: 1
      1374: 1
      1375: 1
      1381: 1
      1382: 1
      1383: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1408: 1
      1455: 1
      1475: 1
      1537: 1
      1544: 1
      1551: 1
      1552: 1
      1553: 1
      1681: 1

1682:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q+1
        62: q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       114: q+1
       115: q+1
       116: q^2+q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       191: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       199: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       208: q+1
       209: q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       259: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       268: q+1
       269: q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       312: q+1
       314: q+1
       316: q+1
       317: 1
       318: 1
       321: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       329: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       405: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       414: q+1
       415: q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       469: q+1
       471: 1
       472: 1
       476: q+1
       478: q+1
       480: q+1
       481: 1
       482: 1
       485: q+1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       519: 1
       521: 1
       523: 1
       524: 1
       525: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: q+1
       568: q+1
       570: q+1
       571: 1
       572: 1
       575: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       583: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       591: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       654: 1
       656: 1
       662: q+1
       664: 1
       665: 1
       669: q+1
       671: q+1
       673: q+1
       674: 1
       675: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 1
       710: 1
       711: 1
       715: 1
       717: 1
       719: 1
       721: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       760: q+1
       762: 1
       763: 1
       767: q+1
       769: q+1
       771: q+1
       772: 1
       773: 1
       776: q+1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       793: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: 1
       816: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       859: 1
       866: 1
       868: 1
       874: q+1
       876: 1
       877: 1
       883: 1
       885: 1
       886: 1
       890: 1
       892: 1
       894: 1
       895: 1
       896: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       911: 1
       913: 1
       919: 1
       936: 1
       938: 1
       940: 1
       942: 1
       953: 1
       965: 1
       967: 1
       973: q+1
       975: 1
       976: 1
       980: q+1
       982: q+1
       984: q+1
       985: 1
       986: 1
       990: 1
       992: 1
       994: 1
       995: 1
       996: 1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1022: 1
      1026: 1
      1028: 1
      1030: 1
      1032: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1076: 1
      1083: 1
      1085: 1
      1091: 1
      1093: 1
      1099: 1
      1101: 1
      1102: 1
      1106: 1
      1108: 1
      1110: 1
      1112: 1
      1118: 1
      1142: 1
      1170: 1
      1177: 1
      1179: 1
      1185: q+1
      1187: 1
      1188: 1
      1194: 1
      1196: 1
      1197: 1
      1201: 1
      1203: 1
      1205: 1
      1206: 1
      1207: 1
      1210: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1222: 1
      1224: 1
      1230: 1
      1247: 1
      1249: 1
      1251: 1
      1253: 1
      1264: 1
      1284: 1
      1291: 1
      1298: 1
      1300: 1
      1306: 1
      1367: 1
      1374: 1
      1376: 1
      1382: 1
      1384: 1
      1390: 1
      1392: 1
      1393: 1
      1397: 1
      1399: 1
      1401: 1
      1403: 1
      1409: 1
      1433: 1
      1476: 1
      1538: 1
      1545: 1
      1552: 1
      1554: 1
      1560: 1
      1682: 1

1683:    0: 2q+1
         1: 2q+1
         2: 2q+1
         3: 2q+1
         4: 2q+1
         5: 2q+1
         6: q+1
         7: 2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: 2q+1
        14: 2q+1
        15: 2q+1
        16: 2q+1
        17: 2q+1
        18: 2q+1
        19: 2q+1
        20: q+1
        21: q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q+1
        34: 2q+1
        35: 2q+1
        36: 2q+1
        37: q+1
        38: q+1
        39: 2q+1
        40: q+1
        41: 2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: 2q+1
        48: 2q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q+1
        63: 2q+1
        64: 2q+1
        65: q+1
        66: 2q+1
        67: 2q+1
        68: 2q+1
        69: 2q+1
        70: 2q+1
        71: q+1
        72: q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: 1
        77: q+1
        78: q+1
        79: q+1
        80: 1
        81: 2q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q+1
        98: 2q+1
        99: 2q+1
       100: 2q+1
       101: q+1
       102: q+1
       103: 2q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q+1
       130: 2q+1
       131: 2q+1
       132: 2q+1
       133: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: 2q+1
       140: q+1
       141: 1
       142: 1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: 1
       150: q+1
       151: q+1
       152: q+1
       153: 1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: 2q+1
       172: 2q+1
       173: 2q+1
       174: 2q+1
       175: 2q+1
       176: q+1
       177: q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: 1
       182: q+1
       183: q+1
       184: q+1
       185: 1
       186: 2q+1
       187: q+1
       188: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       207: q+1
       208: q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: 1
       226: q+1
       227: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: 2q+1
       265: 2q+1
       267: q+1
       268: q+1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: 2q+1
       281: q+1
       282: 2q+1
       283: q+1
       284: 2q+1
       285: 2q+1
       286: 2q+1
       287: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: 2q+1
       294: q+1
       295: 1
       296: 1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: 1
       304: q+1
       305: q+1
       306: q+1
       307: 1
       308: q+1
       313: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: 1
       352: 1
       353: q+1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: 2q+1
       403: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: 2q+1
       411: 2q+1
       413: q+1
       414: q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: 1
       432: q+1
       433: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: q+1
       457: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       470: q+1
       471: 1
       472: 1
       477: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       525: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       537: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: q+1
       569: q+1
       570: q+1
       571: 1
       572: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: 2q+1
       581: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: 2q+1
       604: q+1
       605: 1
       606: 1
       607: q+1
       608: 1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       655: 1
       656: 1
       663: q+1
       664: 1
       665: 1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       680: 1
       682: 1
       683: 1
       684: 1
       685: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 1
       710: 1
       711: 1
       716: 1
       718: 1
       719: 1
       721: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       742: 1
       746: 1
       747: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       761: q+1
       762: 1
       763: 1
       768: q+1
       770: q+1
       771: q+1
       772: 1
       773: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       801: 1
       802: 1
       803: 1
       804: 1
       805: q+1
       806: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       828: 1
       832: 1
       833: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       860: 1
       867: 1
       868: 1
       875: q+1
       876: 1
       877: 1
       884: 1
       885: 1
       886: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       912: 1
       913: 1
       920: 1
       932: 1
       937: 1
       939: 1
       940: 1
       942: 1
       950: 1
       951: 1
       954: 1
       958: 1
       959: 1
       966: 1
       967: 1
       974: q+1
       975: 1
       976: 1
       981: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       991: 1
       993: 1
       994: 1
       995: 1
       996: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1040: 1
      1041: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1053: 1
      1057: 1
      1058: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1077: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1100: 1
      1101: 1
      1102: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1119: 1
      1143: 1
      1155: 1
      1163: 1
      1164: 1
      1171: 1
      1178: 1
      1179: 1
      1186: q+1
      1187: 1
      1188: 1
      1195: 1
      1196: 1
      1197: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1223: 1
      1224: 1
      1231: 1
      1243: 1
      1248: 1
      1250: 1
      1251: 1
      1253: 1
      1261: 1
      1262: 1
      1265: 1
      1269: 1
      1270: 1
      1285: 1
      1292: 1
      1299: 1
      1300: 1
      1307: 1
      1356: 1
      1368: 1
      1375: 1
      1376: 1
      1383: 1
      1384: 1
      1391: 1
      1392: 1
      1393: 1
      1398: 1
      1400: 1
      1401: 1
      1403: 1
      1410: 1
      1434: 1
      1446: 1
      1454: 1
      1455: 1
      1477: 1
      1539: 1
      1546: 1
      1553: 1
      1554: 1
      1561: 1
      1610: 1
      1683: 1

1684:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q+1
         5: q^3+q^2+q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^2+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q^3+q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^3+q^2+q+1
        17: q^3+q^2+q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q^2+1
        21: q^3+q^2+q+1
        22: q^2+1
        23: q^2+1
        24: 1
        25: q^3+q^2+q+1
        26: q^3+q^2+q+1
        27: q^2+1
        28: q^3+q^2+q+1
        29: q^3+q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^3+q^2+q+1
        41: q^3+q^2+q+1
        42: q^2+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+1
        51: 1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: 1
        56: 1
        57: q^2+1
        58: q^3+q^2+q+1
        59: q^2+1
        60: q^2+1
        61: 1
        62: q^3+q^2+q+1
        63: q^3+q^2+q+1
        64: q^2+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+1
        85: q^3+q^2+q+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^2+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: q^2+1
       106: 1
       107: q^2+1
       108: q^2+1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       113: 1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: 1
       118: 1
       119: q^2+1
       120: q^3+q^2+q+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+1
       156: 1
       157: q^2+1
       158: q^2+1
       159: q^2+1
       160: 1
       161: 1
       162: q^2+1
       163: q^3+q^2+q+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^3+q^2+q+1
       168: q^3+q^2+q+1
       169: q^2+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q^2+1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q^2+1
       200: 1
       201: q^2+1
       202: q^2+1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       207: 1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: q^2+1
       260: 1
       261: q^2+1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       267: 1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: 1
       273: q^2+1
       274: q^3+q^2+q+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q^2+1
       322: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q^2+1
       330: 1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       395: 1
       396: 1
       397: q^2+1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q^2+1
       406: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q^2+1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q^2+1
       576: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q^2+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       647: q+1
       648: 1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: 1
       720: 1
       721: 1
       724: 1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       861: 1
       869: 1
       870: 1
       877: 1
       878: 1
       879: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       906: 1
       914: 1
       915: 1
       922: 1
       933: 1
       934: 1
       935: 1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       960: 1
       968: 1
       969: 1
       976: 1
       977: 1
       978: 1
       979: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1032: 1
      1035: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1120: 1
      1137: 1
      1138: 1
      1145: 1
      1158: 1
      1172: 1
      1180: 1
      1181: 1
      1188: 1
      1189: 1
      1190: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1225: 1
      1226: 1
      1233: 1
      1244: 1
      1245: 1
      1246: 1
      1252: 1
      1253: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1293: 1
      1301: 1
      1302: 1
      1309: 1
      1330: 1
      1369: 1
      1377: 1
      1385: 1
      1386: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1402: 1
      1403: 1
      1411: 1
      1428: 1
      1429: 1
      1436: 1
      1449: 1
      1478: 1
      1547: 1
      1555: 1
      1556: 1
      1563: 1
      1584: 1
      1684: 1

1685:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: q^3+3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: 2q^2+2q+1
         5: q^3+3q^2+2q+1
         6: q^3+3q^2+2q+1
         7: q^2+2q+1
         8: q^3+3q^2+2q+1
         9: q^3+3q^2+2q+1
        10: q^3+3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: q^3+3q^2+2q+1
        17: q^3+3q^2+2q+1
        18: q^3+3q^2+2q+1
        19: 2q^2+2q+1
        20: q^3+3q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+q+1
        24: q^2+1
        25: q^3+3q^2+2q+1
        26: q^2+2q+1
        27: q^3+3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^3+3q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: q^3+3q^2+2q+1
        41: q^2+2q+1
        42: q^3+3q^2+2q+1
        43: q^3+3q^2+2q+1
        44: q^3+3q^2+2q+1
        45: q^3+3q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+q+1
        51: q^2+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: 1
        57: q^3+3q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+q+1
        61: q^2+1
        62: q^3+3q^2+2q+1
        63: q^2+2q+1
        64: q^3+3q^2+2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: 2q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: 2q^2+2q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+1
        76: 2q^2+2q+1
        77: q+1
        78: 2q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: q^3+3q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+q+1
        88: q^2+1
        89: q^3+3q^2+2q+1
        90: q^2+2q+1
        91: q^3+3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^3+3q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       104: 1
       105: q+1
       106: 1
       107: q^2+2q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q^2+q+1
       113: q^2+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q+1
       117: 1
       118: 1
       119: q^3+3q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^2+q+1
       123: q^2+1
       124: 2q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: 2q^2+2q+1
       132: 2q^2+2q+1
       133: 2q^2+2q+1
       134: q+1
       135: q^2+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 1
       140: 1
       141: 2q^2+2q+1
       142: q+1
       143: q+1
       144: q+1
       145: q^2+1
       146: q^2+2q+1
       147: q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: q+1
       151: 2q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q^2+q+1
       156: q^2+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: 1
       162: q^3+3q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+q+1
       166: q^2+1
       167: q^3+3q^2+2q+1
       168: q^2+2q+1
       169: q^3+3q^2+2q+1
       170: 2q^2+2q+1
       171: q^2+2q+1
       172: 2q^2+2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: 2q^2+2q+1
       176: 2q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+1
       181: 2q^2+2q+1
       182: q+1
       183: 2q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: 2q^2+2q+1
       187: 2q^2+2q+1
       188: q^2+2q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q^2+2q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q^2+q+1
       207: q^2+1
       208: q^2+2q+1
       209: q^2+2q+1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: q^2+1
       215: q^2+2q+1
       216: q^2+2q+1
       217: q+1
       218: 1
       219: 1
       220: 2q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q+1
       224: q^2+1
       225: 2q^2+2q+1
       226: q+1
       227: 2q^2+2q+1
       228: 1
       229: q+1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q^2+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: q^2+2q+1
       244: q+1
       245: q+1
       246: q+1
       248: 2q^2+2q+1
       249: q+1
       250: q+1
       251: q+1
       252: q^2+1
       253: q^2+2q+1
       254: q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 1
       259: q+1
       260: 1
       261: q^2+2q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q^2+q+1
       267: q^2+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q+1
       271: 1
       272: 1
       273: q^3+3q^2+2q+1
       274: q^2+2q+1
       275: q^2+2q+1
       276: q^2+q+1
       277: q^2+1
       278: 2q^2+2q+1
       279: q^2+2q+1
       280: q^2+2q+1
       281: q+1
       282: q^2+1
       283: 2q^2+2q+1
       284: q^2+2q+1
       285: 2q^2+2q+1
       286: 2q^2+2q+1
       287: 2q^2+2q+1
       288: q+1
       289: q^2+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q+1
       293: 1
       294: 1
       295: 2q^2+2q+1
       296: q+1
       297: q+1
       298: q+1
       299: q^2+1
       300: q^2+2q+1
       301: q+1
       302: q^2+2q+1
       303: 2q^2+2q+1
       304: q+1
       305: 2q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: 1
       310: 1
       311: 1
       312: q+1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q+1
       330: 1
       331: q^2+2q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: q^2+2q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: q^2+1
       346: q^2+2q+1
       347: q^2+2q+1
       348: q+1
       349: 1
       350: 1
       351: 2q^2+2q+1
       352: q+1
       353: q+1
       354: q+1
       355: q^2+1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       376: q+1
       377: 1
       380: q+1
       381: q^2+1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: 1
       387: q^2+2q+1
       388: q+1
       389: q+1
       390: q+1
       392: q^2+2q+1
       393: q+1
       394: q^2+2q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q^2+2q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q^2+q+1
       413: q^2+1
       414: q^2+2q+1
       415: q^2+2q+1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: q^2+1
       421: q^2+2q+1
       422: q^2+2q+1
       423: q+1
       424: 1
       425: 1
       426: 2q^2+2q+1
       427: q^2+2q+1
       428: q^2+2q+1
       429: q+1
       430: q^2+1
       431: 2q^2+2q+1
       432: q+1
       433: 2q^2+2q+1
       434: 1
       435: q+1
       436: 1
       437: q^2+2q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: q^2+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: q^2+2q+1
       450: q+1
       451: q+1
       452: q+1
       454: 2q^2+2q+1
       455: q+1
       456: q+1
       457: q+1
       458: q^2+1
       459: q^2+2q+1
       460: q+1
       461: q^2+2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: q+1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q^2+2q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: q^2+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: q+1
       539: 1
       543: 1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q+1
       553: q+1
       554: q+1
       555: 1
       558: q^2+2q+1
       559: q+1
       560: q+1
       561: q+1
       563: 1
       564: 1
       565: 1
       566: q+1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q^2+2q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q^2+2q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: q^2+1
       600: q^2+2q+1
       601: q^2+2q+1
       602: q+1
       603: 1
       604: 1
       605: 2q^2+2q+1
       606: q+1
       607: q+1
       608: q+1
       609: q^2+1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       630: q+1
       631: 1
       634: q+1
       635: q^2+1
       636: q+1
       637: q+1
       638: 1
       639: 1
       640: 1
       641: q^2+2q+1
       642: q+1
       643: q+1
       644: q+1
       646: q^2+2q+1
       647: q+1
       648: q^2+2q+1
       650: 1
       658: 1
       659: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q+1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       705: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: q+1
       750: q+1
       751: q+1
       752: 1
       756: 1
       757: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       787: q+1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q^2+2q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: q^2+1
       802: q+1
       803: q+1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       813: 1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: q+1
       830: 1
       834: 1
       835: 1
       836: 1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: q+1
       845: q+1
       846: 1
       849: q^2+2q+1
       850: q+1
       851: q+1
       852: q+1
       862: 1
       870: 1
       871: 1
       876: 1
       879: 1
       880: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       893: 1
       894: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       907: 1
       915: 1
       916: 1
       921: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       945: 1
       947: 1
       953: 1
       955: q+1
       956: 1
       961: 1
       969: 1
       970: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: q+1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: q+1
      1055: 1
      1059: q+1
      1061: q+1
      1062: q+1
      1063: 1
      1079: 1
      1087: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1121: 1
      1138: 1
      1139: 1
      1144: 1
      1149: 1
      1158: 1
      1160: 1
      1173: 1
      1181: 1
      1182: 1
      1187: 1
      1190: 1
      1191: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1218: 1
      1226: 1
      1227: 1
      1232: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1252: 1
      1256: 1
      1258: 1
      1264: 1
      1266: q+1
      1267: 1
      1294: 1
      1302: 1
      1303: 1
      1308: 1
      1331: 1
      1350: 1
      1370: 1
      1378: 1
      1386: 1
      1387: 1
      1392: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1402: 1
      1412: 1
      1429: 1
      1430: 1
      1435: 1
      1440: 1
      1449: 1
      1451: 1
      1479: 1
      1548: 1
      1556: 1
      1557: 1
      1562: 1
      1585: 1
      1604: 1
      1685: 1

1686:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: q^2+2q+1
         3: q^3+3q^2+2q+1
         4: q^3+3q^2+2q+1
         5: q^3+3q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+3q^2+2q+1
        10: q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: q^2+2q+1
        15: q^3+3q^2+2q+1
        16: q^3+3q^2+2q+1
        17: q^2+2q+1
        18: q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+3q^2+2q+1
        29: q^2+2q+1
        30: q^3+3q^2+2q+1
        31: q^2+2q+1
        32: q^3+3q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^3+3q^2+2q+1
        37: q+1
        38: q^3+2q^2+2q+1
        39: q^3+3q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^3+3q^2+2q+1
        44: q^2+2q+1
        45: q^3+3q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 1
        54: q+1
        55: q^2+2q+1
        56: q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q+1
        61: q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^3+3q^2+2q+1
        69: q^2+2q+1
        70: q^3+3q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^3+2q^2+2q+1
        80: q+1
        81: q^3+3q^2+2q+1
        82: q+1
        83: q^3+2q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^3+3q^2+2q+1
        93: q^2+2q+1
        94: q^3+3q^2+2q+1
        95: q^2+2q+1
        96: q^3+3q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^3+3q^2+2q+1
       101: q+1
       102: q^3+2q^2+2q+1
       103: q^3+3q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: 1
       116: q+1
       117: q^2+2q+1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^3+3q^2+2q+1
       133: q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^3+2q^2+2q+1
       153: q+1
       154: q^3+2q^2+2q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^3+3q^2+2q+1
       174: q^2+2q+1
       175: q^3+3q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^3+2q^2+2q+1
       185: q+1
       186: q^3+3q^2+2q+1
       187: q+1
       188: q^3+2q^2+2q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: q+1
       199: q+1
       200: q^2+2q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       206: q+1
       207: q^2+2q+1
       208: q^2+2q+1
       209: 1
       210: q+1
       211: q^2+2q+1
       212: q+1
       213: q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: 1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^3+2q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: q^2+2q+1
       268: q^2+2q+1
       269: 1
       270: q+1
       271: q^2+2q+1
       272: q+1
       273: q^2+2q+1
       274: q^2+2q+1
       275: q^2+2q+1
       276: q+1
       277: q^2+2q+1
       278: q^2+2q+1
       279: q^2+2q+1
       280: q^2+2q+1
       281: q+1
       282: q^2+2q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q^2+2q+1
       286: q^3+3q^2+2q+1
       287: q+1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^3+2q^2+2q+1
       307: q+1
       308: q^3+2q^2+2q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       328: q+1
       329: q+1
       330: q^2+2q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q^2+2q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: 1
       348: q+1
       349: q^2+2q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: q+1
       405: q+1
       406: q^2+2q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       412: q+1
       413: q^2+2q+1
       414: q^2+2q+1
       415: 1
       416: q+1
       417: q^2+2q+1
       418: q+1
       419: q+1
       420: q^2+2q+1
       421: q^2+2q+1
       422: 1
       423: q+1
       424: q^2+2q+1
       425: q+1
       426: q^2+2q+1
       427: q^2+2q+1
       428: q^2+2q+1
       429: q+1
       430: q^2+2q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: q+1
       444: q+1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^3+2q^2+2q+1
       463: q+1
       466: 1
       467: 1
       470: 1
       474: q+1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: q+1
       502: q+1
       503: q^2+2q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       511: q+1
       512: 1
       513: 1
       514: q+1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: q+1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       582: q+1
       583: q+1
       584: q^2+2q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q+1
       590: q+1
       591: q+1
       592: q^2+2q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: q^2+2q+1
       600: q^2+2q+1
       601: 1
       602: q+1
       603: q^2+2q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: q+1
       629: q+1
       631: 1
       632: q+1
       633: 1
       634: 1
       635: q+1
       636: q+1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       651: 1
       659: 1
       660: 1
       663: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: 1
       696: 1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       752: 1
       753: q+1
       754: 1
       757: 1
       758: 1
       761: 1
       765: q+1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: q+1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       792: q+1
       793: q+1
       794: q^2+2q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       802: q+1
       803: 1
       804: 1
       805: q+1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: q+1
       832: 1
       833: 1
       834: 1
       835: 1
       836: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: q+1
       844: q+1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       863: 1
       871: 1
       872: 1
       875: 1
       880: 1
       881: 1
       884: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: 1
       940: 1
       943: 1
       944: 1
       950: 1
       952: 1
       953: 1
       954: q+1
       958: 1
       959: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: q+1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       988: q+1
       989: 1
       990: 1
       991: 1
       993: 1
       994: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1006: 1
      1007: 1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1040: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: 1
      1053: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1061: q+1
      1063: 1
      1064: q+1
      1065: 1
      1080: 1
      1088: 1
      1096: 1
      1097: 1
      1100: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1122: 1
      1139: 1
      1140: 1
      1143: 1
      1147: 1
      1156: 1
      1157: 1
      1163: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1191: 1
      1192: 1
      1195: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1219: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1261: 1
      1263: 1
      1264: 1
      1265: q+1
      1269: 1
      1270: 1
      1295: 1
      1303: 1
      1304: 1
      1307: 1
      1332: 1
      1348: 1
      1371: 1
      1379: 1
      1387: 1
      1388: 1
      1391: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: 1
      1401: 1
      1413: 1
      1430: 1
      1431: 1
      1434: 1
      1438: 1
      1447: 1
      1448: 1
      1454: 1
      1480: 1
      1549: 1
      1557: 1
      1558: 1
      1561: 1
      1586: 1
      1602: 1
      1686: 1

1687:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       422: 1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: 1
       602: q+1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       652: 1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       707: 1
       708: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: 1
       748: 1
       750: 1
       752: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       864: 1
       871: 1
       873: 1
       874: 1
       880: 1
       882: 1
       883: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       909: 1
       916: 1
       918: 1
       919: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       953: 1
       963: 1
       970: 1
       972: 1
       973: 1
       978: 1
       979: 1
       980: 1
       982: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1081: 1
      1089: 1
      1096: 1
      1098: 1
      1099: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1123: 1
      1139: 1
      1141: 1
      1142: 1
      1175: 1
      1182: 1
      1184: 1
      1185: 1
      1191: 1
      1193: 1
      1194: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1220: 1
      1227: 1
      1229: 1
      1230: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1264: 1
      1296: 1
      1303: 1
      1305: 1
      1306: 1
      1333: 1
      1372: 1
      1380: 1
      1387: 1
      1389: 1
      1390: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1414: 1
      1430: 1
      1432: 1
      1433: 1
      1481: 1
      1550: 1
      1557: 1
      1559: 1
      1560: 1
      1587: 1
      1687: 1

1688:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: 2q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: 2q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q+1
        92: 2q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+2q+1
        95: q^2+2q+1
        96: 2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: 2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: q+1
       409: q+1
       410: 2q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: q+1
       427: q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: 2q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: q+1
       587: q+1
       588: 2q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: q+1
       595: q+1
       596: 2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: 1
       729: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: q+1
       797: q+1
       798: 2q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       944: 1
       950: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1034: 1
      1040: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1082: 1
      1090: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1124: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1157: 1
      1163: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: 1
      1221: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1255: 1
      1261: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1297: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1334: 1
      1373: 1
      1381: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1415: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1448: 1
      1454: 1
      1482: 1
      1551: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1588: 1
      1688: 1

1689:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: 1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: 1
        62: q^2+q+1
        63: q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: 1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: 1
        89: q^2+q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q^2+q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q^2+q+1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: 1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: 1
       167: q^2+q+1
       168: q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       191: q+1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       199: q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q^2+q+1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: q+1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: q+1
       229: q+1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: q+1
       249: 1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q^2+q+1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q^2+q+1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: 1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       312: q+1
       314: 1
       316: 1
       317: 1
       321: q+1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       329: q+1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       337: q+1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q+1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: 1
       358: q+1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: 1
       389: 1
       390: q+1
       392: q+1
       393: 1
       394: q+1
       397: q+1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       405: q+1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q^2+q+1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       419: q+1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: 1
       433: q+1
       435: q+1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: q+1
       455: 1
       456: 1
       457: q+1
       458: 1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       469: 1
       471: 1
       476: q+1
       478: 1
       480: 1
       481: 1
       485: q+1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       494: q+1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       502: q+1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       519: q+1
       521: 1
       523: 1
       524: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q+1
       553: 1
       554: 1
       555: 1
       558: q+1
       559: 1
       560: 1
       561: q+1
       566: q+1
       568: 1
       570: 1
       571: 1
       575: q+1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       583: q+1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       591: q+1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: 1
       607: 1
       608: q+1
       609: 1
       612: q+1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: q+1
       642: 1
       643: 1
       644: q+1
       646: q+1
       647: 1
       648: q+1
       654: 1
       662: 1
       664: 1
       669: q+1
       671: 1
       673: 1
       674: 1
       679: q+1
       681: 1
       683: 1
       684: 1
       688: q+1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 1
       710: 1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: q+1
       750: 1
       751: 1
       752: 1
       760: 1
       762: 1
       767: q+1
       769: 1
       771: 1
       772: 1
       776: q+1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       785: q+1
       787: q+1
       788: 1
       789: 1
       790: 1
       791: 1
       793: q+1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       810: q+1
       812: 1
       814: 1
       815: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: 1
       845: 1
       846: 1
       849: q+1
       850: 1
       851: 1
       852: q+1
       866: 1
       874: 1
       876: 1
       883: 1
       885: 1
       890: q+1
       892: 1
       894: 1
       895: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       911: 1
       919: 1
       921: 1
       926: 1
       936: 1
       938: 1
       940: 1
       941: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       965: 1
       973: 1
       975: 1
       980: q+1
       982: 1
       984: 1
       985: 1
       990: q+1
       992: 1
       994: 1
       995: 1
       999: q+1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: q+1
      1061: 1
      1062: 1
      1063: 1
      1083: 1
      1091: 1
      1099: 1
      1101: 1
      1106: 1
      1108: 1
      1110: 1
      1111: 1
      1125: 1
      1142: 1
      1144: 1
      1149: 1
      1158: 1
      1160: 1
      1177: 1
      1185: 1
      1187: 1
      1194: 1
      1196: 1
      1201: q+1
      1203: 1
      1205: 1
      1206: 1
      1210: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1222: 1
      1230: 1
      1232: 1
      1237: 1
      1247: 1
      1249: 1
      1251: 1
      1252: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1267: 1
      1298: 1
      1306: 1
      1308: 1
      1335: 1
      1350: 1
      1374: 1
      1382: 1
      1390: 1
      1392: 1
      1397: 1
      1399: 1
      1401: 1
      1402: 1
      1416: 1
      1433: 1
      1435: 1
      1440: 1
      1449: 1
      1451: 1
      1483: 1
      1552: 1
      1560: 1
      1562: 1
      1589: 1
      1604: 1
      1689: 1

1690:    0: 3q^2+2q+1
         1: 2q^2+2q+1
         2: 3q^2+2q+1
         3: 3q^2+2q+1
         4: 3q^2+2q+1
         5: 3q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 3q^2+2q+1
        11: 3q^2+2q+1
        12: 3q^2+2q+1
        13: 2q^2+2q+1
        14: 3q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 3q^2+2q+1
        18: 3q^2+2q+1
        19: 3q^2+2q+1
        20: q^2+q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: 2q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 3q^2+2q+1
        30: 2q^2+2q+1
        31: 3q^2+2q+1
        32: 3q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: 2q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 3q^2+2q+1
        45: 3q^2+2q+1
        46: 3q^2+2q+1
        47: 2q^2+2q+1
        48: 3q^2+2q+1
        49: 2q^2+2q+1
        51: q^2+q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^2+q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: 2q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: 2q^2+2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 3q^2+2q+1
        70: 2q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: q^2+2q+1
        76: q^2+2q+1
        77: q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: q^2+q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 3q^2+2q+1
        94: 2q^2+2q+1
        95: 3q^2+2q+1
        96: 3q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: 2q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       113: q^2+q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: q^2+q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+2q+1
       123: 2q^2+2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: 2q^2+2q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: q+1
       149: q^2+2q+1
       150: q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       156: q^2+q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: q^2+2q+1
       162: q^2+q+1
       163: q^2+2q+1
       164: 2q+1
       165: q^2+2q+1
       166: 2q^2+2q+1
       167: 2q^2+2q+1
       168: q^2+2q+1
       169: 2q^2+2q+1
       170: 2q^2+2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: 2q^2+2q+1
       174: 3q^2+2q+1
       175: 2q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q^2+2q+1
       181: q^2+2q+1
       182: q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: 2q^2+2q+1
       188: q^2+2q+1
       192: q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       200: q+1
       201: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       207: q^2+q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: q^2+2q+1
       214: q+1
       215: q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q+1
       227: q^2+2q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       237: q+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       267: q^2+q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: q^2+2q+1
       273: q^2+q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+2q+1
       277: 2q^2+2q+1
       278: q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: q^2+2q+1
       283: 2q^2+2q+1
       284: q^2+2q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: 2q^2+2q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: q^2+2q+1
       300: q^2+2q+1
       301: q+1
       302: q+1
       303: q^2+2q+1
       304: q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       313: q+1
       315: 1
       316: 1
       317: q+1
       322: q+1
       323: q+1
       324: 1
       325: 2q+1
       326: q+1
       327: q+1
       330: q+1
       331: q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       338: q+1
       339: q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       345: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: q+1
       352: q+1
       353: q+1
       354: 2q+1
       355: q^2+2q+1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       381: q+1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: 2q+1
       387: q+1
       388: q+1
       389: 1
       390: q+1
       391: q+1
       392: q^2+2q+1
       393: q+1
       394: q+1
       398: q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q+1
       413: q^2+q+1
       414: q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: q^2+2q+1
       420: q+1
       421: q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: q+1
       427: q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: q^2+2q+1
       431: q^2+2q+1
       432: q+1
       433: q^2+2q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       443: q+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       457: 2q+1
       458: q^2+2q+1
       459: q^2+2q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       470: 1
       471: 1
       477: q+1
       479: 1
       480: 1
       481: q+1
       486: q+1
       487: q+1
       488: 1
       489: 2q+1
       490: q+1
       491: q+1
       495: q+1
       496: q+1
       497: 1
       498: 2q+1
       499: q+1
       500: q+1
       503: q+1
       504: q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: 2q+1
       520: q+1
       522: 1
       523: 1
       524: q+1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       552: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q+1
       558: q+1
       559: q+1
       560: 1
       561: q+1
       562: q+1
       567: q+1
       569: 1
       570: 1
       571: q+1
       576: q+1
       577: q+1
       578: 1
       579: 2q+1
       580: q+1
       581: q+1
       584: q+1
       585: q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q+1
       592: q+1
       593: q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: q+1
       606: q+1
       607: q+1
       608: 2q+1
       609: q^2+2q+1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: q+1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: 2q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q+1
       655: 1
       663: 1
       664: 1
       670: q+1
       672: 1
       673: 1
       674: q+1
       680: q+1
       682: 1
       683: 1
       684: q+1
       689: q+1
       690: q+1
       691: 1
       692: 2q+1
       693: q+1
       694: q+1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       709: 1
       710: 1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       761: 1
       762: 1
       768: q+1
       770: 1
       771: 1
       772: q+1
       777: q+1
       778: q+1
       779: 1
       780: 2q+1
       781: q+1
       782: q+1
       786: q+1
       787: q+1
       788: 1
       789: 2q+1
       790: q+1
       791: q+1
       794: q+1
       795: q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: q+1
       801: q+1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: 2q+1
       811: q+1
       813: 1
       814: 1
       815: q+1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       867: 1
       875: 1
       876: 1
       884: 1
       885: 1
       891: q+1
       893: 1
       894: 1
       895: q+1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       912: 1
       920: 1
       921: 1
       927: 1
       931: 1
       937: 1
       939: 1
       940: 1
       941: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: 1
       974: 1
       975: 1
       981: q+1
       983: 1
       984: 1
       985: q+1
       991: q+1
       993: 1
       994: 1
       995: q+1
      1000: q+1
      1001: q+1
      1002: 1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1020: 1
      1021: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1084: 1
      1092: 1
      1100: 1
      1101: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1126: 1
      1143: 1
      1144: 1
      1150: 1
      1154: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1178: 1
      1186: 1
      1187: 1
      1195: 1
      1196: 1
      1202: q+1
      1204: 1
      1205: 1
      1206: q+1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: 1
      1216: 1
      1223: 1
      1231: 1
      1232: 1
      1238: 1
      1242: 1
      1248: 1
      1250: 1
      1251: 1
      1252: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1299: 1
      1307: 1
      1308: 1
      1336: 1
      1351: 1
      1355: 1
      1375: 1
      1383: 1
      1391: 1
      1392: 1
      1398: 1
      1400: 1
      1401: 1
      1402: 1
      1417: 1
      1434: 1
      1435: 1
      1441: 1
      1445: 1
      1450: 1
      1451: 1
      1453: 1
      1454: 1
      1455: 1
      1484: 1
      1553: 1
      1561: 1
      1562: 1
      1590: 1
      1605: 1
      1609: 1
      1690: 1

1691:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: 1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: 1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: q^2+1
       108: q^2+1
       109: 1
       110: 1
       111: 1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: 1
       118: 1
       119: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: q^2+1
       158: q^2+1
       159: q^2+1
       160: 1
       161: 1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       193: q^2+1
       194: 1
       195: 1
       196: 1
       197: 1
       201: q^2+1
       202: q^2+1
       203: 1
       204: 1
       205: 1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: q^2+1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: 1
       273: q^2+1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       318: 1
       323: q^2+1
       324: 1
       325: 1
       326: 1
       327: 1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       399: q^2+1
       400: 1
       401: 1
       402: 1
       403: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: q^2+1
       488: 1
       489: 1
       490: 1
       491: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       570: 1
       571: 1
       572: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       673: 1
       674: 1
       675: 1
       683: 1
       684: 1
       685: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       711: 1
       719: 1
       720: 1
       721: 1
       726: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       750: 1
       751: 1
       752: 1
       762: 1
       763: 1
       771: 1
       772: 1
       773: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       868: 1
       876: 1
       877: 1
       885: 1
       886: 1
       894: 1
       895: 1
       896: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       913: 1
       921: 1
       922: 1
       940: 1
       941: 1
       942: 1
       947: 1
       955: 1
       956: 1
       967: 1
       975: 1
       976: 1
       984: 1
       985: 1
       986: 1
       994: 1
       995: 1
       996: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1021: 1
      1022: 1
      1030: 1
      1031: 1
      1032: 1
      1037: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1054: 1
      1055: 1
      1061: 1
      1062: 1
      1063: 1
      1085: 1
      1093: 1
      1101: 1
      1102: 1
      1110: 1
      1111: 1
      1112: 1
      1127: 1
      1144: 1
      1145: 1
      1160: 1
      1179: 1
      1187: 1
      1188: 1
      1196: 1
      1197: 1
      1205: 1
      1206: 1
      1207: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1224: 1
      1232: 1
      1233: 1
      1251: 1
      1252: 1
      1253: 1
      1258: 1
      1266: 1
      1267: 1
      1300: 1
      1308: 1
      1309: 1
      1337: 1
      1376: 1
      1384: 1
      1392: 1
      1393: 1
      1401: 1
      1402: 1
      1403: 1
      1418: 1
      1435: 1
      1436: 1
      1451: 1
      1485: 1
      1554: 1
      1562: 1
      1563: 1
      1591: 1
      1691: 1

1692:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q^2+3q+1
         9: 2q^2+3q+1
        10: 2q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q^2+3q+1
        29: 2q+1
        30: 2q^2+3q+1
        31: 2q+1
        32: 2q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: 2q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: 2q^2+3q+1
        69: 2q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+3q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q^2+3q+1
        80: 2q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^3+3q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 2q^2+3q+1
       105: 2q^2+3q+1
       106: 2q^2+3q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q^2+3q+1
       111: q^2+2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: 2q+1
       131: 1
       132: q^2+2q+1
       133: q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: 2q^2+3q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q^2+3q+1
       153: 2q+1
       154: q^2+2q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 2q^2+3q+1
       158: 2q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q^2+3q+1
       174: 2q+1
       175: q^2+2q+1
       176: 2q^2+3q+1
       177: q^3+3q^2+3q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: 2q^2+3q+1
       189: q^2+2q+1
       190: 2q^2+3q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 2q^2+3q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q^2+3q+1
       235: q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: 2q^2+3q+1
       259: 2q^2+3q+1
       260: 2q^2+3q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q^2+3q+1
       265: q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: 2q^2+3q+1
       289: 2q^2+3q+1
       290: 2q^2+3q+1
       291: 2q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: 2q^2+3q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q^2+3q+1
       307: 2q+1
       308: q^2+2q+1
       309: q+1
       310: q^2+2q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+2q+1
       357: 2q^2+3q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q^2+2q+1
       396: 2q^2+3q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 2q^2+3q+1
       435: 2q^2+3q+1
       436: 2q^2+3q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       482: 1
       483: 1
       484: q+1
       490: 1
       491: 1
       492: 1
       493: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       773: 1
       774: 1
       775: q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       898: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       977: 1
       978: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1074: 1
      1094: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1146: 1
      1147: 1
      1155: 1
      1157: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1209: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1271: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1318: 1
      1338: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1365: 1
      1385: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1448: 1
      1486: 1
      1525: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1572: 1
      1592: 1
      1692: 1

1693:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        60: 1
        61: 1
        62: 1
        64: 1
        65: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       118: 1
       119: 1
       122: 1
       123: 1
       124: 1
       127: 1
       128: 1
       129: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       205: 1
       206: 1
       207: 1
       212: 1
       213: 1
       214: 1
       219: 1
       220: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       327: 1
       328: 1
       335: 1
       336: 1
       343: 1
       344: 1
       345: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       483: 1
       491: 1
       492: 1
       500: 1
       501: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       666: 1
       676: 1
       686: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       887: 1
       897: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1068: 1
      1069: 1
      1103: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1156: 1
      1164: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1208: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1272: 1
      1312: 1
      1313: 1
      1347: 1
      1359: 1
      1360: 1
      1394: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1447: 1
      1455: 1
      1487: 1
      1526: 1
      1566: 1
      1567: 1
      1601: 1
      1693: 1

1694:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q+1
        30: q^2+2q+1
        31: q+1
        32: q^2+2q+1
        33: q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 1
        58: 1
        59: q+1
        60: q+1
        61: q+1
        62: 1
        63: q+1
        64: q+1
        65: 1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: 1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: 1
       126: q+1
       127: q+1
       128: q+1
       129: 1
       130: q+1
       131: q+1
       132: q^2+2q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 1
       142: 1
       143: q+1
       144: q+1
       145: q+1
       146: 1
       147: q+1
       148: q+1
       149: 1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 1
       163: 1
       164: q+1
       165: q+1
       166: q+1
       167: 1
       168: q+1
       169: q+1
       170: 1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q+1
       177: q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: 1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q^2+2q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       206: 1
       207: 1
       208: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: 1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: 1
       250: q+1
       251: q+1
       252: q+1
       253: 1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: 1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: 1
       280: q+1
       281: q+1
       282: q+1
       283: 1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 1
       296: 1
       297: q+1
       298: q+1
       299: q+1
       300: 1
       301: q+1
       302: q+1
       303: 1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       327: 1
       328: 1
       329: 1
       330: 1
       334: q+1
       335: q+1
       336: 1
       337: 1
       338: 1
       342: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q^2+2q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: 1
       374: 1
       375: 1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q^2+2q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       412: 1
       413: 1
       414: 1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: 1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: 1
       456: q+1
       457: q+1
       458: q+1
       459: 1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       482: 1
       483: 1
       484: 1
       490: q+1
       491: 1
       492: 1
       493: 1
       499: q+1
       500: 1
       501: 1
       502: 1
       503: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       534: 1
       535: 1
       536: 1
       537: 1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: 1
       549: q+1
       550: q+1
       551: 1
       552: 1
       553: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       581: 1
       582: 1
       583: 1
       584: 1
       588: q+1
       589: q+1
       590: 1
       591: 1
       592: 1
       596: q+1
       597: q+1
       598: 1
       599: 1
       600: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+2q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: q+1
       626: q+1
       627: 1
       628: 1
       629: 1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 1
       643: q+1
       644: q+1
       645: q+1
       646: 1
       647: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       675: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       722: 1
       723: 1
       729: q+1
       730: 1
       731: 1
       732: 1
       738: q+1
       739: 1
       740: 1
       741: 1
       742: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       781: q+1
       782: 1
       783: 1
       784: 1
       790: q+1
       791: 1
       792: 1
       793: 1
       794: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: q+1
       825: 1
       826: 1
       827: 1
       828: 1
       832: q+1
       833: q+1
       834: 1
       835: 1
       836: 1
       840: q+1
       841: q+1
       842: 1
       843: 1
       844: 1
       846: q+1
       847: q+1
       848: q+1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       932: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       986: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: q+1
      1041: 1
      1042: 1
      1043: 1
      1049: q+1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: q+1
      1058: q+1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1069: 1
      1070: 1
      1074: 1
      1104: 1
      1112: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1243: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1273: 1
      1313: 1
      1314: 1
      1318: 1
      1348: 1
      1356: 1
      1360: 1
      1361: 1
      1365: 1
      1395: 1
      1403: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1488: 1
      1527: 1
      1567: 1
      1568: 1
      1572: 1
      1602: 1
      1610: 1
      1694: 1

1695:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q+1
        55: q^2+2q+1
        56: q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q+1
        61: q^2+2q+1
        62: q+1
        63: q+1
        64: 1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q+1
       109: q^2+2q+1
       110: q+1
       111: q+1
       112: q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q+1
       117: q^2+2q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q^2+2q+1
       126: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q+1
       145: q^2+2q+1
       146: q+1
       147: q+1
       148: 1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q+1
       166: q^2+2q+1
       167: q+1
       168: q+1
       169: 1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^3+2q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q+1
       185: q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^2+2q+1
       193: 1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q+1
       203: q^2+2q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       216: q+1
       218: q+1
       220: 1
       221: q+1
       222: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: q^2+2q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+2q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: q+1
       241: q^2+2q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q^2+2q+1
       250: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: q+1
       263: q^2+2q+1
       264: q+1
       265: q+1
       266: q+1
       267: q^2+2q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q+1
       271: q^2+2q+1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q^2+2q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q+1
       299: q^2+2q+1
       300: q+1
       301: q+1
       302: 1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: q+1
       321: q+1
       322: q^2+2q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: q+1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: q+1
       353: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+2q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       383: q+1
       385: q+1
       387: 1
       388: q+1
       389: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q^2+2q+1
       399: 1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q^2+2q+1
       407: q^2+2q+1
       408: q+1
       409: q^2+2q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       422: q+1
       424: q+1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: q^2+2q+1
       438: q+1
       439: q^2+2q+1
       440: q+1
       441: q+1
       442: q+1
       443: q^2+2q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: q+1
       447: q^2+2q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q^2+2q+1
       456: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       467: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       495: q+1
       497: q+1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q^2+2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: q+1
       560: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q^2+2q+1
       577: 1
       578: q+1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: q+1
       593: q+1
       595: q+1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q^2+2q+1
       614: 1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q^2+2q+1
       622: q^2+2q+1
       623: q+1
       624: q^2+2q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       637: q+1
       639: q+1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       682: q+1
       689: 1
       697: 1
       698: 1
       700: 1
       703: q+1
       704: q+1
       705: 1
       706: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: q+1
       736: q+1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       755: q+1
       756: q+1
       757: 1
       758: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: q+1
       788: q+1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q^2+2q+1
       821: 1
       822: q+1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: q+1
       837: q+1
       839: q+1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: q+1
       851: 1
       853: 1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       900: 1
       906: q+1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       939: q+1
       946: 1
       954: 1
       955: 1
       957: 1
       960: q+1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       986: 1
       993: q+1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: q+1
      1047: q+1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1159: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: 1
      1188: 1
      1211: 1
      1217: q+1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1250: q+1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1274: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: 1
      1427: 1
      1450: 1
      1489: 1
      1528: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1695: 1

1696:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^2+2q+1
       113: q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: q+1
       118: q+1
       119: q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^3+2q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q^2+2q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q^2+2q+1
       200: q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       208: q+1
       209: q+1
       210: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q+1
       234: q+1
       235: q+1
       236: q^2+2q+1
       237: q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: q^2+2q+1
       241: q+1
       242: q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: q^2+2q+1
       262: q^2+2q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+2q+1
       267: q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q^2+2q+1
       271: q+1
       272: q+1
       273: q+1
       274: q^2+2q+1
       275: q+1
       276: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q^2+2q+1
       299: q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: q+1
       321: q^2+2q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       329: q+1
       331: q+1
       332: q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       356: q+1
       357: q+1
       358: q^2+2q+1
       359: q+1
       360: q+1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q^2+2q+1
       367: q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       375: q+1
       376: q+1
       377: q+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q^2+2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q^2+2q+1
       406: q+1
       407: q^2+2q+1
       408: q^2+2q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       414: q+1
       415: q+1
       416: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: q^2+2q+1
       438: q^2+2q+1
       439: q+1
       440: q+1
       441: q+1
       442: q^2+2q+1
       443: q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: q^2+2q+1
       447: q+1
       448: q+1
       449: q+1
       450: q^2+2q+1
       451: q+1
       452: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       468: 1
       469: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: q+1
       487: q+1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q^2+2q+1
       529: q+1
       530: q+1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: q+1
       538: q+1
       539: q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q^2+2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: q+1
       585: q+1
       586: q+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       610: q+1
       611: q+1
       612: q^2+2q+1
       613: q+1
       614: q+1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q^2+2q+1
       621: q+1
       622: q^2+2q+1
       623: q^2+2q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       629: q+1
       630: q+1
       631: q+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       665: 1
       669: q+1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       688: 1
       696: 1
       698: 1
       699: 1
       703: q+1
       704: q+1
       705: 1
       707: 1
       708: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: q+1
       726: q+1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: q+1
       756: q+1
       757: 1
       759: 1
       760: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       776: q+1
       778: q+1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q^2+2q+1
       820: q+1
       821: q+1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: q+1
       829: q+1
       830: q+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       878: 1
       879: 1
       882: 1
       886: 1
       899: 1
       906: q+1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: q+1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       960: q+1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       976: 1
       980: q+1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       999: 1
      1007: 1
      1009: 1
      1010: 1
      1014: q+1
      1015: q+1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: q+1
      1037: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1086: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1141: 1
      1145: 1
      1158: 1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: 1
      1177: 1
      1179: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1210: 1
      1217: q+1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: q+1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1275: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1377: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1428: 1
      1429: 1
      1432: 1
      1436: 1
      1449: 1
      1490: 1
      1529: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1584: 1
      1696: 1

1697:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 3q+1
         9: 3q+1
        10: 3q+1
        11: 3q+1
        12: 3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 3q+1
        19: 2q^2+3q+1
        20: 3q+1
        21: 2q^2+3q+1
        22: 3q+1
        23: 3q+1
        24: 3q+1
        25: 3q+1
        26: q+1
        27: 3q+1
        28: 3q+1
        29: 3q+1
        30: 3q+1
        31: 3q+1
        32: 3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 3q+1
        36: 3q+1
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 3q+1
        43: 3q+1
        44: 3q+1
        45: 3q+1
        46: 3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 3q+1
        50: 3q+1
        51: 3q+1
        52: 3q+1
        53: 3q+1
        54: 3q+1
        55: 3q+1
        56: 3q+1
        57: 3q+1
        58: q+1
        59: q+1
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: q+1
        64: q+1
        65: 3q+1
        66: q+1
        67: q+1
        68: 3q+1
        69: 3q+1
        70: 2q+1
        71: 3q+1
        72: 2q^2+3q+1
        73: 3q+1
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: q+1
        78: 3q+1
        79: 3q+1
        80: 3q+1
        81: 3q+1
        82: 3q+1
        83: 3q+1
        84: 3q+1
        85: 2q^2+3q+1
        86: 3q+1
        87: 3q+1
        88: 3q+1
        89: 3q+1
        90: q+1
        91: 3q+1
        92: 3q+1
        93: 3q+1
        94: 3q+1
        95: 3q+1
        96: 3q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: 3q+1
       102: 3q+1
       103: 3q+1
       104: 3q+1
       105: 3q+1
       106: 3q+1
       107: 3q+1
       108: 3q+1
       109: 3q+1
       110: 3q+1
       111: 2q+1
       112: 3q+1
       113: 3q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 3q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 3q+1
       130: q+1
       131: 1
       132: 2q+1
       133: 2q+1
       134: 3q+1
       135: 3q+1
       136: 3q+1
       137: 3q+1
       138: 3q+1
       139: 3q+1
       140: 3q+1
       141: 3q+1
       142: q+1
       143: q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: q+1
       148: q+1
       149: 3q+1
       150: q+1
       151: q+1
       152: 3q+1
       153: 3q+1
       154: 2q+1
       155: 3q+1
       156: 3q+1
       157: 3q+1
       158: 3q+1
       159: 3q+1
       160: 3q+1
       161: 3q+1
       162: 3q+1
       163: q+1
       164: q+1
       165: 3q+1
       166: 3q+1
       167: 3q+1
       168: q+1
       169: q+1
       170: 3q+1
       171: q+1
       172: q+1
       173: 3q+1
       174: 3q+1
       175: 2q+1
       176: 3q+1
       177: 2q^2+3q+1
       178: 3q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: q+1
       183: 3q+1
       184: 3q+1
       185: 3q+1
       186: 3q+1
       187: 3q+1
       188: 3q+1
       189: 2q+1
       190: 3q+1
       191: 3q+1
       192: 3q+1
       193: q+1
       194: q+1
       195: 3q+1
       196: 2q+1
       197: 2q+1
       198: 3q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 2q+1
       227: 1
       228: 3q+1
       229: 3q+1
       230: 3q+1
       231: 3q+1
       232: 3q+1
       233: 3q+1
       234: 3q+1
       235: 2q+1
       236: 3q+1
       237: 3q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 3q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 3q+1
       254: q+1
       255: 1
       256: 2q+1
       257: 2q+1
       258: 3q+1
       259: 3q+1
       260: 3q+1
       261: 3q+1
       262: 3q+1
       263: 3q+1
       264: 3q+1
       265: 2q+1
       266: 3q+1
       267: 3q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 3q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 3q+1
       284: q+1
       285: 1
       286: 2q+1
       287: 2q+1
       288: 3q+1
       289: 3q+1
       290: 3q+1
       291: 3q+1
       292: 3q+1
       293: 3q+1
       294: 3q+1
       295: 3q+1
       296: q+1
       297: q+1
       298: 3q+1
       299: 3q+1
       300: 3q+1
       301: q+1
       302: q+1
       303: 3q+1
       304: q+1
       305: q+1
       306: 3q+1
       307: 3q+1
       308: 2q+1
       309: 2q+1
       310: 2q+1
       311: 3q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: 2q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 2q+1
       357: 3q+1
       358: 3q+1
       359: 3q+1
       360: q+1
       361: q+1
       362: 3q+1
       363: 2q+1
       364: 2q+1
       365: 3q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 2q+1
       394: 1
       395: 2q+1
       396: 3q+1
       397: 3q+1
       398: 3q+1
       399: q+1
       400: q+1
       401: 3q+1
       402: 2q+1
       403: 2q+1
       404: 3q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 2q+1
       433: 1
       434: 3q+1
       435: 3q+1
       436: 3q+1
       437: 3q+1
       438: 3q+1
       439: 3q+1
       440: 3q+1
       441: 2q+1
       442: 3q+1
       443: 3q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 3q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 3q+1
       460: q+1
       461: 1
       462: 2q+1
       463: 2q+1
       465: 2q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 2q+1
       517: 2q+1
       518: 3q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: 2q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 2q+1
       564: 2q+1
       565: 3q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: 2q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 2q+1
       611: 3q+1
       612: 3q+1
       613: 3q+1
       614: q+1
       615: q+1
       616: 3q+1
       617: 2q+1
       618: 2q+1
       619: 3q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: 2q+1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: 2q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 2q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 2q+1
       808: 2q+1
       809: 3q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: 2q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       872: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       895: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: 2q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1095: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1131: 1
      1138: 1
      1141: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1183: 1
      1190: 1
      1193: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1276: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1339: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1386: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1422: 1
      1429: 1
      1432: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1491: 1
      1530: 1
      1566: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1593: 1
      1697: 1

1698:    0: q^4+4q^3+11q^2+6q+1
         1: 2q^3+10q^2+6q+1
         2: q^4+4q^3+11q^2+6q+1
         3: q^4+4q^3+11q^2+6q+1
         4: q^4+4q^3+11q^2+6q+1
         5: q^4+4q^3+11q^2+6q+1
         6: q^3+8q^2+6q+1
         7: 2q^3+10q^2+6q+1
         8: q^4+4q^3+11q^2+6q+1
         9: 2q^3+10q^2+6q+1
        10: 2q^3+7q^2+6q+1
        11: 2q^3+7q^2+6q+1
        12: 2q^3+7q^2+6q+1
        13: 2q^3+10q^2+6q+1
        14: q^4+4q^3+11q^2+6q+1
        15: q^4+4q^3+11q^2+6q+1
        16: 2q^3+10q^2+6q+1
        17: q^4+4q^3+11q^2+6q+1
        18: q^4+4q^3+11q^2+6q+1
        19: q^4+4q^3+11q^2+6q+1
        20: q^3+8q^2+6q+1
        21: q^3+8q^2+6q+1
        22: 2q^3+10q^2+6q+1
        23: 2q^3+7q^2+6q+1
        24: 2q^3+7q^2+6q+1
        25: 4q^2+6q+1
        26: 3q^2+4q+1
        27: 2q^3+7q^2+6q+1
        28: q^3+6q^2+6q+1
        29: q^3+4q^2+6q+1
        30: q^3+6q^2+6q+1
        31: q^3+4q^2+6q+1
        32: 4q^2+6q+1
        33: q^3+8q^2+6q+1
        34: 2q^3+10q^2+6q+1
        35: q^4+4q^3+11q^2+6q+1
        36: 2q^3+10q^2+6q+1
        37: 2q^3+7q^2+6q+1
        38: 2q^3+7q^2+6q+1
        39: 2q^3+7q^2+6q+1
        40: q^3+8q^2+6q+1
        41: 2q^3+10q^2+6q+1
        42: q^4+4q^3+11q^2+6q+1
        43: 2q^3+10q^2+6q+1
        44: 2q^3+7q^2+6q+1
        45: 2q^3+7q^2+6q+1
        46: 2q^3+7q^2+6q+1
        47: 2q^3+10q^2+6q+1
        48: q^4+4q^3+11q^2+6q+1
        49: q^4+4q^3+11q^2+6q+1
        50: 3q^2+4q+1
        51: 3q^2+4q+1
        52: q^3+8q^2+6q+1
        53: 4q^2+6q+1
        54: q^3+6q^2+6q+1
        55: q^3+6q^2+6q+1
        56: 4q^2+6q+1
        57: 4q^2+6q+1
        58: q^2+4q+1
        59: 3q^2+4q+1
        60: q^3+4q^2+6q+1
        61: q^3+4q^2+6q+1
        62: 2q^2+6q+1
        63: q^2+4q+1
        64: q^3+4q^2+6q+1
        65: 2q^2+6q+1
        66: q^2+4q+1
        67: q^3+4q^2+6q+1
        68: 3q^2+6q+1
        69: 2q^2+6q+1
        70: 4q^2+6q+1
        71: q^3+8q^2+6q+1
        72: q^3+8q^2+6q+1
        73: 2q^3+10q^2+6q+1
        74: 2q^3+7q^2+6q+1
        75: 2q^3+7q^2+6q+1
        76: 4q^2+6q+1
        77: 3q^2+4q+1
        78: 2q^3+7q^2+6q+1
        79: q^3+6q^2+6q+1
        80: q^3+4q^2+6q+1
        81: q^3+6q^2+6q+1
        82: q^3+4q^2+6q+1
        83: 4q^2+6q+1
        84: q^3+8q^2+6q+1
        85: q^3+8q^2+6q+1
        86: 2q^3+10q^2+6q+1
        87: 2q^3+7q^2+6q+1
        88: 2q^3+7q^2+6q+1
        89: 4q^2+6q+1
        90: 3q^2+4q+1
        91: 2q^3+7q^2+6q+1
        92: q^3+6q^2+6q+1
        93: q^3+4q^2+6q+1
        94: q^3+6q^2+6q+1
        95: q^3+4q^2+6q+1
        96: 4q^2+6q+1
        97: q^3+8q^2+6q+1
        98: 2q^3+10q^2+6q+1
        99: q^4+4q^3+11q^2+6q+1
       100: 2q^3+10q^2+6q+1
       101: 2q^3+7q^2+6q+1
       102: 2q^3+7q^2+6q+1
       103: 2q^3+7q^2+6q+1
       104: 3q+1
       105: 3q^2+4q+1
       106: 3q^2+4q+1
       107: 4q^2+6q+1
       108: 2q^2+6q+1
       109: 2q^2+6q+1
       110: 3q^2+6q+1
       111: 4q^2+6q+1
       112: q^2+4q+1
       113: q^2+4q+1
       114: q^2+4q+1
       115: q^2+4q+1
       116: q^2+4q+1
       117: q^2+4q+1
       118: 2q^2+6q+1
       119: 2q^2+6q+1
       120: 4q+1
       121: q^2+4q+1
       122: q^3+4q^2+6q+1
       123: q^2+3q+1
       124: 2q^2+6q+1
       125: 4q+1
       126: q^2+4q+1
       127: q^2+3q+1
       128: q^3+4q^2+6q+1
       129: q^2+6q+1
       130: 4q+1
       131: 2q^2+6q+1
       132: 3q^2+6q+1
       133: 3q+1
       134: 3q^2+4q+1
       135: 3q^2+4q+1
       136: q^3+8q^2+6q+1
       137: 4q^2+6q+1
       138: q^3+6q^2+6q+1
       139: q^3+6q^2+6q+1
       140: 4q^2+6q+1
       141: 4q^2+6q+1
       142: q^2+4q+1
       143: 3q^2+4q+1
       144: q^3+4q^2+6q+1
       145: q^3+4q^2+6q+1
       146: 2q^2+6q+1
       147: q^2+4q+1
       148: q^3+4q^2+6q+1
       149: 2q^2+6q+1
       150: q^2+4q+1
       151: q^3+4q^2+6q+1
       152: 3q^2+6q+1
       153: 2q^2+6q+1
       154: 4q^2+6q+1
       155: 3q^2+4q+1
       156: 3q^2+4q+1
       157: q^3+8q^2+6q+1
       158: 4q^2+6q+1
       159: q^3+6q^2+6q+1
       160: q^3+6q^2+6q+1
       161: 4q^2+6q+1
       162: 4q^2+6q+1
       163: q^2+4q+1
       164: 3q^2+4q+1
       165: q^3+4q^2+6q+1
       166: q^3+4q^2+6q+1
       167: 2q^2+6q+1
       168: q^2+4q+1
       169: q^3+4q^2+6q+1
       170: 2q^2+6q+1
       171: q^2+4q+1
       172: q^3+4q^2+6q+1
       173: 3q^2+6q+1
       174: 2q^2+6q+1
       175: 4q^2+6q+1
       176: q^3+8q^2+6q+1
       177: q^3+8q^2+6q+1
       178: 2q^3+10q^2+6q+1
       179: 2q^3+7q^2+6q+1
       180: 2q^3+7q^2+6q+1
       181: 4q^2+6q+1
       182: 3q^2+4q+1
       183: 2q^3+7q^2+6q+1
       184: q^3+6q^2+6q+1
       185: q^3+4q^2+6q+1
       186: q^3+6q^2+6q+1
       187: q^3+4q^2+6q+1
       188: 4q^2+6q+1
       189: 3q+1
       190: 3q+1
       191: q^2+4q+1
       192: q^2+4q+1
       193: 2q^2+6q+1
       194: 2q^2+6q+1
       195: q^2+6q+1
       196: 3q^2+6q+1
       197: 3q+1
       198: 3q+1
       199: 2q+1
       200: 2q+1
       201: q^2+4q+1
       202: 4q+1
       203: 4q+1
       204: 4q+1
       205: 2q^2+6q+1
       206: q^2+4q+1
       207: 2q+1
       208: 4q+1
       209: 2q+1
       210: q^2+4q+1
       211: 2q+1
       212: q^2+3q+1
       213: 2q+1
       214: q^2+4q+1
       215: 4q+1
       216: 2q+1
       217: 2q+1
       218: q^2+4q+1
       219: q^2+3q+1
       220: q^2+6q+1
       221: 4q+1
       222: 4q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: 3q+1
       227: 3q+1
       228: 3q+1
       229: 3q^2+4q+1
       230: 3q^2+4q+1
       231: 4q^2+6q+1
       232: 2q^2+6q+1
       233: 2q^2+6q+1
       234: 3q^2+6q+1
       235: 4q^2+6q+1
       236: q^2+4q+1
       237: q^2+4q+1
       238: q^2+4q+1
       239: q^2+4q+1
       240: q^2+4q+1
       241: q^2+4q+1
       242: 2q^2+6q+1
       243: 2q^2+6q+1
       244: 4q+1
       245: q^2+4q+1
       246: q^3+4q^2+6q+1
       247: q^2+3q+1
       248: 2q^2+6q+1
       249: 4q+1
       250: q^2+4q+1
       251: q^2+3q+1
       252: q^3+4q^2+6q+1
       253: q^2+6q+1
       254: 4q+1
       255: 2q^2+6q+1
       256: 3q^2+6q+1
       257: 3q+1
       258: 3q+1
       259: 3q^2+4q+1
       260: 3q^2+4q+1
       261: 4q^2+6q+1
       262: 2q^2+6q+1
       263: 2q^2+6q+1
       264: 3q^2+6q+1
       265: 4q^2+6q+1
       266: q^2+4q+1
       267: q^2+4q+1
       268: q^2+4q+1
       269: q^2+4q+1
       270: q^2+4q+1
       271: q^2+4q+1
       272: 2q^2+6q+1
       273: 2q^2+6q+1
       274: 4q+1
       275: q^2+4q+1
       276: q^3+4q^2+6q+1
       277: q^2+3q+1
       278: 2q^2+6q+1
       279: 4q+1
       280: q^2+4q+1
       281: q^2+3q+1
       282: q^3+4q^2+6q+1
       283: q^2+6q+1
       284: 4q+1
       285: 2q^2+6q+1
       286: 3q^2+6q+1
       287: 3q+1
       288: 3q^2+4q+1
       289: 3q^2+4q+1
       290: q^3+8q^2+6q+1
       291: 4q^2+6q+1
       292: q^3+6q^2+6q+1
       293: q^3+6q^2+6q+1
       294: 4q^2+6q+1
       295: 4q^2+6q+1
       296: q^2+4q+1
       297: 3q^2+4q+1
       298: q^3+4q^2+6q+1
       299: q^3+4q^2+6q+1
       300: 2q^2+6q+1
       301: q^2+4q+1
       302: q^3+4q^2+6q+1
       303: 2q^2+6q+1
       304: q^2+4q+1
       305: q^3+4q^2+6q+1
       306: 3q^2+6q+1
       307: 2q^2+6q+1
       308: 4q^2+6q+1
       310: 3q+1
       311: 3q+1
       312: q^2+4q+1
       313: 2q+1
       314: 2q+1
       315: q^2+4q+1
       316: q^2+6q+1
       317: 3q+1
       319: 3q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: 4q+1
       324: 4q+1
       325: 4q+1
       326: 4q+1
       327: 3q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: 2q+1
       335: q^2+3q+1
       336: q+1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: 2q+1
       343: q^2+3q+1
       344: 2q+1
       345: 2q+1
       346: 4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: 3q+1
       354: q+1
       355: q+1
       356: 3q+1
       357: 3q+1
       358: q^2+4q+1
       359: q^2+4q+1
       360: 2q^2+6q+1
       361: 2q^2+6q+1
       362: q^2+6q+1
       363: 3q^2+6q+1
       364: 3q+1
       365: 3q+1
       366: 2q+1
       367: 2q+1
       368: q^2+4q+1
       369: 4q+1
       370: 4q+1
       371: 4q+1
       372: 2q^2+6q+1
       373: q^2+4q+1
       374: 2q+1
       375: 4q+1
       376: 2q+1
       377: q^2+4q+1
       378: 2q+1
       379: q^2+3q+1
       380: 2q+1
       381: q^2+4q+1
       382: 4q+1
       383: 2q+1
       384: 2q+1
       385: q^2+4q+1
       386: q^2+3q+1
       387: q^2+6q+1
       388: 4q+1
       389: 4q+1
       390: q^2+3q+1
       391: q^2+3q+1
       392: 3q+1
       394: 3q+1
       395: 3q+1
       396: 3q+1
       397: q^2+4q+1
       398: q^2+4q+1
       399: 2q^2+6q+1
       400: 2q^2+6q+1
       401: q^2+6q+1
       402: 3q^2+6q+1
       403: 3q+1
       404: 3q+1
       405: 2q+1
       406: 2q+1
       407: q^2+4q+1
       408: 4q+1
       409: 4q+1
       410: 4q+1
       411: 2q^2+6q+1
       412: q^2+4q+1
       413: 2q+1
       414: 4q+1
       415: 2q+1
       416: q^2+4q+1
       417: 2q+1
       418: q^2+3q+1
       419: 2q+1
       420: q^2+4q+1
       421: 4q+1
       422: 2q+1
       423: 2q+1
       424: q^2+4q+1
       425: q^2+3q+1
       426: q^2+6q+1
       427: 4q+1
       428: 4q+1
       429: q^2+3q+1
       430: q^2+3q+1
       431: 3q+1
       433: 3q+1
       434: 3q+1
       435: 3q^2+4q+1
       436: 3q^2+4q+1
       437: 4q^2+6q+1
       438: 2q^2+6q+1
       439: 2q^2+6q+1
       440: 3q^2+6q+1
       441: 4q^2+6q+1
       442: q^2+4q+1
       443: q^2+4q+1
       444: q^2+4q+1
       445: q^2+4q+1
       446: q^2+4q+1
       447: q^2+4q+1
       448: 2q^2+6q+1
       449: 2q^2+6q+1
       450: 4q+1
       451: q^2+4q+1
       452: q^3+4q^2+6q+1
       453: q^2+3q+1
       454: 2q^2+6q+1
       455: 4q+1
       456: q^2+4q+1
       457: q^2+3q+1
       458: q^3+4q^2+6q+1
       459: q^2+6q+1
       460: 4q+1
       461: 2q^2+6q+1
       462: 3q^2+6q+1
       463: 3q+1
       466: 3q+1
       467: q+1
       468: q+1
       469: 2q+1
       470: 2q+1
       471: 3q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 4q+1
       481: q+1
       483: q+1
       484: 1
       485: q+1
       486: 1
       487: 2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: q+1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: 2q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       515: 1
       517: 3q+1
       518: 3q+1
       519: q^2+4q+1
       520: 2q+1
       521: 2q+1
       522: q^2+4q+1
       523: q^2+6q+1
       524: 3q+1
       526: 3q+1
       527: q+1
       528: 2q+1
       529: 2q+1
       530: 4q+1
       531: 4q+1
       532: 4q+1
       533: 4q+1
       534: 3q+1
       535: q+1
       536: 2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: 2q+1
       542: q^2+3q+1
       543: q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: 2q+1
       550: q^2+3q+1
       551: 2q+1
       552: 2q+1
       553: 4q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: q+1
       558: 3q+1
       561: q+1
       562: q+1
       564: 3q+1
       565: 3q+1
       566: q^2+4q+1
       567: 2q+1
       568: 2q+1
       569: q^2+4q+1
       570: q^2+6q+1
       571: 3q+1
       573: 3q+1
       574: q+1
       575: 2q+1
       576: 2q+1
       577: 4q+1
       578: 4q+1
       579: 4q+1
       580: 4q+1
       581: 3q+1
       582: q+1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: 2q+1
       589: q^2+3q+1
       590: q+1
       591: q+1
       592: 2q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       597: q^2+3q+1
       598: 2q+1
       599: 2q+1
       600: 4q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: q+1
       605: 3q+1
       608: q+1
       609: q+1
       610: 3q+1
       611: 3q+1
       612: q^2+4q+1
       613: q^2+4q+1
       614: 2q^2+6q+1
       615: 2q^2+6q+1
       616: q^2+6q+1
       617: 3q^2+6q+1
       618: 3q+1
       619: 3q+1
       620: 2q+1
       621: 2q+1
       622: q^2+4q+1
       623: 4q+1
       624: 4q+1
       625: 4q+1
       626: 2q^2+6q+1
       627: q^2+4q+1
       628: 2q+1
       629: 4q+1
       630: 2q+1
       631: q^2+4q+1
       632: 2q+1
       633: q^2+3q+1
       634: 2q+1
       635: q^2+4q+1
       636: 4q+1
       637: 2q+1
       638: 2q+1
       639: q^2+4q+1
       640: q^2+3q+1
       641: q^2+6q+1
       642: 4q+1
       643: 4q+1
       644: q^2+3q+1
       645: q^2+3q+1
       646: 3q+1
       648: 3q+1
       651: q+1
       652: q+1
       653: 1
       654: q+1
       655: q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: q+1
       674: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: q+1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: 3q+1
       706: q+1
       707: q+1
       708: 2q+1
       709: 2q+1
       710: 3q+1
       713: q+1
       714: q+1
       715: 2q+1
       716: q+1
       717: q+1
       718: 2q+1
       719: 4q+1
       720: q+1
       722: q+1
       723: 1
       724: q+1
       725: 1
       726: 2q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       731: q+1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: 2q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: 1
       741: q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: q+1
       754: 1
       757: 3q+1
       758: q+1
       759: q+1
       760: 2q+1
       761: 2q+1
       762: 3q+1
       765: q+1
       766: q+1
       767: 2q+1
       768: q+1
       769: q+1
       770: 2q+1
       771: 4q+1
       772: q+1
       774: q+1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: q+1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: 2q+1
       789: q+1
       790: 2q+1
       791: q+1
       792: 1
       793: q+1
       794: q+1
       795: q+1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: q+1
       806: 1
       808: 3q+1
       809: 3q+1
       810: q^2+4q+1
       811: 2q+1
       812: 2q+1
       813: q^2+4q+1
       814: q^2+6q+1
       815: 3q+1
       817: 3q+1
       818: q+1
       819: 2q+1
       820: 2q+1
       821: 4q+1
       822: 4q+1
       823: 4q+1
       824: 4q+1
       825: 3q+1
       826: q+1
       827: 2q+1
       828: q+1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: 2q+1
       833: q^2+3q+1
       834: q+1
       835: q+1
       836: 2q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: 2q+1
       841: q^2+3q+1
       842: 2q+1
       843: 2q+1
       844: 4q+1
       845: q+1
       846: 2q+1
       847: 2q+1
       848: q+1
       849: 3q+1
       852: q+1
       853: q+1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       875: 1
       876: 1
       880: 1
       882: 1
       883: 1
       885: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: q+1
       909: q+1
       910: 1
       911: q+1
       912: q+1
       916: q+1
       917: 1
       918: 1
       919: q+1
       920: q+1
       921: q+1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: q+1
       931: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: q+1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       959: 1
       962: q+1
       963: q+1
       964: 1
       965: q+1
       966: q+1
       970: q+1
       971: 1
       972: 1
       973: q+1
       974: q+1
       975: q+1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: q+1
       985: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: q+1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1013: 1
      1016: 3q+1
      1017: q+1
      1018: q+1
      1019: 2q+1
      1020: 2q+1
      1021: 3q+1
      1024: q+1
      1025: q+1
      1026: 2q+1
      1027: q+1
      1028: q+1
      1029: 2q+1
      1030: 4q+1
      1031: q+1
      1033: q+1
      1034: 1
      1035: q+1
      1036: 1
      1037: 2q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1042: q+1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: 2q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1051: 1
      1052: q+1
      1053: q+1
      1054: q+1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: q+1
      1065: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1084: 1
      1089: 1
      1091: 1
      1096: 1
      1101: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1168: 1
      1169: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1219: q+1
      1220: q+1
      1221: 1
      1222: q+1
      1223: q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: q+1
      1231: q+1
      1232: q+1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: q+1
      1242: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: q+1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1270: 1
      1277: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1328: 1
      1333: 1
      1335: 1
      1340: 1
      1345: 1
      1360: 1
      1365: 1
      1366: 1
      1371: 1
      1375: 1
      1380: 1
      1382: 1
      1387: 1
      1392: 1
      1407: 1
      1408: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1455: 1
      1492: 1
      1531: 1
      1567: 1
      1572: 1
      1573: 1
      1578: 1
      1582: 1
      1587: 1
      1589: 1
      1594: 1
      1599: 1
      1698: 1

1699:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 2q^2+3q+1
         3: 3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 3q+1
         9: 3q+1
        10: 3q+1
        11: 3q+1
        12: 3q+1
        13: 2q^2+3q+1
        14: 2q^2+3q+1
        15: 3q+1
        16: 2q^2+3q+1
        17: 2q^2+3q+1
        18: 3q+1
        19: 2q^2+3q+1
        20: q+1
        21: 2q^2+3q+1
        22: 3q+1
        23: 3q+1
        24: 3q+1
        25: 3q+1
        26: 3q+1
        27: 3q+1
        28: 3q+1
        29: 3q+1
        30: 3q+1
        31: 3q+1
        32: 3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 3q+1
        36: 3q+1
        37: 3q+1
        38: 3q+1
        39: 3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 3q+1
        43: 3q+1
        44: 3q+1
        45: 3q+1
        46: 3q+1
        47: 2q^2+3q+1
        48: 2q^2+3q+1
        49: 3q+1
        50: q+1
        51: q+1
        52: q+1
        53: 3q+1
        54: 3q+1
        55: 3q+1
        56: 3q+1
        57: q+1
        58: 3q+1
        59: 3q+1
        60: 3q+1
        61: 3q+1
        62: 3q+1
        63: 3q+1
        64: q+1
        65: 3q+1
        66: 3q+1
        67: q+1
        68: 3q+1
        69: 3q+1
        70: 2q+1
        71: q+1
        72: 2q^2+3q+1
        73: 3q+1
        74: 3q+1
        75: 3q+1
        76: 3q+1
        77: 3q+1
        78: 3q+1
        79: 3q+1
        80: 3q+1
        81: 3q+1
        82: 3q+1
        83: 3q+1
        84: q+1
        85: 2q^2+3q+1
        86: 3q+1
        87: 3q+1
        88: 3q+1
        89: 3q+1
        90: 3q+1
        91: 3q+1
        92: 3q+1
        93: 3q+1
        94: 3q+1
        95: 3q+1
        96: 3q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: 3q+1
       102: 3q+1
       103: 3q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 3q+1
       109: 3q+1
       110: 3q+1
       111: 2q+1
       112: q+1
       113: q+1
       114: q+1
       115: 3q+1
       116: 3q+1
       117: 3q+1
       118: 3q+1
       119: 1
       120: 3q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: 3q+1
       126: q+1
       127: q+1
       128: q+1
       129: 3q+1
       130: 3q+1
       131: 1
       132: 2q+1
       133: 2q+1
       134: q+1
       135: q+1
       136: q+1
       137: 3q+1
       138: 3q+1
       139: 3q+1
       140: 3q+1
       141: q+1
       142: 3q+1
       143: 3q+1
       144: 3q+1
       145: 3q+1
       146: 3q+1
       147: 3q+1
       148: q+1
       149: 3q+1
       150: 3q+1
       151: q+1
       152: 3q+1
       153: 3q+1
       154: 2q+1
       155: q+1
       156: q+1
       157: q+1
       158: 3q+1
       159: 3q+1
       160: 3q+1
       161: 3q+1
       162: q+1
       163: 3q+1
       164: 3q+1
       165: 3q+1
       166: 3q+1
       167: 3q+1
       168: 3q+1
       169: q+1
       170: 3q+1
       171: 3q+1
       172: q+1
       173: 3q+1
       174: 3q+1
       175: 2q+1
       176: q+1
       177: 2q^2+3q+1
       178: 3q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       183: 3q+1
       184: 3q+1
       185: 3q+1
       186: 3q+1
       187: 3q+1
       188: 3q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: 3q+1
       196: 2q+1
       197: 2q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: 3q+1
       203: 3q+1
       204: 3q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 3q+1
       222: 1
       223: 1
       224: 1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 3q+1
       233: 3q+1
       234: 3q+1
       235: 2q+1
       236: q+1
       237: q+1
       238: q+1
       239: 3q+1
       240: 3q+1
       241: 3q+1
       242: 3q+1
       243: 1
       244: 3q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: 3q+1
       250: q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: 1
       256: 2q+1
       257: 2q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 3q+1
       263: 3q+1
       264: 3q+1
       265: 2q+1
       266: q+1
       267: q+1
       268: q+1
       269: 3q+1
       270: 3q+1
       271: 3q+1
       272: 3q+1
       273: 1
       274: 3q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: 3q+1
       280: q+1
       281: q+1
       282: q+1
       283: 3q+1
       284: 3q+1
       285: 1
       286: 2q+1
       287: 2q+1
       288: q+1
       289: q+1
       290: q+1
       291: 3q+1
       292: 3q+1
       293: 3q+1
       294: 3q+1
       295: q+1
       296: 3q+1
       297: 3q+1
       298: 3q+1
       299: 3q+1
       300: 3q+1
       301: 3q+1
       302: q+1
       303: 3q+1
       304: 3q+1
       305: q+1
       306: 3q+1
       307: 3q+1
       308: 2q+1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 2q+1
       318: 2q+1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: 3q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 2q+1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: 1
       362: 3q+1
       363: 2q+1
       364: 2q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 3q+1
       370: 3q+1
       371: 3q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 3q+1
       389: 1
       390: 1
       391: 1
       392: 2q+1
       393: 2q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       400: 1
       401: 3q+1
       402: 2q+1
       403: 2q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: 3q+1
       409: 3q+1
       410: 3q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 3q+1
       428: 1
       429: 1
       430: 1
       431: 2q+1
       432: 2q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 3q+1
       439: 3q+1
       440: 3q+1
       441: 2q+1
       442: q+1
       443: q+1
       444: q+1
       445: 3q+1
       446: 3q+1
       447: 3q+1
       448: 3q+1
       449: 1
       450: 3q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: 3q+1
       456: q+1
       457: q+1
       458: q+1
       459: 3q+1
       460: 3q+1
       461: 1
       462: 2q+1
       463: 2q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 2q+1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: q+1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 2q+1
       525: 2q+1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: 3q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 2q+1
       560: 1
       561: 1
       562: 1
       565: q+1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 2q+1
       572: 2q+1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: 3q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 2q+1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: 1
       616: 3q+1
       617: 2q+1
       618: 2q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: 3q+1
       624: 3q+1
       625: 3q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 3q+1
       643: 1
       644: 1
       645: 1
       646: 2q+1
       647: 2q+1
       648: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 2q+1
       714: q+1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: q+1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 2q+1
       766: q+1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: q+1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 2q+1
       816: 2q+1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: 3q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 2q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: 1
       877: 1
       882: 1
       886: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       935: 1
       938: 1
       939: 1
       941: 1
       942: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       979: 1
       980: 1
       981: 1
       985: 1
       986: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 2q+1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1102: 1
      1105: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1136: 1
      1141: 1
      1145: 1
      1148: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1183: 1
      1188: 1
      1193: 1
      1197: 1
      1200: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1278: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1346: 1
      1349: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1393: 1
      1396: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1422: 1
      1427: 1
      1432: 1
      1436: 1
      1439: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1493: 1
      1532: 1
      1568: 1
      1573: 1
      1574: 1
      1575: 1
      1600: 1
      1603: 1
      1699: 1

1700:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: 1
        24: q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q+1
        29: q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 1
        51: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: 1
        55: q+1
        56: 1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 1
        75: q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q+1
        80: q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: 1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q+1
        93: q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q+1
       103: q^2+2q+1
       104: 1
       105: 1
       106: q+1
       107: q^2+2q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: 1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 1
       139: q+1
       140: 1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: 1
       160: q+1
       161: 1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: 1
       180: q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q+1
       185: q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q^2+2q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q^2+2q+1
       216: q^2+2q+1
       218: q+1
       220: q+1
       221: q+1
       222: q+1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: q^2+2q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: 1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q^2+2q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: 1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: 1
       278: q^2+2q+1
       279: q^2+2q+1
       280: q^2+2q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: 1
       293: q+1
       294: 1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: q+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: q^2+2q+1
       341: q+1
       345: 1
       346: q+1
       347: q+1
       349: 1
       351: q+1
       352: q+1
       353: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q^2+2q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: q+1
       376: q+1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q^2+2q+1
       383: q^2+2q+1
       385: q+1
       387: q+1
       388: q+1
       389: q+1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q^2+2q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       412: 1
       413: 1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q^2+2q+1
       422: q^2+2q+1
       424: q+1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: 1
       436: q+1
       437: q^2+2q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: 1
       454: q^2+2q+1
       455: q^2+2q+1
       456: q^2+2q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: q+1
       497: q+1
       503: 1
       504: q+1
       506: 1
       510: 1
       511: q+1
       512: q+1
       514: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: q^2+2q+1
       548: q+1
       552: 1
       553: q+1
       554: q+1
       556: 1
       558: q+1
       559: q+1
       560: q+1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: q+1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: q+1
       593: q^2+2q+1
       595: q+1
       599: 1
       600: q+1
       601: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q^2+2q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: 1
       629: q+1
       630: q+1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q^2+2q+1
       637: q^2+2q+1
       639: q+1
       641: q+1
       642: q+1
       643: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: q+1
       689: 1
       691: 1
       697: 1
       698: q+1
       700: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: q+1
       736: q+1
       742: 1
       743: q+1
       745: 1
       749: 1
       750: q+1
       751: q+1
       753: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: q+1
       788: q+1
       794: 1
       795: q+1
       797: 1
       801: 1
       802: q+1
       803: q+1
       805: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       836: q+1
       837: q^2+2q+1
       839: q+1
       843: 1
       844: q+1
       845: q+1
       847: 1
       849: q+1
       850: q+1
       851: q+1
       853: 1
       854: 1
       861: 1
       862: 1
       868: 1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       906: 1
       907: 1
       913: 1
       914: 1
       915: 1
       916: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       932: 1
       939: q+1
       946: 1
       948: 1
       954: 1
       955: q+1
       957: 1
       960: 1
       961: 1
       967: 1
       968: 1
       969: 1
       970: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: q+1
      1000: 1
      1002: 1
      1008: 1
      1009: q+1
      1011: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: q+1
      1047: q+1
      1053: 1
      1054: q+1
      1056: 1
      1060: 1
      1061: q+1
      1062: q+1
      1064: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1109: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1135: 1
      1136: 1
      1152: 1
      1159: 1
      1161: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1250: q+1
      1257: 1
      1259: 1
      1265: 1
      1266: q+1
      1268: 1
      1279: 1
      1315: 1
      1322: 1
      1323: 1
      1329: 1
      1353: 1
      1362: 1
      1369: 1
      1370: 1
      1376: 1
      1400: 1
      1404: 1
      1411: 1
      1412: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1426: 1
      1427: 1
      1443: 1
      1450: 1
      1452: 1
      1494: 1
      1533: 1
      1569: 1
      1576: 1
      1577: 1
      1583: 1
      1607: 1
      1700: 1

1701:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: 1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: 1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: 1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: 1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: 1
       126: 1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: 1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: 1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: 1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: 1
       216: 1
       218: 1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: 1
       250: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: 1
       305: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       341: 1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: 1
       383: 1
       385: 1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       497: 1
       503: 1
       504: 1
       506: 1
       510: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       548: 1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       648: 1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       682: 1
       689: 1
       691: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: 1
       736: 1
       742: 1
       743: 1
       745: 1
       749: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       853: 1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       893: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       939: 1
       946: 1
       948: 1
       961: 1
       962: 1
       966: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1152: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1204: 1
      1218: 1
      1219: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1250: 1
      1257: 1
      1259: 1
      1280: 1
      1316: 1
      1323: 1
      1324: 1
      1328: 1
      1363: 1
      1370: 1
      1371: 1
      1375: 1
      1405: 1
      1412: 1
      1413: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1443: 1
      1495: 1
      1534: 1
      1570: 1
      1577: 1
      1578: 1
      1582: 1
      1701: 1

1702:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: 3q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 3q^2+3q+1
        16: q^3+4q^2+3q+1
        17: q^3+4q^2+3q+1
        18: 3q^2+3q+1
        19: q^3+4q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: 2q^2+3q+1
        24: 2q+1
        25: 3q^2+3q+1
        26: q^2+2q+1
        27: 2q^2+3q+1
        28: 3q^2+3q+1
        29: 3q^2+3q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+4q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+3q+1
        37: 3q^2+3q+1
        38: 3q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+4q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q^2+3q+1
        43: 3q^2+3q+1
        44: 3q^2+3q+1
        45: 3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+4q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 3q^2+3q+1
        50: 2q^2+3q+1
        51: 2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: 2q+1
        56: 2q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q^2+3q+1
        61: 2q+1
        62: 3q^2+3q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+3q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        75: 2q+1
        76: 3q^2+3q+1
        77: q^2+2q+1
        78: 2q^2+3q+1
        79: 3q^2+3q+1
        80: 3q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: 2q^2+3q+1
        88: 2q+1
        89: 3q^2+3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: 3q^2+3q+1
        93: 3q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 3q^2+3q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: q^2+3q+1
       106: 2q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q^2+3q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q+1
       118: 2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+2q+1
       123: q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q+1
       127: q^2+2q+1
       128: q+1
       129: 2q^2+3q+1
       130: q^2+2q+1
       131: q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: 2q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q^2+3q+1
       145: 2q+1
       146: 3q^2+3q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+2q+1
       155: 2q^2+3q+1
       156: 2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: 2q^2+3q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q^2+3q+1
       166: 2q+1
       167: 3q^2+3q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q^2+3q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+2q+1
       176: 2q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+3q+1
       180: 2q+1
       181: 3q^2+3q+1
       182: q^2+2q+1
       183: 2q^2+3q+1
       184: 3q^2+3q+1
       185: 3q^2+3q+1
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: 2q^2+3q+1
       189: q+1
       190: 2q+1
       191: q^2+3q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: q+1
       204: q+1
       205: 1
       206: q^2+2q+1
       207: q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: q^2+2q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: q+1
       224: 1
       225: q^2+2q+1
       227: q+1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q^2+3q+1
       232: q^2+3q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q^2+3q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q+1
       242: 2q+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: 2q+1
       246: q^2+2q+1
       247: q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: 2q^2+3q+1
       254: q^2+2q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: q^2+3q+1
       260: 2q+1
       261: q^2+3q+1
       262: q^2+3q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q^2+3q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: 2q+1
       273: q^2+2q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q+1
       278: q^2+2q+1
       279: q^2+2q+1
       280: q+1
       281: q^2+2q+1
       282: q+1
       283: 2q^2+3q+1
       284: q^2+2q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q^2+3q+1
       289: 2q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: q^2+3q+1
       293: 2q+1
       294: 2q+1
       295: 2q^2+3q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q^2+3q+1
       299: 2q+1
       300: 3q^2+3q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: 2q^2+3q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: 2q^2+3q+1
       307: 2q^2+3q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: 2q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: 1
       356: q+1
       357: 2q+1
       358: q^2+3q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: q+1
       368: 2q+1
       369: 2q+1
       370: q+1
       371: q+1
       372: 1
       373: q^2+2q+1
       374: q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: q+1
       379: q+1
       380: q^2+2q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: 1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: q+1
       391: 1
       392: q^2+2q+1
       394: q+1
       395: q+1
       396: 2q+1
       397: q^2+3q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: q^2+2q+1
       413: q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: q+1
       419: q^2+2q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: q+1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: 1
       431: q^2+2q+1
       433: q+1
       434: 2q+1
       435: q^2+3q+1
       436: 2q+1
       437: q^2+3q+1
       438: q^2+3q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q^2+3q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: q+1
       448: 2q+1
       449: q^2+2q+1
       450: q^2+2q+1
       451: 2q+1
       452: q^2+2q+1
       453: q+1
       454: q^2+2q+1
       455: q^2+2q+1
       456: q+1
       457: q^2+2q+1
       458: q+1
       459: 2q^2+3q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: 1
       468: q+1
       469: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: q+1
       485: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: 2q+1
       529: q+1
       530: q+1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: 1
       546: q+1
       547: q+1
       548: 1
       549: 1
       550: 1
       551: q+1
       552: 1
       553: q+1
       554: q+1
       555: q+1
       556: 1
       557: 1
       558: q+1
       561: q+1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: q+1
       611: 2q+1
       612: q^2+3q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: q+1
       622: 2q+1
       623: 2q+1
       624: q+1
       625: q+1
       626: 1
       627: q^2+2q+1
       628: q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: q+1
       633: q+1
       634: q^2+2q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: q+1
       645: 1
       646: q^2+2q+1
       648: q+1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       707: q+1
       708: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: q+1
       724: 2q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: 1
       733: q+1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: q+1
       742: 1
       743: q+1
       744: q+1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       754: 1
       756: q+1
       757: 1
       759: q+1
       760: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: q+1
       776: 2q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: 2q+1
       820: q+1
       821: q+1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 2q+1
       828: q+1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       841: 1
       842: q+1
       843: 1
       844: q+1
       845: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       852: q+1
       853: 1
       856: 1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       907: 1
       909: 1
       911: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       943: 1
       944: 1
       945: q+1
       946: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: q+1
      1016: 1
      1018: q+1
      1019: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: q+1
      1035: 2q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: q+1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: q+1
      1053: 1
      1054: q+1
      1055: q+1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1065: 1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1095: 1
      1098: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1129: 1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1138: 1
      1141: 1
      1146: 1
      1147: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1190: 1
      1193: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1218: 1
      1220: 1
      1222: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1254: 1
      1255: 1
      1256: q+1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1281: 1
      1317: 1
      1323: 1
      1325: 1
      1327: 1
      1339: 1
      1342: 1
      1364: 1
      1370: 1
      1372: 1
      1374: 1
      1386: 1
      1389: 1
      1406: 1
      1412: 1
      1414: 1
      1416: 1
      1420: 1
      1421: 1
      1423: 1
      1424: 1
      1426: 1
      1429: 1
      1432: 1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1496: 1
      1535: 1
      1571: 1
      1577: 1
      1579: 1
      1581: 1
      1593: 1
      1596: 1
      1702: 1

1703:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       888: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       934: 1
       943: 1
       944: 1
       950: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1147: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1199: 1
      1219: 1
      1220: 1
      1221: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1245: 1
      1254: 1
      1255: 1
      1261: 1
      1282: 1
      1318: 1
      1324: 1
      1325: 1
      1326: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1407: 1
      1413: 1
      1414: 1
      1415: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1438: 1
      1497: 1
      1536: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1703: 1

1704:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: q+1
       566: 1
       567: 1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       678: 1
       681: 1
       682: 1
       684: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: 1
       759: q+1
       760: 1
       761: 1
       762: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: q+1
       810: 1
       811: 1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       882: 1
       889: 1
       892: 1
       893: 1
       895: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       935: 1
       938: 1
       939: 1
       941: 1
       944: 1
       945: 1
       946: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       964: 1
       965: 1
       966: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       989: 1
       992: 1
       993: 1
       995: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1017: 1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1098: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1141: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1193: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1221: 1
      1222: 1
      1223: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1283: 1
      1319: 1
      1326: 1
      1327: 1
      1328: 1
      1342: 1
      1366: 1
      1373: 1
      1374: 1
      1375: 1
      1389: 1
      1408: 1
      1415: 1
      1416: 1
      1417: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1432: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1498: 1
      1537: 1
      1573: 1
      1580: 1
      1581: 1
      1582: 1
      1596: 1
      1704: 1

1705:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       105: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 1
       120: 2q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       191: q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       199: q+1
       201: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 1
       206: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       229: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: 1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       312: 1
       314: q+1
       316: 1
       317: q+1
       318: q+1
       321: q+1
       323: 1
       324: q+1
       325: 2q+1
       326: 1
       327: 1
       329: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       337: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       358: q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       366: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       397: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       405: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       435: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q+1
       463: q+1
       469: 1
       471: 1
       472: q+1
       476: 1
       478: q+1
       480: 1
       481: 1
       482: 1
       485: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       494: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       519: 1
       521: q+1
       523: 1
       524: q+1
       525: q+1
       528: q+1
       530: 1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       544: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       566: 1
       568: q+1
       570: 1
       571: q+1
       572: q+1
       575: q+1
       577: 1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       591: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       612: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       620: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       654: 1
       656: 1
       662: 1
       664: 1
       665: 1
       669: 1
       671: 1
       673: 1
       674: 1
       675: 1
       681: q+1
       684: 1
       685: 1
       688: 1
       691: 1
       692: 1
       693: 1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       708: 1
       710: 1
       711: q+1
       715: 1
       717: q+1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       727: 1
       728: q+1
       729: 1
       730: 1
       733: q+1
       736: q+1
       737: q+1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       760: 1
       762: 1
       763: q+1
       767: 1
       769: q+1
       771: 1
       772: 1
       773: 1
       776: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       785: q+1
       788: q+1
       789: q+1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: q+1
       814: 1
       815: q+1
       816: q+1
       819: q+1
       821: 1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       835: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       859: 1
       866: 1
       868: 1
       874: 1
       876: 1
       877: 1
       886: 1
       892: 1
       895: 1
       896: 1
       899: 1
       902: 1
       903: 1
       911: 1
       913: 1
       919: 1
       921: 1
       922: 1
       926: 1
       928: 1
       930: 1
       931: 1
       932: 1
       938: q+1
       941: 1
       942: 1
       945: 1
       948: 1
       949: 1
       950: 1
       951: 1
       953: 1
       955: 1
       956: 1
       957: 1
       958: 1
       965: 1
       967: 1
       973: 1
       975: 1
       976: 1
       980: 1
       982: 1
       984: 1
       985: 1
       986: 1
       992: q+1
       995: 1
       996: 1
       999: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1019: 1
      1021: 1
      1022: q+1
      1026: 1
      1028: q+1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1044: q+1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1076: 1
      1083: 1
      1085: 1
      1102: 1
      1108: 1
      1118: 1
      1125: 1
      1127: 1
      1133: 1
      1135: 1
      1136: 1
      1145: 1
      1151: 1
      1154: 1
      1155: 1
      1158: 1
      1161: 1
      1162: 1
      1170: 1
      1177: 1
      1179: 1
      1185: 1
      1187: 1
      1188: 1
      1197: 1
      1203: 1
      1206: 1
      1207: 1
      1210: 1
      1213: 1
      1214: 1
      1222: 1
      1224: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1239: 1
      1241: 1
      1242: 1
      1243: 1
      1249: q+1
      1252: 1
      1253: 1
      1256: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1264: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1284: 1
      1320: 1
      1327: 1
      1329: 1
      1346: 1
      1352: 1
      1367: 1
      1374: 1
      1376: 1
      1393: 1
      1399: 1
      1409: 1
      1416: 1
      1418: 1
      1424: 1
      1426: 1
      1427: 1
      1436: 1
      1442: 1
      1445: 1
      1446: 1
      1449: 1
      1452: 1
      1453: 1
      1499: 1
      1538: 1
      1574: 1
      1581: 1
      1583: 1
      1600: 1
      1606: 1
      1705: 1

1706:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       216: q+1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       318: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: q+1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       383: q+1
       385: q+1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       422: q+1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       470: 1
       471: 1
       472: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       482: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: q+1
       497: q+1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       572: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: q+1
       593: q+1
       595: q+1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       637: q+1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       655: 1
       656: 1
       663: 1
       664: 1
       665: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: q+1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       709: 1
       710: 1
       711: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: q+1
       736: q+1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       761: 1
       762: 1
       763: 1
       768: 1
       770: q+1
       771: 1
       772: 1
       773: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: q+1
       788: q+1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: q+1
       837: q+1
       839: q+1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       860: 1
       867: 1
       868: 1
       875: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       912: 1
       913: 1
       920: 1
       921: 1
       922: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       939: q+1
       946: 1
       948: 1
       954: 1
       955: 1
       957: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: q+1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: q+1
      1047: q+1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1077: 1
      1084: 1
      1085: 1
      1109: 1
      1119: 1
      1126: 1
      1127: 1
      1134: 1
      1135: 1
      1136: 1
      1152: 1
      1159: 1
      1161: 1
      1171: 1
      1178: 1
      1179: 1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1223: 1
      1224: 1
      1231: 1
      1232: 1
      1233: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1250: q+1
      1257: 1
      1259: 1
      1265: 1
      1266: 1
      1268: 1
      1285: 1
      1321: 1
      1328: 1
      1329: 1
      1353: 1
      1368: 1
      1375: 1
      1376: 1
      1400: 1
      1410: 1
      1417: 1
      1418: 1
      1425: 1
      1426: 1
      1427: 1
      1443: 1
      1450: 1
      1452: 1
      1500: 1
      1539: 1
      1575: 1
      1582: 1
      1583: 1
      1607: 1
      1706: 1

1707:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: 1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: 1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q+1
        55: 1
        56: 1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q+1
        61: 1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: 1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: 1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: q^2+2q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q+1
       117: 1
       118: 1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 1
       140: 1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q+1
       145: 1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q+1
       160: 1
       161: 1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q+1
       166: 1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: 1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q^2+2q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: q^2+2q+1
       209: q^2+2q+1
       210: q+1
       213: 1
       214: 1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: q^2+2q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q^2+2q+1
       239: q^2+2q+1
       240: q+1
       241: 1
       242: 1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: q^2+2q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q+1
       271: 1
       272: 1
       273: q^2+2q+1
       274: q^2+2q+1
       275: q^2+2q+1
       276: q+1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q+1
       293: 1
       294: 1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q+1
       299: 1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: q+1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       329: q+1
       331: q^2+2q+1
       332: q+1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: q+1
       347: q+1
       348: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q^2+2q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q^2+2q+1
       376: q^2+2q+1
       377: q+1
       380: 1
       381: 1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q^2+2q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q^2+2q+1
       415: q^2+2q+1
       416: q+1
       419: 1
       420: 1
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q^2+2q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q^2+2q+1
       445: q^2+2q+1
       446: q+1
       447: 1
       448: 1
       449: q^2+2q+1
       450: q^2+2q+1
       451: q^2+2q+1
       452: q+1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: q+1
       479: 1
       480: 1
       481: 1
       482: 1
       485: q+1
       487: q+1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: q+1
       505: 1
       509: 1
       511: q+1
       512: q+1
       513: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       538: q^2+2q+1
       539: q+1
       543: 1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       554: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       583: q+1
       585: q^2+2q+1
       586: q+1
       590: 1
       591: 1
       592: 1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: q+1
       601: q+1
       602: 1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q^2+2q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q^2+2q+1
       630: q^2+2q+1
       631: q+1
       634: 1
       635: 1
       636: q+1
       637: q+1
       638: 1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       669: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: q+1
       699: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: q+1
       718: 1
       719: 1
       720: 1
       721: 1
       724: q+1
       726: q+1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: 1
       750: q+1
       751: q+1
       752: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       770: 1
       771: 1
       772: 1
       773: 1
       776: q+1
       778: q+1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: q+1
       796: 1
       800: 1
       802: q+1
       803: q+1
       804: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       829: q^2+2q+1
       830: q+1
       834: 1
       835: 1
       836: 1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: q+1
       845: q+1
       846: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       854: 1
       861: 1
       862: 1
       868: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       906: 1
       907: 1
       913: 1
       914: 1
       915: 1
       916: 1
       921: 1
       922: 1
       926: q+1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: q+1
       956: 1
       960: 1
       961: 1
       967: 1
       968: 1
       969: 1
       970: 1
       975: 1
       976: 1
       980: q+1
       987: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       996: 1
       999: 1
      1001: 1
      1007: 1
      1009: q+1
      1010: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: q+1
      1037: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: q+1
      1055: 1
      1059: 1
      1061: q+1
      1062: q+1
      1063: 1
      1071: 1
      1086: 1
      1087: 1
      1093: 1
      1106: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1189: 1
      1190: 1
      1191: 1
      1196: 1
      1197: 1
      1201: 1
      1210: 1
      1212: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1237: q+1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1256: 1
      1258: 1
      1264: 1
      1266: q+1
      1267: 1
      1286: 1
      1315: 1
      1330: 1
      1331: 1
      1337: 1
      1350: 1
      1362: 1
      1377: 1
      1378: 1
      1384: 1
      1397: 1
      1404: 1
      1411: 1
      1412: 1
      1418: 1
      1428: 1
      1429: 1
      1430: 1
      1435: 1
      1436: 1
      1440: 1
      1449: 1
      1451: 1
      1501: 1
      1540: 1
      1569: 1
      1584: 1
      1585: 1
      1591: 1
      1604: 1
      1707: 1

1708:    0: q^3+4q^2+3q+1
         1: q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: 3q^2+3q+1
         4: q^3+4q^2+3q+1
         5: q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 2q^2+3q+1
        12: 3q^2+3q+1
        13: q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 3q^2+3q+1
        16: q^3+4q^2+3q+1
        17: q^3+4q^2+3q+1
        18: 3q^2+3q+1
        19: q^3+4q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: 2q+1
        24: 2q^2+3q+1
        25: 3q^2+3q+1
        26: q^2+2q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: 3q^2+3q+1
        31: 3q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+4q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q^2+3q+1
        36: 3q^2+3q+1
        37: 3q^2+3q+1
        38: 2q^2+3q+1
        39: 3q^2+3q+1
        40: q^3+4q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q^2+3q+1
        43: 3q^2+3q+1
        44: 3q^2+3q+1
        45: 2q^2+3q+1
        46: 3q^2+3q+1
        47: q^3+4q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 3q^2+3q+1
        50: 2q+1
        51: 2q^2+3q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: 2q+1
        55: q^2+3q+1
        56: 2q+1
        57: 2q^2+3q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q+1
        61: 2q^2+3q+1
        62: 2q^2+3q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 3q^2+3q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: 2q+1
        75: 2q^2+3q+1
        76: 3q^2+3q+1
        77: q^2+2q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 3q^2+3q+1
        82: 3q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: 2q^2+3q+1
        89: 3q^2+3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 3q^2+3q+1
        95: 3q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 2q^2+3q+1
       103: 3q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: q^2+3q+1
       107: q^2+3q+1
       108: 2q+1
       109: q^2+3q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q^2+3q+1
       114: 2q+1
       115: 2q+1
       116: q+1
       117: 2q+1
       118: 2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q+1
       122: q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: 2q+1
       127: q+1
       128: q^2+2q+1
       129: 2q^2+3q+1
       130: q^2+2q+1
       131: q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q+1
       145: 2q^2+3q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 3q^2+3q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q^2+3q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: 2q+1
       160: q^2+3q+1
       161: 2q+1
       162: 2q^2+3q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 3q^2+3q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+2q+1
       176: 2q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: 2q+1
       180: 2q^2+3q+1
       181: 3q^2+3q+1
       182: q^2+2q+1
       183: 2q^2+3q+1
       184: 2q^2+3q+1
       185: 2q^2+3q+1
       186: 3q^2+3q+1
       187: 3q^2+3q+1
       188: 2q^2+3q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: q^2+3q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: q+1
       203: 2q+1
       204: q+1
       205: 1
       206: q+1
       207: q^2+2q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: q+1
       213: q+1
       214: q^2+2q+1
       215: 2q+1
       216: 2q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: q^2+2q+1
       222: q+1
       223: 1
       224: q+1
       225: q^2+2q+1
       227: q+1
       228: 2q+1
       229: 2q+1
       230: q^2+3q+1
       231: q^2+3q+1
       232: 2q+1
       233: q^2+3q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q^2+3q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: 2q+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: 2q+1
       251: q+1
       252: q^2+2q+1
       253: 2q^2+3q+1
       254: q^2+2q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q^2+3q+1
       262: 2q+1
       263: q^2+3q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q^2+3q+1
       268: 2q+1
       269: 2q+1
       270: q+1
       271: 2q+1
       272: 2q+1
       273: q^2+2q+1
       274: q^2+2q+1
       275: q+1
       276: q+1
       277: q^2+2q+1
       278: q^2+2q+1
       279: q^2+2q+1
       280: 2q+1
       281: q+1
       282: q^2+2q+1
       283: 2q^2+3q+1
       284: q^2+2q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q^2+3q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: 2q+1
       293: q^2+3q+1
       294: 2q+1
       295: 2q^2+3q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q+1
       299: 2q^2+3q+1
       300: 2q^2+3q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: 3q^2+3q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: 2q^2+3q+1
       307: 2q^2+3q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: 2q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q+1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       354: 1
       355: q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: q^2+3q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: q+1
       374: q^2+2q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: q+1
       380: q+1
       381: q^2+2q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: 1
       391: q+1
       392: q^2+2q+1
       394: q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: q^2+3q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: 2q+1
       407: 2q+1
       408: q+1
       409: 2q+1
       410: q+1
       411: 1
       412: q+1
       413: q^2+2q+1
       414: q+1
       415: q+1
       416: 1
       417: q+1
       418: q+1
       419: q+1
       420: q^2+2q+1
       421: 2q+1
       422: 2q+1
       423: q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: 1
       430: q+1
       431: q^2+2q+1
       433: q+1
       434: 2q+1
       435: 2q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: 2q+1
       439: q^2+3q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q^2+3q+1
       444: 2q+1
       445: 2q+1
       446: q+1
       447: 2q+1
       448: 2q+1
       449: q^2+2q+1
       450: q^2+2q+1
       451: q+1
       452: q+1
       453: q^2+2q+1
       454: q^2+2q+1
       455: q^2+2q+1
       456: 2q+1
       457: q+1
       458: q^2+2q+1
       459: 2q^2+3q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: 1
       467: q+1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: q+1
       576: 2q+1
       577: 1
       578: q+1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: q+1
       585: q+1
       586: 1
       587: q+1
       588: 1
       589: 1
       590: q+1
       591: q+1
       592: 2q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: q+1
       597: 1
       598: 1
       599: q+1
       600: q+1
       601: q+1
       602: 1
       603: q+1
       604: 1
       605: q+1
       608: 1
       609: q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: q^2+3q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: 2q+1
       622: 2q+1
       623: q+1
       624: 2q+1
       625: q+1
       626: 1
       627: q+1
       628: q^2+2q+1
       629: q+1
       630: q+1
       631: 1
       632: q+1
       633: q+1
       634: q+1
       635: q^2+2q+1
       636: 2q+1
       637: 2q+1
       638: q+1
       639: 2q+1
       640: q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: 1
       645: q+1
       646: q^2+2q+1
       648: q+1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       706: q+1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       756: q+1
       757: 1
       758: q+1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       770: q+1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: q+1
       778: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: q+1
       785: q+1
       786: 2q+1
       787: 1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: q+1
       796: 1
       797: q+1
       798: 1
       799: 1
       800: 1
       801: q+1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: 2q+1
       821: 1
       822: q+1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: q+1
       829: q+1
       830: 1
       831: q+1
       832: 1
       833: 1
       834: q+1
       835: q+1
       836: 2q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: q+1
       841: 1
       842: 1
       843: q+1
       844: q+1
       845: q+1
       846: 1
       847: q+1
       848: 1
       849: q+1
       852: 1
       853: q+1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       872: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       961: 1
       962: 1
       966: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       987: 1
       988: 1
       989: q+1
       990: 1
       991: 1
       993: q+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: q+1
      1016: 1
      1017: q+1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: q+1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: 2q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: q+1
      1055: 1
      1056: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1065: 1
      1072: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1097: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1131: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1183: 1
      1190: 1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1218: 1
      1219: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1250: q+1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: q+1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1287: 1
      1316: 1
      1331: 1
      1332: 1
      1336: 1
      1339: 1
      1341: 1
      1363: 1
      1378: 1
      1379: 1
      1383: 1
      1386: 1
      1388: 1
      1405: 1
      1412: 1
      1413: 1
      1417: 1
      1420: 1
      1422: 1
      1429: 1
      1430: 1
      1431: 1
      1434: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1502: 1
      1541: 1
      1570: 1
      1585: 1
      1586: 1
      1590: 1
      1593: 1
      1595: 1
      1708: 1

1709:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: 1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: 1
        59: 1
        60: q+1
        61: 1
        62: q+1
        63: 1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: 1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: 1
       121: 1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: 1
       146: q+1
       147: 1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: 1
       167: q+1
       168: 1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: 1
       209: 1
       210: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: 1
       300: q+1
       301: 1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: 1
       415: 1
       416: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       481: 1
       485: 1
       487: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       648: 1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       669: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       688: 1
       690: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       772: 1
       776: 1
       778: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       852: 1
       856: 1
       862: 1
       864: 1
       866: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       890: 1
       907: 1
       909: 1
       911: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       945: 1
       947: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       980: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       999: 1
      1001: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1073: 1
      1087: 1
      1089: 1
      1091: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1149: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1201: 1
      1218: 1
      1220: 1
      1222: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1256: 1
      1258: 1
      1288: 1
      1317: 1
      1331: 1
      1333: 1
      1335: 1
      1364: 1
      1378: 1
      1380: 1
      1382: 1
      1406: 1
      1412: 1
      1414: 1
      1416: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1440: 1
      1503: 1
      1542: 1
      1571: 1
      1585: 1
      1587: 1
      1589: 1
      1709: 1

1710:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       693: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       857: 1
       863: 1
       864: 1
       865: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       943: 1
       944: 1
       950: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       997: 1
       998: 1
      1004: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1040: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1074: 1
      1088: 1
      1089: 1
      1090: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1199: 1
      1219: 1
      1220: 1
      1221: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1261: 1
      1289: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1365: 1
      1379: 1
      1380: 1
      1381: 1
      1407: 1
      1413: 1
      1414: 1
      1415: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1438: 1
      1504: 1
      1543: 1
      1572: 1
      1586: 1
      1587: 1
      1588: 1
      1710: 1

1711:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: 1
       523: 1
       524: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       674: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       706: q+1
       707: 1
       708: 1
       709: 1
       710: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: 1
       814: 1
       815: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       889: 1
       890: 1
       891: 1
       895: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       931: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       964: 1
       965: 1
       966: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       985: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1017: q+1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1075: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1221: 1
      1222: 1
      1223: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1290: 1
      1319: 1
      1334: 1
      1335: 1
      1336: 1
      1341: 1
      1366: 1
      1381: 1
      1382: 1
      1383: 1
      1388: 1
      1408: 1
      1415: 1
      1416: 1
      1417: 1
      1422: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1505: 1
      1544: 1
      1573: 1
      1588: 1
      1589: 1
      1590: 1
      1595: 1
      1711: 1

1712:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       105: q+1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       191: q+1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       199: q+1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: q+1
       209: q+1
       210: q+1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       229: q+1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: q+1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: q+1
       314: 1
       316: 1
       317: 1
       318: 1
       321: q+1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       329: q+1
       331: q+1
       332: q+1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       358: q+1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       366: q+1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       376: q+1
       377: q+1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: q+1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       405: q+1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       415: q+1
       416: q+1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       435: q+1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       469: 1
       471: 1
       472: 1
       476: q+1
       478: 1
       480: 1
       481: 1
       482: 1
       485: q+1
       487: q+1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       519: q+1
       521: 1
       523: 1
       524: 1
       525: 1
       528: q+1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       538: q+1
       539: q+1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: q+1
       568: 1
       570: 1
       571: 1
       572: 1
       575: q+1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       583: q+1
       585: q+1
       586: q+1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       612: q+1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       620: q+1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       630: q+1
       631: q+1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       654: 1
       656: 1
       662: 1
       664: 1
       665: 1
       669: q+1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       708: 1
       710: 1
       711: 1
       715: q+1
       717: 1
       719: 1
       720: 1
       721: 1
       724: q+1
       726: q+1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       760: 1
       762: 1
       763: 1
       767: q+1
       769: 1
       771: 1
       772: 1
       773: 1
       776: q+1
       778: q+1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       810: q+1
       812: 1
       814: 1
       815: 1
       816: 1
       819: q+1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       829: q+1
       830: q+1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       859: 1
       866: 1
       868: 1
       883: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       911: 1
       913: 1
       919: 1
       921: 1
       922: 1
       926: q+1
       936: 1
       938: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       965: 1
       967: 1
       973: 1
       975: 1
       976: 1
       980: q+1
       990: 1
       992: 1
       994: 1
       995: 1
       996: 1
       999: 1
      1001: 1
      1007: 1
      1009: 1
      1010: 1
      1019: 1
      1021: 1
      1022: 1
      1026: q+1
      1028: 1
      1030: 1
      1031: 1
      1032: 1
      1035: q+1
      1037: q+1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1076: 1
      1091: 1
      1093: 1
      1106: 1
      1118: 1
      1125: 1
      1127: 1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1170: 1
      1177: 1
      1179: 1
      1194: 1
      1196: 1
      1197: 1
      1201: 1
      1210: 1
      1212: 1
      1222: 1
      1224: 1
      1230: 1
      1232: 1
      1233: 1
      1237: q+1
      1247: 1
      1249: 1
      1251: 1
      1252: 1
      1253: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1267: 1
      1291: 1
      1320: 1
      1335: 1
      1337: 1
      1350: 1
      1367: 1
      1382: 1
      1384: 1
      1397: 1
      1409: 1
      1416: 1
      1418: 1
      1433: 1
      1435: 1
      1436: 1
      1440: 1
      1449: 1
      1451: 1
      1506: 1
      1545: 1
      1574: 1
      1589: 1
      1591: 1
      1604: 1
      1712: 1

1713:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: 2q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       192: q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       200: q+1
       201: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       237: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q+1
       257: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       267: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       313: q+1
       315: 1
       316: 1
       317: q+1
       318: q+1
       322: q+1
       323: q+1
       324: 1
       325: 2q+1
       326: 1
       327: 1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       398: q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q+1
       463: q+1
       470: 1
       471: 1
       472: q+1
       477: q+1
       479: 1
       480: 1
       481: 1
       482: 1
       486: q+1
       487: q+1
       489: q+1
       490: 1
       491: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       520: q+1
       522: 1
       523: 1
       524: q+1
       525: q+1
       529: q+1
       530: q+1
       531: 1
       532: 2q+1
       533: 1
       534: 1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       567: q+1
       569: 1
       570: 1
       571: q+1
       572: q+1
       576: q+1
       577: q+1
       578: 1
       579: 2q+1
       580: 1
       581: 1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       655: 1
       656: 1
       663: 1
       664: 1
       665: 1
       670: q+1
       674: 1
       675: 1
       680: 1
       682: 1
       683: 1
       684: 1
       685: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       709: 1
       710: 1
       711: q+1
       716: q+1
       718: 1
       719: 1
       720: 1
       721: 1
       725: q+1
       726: q+1
       728: q+1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       761: 1
       762: 1
       763: q+1
       768: q+1
       770: 1
       771: 1
       772: 1
       773: 1
       777: q+1
       778: q+1
       780: q+1
       781: 1
       782: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       811: q+1
       813: 1
       814: 1
       815: q+1
       816: q+1
       820: q+1
       821: q+1
       822: 1
       823: 2q+1
       824: 1
       825: 1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       860: 1
       867: 1
       868: 1
       877: 1
       884: 1
       885: 1
       886: 1
       891: 1
       895: 1
       896: 1
       900: 1
       901: 1
       903: 1
       912: 1
       913: 1
       920: 1
       921: 1
       922: 1
       927: q+1
       931: 1
       932: 1
       937: 1
       939: 1
       940: 1
       941: 1
       942: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       981: q+1
       985: 1
       986: 1
       991: 1
       993: 1
       994: 1
       995: 1
       996: 1
      1000: 1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1020: 1
      1021: 1
      1022: q+1
      1027: q+1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1036: q+1
      1037: q+1
      1039: q+1
      1040: 1
      1041: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1077: 1
      1092: 1
      1093: 1
      1102: 1
      1107: 1
      1119: 1
      1126: 1
      1127: 1
      1136: 1
      1143: 1
      1144: 1
      1145: 1
      1150: 1
      1154: 1
      1155: 1
      1159: 1
      1160: 1
      1162: 1
      1171: 1
      1178: 1
      1179: 1
      1188: 1
      1195: 1
      1196: 1
      1197: 1
      1202: 1
      1206: 1
      1207: 1
      1211: 1
      1212: 1
      1214: 1
      1223: 1
      1224: 1
      1231: 1
      1232: 1
      1233: 1
      1238: q+1
      1242: 1
      1243: 1
      1248: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1292: 1
      1321: 1
      1336: 1
      1337: 1
      1346: 1
      1351: 1
      1368: 1
      1383: 1
      1384: 1
      1393: 1
      1398: 1
      1410: 1
      1417: 1
      1418: 1
      1427: 1
      1434: 1
      1435: 1
      1436: 1
      1441: 1
      1445: 1
      1446: 1
      1450: 1
      1451: 1
      1453: 1
      1507: 1
      1546: 1
      1575: 1
      1590: 1
      1591: 1
      1600: 1
      1605: 1
      1713: 1

1714:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q+1
         9: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q+1
        21: q^3+3q^2+3q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: 2q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q+1
        36: 2q^2+3q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: 2q^2+3q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q^2+3q+1
        63: 2q^2+3q+1
        64: q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+2q+1
        71: 2q+1
        72: q^3+3q^2+3q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: 2q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q+1
        85: q^3+3q^2+3q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q^2+3q+1
        90: 2q^2+3q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: 2q^2+3q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2q^2+3q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q^2+3q+1
       130: 2q^2+3q+1
       131: 1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: 2q^2+3q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q^2+3q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: q+1
       170: 2q^2+3q+1
       171: 2q^2+3q+1
       172: q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^3+3q^2+3q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q^2+3q+1
       182: 2q^2+3q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q^2+3q+1
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: 2q^2+3q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 2q^2+3q+1
       222: 1
       223: 1
       224: 1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: 2q^2+3q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: 2q^2+3q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: 2q^2+3q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: 2q^2+3q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: 1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q^2+3q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q^2+3q+1
       301: 2q^2+3q+1
       302: q+1
       303: 2q^2+3q+1
       304: 2q^2+3q+1
       305: q+1
       306: 2q^2+3q+1
       307: 2q^2+3q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       317: q+1
       318: q+1
       319: 1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       325: 2q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q^2+2q+1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q^2+3q+1
       389: 1
       390: 1
       391: 1
       392: q^2+2q+1
       393: q^2+2q+1
       394: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q^2+3q+1
       428: 1
       429: 1
       430: 1
       431: q^2+2q+1
       432: q^2+2q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q^2+3q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q^2+3q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q^2+3q+1
       460: 2q^2+3q+1
       461: 1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       472: q+1
       473: 1
       474: 1
       475: 2q+1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q^2+2q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       579: 2q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q^2+2q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q^2+3q+1
       643: 1
       644: 1
       645: 1
       646: q^2+2q+1
       647: q^2+2q+1
       648: 1
       649: q+1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       674: 1
       675: 1
       676: 1
       677: 1
       678: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: q+1
       704: q+1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       720: 1
       721: 1
       722: 1
       723: q+1
       724: q+1
       725: q+1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       785: q+1
       786: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q^2+2q+1
       851: 1
       852: 1
       853: 1
       861: 1
       869: 1
       870: 1
       877: 1
       878: 1
       879: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       906: q+1
       914: 1
       915: 1
       922: 1
       923: 1
       924: 1
       925: q+1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       960: q+1
       968: 1
       969: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       985: 1
       986: 1
       987: 1
       988: 1
       989: q+1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1014: q+1
      1015: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1105: 1
      1120: 1
      1128: 1
      1129: 1
      1136: 1
      1137: 1
      1138: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1172: 1
      1180: 1
      1181: 1
      1188: 1
      1189: 1
      1190: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1217: q+1
      1225: 1
      1226: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1293: 1
      1322: 1
      1330: 1
      1338: 1
      1339: 1
      1346: 1
      1349: 1
      1369: 1
      1377: 1
      1385: 1
      1386: 1
      1393: 1
      1396: 1
      1411: 1
      1419: 1
      1420: 1
      1427: 1
      1428: 1
      1429: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1508: 1
      1547: 1
      1576: 1
      1584: 1
      1592: 1
      1593: 1
      1600: 1
      1603: 1
      1714: 1

1715:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: 3q^2+3q+1
         7: q^2+2q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: 3q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: 3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 3q^2+3q+1
        26: q+1
        27: 3q^2+3q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: q^2+3q+1
        33: 3q^2+3q+1
        34: q^2+2q+1
        35: 3q^2+3q+1
        36: 3q^2+3q+1
        37: 3q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 3q^2+3q+1
        41: q^2+2q+1
        42: 3q^2+3q+1
        43: 3q^2+3q+1
        44: 3q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 3q^2+3q+1
        48: 3q^2+3q+1
        49: 3q^2+3q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q+1
        55: q+1
        56: 2q+1
        57: 3q^2+3q+1
        58: q+1
        59: q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+3q+1
        63: q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: q+1
        67: 2q^2+3q+1
        68: q^2+3q+1
        69: q^2+3q+1
        70: q^2+3q+1
        71: 3q^2+3q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 3q^2+3q+1
        77: q+1
        78: 3q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: q^2+3q+1
        84: 3q^2+3q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 3q^2+3q+1
        90: q+1
        91: 3q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+3q+1
        97: 3q^2+3q+1
        98: q^2+2q+1
        99: 3q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: q+1
       106: q+1
       107: q^2+2q+1
       108: q+1
       109: q+1
       110: q+1
       111: 2q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 2q+1
       119: 2q^2+3q+1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: q+1
       124: 2q^2+3q+1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+2q+1
       129: q^2+3q+1
       130: q+1
       131: q^2+3q+1
       132: q^2+3q+1
       133: q^2+3q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: q+1
       140: 2q+1
       141: 3q^2+3q+1
       142: q+1
       143: q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: 2q^2+3q+1
       147: q+1
       148: 2q^2+3q+1
       149: 2q^2+3q+1
       150: q+1
       151: 2q^2+3q+1
       152: q^2+3q+1
       153: q^2+3q+1
       154: q^2+3q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q+1
       160: q+1
       161: 2q+1
       162: 3q^2+3q+1
       163: q+1
       164: q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: 2q^2+3q+1
       168: q+1
       169: 2q^2+3q+1
       170: 2q^2+3q+1
       171: q+1
       172: 2q^2+3q+1
       173: q^2+3q+1
       174: q^2+3q+1
       175: q^2+3q+1
       176: 3q^2+3q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: 3q^2+3q+1
       182: q+1
       183: 3q^2+3q+1
       184: 2q^2+3q+1
       185: 2q^2+3q+1
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: q^2+3q+1
       189: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 2q+1
       198: 2q+1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 2q+1
       206: q^2+2q+1
       207: q+1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: q+1
       213: q+1
       214: q^2+2q+1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: q+1
       220: q^2+3q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q^2+3q+1
       227: q^2+3q+1
       228: 2q+1
       229: q+1
       230: q+1
       231: q^2+2q+1
       232: q+1
       233: q+1
       234: q+1
       235: 2q+1
       236: q^2+2q+1
       237: q^2+2q+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 2q+1
       243: 2q^2+3q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: q+1
       248: 2q^2+3q+1
       249: q+1
       250: q+1
       251: q+1
       252: q^2+2q+1
       253: q^2+3q+1
       254: q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q+1
       259: q+1
       260: q+1
       261: q^2+2q+1
       262: q+1
       263: q+1
       264: q+1
       265: 2q+1
       266: q^2+2q+1
       267: q^2+2q+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 2q+1
       273: 2q^2+3q+1
       274: q+1
       275: q+1
       276: q^2+2q+1
       277: q+1
       278: 2q^2+3q+1
       279: q+1
       280: q+1
       281: q+1
       282: q^2+2q+1
       283: q^2+3q+1
       284: q+1
       285: q^2+3q+1
       286: q^2+3q+1
       287: q^2+3q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q+1
       293: q+1
       294: 2q+1
       295: 3q^2+3q+1
       296: q+1
       297: q+1
       298: q^2+2q+1
       299: q^2+2q+1
       300: 2q^2+3q+1
       301: q+1
       302: 2q^2+3q+1
       303: 2q^2+3q+1
       304: q+1
       305: 2q^2+3q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: 2q+1
       310: q+1
       311: q+1
       312: q+1
       315: q+1
       316: q+1
       317: q+1
       319: 2q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 2q+1
       328: q+1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: q+1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q^2+3q+1
       354: q+1
       355: q+1
       356: 2q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: 2q+1
       365: 2q+1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 2q+1
       373: q^2+2q+1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: 1
       379: q+1
       380: q+1
       381: q^2+2q+1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: q+1
       387: q^2+3q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: q^2+3q+1
       394: q^2+3q+1
       395: 2q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: 2q+1
       404: 2q+1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 2q+1
       412: q^2+2q+1
       413: q+1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: q+1
       419: q+1
       420: q^2+2q+1
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: q+1
       426: q^2+3q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: q^2+3q+1
       433: q^2+3q+1
       434: 2q+1
       435: q+1
       436: q+1
       437: q^2+2q+1
       438: q+1
       439: q+1
       440: q+1
       441: 2q+1
       442: q^2+2q+1
       443: q^2+2q+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 2q+1
       449: 2q^2+3q+1
       450: q+1
       451: q+1
       452: q^2+2q+1
       453: q+1
       454: 2q^2+3q+1
       455: q+1
       456: q+1
       457: q+1
       458: q^2+2q+1
       459: q^2+3q+1
       460: q+1
       461: q^2+3q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: q+1
       466: q+1
       471: q+1
       473: 2q+1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: q+1
       515: 1
       516: 2q+1
       517: q+1
       518: q+1
       519: q+1
       522: q+1
       523: q+1
       524: q+1
       526: 2q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 2q+1
       535: q+1
       536: 1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: q+1
       543: q+1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: 1
       557: 1
       558: q^2+3q+1
       561: q+1
       562: q+1
       563: 2q+1
       564: q+1
       565: q+1
       566: q+1
       569: q+1
       570: q+1
       571: q+1
       573: 2q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 2q+1
       582: q+1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: q+1
       590: q+1
       591: 1
       592: 1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: q+1
       602: 1
       603: 1
       604: 1
       605: q^2+3q+1
       608: q+1
       609: q+1
       610: 2q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: 2q+1
       619: 2q+1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 2q+1
       627: q^2+2q+1
       628: q+1
       629: q+1
       630: q+1
       631: 1
       632: 1
       633: q+1
       634: q+1
       635: q^2+2q+1
       636: q+1
       637: q+1
       638: 1
       639: 1
       640: q+1
       641: q^2+3q+1
       642: q+1
       643: q+1
       644: q+1
       645: q+1
       646: q^2+3q+1
       648: q^2+3q+1
       650: q+1
       658: 1
       659: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: q+1
       705: q+1
       710: q+1
       712: 2q+1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       722: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: q+1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: q+1
       754: 1
       756: q+1
       757: q+1
       762: q+1
       764: 2q+1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       783: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: q+1
       792: 1
       793: 1
       794: 1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: q+1
       806: 1
       807: 2q+1
       808: q+1
       809: q+1
       810: q+1
       813: q+1
       814: q+1
       815: q+1
       817: 2q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 2q+1
       826: q+1
       827: 1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: q+1
       834: q+1
       835: 1
       836: 1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: q+1
       843: q+1
       844: q+1
       845: q+1
       846: 1
       847: 1
       848: 1
       849: q^2+3q+1
       852: q+1
       853: q+1
       862: 1
       870: 1
       871: 1
       876: 1
       879: 1
       880: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: q+1
       915: 1
       916: 1
       921: 1
       923: q+1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: q+1
       969: 1
       970: 1
       975: 1
       977: q+1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       987: q+1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: q+1
      1016: q+1
      1021: q+1
      1023: 2q+1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q+1
      1042: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1051: 1
      1052: 1
      1053: 1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1065: 1
      1079: 1
      1087: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1121: 1
      1129: 1
      1130: 1
      1135: 1
      1138: 1
      1139: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1173: 1
      1181: 1
      1182: 1
      1187: 1
      1190: 1
      1191: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: q+1
      1226: 1
      1227: 1
      1232: 1
      1234: q+1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1242: 1
      1244: q+1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1270: 1
      1294: 1
      1323: 1
      1331: 1
      1339: 1
      1340: 1
      1345: 1
      1347: 1
      1370: 1
      1378: 1
      1386: 1
      1387: 1
      1392: 1
      1394: 1
      1412: 1
      1420: 1
      1421: 1
      1426: 1
      1429: 1
      1430: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1455: 1
      1509: 1
      1548: 1
      1577: 1
      1585: 1
      1593: 1
      1594: 1
      1599: 1
      1601: 1
      1715: 1

1716:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: q^2+2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: 2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: 2q+1
        45: q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q+1
        55: q^2+2q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: q^2+2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 2q^2+2q+1
       101: 2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: 2q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: 2q+1
       182: q+1
       183: 2q+1
       184: q^2+2q+1
       185: 2q+1
       186: 2q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: q+1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: 2q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: q+1
       213: 1
       214: 2q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: 2q+1
       221: q+1
       222: q+1
       223: 1
       224: 2q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: 1
       252: 2q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: 2q+1
       268: q+1
       269: 1
       270: 1
       271: q+1
       272: q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: q+1
       277: 2q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: q+1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: 2q+1
       303: 2q+1
       304: q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       315: q+1
       316: q+1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: q+1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 2q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       365: q+1
       366: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: q+1
       374: 2q+1
       375: q+1
       376: 1
       377: 1
       378: q+1
       379: q+1
       380: 1
       381: 2q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: 2q+1
       388: q+1
       389: q+1
       390: 1
       391: 2q+1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       404: q+1
       405: 1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: q+1
       413: 2q+1
       414: q+1
       415: 1
       416: 1
       417: q+1
       418: q+1
       419: 1
       420: 2q+1
       421: q+1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: 2q+1
       427: q+1
       428: q+1
       429: 1
       430: 2q+1
       431: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: 2q+1
       444: q+1
       445: 1
       446: 1
       447: q+1
       448: q+1
       449: 2q+1
       450: q+1
       451: q+1
       452: q+1
       453: 2q+1
       454: 2q+1
       455: q+1
       456: q+1
       457: 1
       458: 2q+1
       459: 2q+1
       460: q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       466: q+1
       467: q+1
       470: q+1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q+1
       523: q+1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: q+1
       536: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q+1
       543: 1
       544: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 2q+1
       553: q+1
       554: 1
       555: 1
       556: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       569: q+1
       570: q+1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: q+1
       583: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       590: 1
       591: 1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 2q+1
       600: q+1
       601: 1
       602: 1
       603: q+1
       604: 1
       605: q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       619: q+1
       620: 1
       621: q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q+1
       627: q+1
       628: 2q+1
       629: q+1
       630: 1
       631: 1
       632: q+1
       633: q+1
       634: 1
       635: 2q+1
       636: q+1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: 2q+1
       642: q+1
       643: q+1
       644: 1
       645: 2q+1
       646: q+1
       648: q+1
       651: q+1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: q+1
       706: q+1
       709: q+1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       757: q+1
       758: q+1
       761: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: q+1
       806: 1
       808: q+1
       809: q+1
       810: q+1
       811: q+1
       813: q+1
       814: q+1
       817: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: q+1
       827: 1
       828: q+1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       834: 1
       835: 1
       836: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 2q+1
       844: q+1
       845: 1
       846: 1
       847: q+1
       848: 1
       849: q+1
       852: 1
       853: q+1
       863: 1
       871: 1
       872: 1
       875: 1
       880: 1
       881: 1
       884: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       897: 1
       908: q+1
       916: 1
       917: 1
       920: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       959: 1
       962: q+1
       970: 1
       971: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       991: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1013: 1
      1016: q+1
      1017: q+1
      1020: q+1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1065: 1
      1080: 1
      1088: 1
      1096: 1
      1097: 1
      1100: 1
      1122: 1
      1130: 1
      1131: 1
      1134: 1
      1139: 1
      1140: 1
      1143: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1156: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1191: 1
      1192: 1
      1195: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1208: 1
      1219: q+1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1263: 1
      1270: 1
      1295: 1
      1324: 1
      1332: 1
      1340: 1
      1341: 1
      1344: 1
      1371: 1
      1379: 1
      1387: 1
      1388: 1
      1391: 1
      1413: 1
      1421: 1
      1422: 1
      1425: 1
      1430: 1
      1431: 1
      1434: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1447: 1
      1510: 1
      1549: 1
      1578: 1
      1586: 1
      1594: 1
      1595: 1
      1598: 1
      1716: 1

1717:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q^2+2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: 2q+1
        38: 2q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: 2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q^2+2q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q^2+2q+1
        93: 2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: 2q^2+2q+1
       101: 2q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: 2q+1
       182: q+1
       183: 2q+1
       184: 2q^2+2q+1
       185: 2q+1
       186: q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       198: q+1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: 2q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: 2q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 1
       225: q+1
       227: q+1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 2q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: 1
       242: q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 1
       248: 2q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: 2q+1
       277: 1
       278: 2q+1
       279: q+1
       280: q+1
       281: 2q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: q+1
       300: 2q+1
       301: q+1
       302: 2q+1
       303: 2q+1
       304: q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: q+1
       314: q+1
       315: q+1
       316: q+1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: 2q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       365: q+1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: 2q+1
       374: 1
       375: q+1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: 2q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: 1
       386: q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: 1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       404: q+1
       405: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: 2q+1
       413: 1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: 2q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: 1
       425: q+1
       426: 2q+1
       427: q+1
       428: q+1
       429: 2q+1
       430: 1
       431: q+1
       433: q+1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 2q+1
       443: q+1
       444: q+1
       445: 1
       446: q+1
       447: 1
       448: q+1
       449: 2q+1
       450: q+1
       451: q+1
       452: 2q+1
       453: 1
       454: 2q+1
       455: q+1
       456: q+1
       457: 2q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       466: q+1
       468: q+1
       469: q+1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       517: q+1
       518: q+1
       519: q+1
       521: q+1
       522: q+1
       523: q+1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: 2q+1
       552: 1
       553: q+1
       554: 1
       555: q+1
       556: 1
       557: 1
       558: q+1
       561: q+1
       562: 1
       564: q+1
       565: q+1
       566: q+1
       568: q+1
       569: q+1
       570: q+1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q+1
       598: 2q+1
       599: 1
       600: q+1
       601: 1
       602: q+1
       603: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       619: q+1
       620: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q+1
       627: 2q+1
       628: 1
       629: q+1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: 2q+1
       635: q+1
       636: q+1
       637: 1
       638: q+1
       639: 1
       640: q+1
       641: 2q+1
       642: q+1
       643: q+1
       644: 2q+1
       645: 1
       646: q+1
       648: q+1
       652: q+1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       702: 1
       705: q+1
       707: q+1
       708: q+1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: q+1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       754: 1
       757: q+1
       759: q+1
       760: q+1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       808: q+1
       809: q+1
       810: q+1
       812: q+1
       813: q+1
       814: q+1
       817: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: q+1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: q+1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: 2q+1
       843: 1
       844: q+1
       845: 1
       846: q+1
       847: 1
       848: 1
       849: q+1
       852: q+1
       853: 1
       864: 1
       871: 1
       873: 1
       874: 1
       880: 1
       882: 1
       883: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       897: 1
       909: q+1
       916: 1
       918: 1
       919: 1
       924: 1
       925: 1
       926: 1
       928: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       959: 1
       963: q+1
       970: 1
       972: 1
       973: 1
       978: 1
       979: 1
       980: 1
       982: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1013: 1
      1016: q+1
      1018: q+1
      1019: q+1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: q+1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1065: 1
      1081: 1
      1089: 1
      1096: 1
      1098: 1
      1099: 1
      1123: 1
      1130: 1
      1132: 1
      1133: 1
      1139: 1
      1141: 1
      1142: 1
      1147: 1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1156: 1
      1175: 1
      1182: 1
      1184: 1
      1185: 1
      1191: 1
      1193: 1
      1194: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1208: 1
      1220: q+1
      1227: 1
      1229: 1
      1230: 1
      1235: 1
      1236: 1
      1237: 1
      1239: 1
      1240: 1
      1241: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1263: 1
      1270: 1
      1296: 1
      1325: 1
      1333: 1
      1340: 1
      1342: 1
      1343: 1
      1372: 1
      1380: 1
      1387: 1
      1389: 1
      1390: 1
      1414: 1
      1421: 1
      1423: 1
      1424: 1
      1430: 1
      1432: 1
      1433: 1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1447: 1
      1511: 1
      1550: 1
      1579: 1
      1587: 1
      1594: 1
      1596: 1
      1597: 1
      1717: 1

1718:    0: q^5+q^4+3q^3+5q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: 2q^3+4q^2+3q+1
         3: q^4+q^3+5q^2+3q+1
         4: q^5+q^4+3q^3+5q^2+3q+1
         5: q^5+q^4+3q^3+5q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+3q+1
         9: q^3+4q^2+3q+1
        10: 3q^2+3q+1
        11: q^4+q^3+5q^2+3q+1
        12: q^4+q^3+5q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: 2q^3+4q^2+3q+1
        15: q^4+q^3+5q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: q^4+q^3+5q^2+3q+1
        19: q^5+q^4+3q^3+5q^2+3q+1
        20: q^2+2q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: 2q^2+3q+1
        26: q^2+2q+1
        27: 2q^2+3q+1
        28: q^3+4q^2+3q+1
        29: 3q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 3q^2+3q+1
        32: q^4+q^3+5q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 3q^2+3q+1
        36: q^3+4q^2+3q+1
        37: 3q^2+3q+1
        38: q^4+q^3+5q^2+3q+1
        39: q^4+q^3+5q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 3q^2+3q+1
        43: q^3+4q^2+3q+1
        44: 3q^2+3q+1
        45: q^4+q^3+5q^2+3q+1
        46: q^4+q^3+5q^2+3q+1
        47: 2q^3+4q^2+3q+1
        48: 2q^3+4q^2+3q+1
        49: q^4+q^3+5q^2+3q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 3q^2+3q+1
        57: 2q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q^2+3q+1
        61: 2q^2+3q+1
        62: 2q^2+3q+1
        63: q^2+2q+1
        64: q^2+3q+1
        65: 2q^2+3q+1
        66: q^2+2q+1
        67: q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 3q^2+3q+1
        70: q^3+3q^2+3q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: 2q^2+3q+1
        74: 3q^2+3q+1
        75: 3q^2+3q+1
        76: 2q^2+3q+1
        77: q^2+2q+1
        78: 2q^2+3q+1
        79: q^3+4q^2+3q+1
        80: 3q^2+3q+1
        81: q^3+4q^2+3q+1
        82: 3q^2+3q+1
        83: q^4+q^3+5q^2+3q+1
        84: q^2+2q+1
        85: q^3+3q^2+3q+1
        86: 2q^2+3q+1
        87: 3q^2+3q+1
        88: 3q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+4q^2+3q+1
        93: 3q^2+3q+1
        94: q^3+4q^2+3q+1
        95: 3q^2+3q+1
        96: q^4+q^3+5q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 3q^2+3q+1
       100: q^3+4q^2+3q+1
       101: 3q^2+3q+1
       102: q^4+q^3+5q^2+3q+1
       103: q^4+q^3+5q^2+3q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+3q+1
       111: q^2+2q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q^2+3q+1
       119: 2q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+3q+1
       123: q^2+3q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q+1
       127: q^2+3q+1
       128: q^2+3q+1
       129: 2q^2+3q+1
       130: q^2+2q+1
       131: 3q+1
       132: q^3+3q^2+3q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: 3q^2+3q+1
       141: 2q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q^2+3q+1
       145: 2q^2+3q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: q^2+3q+1
       149: 2q^2+3q+1
       150: q^2+2q+1
       151: q^2+3q+1
       152: q^3+4q^2+3q+1
       153: 3q^2+3q+1
       154: q^3+3q^2+3q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 3q^2+3q+1
       162: 2q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q^2+3q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+2q+1
       169: q^2+3q+1
       170: 2q^2+3q+1
       171: q^2+2q+1
       172: q^2+3q+1
       173: q^3+4q^2+3q+1
       174: 3q^2+3q+1
       175: q^3+3q^2+3q+1
       176: q^2+2q+1
       177: q^3+3q^2+3q+1
       178: 2q^2+3q+1
       179: 3q^2+3q+1
       180: 3q^2+3q+1
       181: 2q^2+3q+1
       182: q^2+2q+1
       183: 2q^2+3q+1
       184: q^3+4q^2+3q+1
       185: 3q^2+3q+1
       186: q^3+4q^2+3q+1
       187: 3q^2+3q+1
       188: q^4+q^3+5q^2+3q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: q^2+2q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: q^2+3q+1
       213: 2q+1
       214: 2q+1
       215: q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: q^2+3q+1
       220: 2q+1
       221: q^2+2q+1
       222: 2q+1
       223: 3q+1
       224: 3q+1
       225: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: 2q^2+3q+1
       235: q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: 2q^2+3q+1
       243: 2q+1
       244: q^2+2q+1
       245: 2q+1
       246: q^2+3q+1
       247: q^2+3q+1
       248: 2q+1
       249: q^2+2q+1
       250: 2q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: 2q^2+3q+1
       254: q^2+2q+1
       255: 3q+1
       256: q^3+3q^2+3q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q+1
       262: q^2+2q+1
       263: q^2+2q+1
       264: 2q^2+3q+1
       265: q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: 2q^2+3q+1
       273: 2q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+3q+1
       277: q^2+3q+1
       278: 2q+1
       279: q^2+2q+1
       280: 2q+1
       281: q^2+3q+1
       282: q^2+3q+1
       283: 2q^2+3q+1
       284: q^2+2q+1
       285: 3q+1
       286: q^3+3q^2+3q+1
       287: q^2+2q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: 3q^2+3q+1
       295: 2q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q^2+3q+1
       299: 2q^2+3q+1
       300: 2q^2+3q+1
       301: q^2+2q+1
       302: q^2+3q+1
       303: 2q^2+3q+1
       304: q^2+2q+1
       305: q^2+3q+1
       306: q^3+4q^2+3q+1
       307: 3q^2+3q+1
       308: q^3+3q^2+3q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       328: 2q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: 3q+1
       351: q+1
       354: 2q+1
       355: 2q+1
       357: q^2+2q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q^2+2q+1
       363: q^2+2q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: 1
       369: q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: 2q+1
       374: 2q+1
       375: q+1
       376: q+1
       377: 2q+1
       378: 2q+1
       379: q^2+3q+1
       380: 2q+1
       381: 2q+1
       382: q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: q^2+3q+1
       387: 2q+1
       388: q^2+2q+1
       389: 2q+1
       390: 3q+1
       391: 3q+1
       392: q^2+2q+1
       394: 2q+1
       396: q^2+2q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q^2+2q+1
       402: q^2+2q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: 1
       408: q+1
       409: q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       413: 2q+1
       414: q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: q^2+3q+1
       419: 2q+1
       420: 2q+1
       421: q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: q^2+3q+1
       426: 2q+1
       427: q^2+2q+1
       428: 2q+1
       429: 3q+1
       430: 3q+1
       431: q^2+2q+1
       433: 2q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q+1
       438: q^2+2q+1
       439: q^2+2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: 2q+1
       447: 2q+1
       448: 2q^2+3q+1
       449: 2q+1
       450: q^2+2q+1
       451: 2q+1
       452: q^2+3q+1
       453: q^2+3q+1
       454: 2q+1
       455: q^2+2q+1
       456: 2q+1
       457: q^2+3q+1
       458: q^2+3q+1
       459: 2q^2+3q+1
       460: q^2+2q+1
       461: 3q+1
       462: q^3+3q^2+3q+1
       463: q^2+2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       501: 2q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: 2q+1
       508: 2q+1
       509: q+1
       510: q+1
       515: 2q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       535: 2q+1
       536: q+1
       537: q+1
       538: 1
       539: q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: 2q+1
       544: q+1
       545: q+1
       546: 1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: 2q+1
       553: q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: 3q+1
       558: q+1
       561: 2q+1
       562: 2q+1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       582: 2q+1
       583: q+1
       584: q+1
       585: 1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: 1
       594: q+1
       595: q+1
       596: 2q+1
       597: 2q+1
       598: 2q+1
       599: 2q+1
       600: q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: 3q+1
       605: q+1
       608: 2q+1
       609: 2q+1
       611: q^2+2q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q^2+2q+1
       617: q^2+2q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: 1
       623: q+1
       624: q+1
       625: 2q+1
       626: 2q+1
       627: 2q+1
       628: 2q+1
       629: q+1
       630: q+1
       631: 2q+1
       632: 2q+1
       633: q^2+3q+1
       634: 2q+1
       635: 2q+1
       636: q+1
       637: q+1
       638: 2q+1
       639: 2q+1
       640: q^2+3q+1
       641: 2q+1
       642: q^2+2q+1
       643: 2q+1
       644: 3q+1
       645: 3q+1
       646: q^2+2q+1
       648: 2q+1
       653: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       695: q+1
       702: q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       740: 2q+1
       741: q+1
       742: q+1
       743: 1
       744: q+1
       745: q+1
       746: 2q+1
       747: 2q+1
       748: q+1
       749: q+1
       754: 2q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       792: 2q+1
       793: q+1
       794: q+1
       795: 1
       796: q+1
       797: q+1
       798: 2q+1
       799: 2q+1
       800: q+1
       801: q+1
       806: 2q+1
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: q+1
       818: q+1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: q+1
       826: 2q+1
       827: q+1
       828: q+1
       829: 1
       830: q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       834: 2q+1
       835: q+1
       836: q+1
       837: 1
       838: q+1
       839: q+1
       840: 2q+1
       841: 2q+1
       842: 2q+1
       843: 2q+1
       844: q+1
       845: q+1
       846: 2q+1
       847: 2q+1
       848: 3q+1
       849: q+1
       852: 2q+1
       853: 2q+1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       910: q+1
       917: 1
       918: 1
       919: 1
       920: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       952: q+1
       959: q+1
       964: q+1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1006: q+1
      1013: q+1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1034: q+1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: q+1
      1043: q+1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: q+1
      1051: 2q+1
      1052: q+1
      1053: q+1
      1054: 1
      1055: q+1
      1056: q+1
      1057: 2q+1
      1058: 2q+1
      1059: q+1
      1060: q+1
      1065: 2q+1
      1082: 1
      1090: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1124: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1221: q+1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1255: q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: q+1
      1261: q+1
      1263: q+1
      1270: q+1
      1297: 1
      1326: 1
      1334: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1373: 1
      1381: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1415: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1512: 1
      1551: 1
      1580: 1
      1588: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1718: 1

1719:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q+1
        25: q+1
        26: 1
        27: q^2+q+1
        28: q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        59: 1
        60: q^2+q+1
        61: q+1
        62: q+1
        63: 1
        64: q^2+q+1
        65: q+1
        66: 1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q^2+q+1
        75: q+1
        76: q+1
        77: 1
        78: q^2+q+1
        79: q+1
        80: q^2+q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: q+1
        89: q+1
        90: 1
        91: q^2+q+1
        92: q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: q^2+q+1
       102: q^2+q+1
       103: q+1
       105: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: 1
       121: 1
       122: q^2+q+1
       123: 1
       124: q+1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: q+1
       130: 1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: 1
       143: 1
       144: q^2+q+1
       145: q+1
       146: q+1
       147: 1
       148: q^2+q+1
       149: q+1
       150: 1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: 1
       169: q^2+q+1
       170: q+1
       171: 1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q^2+q+1
       180: q+1
       181: q+1
       182: 1
       183: q^2+q+1
       184: q+1
       185: q^2+q+1
       186: q+1
       187: q+1
       188: q+1
       191: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: q+1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       227: q+1
       229: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q^2+q+1
       247: 1
       248: q+1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       259: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: 1
       275: 1
       276: q^2+q+1
       277: 1
       278: q+1
       279: 1
       280: 1
       281: q+1
       282: q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: 1
       297: 1
       298: q^2+q+1
       299: q+1
       300: q+1
       301: 1
       302: q^2+q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       312: q+1
       314: q+1
       316: q+1
       317: q+1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: 1
       358: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: q+1
       388: 1
       389: 1
       390: q+1
       391: 1
       392: q+1
       394: q+1
       397: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q+1
       427: 1
       428: 1
       429: q+1
       430: 1
       431: q+1
       433: q+1
       435: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: 1
       451: 1
       452: q^2+q+1
       453: 1
       454: q+1
       455: 1
       456: 1
       457: q+1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       469: q+1
       471: q+1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       515: 1
       519: q+1
       521: q+1
       523: q+1
       524: q+1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q+1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: q+1
       561: q+1
       562: 1
       566: q+1
       568: q+1
       570: q+1
       571: q+1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q+1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q+1
       598: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       612: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q+1
       627: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: 1
       643: 1
       644: q+1
       645: 1
       646: q+1
       648: q+1
       654: q+1
       662: 1
       664: 1
       669: 1
       671: 1
       673: 1
       674: 1
       679: 1
       681: 1
       683: 1
       684: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       708: q+1
       710: q+1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       754: 1
       760: q+1
       762: q+1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: q+1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       806: 1
       810: q+1
       812: q+1
       814: q+1
       815: q+1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: q+1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+1
       852: q+1
       853: 1
       866: 1
       874: 1
       876: 1
       883: 1
       885: 1
       890: 1
       892: 1
       894: 1
       895: 1
       905: 1
       911: q+1
       919: 1
       921: 1
       926: 1
       928: 1
       930: 1
       931: 1
       936: 1
       938: 1
       940: 1
       941: 1
       945: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       959: 1
       965: q+1
       973: 1
       975: 1
       980: 1
       982: 1
       984: 1
       985: 1
       990: 1
       992: 1
       994: 1
       995: 1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1013: 1
      1019: q+1
      1021: q+1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1052: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1065: 1
      1083: 1
      1091: 1
      1099: 1
      1101: 1
      1125: 1
      1133: 1
      1135: 1
      1142: 1
      1144: 1
      1149: 1
      1151: 1
      1153: 1
      1154: 1
      1164: 1
      1177: 1
      1185: 1
      1187: 1
      1194: 1
      1196: 1
      1201: 1
      1203: 1
      1205: 1
      1206: 1
      1216: 1
      1222: q+1
      1230: 1
      1232: 1
      1237: 1
      1239: 1
      1241: 1
      1242: 1
      1247: 1
      1249: 1
      1251: 1
      1252: 1
      1256: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1270: 1
      1298: 1
      1327: 1
      1335: 1
      1343: 1
      1345: 1
      1374: 1
      1382: 1
      1390: 1
      1392: 1
      1416: 1
      1424: 1
      1426: 1
      1433: 1
      1435: 1
      1440: 1
      1442: 1
      1444: 1
      1445: 1
      1455: 1
      1513: 1
      1552: 1
      1581: 1
      1589: 1
      1597: 1
      1599: 1
      1719: 1

1720:    0: q^2+q+1
         1: q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q^2+q+1
         9: q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q^2+q+1
        25: q+1
        26: 1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q+1
        31: q^2+q+1
        32: q+1
        33: q+1
        34: q+1
        35: q^2+q+1
        36: q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q^2+q+1
        43: q+1
        44: q^2+q+1
        45: q+1
        46: q^2+q+1
        47: q+1
        48: q^2+q+1
        49: q^2+q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: 1
        59: 1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q^2+q+1
        76: q+1
        77: 1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q^2+q+1
        89: q+1
        90: 1
        91: q^2+q+1
        92: q+1
        93: q+1
        94: q+1
        95: q^2+q+1
        96: q+1
        97: q+1
        98: q+1
        99: q^2+q+1
       100: q+1
       101: q^2+q+1
       102: q+1
       103: q^2+q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: 1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: 1
       126: 1
       127: 1
       128: q^2+q+1
       129: q+1
       130: 1
       131: q+1
       132: q+1
       133: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: q^2+q+1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q^2+q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q^2+q+1
       181: q+1
       182: 1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: q+1
       187: q^2+q+1
       188: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: q+1
       221: 1
       222: 1
       223: 1
       224: q+1
       225: q+1
       227: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: 1
       250: 1
       251: 1
       252: q^2+q+1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: 1
       280: 1
       281: 1
       282: q^2+q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: q^2+q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q^2+q+1
       306: q+1
       307: q+1
       308: q+1
       313: q+1
       315: q+1
       316: q+1
       317: q+1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       354: 1
       355: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: 1
       389: 1
       390: 1
       391: q+1
       392: q+1
       394: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: q+1
       427: 1
       428: 1
       429: 1
       430: q+1
       431: q+1
       433: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: 1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: 1
       456: 1
       457: 1
       458: q^2+q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       470: q+1
       471: q+1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: q+1
       515: 1
       520: q+1
       522: q+1
       523: q+1
       524: q+1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q+1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q+1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: q+1
       561: 1
       562: q+1
       567: q+1
       569: q+1
       570: q+1
       571: q+1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       599: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: q+1
       608: 1
       609: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: q+1
       642: 1
       643: 1
       644: 1
       645: q+1
       646: q+1
       648: q+1
       655: q+1
       663: 1
       664: 1
       670: 1
       672: 1
       673: 1
       674: 1
       680: 1
       682: 1
       683: 1
       684: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       702: 1
       709: q+1
       710: q+1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: q+1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: q+1
       754: 1
       761: q+1
       762: q+1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       801: q+1
       806: 1
       811: q+1
       813: q+1
       814: q+1
       815: q+1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: q+1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+1
       852: 1
       853: q+1
       867: 1
       875: 1
       876: 1
       884: 1
       885: 1
       891: 1
       893: 1
       894: 1
       895: 1
       905: 1
       912: q+1
       920: 1
       921: 1
       927: 1
       929: 1
       930: 1
       931: 1
       937: 1
       939: 1
       940: 1
       941: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       959: 1
       966: q+1
       974: 1
       975: 1
       981: 1
       983: 1
       984: 1
       985: 1
       991: 1
       993: 1
       994: 1
       995: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1013: 1
      1020: q+1
      1021: q+1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q+1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1060: q+1
      1065: 1
      1084: 1
      1092: 1
      1100: 1
      1101: 1
      1126: 1
      1134: 1
      1135: 1
      1143: 1
      1144: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1164: 1
      1178: 1
      1186: 1
      1187: 1
      1195: 1
      1196: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1216: 1
      1223: q+1
      1231: 1
      1232: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1248: 1
      1250: 1
      1251: 1
      1252: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1270: 1
      1299: 1
      1328: 1
      1336: 1
      1344: 1
      1345: 1
      1375: 1
      1383: 1
      1391: 1
      1392: 1
      1417: 1
      1425: 1
      1426: 1
      1434: 1
      1435: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1455: 1
      1514: 1
      1553: 1
      1582: 1
      1590: 1
      1598: 1
      1599: 1
      1720: 1

1721:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: q^2+2q+1
         7: 3q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: 3q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: 3q^2+3q+1
        19: 3q^2+3q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 3q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 2q+1
        26: 2q^2+3q+1
        27: 2q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: q^2+2q+1
        34: 3q^2+3q+1
        35: 3q^2+3q+1
        36: 3q^2+3q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^2+2q+1
        41: 3q^2+3q+1
        42: 3q^2+3q+1
        43: 3q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 3q^2+3q+1
        48: 3q^2+3q+1
        49: 3q^2+3q+1
        52: q^2+2q+1
        53: 2q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: q^2+3q+1
        57: 2q+1
        58: 2q+1
        59: 2q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: 2q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: 2q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: q^2+3q+1
        69: 3q+1
        70: q^2+3q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 3q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 2q+1
        77: 2q^2+3q+1
        78: 2q^2+3q+1
        79: 2q^2+3q+1
        80: q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 3q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q+1
        90: 2q^2+3q+1
        91: 2q^2+3q+1
        92: 2q^2+3q+1
        93: q^2+3q+1
        94: 2q^2+3q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: q^2+2q+1
        98: 3q^2+3q+1
        99: 3q^2+3q+1
       100: 3q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+3q+1
       111: q^2+3q+1
       114: 2q+1
       115: 2q+1
       116: q^2+3q+1
       117: q^2+3q+1
       118: 3q+1
       119: 2q+1
       120: 2q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: 2q+1
       124: 2q+1
       125: 2q+1
       126: q^2+3q+1
       127: 2q+1
       128: q^2+3q+1
       129: 2q+1
       130: 3q+1
       131: 3q+1
       132: q^2+3q+1
       133: 2q+1
       136: q^2+2q+1
       137: 2q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: q^2+3q+1
       141: 2q+1
       142: 2q+1
       143: 2q^2+3q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: 2q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: 2q+1
       150: q^2+3q+1
       151: q^2+3q+1
       152: q^2+3q+1
       153: 3q+1
       154: q^2+3q+1
       157: q^2+2q+1
       158: 2q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: q^2+3q+1
       162: 2q+1
       163: 2q+1
       164: 2q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 2q+1
       168: q^2+3q+1
       169: q^2+3q+1
       170: 2q+1
       171: q^2+3q+1
       172: q^2+3q+1
       173: q^2+3q+1
       174: 3q+1
       175: q^2+3q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 3q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: 2q+1
       182: 2q^2+3q+1
       183: 2q^2+3q+1
       184: 2q^2+3q+1
       185: q^2+3q+1
       186: 2q^2+3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+3q+1
       197: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 3q+1
       205: 3q+1
       208: 2q+1
       209: q+1
       210: q^2+3q+1
       211: 2q+1
       212: 2q+1
       215: 2q+1
       216: q+1
       217: 2q+1
       218: q^2+3q+1
       219: 2q+1
       220: 2q+1
       221: 2q+1
       222: 3q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       226: 2q+1
       227: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+3q+1
       235: q^2+3q+1
       238: 2q+1
       239: 2q+1
       240: q^2+3q+1
       241: q^2+3q+1
       242: 3q+1
       243: 2q+1
       244: 2q+1
       245: q^2+3q+1
       246: q^2+3q+1
       247: 2q+1
       248: 2q+1
       249: 2q+1
       250: q^2+3q+1
       251: 2q+1
       252: q^2+3q+1
       253: 2q+1
       254: 3q+1
       255: 3q+1
       256: q^2+3q+1
       257: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+3q+1
       265: q^2+3q+1
       268: 2q+1
       269: 2q+1
       270: q^2+3q+1
       271: q^2+3q+1
       272: 3q+1
       273: 2q+1
       274: 2q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: 2q+1
       278: 2q+1
       279: 2q+1
       280: q^2+3q+1
       281: 2q+1
       282: q^2+3q+1
       283: 2q+1
       284: 3q+1
       285: 3q+1
       286: q^2+3q+1
       287: 2q+1
       290: q^2+2q+1
       291: 2q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: q^2+3q+1
       295: 2q+1
       296: 2q+1
       297: 2q^2+3q+1
       298: q^2+3q+1
       299: q^2+3q+1
       300: 2q+1
       301: q^2+3q+1
       302: q^2+3q+1
       303: 2q+1
       304: q^2+3q+1
       305: q^2+3q+1
       306: q^2+3q+1
       307: 3q+1
       308: q^2+3q+1
       316: 2q+1
       317: q+1
       318: 2q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: 3q+1
       327: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       346: 2q+1
       347: 1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: q+1
       352: q+1
       353: 2q+1
       354: q+1
       355: q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+3q+1
       364: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 3q+1
       372: 3q+1
       375: 2q+1
       376: q+1
       377: q^2+3q+1
       378: 2q+1
       379: 2q+1
       382: 2q+1
       383: q+1
       384: 2q+1
       385: q^2+3q+1
       386: 2q+1
       387: 2q+1
       388: 2q+1
       389: 3q+1
       390: 2q+1
       391: 2q+1
       392: q+1
       393: 2q+1
       394: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+3q+1
       403: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 3q+1
       411: 3q+1
       414: 2q+1
       415: q+1
       416: q^2+3q+1
       417: 2q+1
       418: 2q+1
       421: 2q+1
       422: q+1
       423: 2q+1
       424: q^2+3q+1
       425: 2q+1
       426: 2q+1
       427: 2q+1
       428: 3q+1
       429: 2q+1
       430: 2q+1
       431: q+1
       432: 2q+1
       433: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+3q+1
       441: q^2+3q+1
       444: 2q+1
       445: 2q+1
       446: q^2+3q+1
       447: q^2+3q+1
       448: 3q+1
       449: 2q+1
       450: 2q+1
       451: q^2+3q+1
       452: q^2+3q+1
       453: 2q+1
       454: 2q+1
       455: 2q+1
       456: q^2+3q+1
       457: 2q+1
       458: q^2+3q+1
       459: 2q+1
       460: 3q+1
       461: 3q+1
       462: q^2+3q+1
       463: 2q+1
       471: q+1
       472: q+1
       480: 2q+1
       481: 1
       482: 2q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       511: q+1
       512: 1
       513: q+1
       514: q+1
       515: 1
       523: 2q+1
       524: q+1
       525: 2q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 3q+1
       534: 2q+1
       538: q+1
       539: q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       553: 2q+1
       554: 1
       555: 2q+1
       556: 2q+1
       557: q+1
       558: q+1
       559: q+1
       560: 2q+1
       561: q+1
       562: q+1
       570: 2q+1
       571: q+1
       572: 2q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 3q+1
       581: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       593: q+1
       594: q+1
       595: q+1
       596: 2q+1
       597: 2q+1
       600: 2q+1
       601: 1
       602: 2q+1
       603: 2q+1
       604: q+1
       605: q+1
       606: q+1
       607: 2q+1
       608: q+1
       609: q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+3q+1
       618: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 3q+1
       626: 3q+1
       629: 2q+1
       630: q+1
       631: q^2+3q+1
       632: 2q+1
       633: 2q+1
       636: 2q+1
       637: q+1
       638: 2q+1
       639: q^2+3q+1
       640: 2q+1
       641: 2q+1
       642: 2q+1
       643: 3q+1
       644: 2q+1
       645: 2q+1
       646: q+1
       647: 2q+1
       648: 2q+1
       656: q+1
       664: 1
       665: 1
       673: q+1
       674: 1
       675: q+1
       683: q+1
       684: 1
       685: q+1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: q+1
       711: q+1
       719: 2q+1
       720: 1
       721: 2q+1
       726: q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       750: q+1
       751: 1
       752: q+1
       753: q+1
       754: 1
       762: q+1
       763: q+1
       771: 2q+1
       772: 1
       773: 2q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       787: q+1
       788: q+1
       789: q+1
       790: 2q+1
       791: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       802: q+1
       803: 1
       804: q+1
       805: q+1
       806: 1
       814: 2q+1
       815: q+1
       816: 2q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 3q+1
       825: 2q+1
       829: q+1
       830: q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       837: q+1
       838: q+1
       839: q+1
       840: 2q+1
       841: 2q+1
       844: 2q+1
       845: 1
       846: 2q+1
       847: 2q+1
       848: q+1
       849: q+1
       850: q+1
       851: 2q+1
       852: q+1
       853: q+1
       868: 1
       876: 1
       877: 1
       885: 1
       886: 1
       894: 1
       895: 1
       896: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       913: q+1
       921: 1
       922: 1
       930: q+1
       931: 1
       932: q+1
       940: q+1
       941: 1
       942: q+1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       967: q+1
       975: 1
       976: 1
       984: q+1
       985: 1
       986: q+1
       994: q+1
       995: 1
       996: q+1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1021: q+1
      1022: q+1
      1030: 2q+1
      1031: 1
      1032: 2q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1061: q+1
      1062: 1
      1063: q+1
      1064: q+1
      1065: 1
      1085: 1
      1093: 1
      1101: 1
      1102: 1
      1110: 1
      1112: 1
      1127: 1
      1135: 1
      1136: 1
      1144: 1
      1145: 1
      1153: 1
      1154: 1
      1155: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1179: 1
      1187: 1
      1188: 1
      1196: 1
      1197: 1
      1205: 1
      1206: 1
      1207: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1224: q+1
      1232: 1
      1233: 1
      1241: q+1
      1242: 1
      1243: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1300: 1
      1329: 1
      1337: 1
      1345: 1
      1346: 1
      1354: 1
      1356: 1
      1376: 1
      1384: 1
      1392: 1
      1393: 1
      1401: 1
      1403: 1
      1418: 1
      1426: 1
      1427: 1
      1435: 1
      1436: 1
      1444: 1
      1445: 1
      1446: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1515: 1
      1554: 1
      1583: 1
      1591: 1
      1599: 1
      1600: 1
      1608: 1
      1610: 1
      1721: 1

1722:    0: q+1
         1: q+1
         2: 1
         3: q+1
         4: q+1
         5: q+1
         6: 1
         7: 1
         8: 1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: 1
        15: q+1
        16: q+1
        17: 1
        18: q+1
        19: q+1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: 1
        34: 1
        35: 1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: 1
        41: 1
        42: 1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: 1
        49: q+1
        50: 1
        51: 1
        52: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: 1
        98: 1
        99: 1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: 1
       135: 1
       136: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: 1
       156: 1
       157: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: 1
       290: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: 1
       318: 1
       319: 1
       320: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       473: 1
       474: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       525: 1
       526: 1
       527: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       572: 1
       573: 1
       574: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       657: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       703: 1
       712: 1
       713: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       764: 1
       765: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       816: 1
       817: 1
       818: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       914: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       968: 1
       977: 1
       978: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1014: 1
      1023: 1
      1024: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1094: 1
      1103: 1
      1104: 1
      1112: 1
      1128: 1
      1137: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1180: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1225: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1301: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1419: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1516: 1
      1555: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1722: 1

1723:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q+1
         8: q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q+1
        21: q+1
        22: 1
        23: q+1
        24: q+1
        25: q^2+2q+1
        26: q+1
        27: q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q+1
        35: q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q+1
        42: q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q+1
        57: q+1
        58: q+1
        59: 1
        60: q+1
        61: q+1
        62: q^2+2q+1
        63: q+1
        64: q+1
        65: q^2+2q+1
        66: q+1
        67: q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q+1
        73: 1
        74: q+1
        75: q+1
        76: q^2+2q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q+1
        85: q+1
        86: 1
        87: q+1
        88: q+1
        89: q^2+2q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q+1
        99: q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: q^2+2q+1
       130: q+1
       131: q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q+1
       135: q+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q+1
       141: q+1
       142: q+1
       143: 1
       144: q+1
       145: q+1
       146: q^2+2q+1
       147: q+1
       148: q+1
       149: q^2+2q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q+1
       162: q+1
       163: q+1
       164: 1
       165: q+1
       166: q+1
       167: q^2+2q+1
       168: q+1
       169: q+1
       170: q^2+2q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: q+1
       177: q+1
       178: 1
       179: q+1
       180: q+1
       181: q^2+2q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: q+1
       221: q+1
       222: 1
       223: q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: q+1
       228: q+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: q^2+2q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q+1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: q^2+2q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q+1
       289: q+1
       290: 1
       291: 1
       292: 1
       293: 1
       294: q+1
       295: q+1
       296: q+1
       297: 1
       298: q+1
       299: q+1
       300: q^2+2q+1
       301: q+1
       302: q+1
       303: q^2+2q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: 1
       310: 1
       311: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: q+1
       351: q+1
       352: q+1
       353: 1
       354: q+1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: q+1
       388: q+1
       389: 1
       390: q+1
       391: q+1
       392: q^2+2q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q+1
       427: q+1
       428: 1
       429: q+1
       430: q+1
       431: q^2+2q+1
       432: q+1
       433: q+1
       434: q+1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: q^2+2q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: 1
       473: 1
       474: 1
       475: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       501: q+1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: 1
       517: 1
       518: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q+1
       552: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q+1
       558: q+1
       559: q+1
       560: 1
       561: q+1
       562: q+1
       563: 1
       564: 1
       565: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q+1
       605: q+1
       606: q+1
       607: 1
       608: q+1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q+1
       658: 1
       666: 1
       667: 1
       668: 1
       674: 1
       676: 1
       677: 1
       678: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: q+1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       712: 1
       713: 1
       714: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       756: 1
       764: 1
       765: 1
       766: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       807: 1
       808: 1
       809: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       870: 1
       879: 1
       887: 1
       888: 1
       889: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       915: 1
       923: 1
       924: 1
       925: 1
       931: 1
       933: 1
       934: 1
       935: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       969: 1
       977: 1
       978: 1
       979: 1
       985: 1
       987: 1
       988: 1
       989: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1015: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1049: 1
      1050: 1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1095: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1129: 1
      1138: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1163: 1
      1164: 1
      1181: 1
      1190: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1215: 1
      1216: 1
      1226: 1
      1234: 1
      1235: 1
      1236: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1302: 1
      1339: 1
      1347: 1
      1348: 1
      1349: 1
      1355: 1
      1386: 1
      1394: 1
      1395: 1
      1396: 1
      1402: 1
      1420: 1
      1429: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1454: 1
      1455: 1
      1517: 1
      1556: 1
      1593: 1
      1601: 1
      1602: 1
      1603: 1
      1609: 1
      1723: 1

1724:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: 3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: 3q+1
         7: 3q+1
         8: 3q+1
         9: 2q^2+3q+1
        10: 3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: 3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: 3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: 3q+1
        21: 3q+1
        22: 3q+1
        23: q+1
        24: q+1
        25: 3q+1
        26: 3q+1
        27: 3q+1
        28: 2q^2+3q+1
        29: 3q+1
        30: 2q^2+3q+1
        31: 3q+1
        32: 2q^2+3q+1
        33: 3q+1
        34: 3q+1
        35: 3q+1
        36: 2q^2+3q+1
        37: 3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 3q+1
        41: 3q+1
        42: 3q+1
        43: 2q^2+3q+1
        44: 3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: 3q+1
        49: 2q^2+3q+1
        50: q+1
        51: q+1
        52: 3q+1
        53: q+1
        54: q+1
        55: q+1
        56: 1
        57: 3q+1
        58: 3q+1
        59: 3q+1
        60: q+1
        61: q+1
        62: 3q+1
        63: 3q+1
        64: 3q+1
        65: 3q+1
        66: 3q+1
        67: 3q+1
        68: 2q^2+3q+1
        69: 3q+1
        70: 2q^2+3q+1
        71: 3q+1
        72: 3q+1
        73: 3q+1
        74: q+1
        75: q+1
        76: 3q+1
        77: 3q+1
        78: 3q+1
        79: 2q^2+3q+1
        80: 3q+1
        81: 2q^2+3q+1
        82: 3q+1
        83: 2q^2+3q+1
        84: 3q+1
        85: 3q+1
        86: 3q+1
        87: q+1
        88: q+1
        89: 3q+1
        90: 3q+1
        91: 3q+1
        92: 2q^2+3q+1
        93: 3q+1
        94: 2q^2+3q+1
        95: 3q+1
        96: 2q^2+3q+1
        97: 3q+1
        98: 3q+1
        99: 3q+1
       100: 2q^2+3q+1
       101: 3q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 1
       105: q+1
       106: q+1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: q+1
       114: 3q+1
       115: q+1
       116: q+1
       117: q+1
       118: 1
       119: 3q+1
       120: 3q+1
       121: 3q+1
       122: q+1
       123: q+1
       124: 3q+1
       125: 3q+1
       126: 3q+1
       127: q+1
       128: q+1
       129: 3q+1
       130: 3q+1
       131: 3q+1
       132: 2q^2+3q+1
       133: 3q+1
       134: q+1
       135: q+1
       136: 3q+1
       137: q+1
       138: q+1
       139: q+1
       140: 1
       141: 3q+1
       142: 3q+1
       143: 3q+1
       144: q+1
       145: q+1
       146: 3q+1
       147: 3q+1
       148: 3q+1
       149: 3q+1
       150: 3q+1
       151: 3q+1
       152: 2q^2+3q+1
       153: 3q+1
       154: 2q^2+3q+1
       155: q+1
       156: q+1
       157: 3q+1
       158: q+1
       159: q+1
       160: q+1
       161: 1
       162: 3q+1
       163: 3q+1
       164: 3q+1
       165: q+1
       166: q+1
       167: 3q+1
       168: 3q+1
       169: 3q+1
       170: 3q+1
       171: 3q+1
       172: 3q+1
       173: 2q^2+3q+1
       174: 3q+1
       175: 2q^2+3q+1
       176: 3q+1
       177: 3q+1
       178: 3q+1
       179: q+1
       180: q+1
       181: 3q+1
       182: 3q+1
       183: 3q+1
       184: 2q^2+3q+1
       185: 3q+1
       186: 2q^2+3q+1
       187: 3q+1
       188: 2q^2+3q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: q+1
       200: q+1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: q+1
       208: 3q+1
       209: q+1
       210: q+1
       211: q+1
       212: 1
       213: q+1
       214: q+1
       215: 3q+1
       216: q+1
       217: q+1
       218: q+1
       219: 1
       220: 3q+1
       221: 3q+1
       222: 3q+1
       223: q+1
       224: q+1
       225: 3q+1
       226: 3q+1
       227: 3q+1
       228: 1
       229: q+1
       230: q+1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: q+1
       238: 3q+1
       239: q+1
       240: q+1
       241: q+1
       242: 1
       243: 3q+1
       244: 3q+1
       245: 3q+1
       246: q+1
       247: q+1
       248: 3q+1
       249: 3q+1
       250: 3q+1
       251: q+1
       252: q+1
       253: 3q+1
       254: 3q+1
       255: 3q+1
       256: 2q^2+3q+1
       257: 3q+1
       258: 1
       259: q+1
       260: q+1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: q+1
       268: 3q+1
       269: q+1
       270: q+1
       271: q+1
       272: 1
       273: 3q+1
       274: 3q+1
       275: 3q+1
       276: q+1
       277: q+1
       278: 3q+1
       279: 3q+1
       280: 3q+1
       281: q+1
       282: q+1
       283: 3q+1
       284: 3q+1
       285: 3q+1
       286: 2q^2+3q+1
       287: 3q+1
       288: q+1
       289: q+1
       290: 3q+1
       291: q+1
       292: q+1
       293: q+1
       294: 1
       295: 3q+1
       296: 3q+1
       297: 3q+1
       298: q+1
       299: q+1
       300: 3q+1
       301: 3q+1
       302: 3q+1
       303: 3q+1
       304: 3q+1
       305: 3q+1
       306: 2q^2+3q+1
       307: 3q+1
       308: 2q^2+3q+1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: q+1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: q+1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: q+1
       346: 3q+1
       347: q+1
       348: q+1
       349: q+1
       350: 1
       351: 3q+1
       352: 3q+1
       353: 3q+1
       354: q+1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: q+1
       367: q+1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       374: q+1
       375: 3q+1
       376: q+1
       377: q+1
       378: q+1
       379: 1
       380: q+1
       381: q+1
       382: 3q+1
       383: q+1
       384: q+1
       385: q+1
       386: 1
       387: 3q+1
       388: 3q+1
       389: 3q+1
       390: q+1
       391: q+1
       392: 3q+1
       393: 3q+1
       394: 3q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: q+1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: q+1
       414: 3q+1
       415: q+1
       416: q+1
       417: q+1
       418: 1
       419: q+1
       420: q+1
       421: 3q+1
       422: q+1
       423: q+1
       424: q+1
       425: 1
       426: 3q+1
       427: 3q+1
       428: 3q+1
       429: q+1
       430: q+1
       431: 3q+1
       432: 3q+1
       433: 3q+1
       434: 1
       435: q+1
       436: q+1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: q+1
       444: 3q+1
       445: q+1
       446: q+1
       447: q+1
       448: 1
       449: 3q+1
       450: 3q+1
       451: 3q+1
       452: q+1
       453: q+1
       454: 3q+1
       455: 3q+1
       456: 3q+1
       457: q+1
       458: q+1
       459: 3q+1
       460: 3q+1
       461: 3q+1
       462: 2q^2+3q+1
       463: 3q+1
       466: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: q+1
       511: 3q+1
       512: q+1
       513: q+1
       514: q+1
       515: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: q+1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: q+1
       545: q+1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q+1
       552: q+1
       553: 3q+1
       554: q+1
       555: q+1
       556: q+1
       557: 1
       558: 3q+1
       559: 3q+1
       560: 3q+1
       561: q+1
       562: q+1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: q+1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: q+1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: q+1
       600: 3q+1
       601: q+1
       602: q+1
       603: q+1
       604: 1
       605: 3q+1
       606: 3q+1
       607: 3q+1
       608: q+1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: q+1
       621: q+1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: q+1
       629: 3q+1
       630: q+1
       631: q+1
       632: q+1
       633: 1
       634: q+1
       635: q+1
       636: 3q+1
       637: q+1
       638: q+1
       639: q+1
       640: 1
       641: 3q+1
       642: 3q+1
       643: 3q+1
       644: q+1
       645: q+1
       646: 3q+1
       647: 3q+1
       648: 3q+1
       659: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       696: q+1
       697: q+1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: q+1
       750: 3q+1
       751: q+1
       752: q+1
       753: q+1
       754: 1
       757: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: q+1
       794: q+1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: q+1
       802: 3q+1
       803: q+1
       804: q+1
       805: q+1
       806: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: q+1
       828: q+1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: q+1
       836: q+1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       843: q+1
       844: 3q+1
       845: q+1
       846: q+1
       847: q+1
       848: 1
       849: 3q+1
       850: 3q+1
       851: 3q+1
       852: q+1
       853: q+1
       871: 1
       880: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       916: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       953: q+1
       954: q+1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       970: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1007: q+1
      1008: q+1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: q+1
      1053: q+1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1061: 3q+1
      1062: q+1
      1063: q+1
      1064: q+1
      1065: 1
      1096: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1130: 1
      1139: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1182: 1
      1191: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1227: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1263: 1
      1264: q+1
      1265: q+1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1303: 1
      1340: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1387: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1421: 1
      1430: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1518: 1
      1557: 1
      1594: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1724: 1

1725:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       320: 1
       321: 1
       322: 1
       323: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       360: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       467: 1
       475: 1
       476: 1
       477: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       493: 1
       494: 1
       495: 1
       496: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       519: 1
       520: 1
       527: 1
       528: 1
       529: 1
       530: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: 1
       566: 1
       567: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       660: 1
       668: 1
       669: 1
       670: 1
       678: 1
       679: 1
       680: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: 1
       714: 1
       715: 1
       716: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       732: 1
       733: 1
       734: 1
       735: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       758: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       784: 1
       785: 1
       786: 1
       787: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: 1
       810: 1
       811: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       872: 1
       881: 1
       889: 1
       890: 1
       891: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       917: 1
       925: 1
       926: 1
       927: 1
       935: 1
       936: 1
       937: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       971: 1
       979: 1
       980: 1
       981: 1
       989: 1
       990: 1
       991: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1017: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1048: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1097: 1
      1105: 1
      1106: 1
      1107: 1
      1131: 1
      1140: 1
      1148: 1
      1149: 1
      1150: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1183: 1
      1192: 1
      1200: 1
      1201: 1
      1202: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1214: 1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1246: 1
      1247: 1
      1248: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1304: 1
      1341: 1
      1349: 1
      1350: 1
      1351: 1
      1388: 1
      1396: 1
      1397: 1
      1398: 1
      1422: 1
      1431: 1
      1439: 1
      1440: 1
      1441: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1453: 1
      1519: 1
      1558: 1
      1595: 1
      1603: 1
      1604: 1
      1605: 1
      1725: 1

1726:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       194: 1
       195: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       314: 1
       315: 1
       320: 1
       321: 1
       322: 1
       324: 1
       325: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: 1
       397: 1
       398: 1
       400: 1
       401: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       468: 1
       475: 1
       478: 1
       479: 1
       484: 1
       485: 1
       486: 1
       488: 1
       489: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: 1
       521: 1
       522: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: 1
       568: 1
       569: 1
       574: 1
       575: 1
       576: 1
       578: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       661: 1
       668: 1
       671: 1
       672: 1
       678: 1
       681: 1
       682: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       707: 1
       714: 1
       717: 1
       718: 1
       723: 1
       724: 1
       725: 1
       727: 1
       728: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       759: 1
       766: 1
       769: 1
       770: 1
       775: 1
       776: 1
       777: 1
       779: 1
       780: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: 1
       812: 1
       813: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       873: 1
       882: 1
       889: 1
       892: 1
       893: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       918: 1
       925: 1
       928: 1
       929: 1
       935: 1
       938: 1
       939: 1
       944: 1
       945: 1
       946: 1
       948: 1
       949: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       972: 1
       979: 1
       982: 1
       983: 1
       989: 1
       992: 1
       993: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1018: 1
      1025: 1
      1028: 1
      1029: 1
      1034: 1
      1035: 1
      1036: 1
      1038: 1
      1039: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1098: 1
      1105: 1
      1108: 1
      1109: 1
      1132: 1
      1141: 1
      1148: 1
      1151: 1
      1152: 1
      1157: 1
      1158: 1
      1159: 1
      1161: 1
      1162: 1
      1184: 1
      1193: 1
      1200: 1
      1203: 1
      1204: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1229: 1
      1236: 1
      1239: 1
      1240: 1
      1246: 1
      1249: 1
      1250: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1305: 1
      1342: 1
      1349: 1
      1352: 1
      1353: 1
      1389: 1
      1396: 1
      1399: 1
      1400: 1
      1423: 1
      1432: 1
      1439: 1
      1442: 1
      1443: 1
      1448: 1
      1449: 1
      1450: 1
      1452: 1
      1453: 1
      1520: 1
      1559: 1
      1596: 1
      1603: 1
      1606: 1
      1607: 1
      1726: 1

1727:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q+1
        49: q^2+q+1
        50: q+1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+q+1
        69: q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q^2+q+1
        95: q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: q+1
       102: q^2+q+1
       103: q^2+q+1
       105: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+q+1
       133: q+1
       134: q+1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+q+1
       153: q+1
       154: q^2+q+1
       155: q+1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+q+1
       174: q+1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+q+1
       185: q+1
       186: q^2+q+1
       187: q+1
       188: q^2+q+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       199: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       229: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       238: q+1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+q+1
       257: q+1
       259: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+q+1
       287: q+1
       288: q+1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+q+1
       307: q+1
       308: q^2+q+1
       312: 1
       314: 1
       316: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       329: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       366: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: q+1
       382: q+1
       383: 1
       384: q+1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       405: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       421: q+1
       422: 1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       435: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       444: q+1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+q+1
       463: q+1
       469: 1
       476: 1
       478: 1
       480: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       502: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       519: 1
       521: 1
       523: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       536: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       544: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q+1
       553: q+1
       554: 1
       555: q+1
       556: 1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       566: 1
       568: 1
       570: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       583: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       600: q+1
       601: 1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       620: q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: q+1
       636: q+1
       637: 1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       662: 1
       669: 1
       671: 1
       673: 1
       679: 1
       681: 1
       683: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       696: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 1
       715: 1
       717: 1
       719: 1
       724: 1
       726: 1
       727: 1
       728: 1
       729: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       741: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       750: q+1
       751: 1
       752: q+1
       753: 1
       754: 1
       760: 1
       767: 1
       769: 1
       771: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       793: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       802: q+1
       803: 1
       804: q+1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       827: q+1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       835: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: q+1
       845: 1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       874: 1
       883: 1
       890: 1
       892: 1
       894: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       919: 1
       926: 1
       928: 1
       930: 1
       936: 1
       938: 1
       940: 1
       945: 1
       947: 1
       948: 1
       949: 1
       950: 1
       953: q+1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       973: 1
       980: 1
       982: 1
       984: 1
       990: 1
       992: 1
       994: 1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1007: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1026: 1
      1028: 1
      1030: 1
      1035: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1052: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1061: q+1
      1062: 1
      1063: q+1
      1064: 1
      1065: 1
      1099: 1
      1106: 1
      1108: 1
      1110: 1
      1133: 1
      1142: 1
      1149: 1
      1151: 1
      1153: 1
      1158: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1185: 1
      1194: 1
      1201: 1
      1203: 1
      1205: 1
      1210: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1230: 1
      1237: 1
      1239: 1
      1241: 1
      1247: 1
      1249: 1
      1251: 1
      1256: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1264: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1306: 1
      1343: 1
      1350: 1
      1352: 1
      1354: 1
      1390: 1
      1397: 1
      1399: 1
      1401: 1
      1424: 1
      1433: 1
      1440: 1
      1442: 1
      1444: 1
      1449: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1521: 1
      1560: 1
      1597: 1
      1604: 1
      1606: 1
      1608: 1
      1727: 1

1728:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q+1
        49: q^2+q+1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+q+1
        69: q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q^2+q+1
        95: q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: q+1
       102: q^2+q+1
       103: q^2+q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+q+1
       133: q+1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+q+1
       153: q+1
       154: q^2+q+1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+q+1
       174: q+1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+q+1
       185: q+1
       186: q^2+q+1
       187: q+1
       188: q^2+q+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: 1
       214: q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+q+1
       257: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: q+1
       268: q+1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+q+1
       287: q+1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+q+1
       307: q+1
       308: q^2+q+1
       313: 1
       315: 1
       316: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: q+1
       375: q+1
       376: 1
       377: 1
       378: q+1
       379: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: q+1
       414: q+1
       415: 1
       416: 1
       417: q+1
       418: 1
       420: q+1
       421: q+1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: q+1
       444: q+1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+q+1
       463: q+1
       470: 1
       477: 1
       479: 1
       480: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: q+1
       511: q+1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: 1
       522: 1
       523: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: q+1
       553: q+1
       554: 1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       567: 1
       569: 1
       570: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       599: q+1
       600: q+1
       601: 1
       602: 1
       603: q+1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       621: q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: q+1
       629: q+1
       630: 1
       631: 1
       632: q+1
       633: 1
       635: q+1
       636: q+1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       663: 1
       670: 1
       672: 1
       673: 1
       680: 1
       682: 1
       683: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 1
       716: 1
       718: 1
       719: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: q+1
       750: q+1
       751: 1
       752: 1
       753: q+1
       754: 1
       761: 1
       768: 1
       770: 1
       771: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       801: q+1
       802: q+1
       803: 1
       804: 1
       805: q+1
       806: 1
       811: 1
       813: 1
       814: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       828: q+1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       843: q+1
       844: q+1
       845: 1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       875: 1
       884: 1
       891: 1
       893: 1
       894: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       920: 1
       927: 1
       929: 1
       930: 1
       937: 1
       939: 1
       940: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       974: 1
       981: 1
       983: 1
       984: 1
       991: 1
       993: 1
       994: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1020: 1
      1027: 1
      1029: 1
      1030: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1060: q+1
      1061: q+1
      1062: 1
      1063: 1
      1064: q+1
      1065: 1
      1100: 1
      1107: 1
      1109: 1
      1110: 1
      1134: 1
      1143: 1
      1150: 1
      1152: 1
      1153: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1186: 1
      1195: 1
      1202: 1
      1204: 1
      1205: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1231: 1
      1238: 1
      1240: 1
      1241: 1
      1248: 1
      1250: 1
      1251: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1307: 1
      1344: 1
      1351: 1
      1353: 1
      1354: 1
      1391: 1
      1398: 1
      1400: 1
      1401: 1
      1425: 1
      1434: 1
      1441: 1
      1443: 1
      1444: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1522: 1
      1561: 1
      1598: 1
      1605: 1
      1607: 1
      1608: 1
      1728: 1

1729:    0: 2q^2+1
         1: q^2+1
         2: 2q^2+1
         3: 2q^2+1
         4: 2q^2+1
         5: 2q^2+1
         6: q^2+1
         7: 1
         8: 2q^2+1
         9: q^2+1
        10: 2q^2+1
        11: 2q^2+1
        12: 2q^2+1
        13: q^2+1
        14: 2q^2+1
        15: 2q^2+1
        16: q^2+1
        17: 2q^2+1
        18: 2q^2+1
        19: 2q^2+1
        20: q^2+1
        21: 1
        22: 1
        23: q^2+1
        24: q^2+1
        25: q^2+1
        26: 1
        27: 2q^2+1
        28: q^2+1
        29: 2q^2+1
        30: q^2+1
        31: 2q^2+1
        32: 2q^2+1
        33: q^2+1
        34: 1
        35: 2q^2+1
        36: q^2+1
        37: 2q^2+1
        38: 2q^2+1
        39: 2q^2+1
        40: q^2+1
        41: 1
        42: 2q^2+1
        43: q^2+1
        44: 2q^2+1
        45: 2q^2+1
        46: 2q^2+1
        47: q^2+1
        48: 2q^2+1
        49: 2q^2+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: q^2+1
        58: 1
        59: 1
        60: q^2+1
        61: q^2+1
        62: q^2+1
        63: 1
        64: 2q^2+1
        65: q^2+1
        66: 1
        67: 2q^2+1
        68: q^2+1
        69: 2q^2+1
        70: 2q^2+1
        71: q^2+1
        72: 1
        73: 1
        74: q^2+1
        75: q^2+1
        76: q^2+1
        77: 1
        78: 2q^2+1
        79: q^2+1
        80: 2q^2+1
        81: q^2+1
        82: 2q^2+1
        83: 2q^2+1
        84: q^2+1
        85: 1
        86: 1
        87: q^2+1
        88: q^2+1
        89: q^2+1
        90: 1
        91: 2q^2+1
        92: q^2+1
        93: 2q^2+1
        94: q^2+1
        95: 2q^2+1
        96: 2q^2+1
        97: q^2+1
        98: 1
        99: 2q^2+1
       100: q^2+1
       101: 2q^2+1
       102: 2q^2+1
       103: 2q^2+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: q^2+1
       120: 1
       121: 1
       122: q^2+1
       123: q^2+1
       124: q^2+1
       125: 1
       126: 1
       127: q^2+1
       128: q^2+1
       129: q^2+1
       130: 1
       131: 2q^2+1
       132: q^2+1
       133: 2q^2+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: q^2+1
       142: 1
       143: 1
       144: q^2+1
       145: q^2+1
       146: q^2+1
       147: 1
       148: 2q^2+1
       149: q^2+1
       150: 1
       151: 2q^2+1
       152: q^2+1
       153: 2q^2+1
       154: 2q^2+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: q^2+1
       163: 1
       164: 1
       165: q^2+1
       166: q^2+1
       167: q^2+1
       168: 1
       169: 2q^2+1
       170: q^2+1
       171: 1
       172: 2q^2+1
       173: q^2+1
       174: 2q^2+1
       175: 2q^2+1
       176: q^2+1
       177: 1
       178: 1
       179: q^2+1
       180: q^2+1
       181: q^2+1
       182: 1
       183: 2q^2+1
       184: q^2+1
       185: 2q^2+1
       186: q^2+1
       187: 2q^2+1
       188: 2q^2+1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: q^2+1
       221: 1
       222: 1
       223: q^2+1
       224: q^2+1
       225: q^2+1
       226: 1
       227: 2q^2+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q^2+1
       244: 1
       245: 1
       246: q^2+1
       247: q^2+1
       248: q^2+1
       249: 1
       250: 1
       251: q^2+1
       252: q^2+1
       253: q^2+1
       254: 1
       255: 2q^2+1
       256: q^2+1
       257: 2q^2+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q^2+1
       274: 1
       275: 1
       276: q^2+1
       277: q^2+1
       278: q^2+1
       279: 1
       280: 1
       281: q^2+1
       282: q^2+1
       283: q^2+1
       284: 1
       285: 2q^2+1
       286: q^2+1
       287: 2q^2+1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: q^2+1
       296: 1
       297: 1
       298: q^2+1
       299: q^2+1
       300: q^2+1
       301: 1
       302: 2q^2+1
       303: q^2+1
       304: 1
       305: 2q^2+1
       306: q^2+1
       307: 2q^2+1
       308: 2q^2+1
       316: 1
       317: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q^2+1
       352: 1
       353: 1
       354: q^2+1
       355: q^2+1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: q^2+1
       388: 1
       389: 1
       390: q^2+1
       391: q^2+1
       392: q^2+1
       393: 1
       394: 2q^2+1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: q^2+1
       427: 1
       428: 1
       429: q^2+1
       430: q^2+1
       431: q^2+1
       432: 1
       433: 2q^2+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q^2+1
       450: 1
       451: 1
       452: q^2+1
       453: q^2+1
       454: q^2+1
       455: 1
       456: 1
       457: q^2+1
       458: q^2+1
       459: q^2+1
       460: 1
       461: 2q^2+1
       462: q^2+1
       463: 2q^2+1
       471: 1
       480: 1
       481: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       523: 1
       524: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: q^2+1
       559: 1
       560: 1
       561: q^2+1
       562: q^2+1
       570: 1
       571: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: q^2+1
       606: 1
       607: 1
       608: q^2+1
       609: q^2+1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: q^2+1
       642: 1
       643: 1
       644: q^2+1
       645: q^2+1
       646: q^2+1
       647: 1
       648: 2q^2+1
       664: 1
       673: 1
       674: 1
       683: 1
       684: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       719: 1
       720: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       762: 1
       771: 1
       772: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       814: 1
       815: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: q^2+1
       850: 1
       851: 1
       852: q^2+1
       853: q^2+1
       876: 1
       885: 1
       894: 1
       895: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       921: 1
       930: 1
       931: 1
       940: 1
       941: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       975: 1
       984: 1
       985: 1
       994: 1
       995: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1021: 1
      1030: 1
      1031: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1101: 1
      1110: 1
      1111: 1
      1135: 1
      1144: 1
      1153: 1
      1154: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1187: 1
      1196: 1
      1205: 1
      1206: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1232: 1
      1241: 1
      1242: 1
      1251: 1
      1252: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1308: 1
      1345: 1
      1354: 1
      1355: 1
      1392: 1
      1401: 1
      1402: 1
      1426: 1
      1435: 1
      1444: 1
      1445: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1523: 1
      1562: 1
      1599: 1
      1608: 1
      1609: 1
      1729: 1

1730:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        53: 1
        54: 1
        55: 1
        56: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       108: 1
       109: 1
       110: 1
       111: 1
       115: 1
       116: 1
       117: 1
       118: 1
       120: 1
       121: 1
       122: 1
       123: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       137: 1
       138: 1
       139: 1
       140: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       158: 1
       159: 1
       160: 1
       161: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       195: 1
       196: 1
       197: 1
       202: 1
       203: 1
       204: 1
       205: 1
       209: 1
       210: 1
       211: 1
       212: 1
       216: 1
       217: 1
       218: 1
       219: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       232: 1
       233: 1
       234: 1
       235: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       245: 1
       246: 1
       247: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       262: 1
       263: 1
       264: 1
       265: 1
       269: 1
       270: 1
       271: 1
       272: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       291: 1
       292: 1
       293: 1
       294: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       317: 1
       318: 1
       325: 1
       326: 1
       327: 1
       332: 1
       333: 1
       334: 1
       335: 1
       340: 1
       341: 1
       342: 1
       343: 1
       347: 1
       348: 1
       349: 1
       350: 1
       352: 1
       353: 1
       354: 1
       355: 1
       362: 1
       363: 1
       364: 1
       369: 1
       370: 1
       371: 1
       372: 1
       376: 1
       377: 1
       378: 1
       379: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       401: 1
       402: 1
       403: 1
       408: 1
       409: 1
       410: 1
       411: 1
       415: 1
       416: 1
       417: 1
       418: 1
       422: 1
       423: 1
       424: 1
       425: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       438: 1
       439: 1
       440: 1
       441: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       472: 1
       481: 1
       482: 1
       489: 1
       490: 1
       491: 1
       498: 1
       499: 1
       500: 1
       505: 1
       506: 1
       507: 1
       508: 1
       512: 1
       513: 1
       514: 1
       515: 1
       524: 1
       525: 1
       532: 1
       533: 1
       534: 1
       539: 1
       540: 1
       541: 1
       542: 1
       547: 1
       548: 1
       549: 1
       550: 1
       554: 1
       555: 1
       556: 1
       557: 1
       559: 1
       560: 1
       561: 1
       562: 1
       571: 1
       572: 1
       579: 1
       580: 1
       581: 1
       586: 1
       587: 1
       588: 1
       589: 1
       594: 1
       595: 1
       596: 1
       597: 1
       601: 1
       602: 1
       603: 1
       604: 1
       606: 1
       607: 1
       608: 1
       609: 1
       616: 1
       617: 1
       618: 1
       623: 1
       624: 1
       625: 1
       626: 1
       630: 1
       631: 1
       632: 1
       633: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       665: 1
       674: 1
       675: 1
       684: 1
       685: 1
       692: 1
       693: 1
       694: 1
       699: 1
       700: 1
       701: 1
       702: 1
       711: 1
       720: 1
       721: 1
       728: 1
       729: 1
       730: 1
       737: 1
       738: 1
       739: 1
       744: 1
       745: 1
       746: 1
       747: 1
       751: 1
       752: 1
       753: 1
       754: 1
       763: 1
       772: 1
       773: 1
       780: 1
       781: 1
       782: 1
       789: 1
       790: 1
       791: 1
       796: 1
       797: 1
       798: 1
       799: 1
       803: 1
       804: 1
       805: 1
       806: 1
       815: 1
       816: 1
       823: 1
       824: 1
       825: 1
       830: 1
       831: 1
       832: 1
       833: 1
       838: 1
       839: 1
       840: 1
       841: 1
       845: 1
       846: 1
       847: 1
       848: 1
       850: 1
       851: 1
       852: 1
       853: 1
       877: 1
       886: 1
       895: 1
       896: 1
       903: 1
       904: 1
       905: 1
       922: 1
       931: 1
       932: 1
       941: 1
       942: 1
       949: 1
       950: 1
       951: 1
       956: 1
       957: 1
       958: 1
       959: 1
       976: 1
       985: 1
       986: 1
       995: 1
       996: 1
      1003: 1
      1004: 1
      1005: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1022: 1
      1031: 1
      1032: 1
      1039: 1
      1040: 1
      1041: 1
      1048: 1
      1049: 1
      1050: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1102: 1
      1111: 1
      1112: 1
      1136: 1
      1145: 1
      1154: 1
      1155: 1
      1162: 1
      1163: 1
      1164: 1
      1188: 1
      1197: 1
      1206: 1
      1207: 1
      1214: 1
      1215: 1
      1216: 1
      1233: 1
      1242: 1
      1243: 1
      1252: 1
      1253: 1
      1260: 1
      1261: 1
      1262: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1309: 1
      1346: 1
      1355: 1
      1356: 1
      1393: 1
      1402: 1
      1403: 1
      1427: 1
      1436: 1
      1445: 1
      1446: 1
      1453: 1
      1454: 1
      1455: 1
      1524: 1
      1563: 1
      1600: 1
      1609: 1
      1610: 1
      1730: 1

1731:    0: q^4+q^2+q+1
         1: q^4+q^2+q+1
         2: q^4+q^2+q+1
         3: q^4+q^2+q+1
         4: q+1
         5: q+1
         6: q^4+q^2+q+1
         7: q^4+q^2+q+1
         8: q^4+q^2+q+1
         9: q^4+q^2+q+1
        10: q^4+q^2+q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^4+q^2+q+1
        21: q^4+q^2+q+1
        22: q^4+q^2+q+1
        23: q+1
        24: q+1
        25: q^4+q^2+q+1
        26: q^4+q^2+q+1
        27: q^4+q^2+q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q^4+q^2+q+1
        53: q^4+q^2+q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^4+q^2+q+1
        58: q^4+q^2+q+1
        59: q^4+q^2+q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q^4+q^2+q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q^4+q^2+q+1
       115: q^4+q^2+q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q^4+q^2+q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       464: q+1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: 1
       478: 1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       646: 1
       647: 1
       648: 1
       649: q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       836: 1
       837: 1
       839: 1
       844: 1
       845: 1
       849: 1
       850: 1
       851: 1
       854: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1045: 1
      1047: 1
      1054: 1
      1061: 1
      1062: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1237: 1
      1250: 1
      1266: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1404: 1
      1411: 1
      1412: 1
      1418: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1467: 1
      1471: 1
      1478: 1
      1479: 1
      1485: 1
      1490: 1
      1501: 1
      1503: 1
      1506: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1569: 1
      1611: 1
      1612: 1
      1613: 1
      1625: 1
      1643: 1
      1667: 1
      1731: 1

1732:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q+1
         5: q^3+q^2+q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q^3+q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^3+q^2+q+1
        17: q^3+q^2+q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q^3+q^2+q+1
        21: q^3+q^2+q+1
        22: q^3+q^2+q+1
        23: q^3+q^2+q+1
        24: q+1
        25: q^3+q^2+q+1
        26: q^3+q^2+q+1
        27: q^3+q^2+q+1
        28: q^3+q^2+q+1
        29: q^3+q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^3+q^2+q+1
        41: q^3+q^2+q+1
        42: q^3+q^2+q+1
        43: q^3+q^2+q+1
        44: q^2+1
        45: q^3+q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^3+q^2+q+1
        51: q+1
        52: q^3+q^2+q+1
        53: q^3+q^2+q+1
        54: q^3+q^2+q+1
        55: q+1
        56: q+1
        57: q^3+q^2+q+1
        58: q^3+q^2+q+1
        59: q^3+q^2+q+1
        60: q^3+q^2+q+1
        61: q+1
        62: q^3+q^2+q+1
        63: q^3+q^2+q+1
        64: q^3+q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q^3+q^2+q+1
        85: q^3+q^2+q+1
        86: q^3+q^2+q+1
        87: q^3+q^2+q+1
        88: q+1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^3+q^2+q+1
        93: q^2+1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q^3+q^2+q+1
       106: q+1
       107: q^3+q^2+q+1
       108: q^3+q^2+q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^3+q^2+q+1
       113: q+1
       114: q^3+q^2+q+1
       115: q^3+q^2+q+1
       116: q^3+q^2+q+1
       117: q+1
       118: q+1
       119: q^3+q^2+q+1
       120: q^3+q^2+q+1
       121: q^3+q^2+q+1
       122: q^3+q^2+q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^3+q^2+q+1
       156: q+1
       157: q^3+q^2+q+1
       158: q^2+1
       159: q^3+q^2+q+1
       160: q+1
       161: q+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q^3+q^2+q+1
       192: q+1
       193: q^3+q^2+q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q^3+q^2+q+1
       200: q+1
       201: q^3+q^2+q+1
       202: q^3+q^2+q+1
       203: q+1
       204: q+1
       205: q+1
       206: q^3+q^2+q+1
       207: q+1
       208: q^3+q^2+q+1
       209: q^2+1
       210: q^3+q^2+q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q^3+q^2+q+1
       260: q+1
       261: q^2+1
       262: q^2+1
       263: 1
       264: q+1
       265: q+1
       266: q^2+1
       267: 1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: 1
       273: q^2+1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q^3+q^2+q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q^3+q^2+q+1
       322: q+1
       323: q^3+q^2+q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q^3+q^2+q+1
       330: q+1
       331: q^2+1
       332: q^2+1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q^2+1
       398: 1
       399: q^2+1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: q^2+1
       406: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q^3+q^2+q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: q^2+1
       486: 1
       487: q^2+1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: q+1
       565: 1
       566: q^2+1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q^2+1
       576: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q^2+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: q^2+1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q^2+1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       942: 1
       953: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: q^2+1
       981: 1
       982: 1
       983: 1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1139: 1
      1141: 1
      1142: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1227: 1
      1229: 1
      1230: 1
      1244: 1
      1245: 1
      1253: 1
      1264: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1303: 1
      1305: 1
      1306: 1
      1311: 1
      1333: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1414: 1
      1428: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1481: 1
      1525: 1
      1526: 1
      1527: 1
      1536: 1
      1555: 1
      1565: 1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1621: 1
      1662: 1
      1732: 1

1733:    0: q^4+4q^3+5q^2+3q+1
         1: 2q^3+5q^2+3q+1
         2: q^4+4q^3+5q^2+3q+1
         3: q^4+4q^3+5q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: q^4+4q^3+5q^2+3q+1
         6: 2q^3+5q^2+3q+1
         7: 2q^3+5q^2+3q+1
         8: q^4+4q^3+5q^2+3q+1
         9: 2q^3+5q^2+3q+1
        10: q^4+4q^3+5q^2+3q+1
        11: q^4+4q^3+5q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: q^3+4q^2+3q+1
        14: 2q^3+4q^2+3q+1
        15: q^3+2q^2+3q+1
        16: 2q^3+5q^2+3q+1
        17: q^4+4q^3+5q^2+3q+1
        18: 2q^3+4q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^3+5q^2+3q+1
        22: 2q^3+5q^2+3q+1
        23: q^4+4q^3+5q^2+3q+1
        24: 2q^3+4q^2+3q+1
        25: 2q^3+5q^2+3q+1
        26: 2q^3+5q^2+3q+1
        27: q^4+4q^3+5q^2+3q+1
        28: 2q^3+5q^2+3q+1
        29: q^4+4q^3+5q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^3+4q^2+3q+1
        32: 2q^3+4q^2+3q+1
        33: q^3+4q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+2q^2+3q+1
        36: 2q^2+3q+1
        37: q^3+2q^2+3q+1
        38: q^3+2q^2+3q+1
        39: q^3+2q^2+3q+1
        40: 2q^3+5q^2+3q+1
        41: 2q^3+5q^2+3q+1
        42: 2q^3+4q^2+3q+1
        43: q^3+4q^2+3q+1
        44: 2q^3+4q^2+3q+1
        45: 2q^3+4q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+4q^2+3q+1
        48: 2q^3+4q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^2+2q+1
        52: q^3+3q^2+3q+1
        53: 2q^3+5q^2+3q+1
        54: 2q^3+5q^2+3q+1
        55: q^3+4q^2+3q+1
        56: 2q^3+4q^2+3q+1
        57: q^3+3q^2+3q+1
        58: 2q^3+5q^2+3q+1
        59: 2q^3+5q^2+3q+1
        60: q^4+4q^3+5q^2+3q+1
        61: 2q^3+4q^2+3q+1
        62: 2q^3+5q^2+3q+1
        63: 2q^3+5q^2+3q+1
        64: 2q^3+4q^2+3q+1
        65: q^3+4q^2+3q+1
        66: q^3+4q^2+3q+1
        67: q^3+2q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^3+4q^2+3q+1
        73: 2q^2+3q+1
        74: q^3+2q^2+3q+1
        75: q^3+2q^2+3q+1
        76: 2q^2+3q+1
        77: q^2+q+1
        78: q^3+2q^2+3q+1
        79: 2q^2+3q+1
        80: q^3+2q^2+3q+1
        81: 2q^2+3q+1
        82: q^3+2q^2+3q+1
        83: q^3+2q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^3+5q^2+3q+1
        86: q^3+4q^2+3q+1
        87: 2q^3+4q^2+3q+1
        88: 2q^2+3q+1
        89: q^3+4q^2+3q+1
        90: 2q^2+2q+1
        91: 2q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: 2q^3+4q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q^2+3q+1
       104: q^2+2q+1
       105: q^3+3q^2+3q+1
       106: q^2+2q+1
       107: q^3+3q^2+3q+1
       108: 2q^3+5q^2+3q+1
       109: q^3+4q^2+3q+1
       110: q^3+4q^2+3q+1
       111: 2q^2+3q+1
       112: q^3+3q^2+3q+1
       113: q^2+2q+1
       114: q^3+3q^2+3q+1
       115: 2q^3+5q^2+3q+1
       116: 2q^3+5q^2+3q+1
       117: q^3+4q^2+3q+1
       118: 2q^3+4q^2+3q+1
       119: 2q^2+3q+1
       120: 2q^3+5q^2+3q+1
       121: q^3+4q^2+3q+1
       122: 2q^3+4q^2+3q+1
       123: 2q^2+3q+1
       124: q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^2+3q+1
       127: q^3+2q^2+3q+1
       128: q^3+2q^2+3q+1
       129: q^3+4q^2+3q+1
       130: q^3+4q^2+3q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^2+3q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: q^3+2q^2+3q+1
       141: q^2+3q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q^3+2q^2+3q+1
       145: q^3+2q^2+3q+1
       146: 2q^2+3q+1
       147: q^2+q+1
       148: q^2+q+1
       149: 2q^2+3q+1
       150: q^2+q+1
       151: q^3+2q^2+3q+1
       152: 2q^2+3q+1
       153: q^3+2q^2+3q+1
       154: 2q^2+3q+1
       155: 2q^2+3q+1
       156: 2q+1
       157: 2q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^2+3q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^3+4q^2+3q+1
       166: 2q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^2+2q+1
       169: 2q^3+4q^2+3q+1
       170: 2q^2+3q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+3q+1
       176: q^2+3q+1
       177: q^3+4q^2+3q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: q^2+3q+1
       181: 2q^2+3q+1
       182: q+1
       183: 2q^2+3q+1
       184: 2q^2+3q+1
       185: 2q^2+3q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: q+1
       190: q^2+2q+1
       191: q^3+3q^2+3q+1
       192: q^2+2q+1
       193: 2q^2+3q+1
       194: q^2+3q+1
       195: q^3+4q^2+3q+1
       196: 2q^2+3q+1
       197: 2q^2+3q+1
       198: q^2+2q+1
       199: q^3+3q^2+3q+1
       200: q^2+2q+1
       201: q^3+3q^2+3q+1
       202: 2q^3+5q^2+3q+1
       203: q^3+4q^2+3q+1
       204: q^3+4q^2+3q+1
       205: 2q^2+3q+1
       206: 2q^2+3q+1
       207: 2q+1
       208: 2q^2+3q+1
       209: q^3+4q^2+3q+1
       210: q^3+4q^2+3q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: q^2+3q+1
       214: 2q+1
       215: q^2+3q+1
       216: 2q^2+3q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: q^3+2q^2+3q+1
       220: q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: q^2+3q+1
       225: 2q^2+3q+1
       226: q+1
       227: 2q^2+3q+1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q^2+3q+1
       232: 2q^2+3q+1
       233: 2q^2+3q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+3q+1
       237: 2q+1
       238: q+1
       239: q^2+q+1
       240: q^2+q+1
       241: q^2+q+1
       242: q^3+2q^2+3q+1
       243: q+1
       244: q^2+q+1
       245: q^2+1
       246: q^2+q+1
       248: q^2+3q+1
       249: q^2+q+1
       250: q^2+q+1
       251: q^3+2q^2+3q+1
       252: q^3+2q^2+3q+1
       253: 2q^2+3q+1
       254: q^2+q+1
       255: q^2+q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: 2q+1
       259: 2q^2+3q+1
       260: 2q+1
       261: 2q^2+3q+1
       262: q^3+4q^2+3q+1
       263: 2q^2+3q+1
       264: 2q^2+3q+1
       265: q^2+3q+1
       266: 2q^2+3q+1
       267: 2q+1
       268: q^2+2q+1
       269: 2q^2+2q+1
       270: 2q^2+2q+1
       271: q^2+2q+1
       272: 2q^2+3q+1
       273: 2q^2+3q+1
       274: 2q^2+2q+1
       275: 2q^2+2q+1
       276: 2q^3+4q^2+3q+1
       277: 2q^2+3q+1
       278: 2q+1
       279: q^2+2q+1
       280: q+1
       281: 2q+1
       282: 2q+1
       283: 2q^2+3q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+3q+1
       287: q^2+3q+1
       288: q^2+3q+1
       289: 2q+1
       290: q^2+3q+1
       291: 2q^2+3q+1
       292: 2q^2+3q+1
       293: q^2+3q+1
       294: q^2+3q+1
       295: q^2+3q+1
       296: q+1
       297: q+1
       298: 2q^2+3q+1
       299: q^2+3q+1
       300: 2q^2+3q+1
       301: q+1
       302: q^2+q+1
       303: q^2+3q+1
       304: q+1
       305: 2q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: q+1
       310: q+1
       311: q^2+2q+1
       312: 2q^2+3q+1
       313: 2q+1
       314: q^2+3q+1
       315: 2q+1
       316: q^2+3q+1
       317: 2q^2+3q+1
       318: q+1
       319: q+1
       320: q^2+2q+1
       321: q^3+3q^2+3q+1
       322: q^2+2q+1
       323: 2q^2+3q+1
       324: q^2+3q+1
       325: q^3+4q^2+3q+1
       326: 2q^2+3q+1
       327: 2q^2+3q+1
       328: 2q+1
       329: 2q^2+3q+1
       330: 2q+1
       331: 2q^2+3q+1
       332: q^3+4q^2+3q+1
       333: 2q^2+3q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: 2q+1
       337: q^2+3q+1
       338: 2q+1
       339: q^2+3q+1
       340: 2q^2+3q+1
       341: 2q^2+3q+1
       342: 2q^2+3q+1
       343: 2q^2+3q+1
       344: q^2+3q+1
       345: 2q+1
       346: q^2+3q+1
       347: 2q^2+3q+1
       348: 2q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q^2+3q+1
       352: q+1
       353: q+1
       354: 2q^2+3q+1
       355: q^2+3q+1
       356: q+1
       357: 2q+1
       358: q^2+3q+1
       359: 2q+1
       360: q+1
       361: q^2+3q+1
       362: 2q^2+3q+1
       363: 2q^2+3q+1
       364: 2q^2+3q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q^2+q+1
       370: q^2+q+1
       371: q^2+q+1
       372: q^2+q+1
       373: q+1
       375: 1
       376: q^2+1
       377: q^2+1
       380: q^2+3q+1
       381: 2q+1
       382: q+1
       383: q^2+q+1
       384: q^2+q+1
       385: q^2+q+1
       386: q^3+2q^2+3q+1
       387: q+1
       388: q^2+q+1
       389: q^2+1
       390: q^2+q+1
       392: 2q^2+3q+1
       393: q+1
       394: q^2+q+1
       395: q+1
       396: 2q+1
       397: 2q^2+3q+1
       398: 2q+1
       399: 2q^2+3q+1
       400: 2q+1
       401: 2q^2+3q+1
       402: q^2+3q+1
       403: q^2+3q+1
       404: 2q+1
       405: q^2+2q+1
       406: q+1
       407: q^2+2q+1
       408: 2q^2+2q+1
       409: q^2+2q+1
       410: q^2+2q+1
       411: 2q+1
       412: 2q^2+3q+1
       413: 2q+1
       414: q^2+2q+1
       415: 2q^2+2q+1
       416: 2q^2+2q+1
       417: q^2+2q+1
       418: 2q^2+3q+1
       419: 2q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: 2q+1
       426: 2q+1
       427: q^2+2q+1
       428: q+1
       429: 2q+1
       430: 2q+1
       431: q^2+3q+1
       432: q+1
       433: 2q+1
       434: 2q+1
       435: q^2+3q+1
       436: 2q+1
       437: q^2+3q+1
       438: 2q^2+3q+1
       439: q^2+3q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: q^2+3q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q^2+3q+1
       449: q+1
       450: q+1
       451: 1
       452: q^2+q+1
       454: 2q+1
       455: q+1
       456: 1
       457: 2q+1
       458: 2q+1
       459: q^2+3q+1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: q+1
       466: q+1
       467: 2q+1
       468: 2q+1
       469: q^2+3q+1
       470: 2q+1
       471: q^2+3q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+2q+1
       476: 2q^2+3q+1
       477: 2q+1
       478: q^2+3q+1
       479: 2q+1
       480: q^2+3q+1
       481: 2q^2+3q+1
       482: q+1
       483: q+1
       484: 2q+1
       485: 2q^2+3q+1
       486: 2q+1
       487: 2q^2+3q+1
       488: 2q+1
       489: 2q^2+3q+1
       490: q^2+3q+1
       491: q^2+3q+1
       492: q+1
       493: 2q+1
       494: q^2+3q+1
       495: 2q+1
       496: q+1
       497: q^2+3q+1
       498: 2q^2+3q+1
       499: 2q^2+3q+1
       500: 2q^2+3q+1
       501: 2q+1
       502: q^2+3q+1
       503: 2q+1
       504: q^2+3q+1
       505: 2q^2+3q+1
       506: q^2+3q+1
       507: q^2+3q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q^2+3q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       521: q^2+3q+1
       522: 2q+1
       523: q+1
       524: 2q^2+3q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q^2+q+1
       533: q^2+1
       534: q^2+q+1
       536: 1
       538: 1
       539: q^2+1
       543: 2q+1
       544: q+1
       545: q+1
       546: q+1
       547: q^2+q+1
       548: q^2+q+1
       549: q^2+q+1
       550: q^2+q+1
       551: q+1
       553: 1
       554: q^2+1
       555: q^2+1
       558: q+1
       559: q+1
       560: 1
       561: q^2+q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: 2q^2+3q+1
       567: 2q+1
       568: 2q+1
       569: q+1
       570: 2q+1
       571: q^2+3q+1
       572: q+1
       573: 1
       574: q+1
       575: q^2+2q+1
       576: q+1
       577: q^2+2q+1
       578: q+1
       579: q^2+2q+1
       580: q+1
       581: 2q+1
       582: 2q+1
       583: q^2+2q+1
       584: q+1
       585: q^2+2q+1
       586: 2q^2+2q+1
       587: q^2+2q+1
       588: q^2+2q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 2q+1
       598: 2q+1
       599: q+1
       600: q+1
       601: q+1
       602: q+1
       603: q+1
       604: 2q+1
       605: 2q+1
       606: q+1
       607: 1
       608: 2q+1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: q^2+3q+1
       613: 2q+1
       614: q+1
       615: 2q+1
       616: q^2+3q+1
       617: q^2+3q+1
       618: q^2+3q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: 2q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 2q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       646: q^2+3q+1
       647: q+1
       648: q+1
       650: q+1
       651: q+1
       652: q+1
       653: 2q+1
       654: q^2+3q+1
       655: 2q+1
       656: q+1
       658: q+1
       659: q+1
       660: 2q+1
       661: 2q+1
       662: q^2+3q+1
       663: 2q+1
       664: q^2+3q+1
       665: q+1
       666: q+1
       667: q+1
       668: 2q+1
       669: 2q^2+3q+1
       670: 2q+1
       671: 2q+1
       672: q+1
       673: 2q+1
       674: q^2+3q+1
       675: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       681: q^2+3q+1
       682: 2q+1
       683: q+1
       684: 2q^2+3q+1
       685: q+1
       686: q+1
       687: 2q+1
       688: q^2+3q+1
       689: 2q+1
       690: q+1
       691: 2q+1
       692: q^2+3q+1
       693: q^2+3q+1
       694: q^2+3q+1
       695: 2q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       704: q+1
       705: 1
       707: 2q+1
       708: q+1
       710: q+1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       717: q+1
       718: q+1
       719: 1
       720: q^2+1
       721: 1
       724: 1
       726: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q^2+q+1
       738: q^2+1
       739: q^2+q+1
       741: 1
       743: 1
       744: q^2+1
       748: q+1
       750: 1
       751: 1
       752: 1
       756: q+1
       757: 1
       758: 2q+1
       759: q+1
       760: 2q+1
       761: q+1
       762: 2q+1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q^2+2q+1
       768: q+1
       769: q+1
       770: 1
       771: q+1
       772: q+1
       773: 1
       774: 1
       775: q+1
       776: q^2+2q+1
       777: q+1
       778: q^2+2q+1
       779: q+1
       780: q^2+2q+1
       781: q+1
       782: 2q+1
       783: 1
       784: 1
       785: q+1
       786: 1
       788: q+1
       789: q+1
       790: q+1
       791: 2q+1
       792: q+1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: q+1
       798: q+1
       799: 2q+1
       800: 2q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       812: 2q+1
       813: q+1
       814: q+1
       815: q^2+3q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: q+1
       827: 1
       829: 1
       830: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: q+1
       844: 1
       845: 1
       846: 1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       855: q+1
       856: q+1
       857: q+1
       858: 2q+1
       859: q+1
       860: q+1
       862: q+1
       863: q+1
       864: q+1
       865: 2q+1
       866: q^2+3q+1
       867: 2q+1
       868: q+1
       870: q+1
       871: 1
       872: 2q+1
       873: q+1
       874: 2q+1
       875: q+1
       876: 2q+1
       877: q+1
       879: q+1
       880: 1
       882: 2q+1
       883: q+1
       885: q+1
       886: q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       892: 2q+1
       893: q+1
       894: q+1
       895: q^2+3q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: q+1
       907: 1
       909: 1
       911: q+1
       913: 1
       915: 1
       916: 1
       918: q+1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       938: q+1
       939: q+1
       940: 1
       941: q^2+1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       961: 1
       962: 1
       963: 1
       964: q+1
       965: 2q+1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: q+1
       974: 1
       975: q+1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q^2+2q+1
       981: q+1
       982: q+1
       983: 1
       984: q+1
       985: q+1
       986: 1
       987: 1
       988: 1
       989: 1
       992: q+1
       993: 1
       995: q+1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: q+1
      1003: q+1
      1004: q+1
      1005: 2q+1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q+1
      1015: q+1
      1016: 1
      1018: q+1
      1019: q+1
      1021: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1052: 1
      1054: 1
      1055: 1
      1059: q+1
      1061: 1
      1062: 1
      1063: 1
      1068: q+1
      1069: 1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: q+1
      1083: 2q+1
      1084: q+1
      1085: 1
      1087: 1
      1089: 1
      1091: q+1
      1093: 1
      1095: q+1
      1096: 1
      1098: q+1
      1099: q+1
      1101: q+1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1115: 1
      1118: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1138: 1
      1139: 1
      1141: q+1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1166: 1
      1167: 1
      1168: 1
      1169: q+1
      1170: 1
      1171: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: q+1
      1178: 1
      1179: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: q+1
      1186: 1
      1187: q+1
      1188: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: q+1
      1204: 1
      1206: q+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: 1
      1220: 1
      1222: q+1
      1224: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1272: 1
      1273: 1
      1276: q+1
      1277: 1
      1278: q+1
      1280: 1
      1281: 1
      1282: 1
      1283: q+1
      1284: 1
      1285: 1
      1288: 1
      1291: 1
      1294: 1
      1296: 1
      1298: q+1
      1300: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1317: 1
      1320: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: q+1
      1375: 1
      1376: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1406: 1
      1409: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1429: 1
      1432: 1
      1436: 1
      1449: 1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1473: 1
      1476: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1503: 1
      1506: 1
      1526: 1
      1527: 1
      1530: 1
      1532: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1556: 1
      1559: 1
      1563: 1
      1571: 1
      1574: 1
      1613: 1
      1615: 1
      1616: 1
      1627: 1
      1630: 1
      1663: 1
      1669: 1
      1671: 1
      1733: 1

1734:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q+1
        12: q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^3+q^2+q+1
        21: q^3+q^2+q+1
        22: q^3+q^2+q+1
        23: q+1
        24: q^3+q^2+q+1
        25: q^3+q^2+q+1
        26: q^3+q^2+q+1
        27: q^3+q^2+q+1
        28: q+1
        29: q+1
        30: q^3+q^2+q+1
        31: q^3+q^2+q+1
        32: q+1
        33: q^3+q^2+q+1
        34: q^3+q^2+q+1
        35: q^3+q^2+q+1
        36: q^3+q^2+q+1
        37: q^2+1
        38: q+1
        39: q^3+q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q^3+q^2+q+1
        52: q^3+q^2+q+1
        53: q^3+q^2+q+1
        54: q+1
        55: q^3+q^2+q+1
        56: q+1
        57: q^3+q^2+q+1
        58: q^3+q^2+q+1
        59: q^3+q^2+q+1
        60: q+1
        61: q^3+q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^3+q^2+q+1
        66: q^3+q^2+q+1
        67: q^3+q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^3+q^2+q+1
        72: q^3+q^2+q+1
        73: q^3+q^2+q+1
        74: q+1
        75: q^3+q^2+q+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: q+1
        80: 1
        81: q^3+q^2+q+1
        82: q^2+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q^3+q^2+q+1
       107: q^3+q^2+q+1
       108: q+1
       109: q^3+q^2+q+1
       110: q+1
       111: q+1
       112: q+1
       113: q^3+q^2+q+1
       114: q^3+q^2+q+1
       115: q^3+q^2+q+1
       116: q+1
       117: q^3+q^2+q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q^3+q^2+q+1
       125: q^3+q^2+q+1
       126: q^3+q^2+q+1
       127: q+1
       128: q^3+q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q^3+q^2+q+1
       136: q^3+q^2+q+1
       137: q^2+1
       138: q+1
       139: q^3+q^2+q+1
       140: q+1
       141: q^2+1
       142: q^2+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^3+q^2+q+1
       193: q+1
       194: q^3+q^2+q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q^3+q^2+q+1
       201: q^3+q^2+q+1
       202: q+1
       203: q^3+q^2+q+1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q^3+q^2+q+1
       215: q^3+q^2+q+1
       216: q^2+1
       217: q+1
       218: q^3+q^2+q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q^3+q^2+q+1
       231: q^2+1
       232: 1
       233: q^2+1
       234: q+1
       235: q+1
       236: 1
       237: q^2+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q^3+q^2+q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q^3+q^2+q+1
       323: q+1
       324: q^3+q^2+q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q^3+q^2+q+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: q^2+1
       360: 1
       361: q^2+1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: q^2+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q^3+q^2+q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: q^2+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: q^2+1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: q^2+1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1182: 1
      1183: 1
      1186: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1265: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1307: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1357: 1
      1371: 1
      1404: 1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1477: 1
      1480: 1
      1486: 1
      1487: 1
      1488: 1
      1504: 1
      1516: 1
      1564: 1
      1612: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1632: 1
      1734: 1

1735:    0: q^4+4q^3+5q^2+3q+1
         1: 2q^3+5q^2+3q+1
         2: q^4+4q^3+5q^2+3q+1
         3: q^4+4q^3+5q^2+3q+1
         4: q^4+4q^3+5q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: 2q^3+5q^2+3q+1
         7: 2q^3+5q^2+3q+1
         8: q^4+4q^3+5q^2+3q+1
         9: 2q^3+5q^2+3q+1
        10: q^4+4q^3+5q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: q^4+4q^3+5q^2+3q+1
        13: 2q^3+5q^2+3q+1
        14: q^4+4q^3+5q^2+3q+1
        15: 2q^3+4q^2+3q+1
        16: q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: q^3+2q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^3+5q^2+3q+1
        22: 2q^3+5q^2+3q+1
        23: 2q^3+4q^2+3q+1
        24: q^4+4q^3+5q^2+3q+1
        25: 2q^3+5q^2+3q+1
        26: 2q^3+5q^2+3q+1
        27: q^4+4q^3+5q^2+3q+1
        28: q^3+4q^2+3q+1
        29: 2q^3+4q^2+3q+1
        30: 2q^3+5q^2+3q+1
        31: q^4+4q^3+5q^2+3q+1
        32: 2q^3+4q^2+3q+1
        33: 2q^3+5q^2+3q+1
        34: 2q^3+5q^2+3q+1
        35: 2q^3+4q^2+3q+1
        36: q^3+4q^2+3q+1
        37: 2q^3+4q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^3+4q^2+3q+1
        40: q^3+4q^2+3q+1
        41: q^3+4q^2+3q+1
        42: q^3+2q^2+3q+1
        43: 2q^2+3q+1
        44: q^3+2q^2+3q+1
        45: q^3+2q^2+3q+1
        46: q^3+2q^2+3q+1
        47: q^3+4q^2+3q+1
        48: 2q^3+4q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+2q+1
        51: q^3+3q^2+3q+1
        52: q^3+3q^2+3q+1
        53: 2q^3+5q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 2q^3+5q^2+3q+1
        56: 2q^3+4q^2+3q+1
        57: q^3+3q^2+3q+1
        58: 2q^3+5q^2+3q+1
        59: 2q^3+5q^2+3q+1
        60: 2q^3+4q^2+3q+1
        61: q^4+4q^3+5q^2+3q+1
        62: q^3+4q^2+3q+1
        63: q^3+4q^2+3q+1
        64: q^3+2q^2+3q+1
        65: 2q^3+5q^2+3q+1
        66: 2q^3+5q^2+3q+1
        67: 2q^3+4q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: 2q^2+3q+1
        71: 2q^2+3q+1
        72: 2q^3+5q^2+3q+1
        73: q^3+4q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^3+4q^2+3q+1
        76: q^3+4q^2+3q+1
        77: 2q^2+2q+1
        78: 2q^3+4q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: q^3+4q^2+3q+1
        82: 2q^3+4q^2+3q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: q^3+4q^2+3q+1
        86: 2q^2+3q+1
        87: q^3+2q^2+3q+1
        88: q^3+2q^2+3q+1
        89: 2q^2+3q+1
        90: q^2+q+1
        91: q^3+2q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+3q+1
        94: 2q^2+3q+1
        95: q^3+2q^2+3q+1
        96: q^3+2q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+3q+1
       103: 2q^2+3q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^3+3q^2+3q+1
       107: q^3+3q^2+3q+1
       108: q^3+4q^2+3q+1
       109: 2q^3+5q^2+3q+1
       110: q^3+4q^2+3q+1
       111: 2q^2+3q+1
       112: q^2+2q+1
       113: q^3+3q^2+3q+1
       114: q^3+3q^2+3q+1
       115: 2q^3+5q^2+3q+1
       116: q^3+4q^2+3q+1
       117: 2q^3+5q^2+3q+1
       118: 2q^3+4q^2+3q+1
       119: q^2+3q+1
       120: q^3+4q^2+3q+1
       121: 2q^2+3q+1
       122: q^3+2q^2+3q+1
       123: q^3+2q^2+3q+1
       124: 2q^2+3q+1
       125: 2q^3+5q^2+3q+1
       126: q^3+4q^2+3q+1
       127: 2q^2+3q+1
       128: 2q^3+4q^2+3q+1
       129: q^3+4q^2+3q+1
       130: q^3+4q^2+3q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^2+3q+1
       134: 2q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: q^3+4q^2+3q+1
       138: 2q^2+3q+1
       139: q^3+4q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^2+3q+1
       142: 2q^2+2q+1
       143: 2q^2+2q+1
       144: 2q^2+3q+1
       145: 2q^3+4q^2+3q+1
       146: 2q^2+3q+1
       147: q^2+2q+1
       148: 2q+1
       149: q^3+4q^2+3q+1
       150: 2q^2+2q+1
       151: 2q^3+4q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+3q+1
       155: 2q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: q^3+2q^2+3q+1
       162: q^2+3q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^3+2q^2+3q+1
       166: q^3+2q^2+3q+1
       167: 2q^2+3q+1
       168: q^2+q+1
       169: q^3+2q^2+3q+1
       170: 2q^2+3q+1
       171: q^2+q+1
       172: q^2+q+1
       173: 2q^2+3q+1
       174: q^3+2q^2+3q+1
       175: 2q^2+3q+1
       176: q^2+3q+1
       177: q^3+4q^2+3q+1
       178: 2q^2+3q+1
       179: q^2+3q+1
       180: 2q^2+3q+1
       181: 2q^2+3q+1
       182: q+1
       183: 2q^2+3q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: q^2+3q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^3+3q^2+3q+1
       193: q^2+3q+1
       194: 2q^2+3q+1
       195: q^3+4q^2+3q+1
       196: 2q^2+3q+1
       197: 2q^2+3q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^3+3q^2+3q+1
       201: q^3+3q^2+3q+1
       202: q^3+4q^2+3q+1
       203: 2q^3+5q^2+3q+1
       204: q^3+4q^2+3q+1
       205: 2q^2+3q+1
       206: 2q+1
       207: q^2+3q+1
       208: q^2+3q+1
       209: 2q^2+3q+1
       210: 2q^2+3q+1
       211: 2q^2+3q+1
       212: q^3+2q^2+3q+1
       213: 2q+1
       214: 2q^2+3q+1
       215: 2q^2+3q+1
       216: q^3+4q^2+3q+1
       217: 2q^2+3q+1
       218: q^3+4q^2+3q+1
       219: 2q^2+3q+1
       220: q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: q^2+3q+1
       224: 2q^2+3q+1
       225: 2q^2+3q+1
       226: q+1
       227: 2q^2+3q+1
       228: 2q+1
       229: 2q+1
       230: 2q^2+3q+1
       231: 2q^2+3q+1
       232: 2q^2+3q+1
       233: q^3+4q^2+3q+1
       234: 2q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       237: 2q^2+3q+1
       238: q^2+2q+1
       239: 2q^2+2q+1
       240: q^2+2q+1
       241: 2q^2+2q+1
       242: 2q^2+3q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: 2q+1
       248: 2q^2+3q+1
       249: 2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+3q+1
       252: 2q^3+4q^2+3q+1
       253: 2q^2+3q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q^2+3q+1
       262: 2q^2+3q+1
       263: 2q^2+3q+1
       264: 2q^2+3q+1
       265: 2q^2+3q+1
       266: 2q+1
       267: q^2+3q+1
       268: q+1
       269: q^2+q+1
       270: q^2+q+1
       271: q^2+q+1
       272: q^3+2q^2+3q+1
       273: q^2+3q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^3+2q^2+3q+1
       277: q^3+2q^2+3q+1
       278: q+1
       279: q^2+q+1
       280: q^2+1
       282: q^2+q+1
       283: 2q^2+3q+1
       284: q^2+q+1
       285: q^2+q+1
       286: 2q^2+3q+1
       287: 2q^2+3q+1
       288: 2q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: 2q^2+3q+1
       292: q^2+3q+1
       293: 2q^2+3q+1
       294: q^2+3q+1
       295: q^2+3q+1
       296: q+1
       297: q+1
       298: q^2+3q+1
       299: 2q^2+3q+1
       300: q^2+3q+1
       301: q+1
       302: 2q+1
       303: 2q^2+3q+1
       304: q+1
       305: q^2+q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: q+1
       310: q+1
       311: q^2+2q+1
       312: 2q+1
       313: q^2+3q+1
       314: 2q+1
       315: 2q^2+3q+1
       316: q^2+3q+1
       317: 2q^2+3q+1
       318: q+1
       319: q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^3+3q^2+3q+1
       323: q^2+3q+1
       324: 2q^2+3q+1
       325: q^3+4q^2+3q+1
       326: 2q^2+3q+1
       327: 2q^2+3q+1
       328: 2q+1
       329: 2q+1
       330: q^2+3q+1
       331: q^2+3q+1
       332: 2q^2+3q+1
       333: 2q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: 2q+1
       337: 2q+1
       338: 2q^2+3q+1
       339: 2q^2+3q+1
       340: 2q^2+3q+1
       341: q^3+4q^2+3q+1
       342: 2q^2+3q+1
       343: q^2+3q+1
       344: 2q+1
       345: q^2+3q+1
       346: q^2+3q+1
       347: 2q^2+3q+1
       348: q^2+3q+1
       349: 2q^2+3q+1
       350: q^2+3q+1
       351: q^2+3q+1
       352: q+1
       353: q+1
       354: q^2+3q+1
       355: 2q^2+3q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q^2+3q+1
       360: 2q+1
       361: 2q^2+3q+1
       362: 2q^2+3q+1
       363: q^2+3q+1
       364: q^2+3q+1
       365: 2q+1
       366: q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: 2q^2+2q+1
       371: q^2+2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: 2q+1
       380: 2q+1
       381: 2q^2+3q+1
       382: q^2+2q+1
       383: 2q^2+2q+1
       384: q^2+2q+1
       385: 2q^2+2q+1
       386: 2q^2+3q+1
       387: 2q+1
       388: q^2+2q+1
       389: q+1
       390: 2q+1
       391: 2q+1
       392: q^2+3q+1
       393: q+1
       394: 2q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: q^2+3q+1
       399: q^2+3q+1
       400: q+1
       401: 2q^2+3q+1
       402: 2q^2+3q+1
       403: 2q^2+3q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q^2+q+1
       409: q^2+q+1
       410: q^2+q+1
       411: q^2+q+1
       412: 2q+1
       413: q^2+3q+1
       414: q+1
       415: q^2+q+1
       416: q^2+q+1
       417: q^2+q+1
       418: q^3+2q^2+3q+1
       420: q+1
       421: 1
       422: q^2+1
       424: q^2+1
       426: q+1
       427: q^2+q+1
       428: q^2+1
       430: q^2+q+1
       431: 2q^2+3q+1
       432: q+1
       433: q^2+q+1
       434: 2q+1
       435: 2q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: q^2+3q+1
       439: 2q^2+3q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: 2q+1
       443: q^2+3q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q^2+3q+1
       449: 2q+1
       450: q+1
       451: 1
       452: 2q+1
       453: 2q+1
       454: q+1
       455: q+1
       456: 1
       458: q^2+q+1
       459: q^2+3q+1
       460: q+1
       461: q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: q+1
       466: q+1
       467: 2q+1
       468: 2q+1
       469: 2q+1
       470: q^2+3q+1
       471: q^2+3q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+2q+1
       476: 2q+1
       477: q^2+3q+1
       478: 2q+1
       479: 2q^2+3q+1
       480: q^2+3q+1
       481: 2q^2+3q+1
       482: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: q^2+3q+1
       487: q^2+3q+1
       488: q+1
       489: 2q^2+3q+1
       490: 2q^2+3q+1
       491: 2q^2+3q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q^2+3q+1
       496: 2q+1
       497: 2q^2+3q+1
       498: 2q^2+3q+1
       499: q^2+3q+1
       500: q^2+3q+1
       501: 2q+1
       502: 2q+1
       503: q^2+3q+1
       504: q^2+3q+1
       505: q^2+3q+1
       506: 2q^2+3q+1
       507: q^2+3q+1
       508: q^2+3q+1
       509: 2q+1
       510: q^2+3q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q^2+3q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: 2q+1
       521: 2q+1
       522: 2q^2+3q+1
       523: 2q+1
       524: q^2+3q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q^2+2q+1
       530: q+1
       531: q^2+2q+1
       532: q^2+2q+1
       533: q+1
       534: 2q+1
       535: q+1
       536: 1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 2q+1
       543: 2q+1
       544: q+1
       545: q^2+2q+1
       546: q^2+2q+1
       547: q^2+2q+1
       548: 2q^2+2q+1
       549: q^2+2q+1
       550: 2q+1
       551: q+1
       552: 2q+1
       553: q+1
       554: q+1
       555: q+1
       556: q+1
       557: 2q+1
       558: 2q+1
       559: q+1
       560: 1
       561: 2q+1
       562: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: 2q+1
       567: q^2+3q+1
       569: q+1
       570: q+1
       571: 2q^2+3q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q^2+q+1
       580: q^2+1
       581: q^2+q+1
       582: 2q+1
       583: q+1
       584: q+1
       585: q+1
       586: q^2+q+1
       587: q^2+q+1
       588: q^2+q+1
       589: q^2+q+1
       592: 1
       593: 1
       595: q^2+1
       599: q+1
       600: 1
       601: q^2+1
       603: q^2+1
       605: q+1
       606: q+1
       607: 1
       609: q^2+q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: q^2+3q+1
       614: 2q+1
       615: q+1
       616: q^2+3q+1
       617: q^2+3q+1
       618: q^2+3q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q+1
       628: 2q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 2q+1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: q+1
       643: 1
       645: q+1
       646: q^2+3q+1
       647: q+1
       648: q+1
       650: q+1
       651: q+1
       652: q+1
       653: 2q+1
       654: 2q+1
       655: q^2+3q+1
       656: q+1
       658: q+1
       659: q+1
       660: 2q+1
       661: 2q+1
       662: 2q+1
       663: q^2+3q+1
       664: q^2+3q+1
       665: q+1
       666: q+1
       667: q+1
       668: 2q+1
       669: 2q+1
       670: q^2+3q+1
       672: q+1
       673: q+1
       674: 2q^2+3q+1
       675: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: 2q+1
       682: 2q^2+3q+1
       683: 2q+1
       684: q^2+3q+1
       685: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: q^2+3q+1
       690: 2q+1
       691: q+1
       692: q^2+3q+1
       693: q^2+3q+1
       694: q^2+3q+1
       695: 2q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       704: q+1
       705: 1
       706: q+1
       707: 2q+1
       708: q+1
       709: 2q+1
       710: 2q+1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: q+1
       717: q+1
       718: q^2+2q+1
       719: q+1
       720: q+1
       721: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: q+1
       728: q+1
       729: q+1
       730: 2q+1
       731: 1
       732: q+1
       733: q+1
       734: q^2+2q+1
       735: q+1
       736: q^2+2q+1
       737: q^2+2q+1
       738: q+1
       739: 2q+1
       740: q+1
       741: 1
       742: q+1
       743: q+1
       744: q+1
       745: q+1
       746: q+1
       747: 2q+1
       748: q+1
       749: 2q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 2q+1
       756: q+1
       757: 1
       758: 2q+1
       761: q+1
       762: q+1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       770: 1
       771: 1
       772: q^2+1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q^2+q+1
       781: q^2+1
       782: q^2+q+1
       786: 1
       788: 1
       794: 1
       795: 1
       797: q^2+1
       801: q+1
       802: 1
       803: 1
       805: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: 2q+1
       813: q+1
       814: q+1
       815: q^2+3q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       836: 1
       837: 1
       839: 1
       843: q+1
       844: 1
       845: 1
       847: 1
       849: q+1
       850: q+1
       851: 1
       853: q+1
       855: q+1
       856: q+1
       857: q+1
       858: 2q+1
       859: q+1
       860: q+1
       862: q+1
       863: q+1
       864: q+1
       865: 2q+1
       866: 2q+1
       867: q^2+3q+1
       868: q+1
       870: q+1
       871: 1
       872: 2q+1
       875: q+1
       876: q+1
       877: q+1
       879: q+1
       880: 1
       881: q+1
       882: 2q+1
       883: q+1
       884: 2q+1
       885: 2q+1
       886: q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: 2q+1
       893: q+1
       894: q+1
       895: q^2+3q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: q+1
       907: 1
       908: 1
       909: 1
       910: q+1
       911: q+1
       912: 2q+1
       913: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: q+1
       921: q+1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: q+1
       931: q+1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: q+1
       938: q+1
       939: q^2+2q+1
       940: q+1
       941: q+1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: q+1
       949: q+1
       950: q+1
       951: 2q+1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q+1
       961: 1
       962: 1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: q+1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       983: 1
       984: 1
       985: q^2+1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1015: q+1
      1016: 1
      1017: q+1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: q+1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: q+1
      1061: 1
      1062: 1
      1064: 1
      1068: q+1
      1069: 1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: q+1
      1079: 1
      1080: 1
      1084: q+1
      1085: 1
      1087: 1
      1088: 1
      1089: 1
      1090: q+1
      1091: q+1
      1092: 2q+1
      1093: 1
      1095: q+1
      1096: 1
      1097: q+1
      1100: q+1
      1101: q+1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: q+1
      1118: 1
      1119: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: q+1
      1127: 1
      1129: 1
      1131: 1
      1136: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: q+1
      1144: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: q+1
      1154: q+1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 1
      1171: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1181: 1
      1182: 1
      1183: q+1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1218: 1
      1219: 1
      1223: q+1
      1224: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1250: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1272: 1
      1273: 1
      1276: q+1
      1277: 1
      1278: q+1
      1280: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: q+1
      1291: 1
      1292: 1
      1294: 1
      1295: 1
      1299: q+1
      1300: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: q+1
      1337: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1363: 1
      1368: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1405: 1
      1410: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1420: 1
      1422: 1
      1427: 1
      1450: 1
      1457: 1
      1459: 1
      1460: 1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1477: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1493: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1517: 1
      1519: 1
      1524: 1
      1534: 1
      1539: 1
      1570: 1
      1575: 1
      1613: 1
      1618: 1
      1619: 1
      1626: 1
      1631: 1
      1633: 1
      1644: 1
      1646: 1
      1735: 1

1736:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: q^3+5q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: 3q^3+6q^2+4q+1
         5: 3q^3+6q^2+4q+1
         6: q^3+5q^2+4q+1
         7: q^3+5q^2+4q+1
         8: 4q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: q^3+5q^2+4q+1
        11: 3q^3+6q^2+4q+1
        12: 3q^3+6q^2+4q+1
        13: 3q^3+6q^2+4q+1
        14: q^3+5q^2+4q+1
        15: 2q^3+5q^2+4q+1
        16: 3q^3+6q^2+4q+1
        17: q^3+5q^2+4q+1
        18: 2q^3+5q^2+4q+1
        19: 3q^3+6q^2+4q+1
        20: 4q^2+4q+1
        21: q^3+5q^2+4q+1
        22: 4q^2+4q+1
        23: 4q^2+4q+1
        24: 4q^2+4q+1
        25: q^3+5q^2+4q+1
        26: q^3+5q^2+4q+1
        27: 4q^2+4q+1
        28: 3q^3+6q^2+4q+1
        29: q^3+5q^2+4q+1
        30: 3q^3+6q^2+4q+1
        31: q^3+5q^2+4q+1
        32: 3q^3+6q^2+4q+1
        33: q^3+5q^2+4q+1
        34: q^3+5q^2+4q+1
        35: 3q^2+4q+1
        36: 2q^3+5q^2+4q+1
        37: 2q^2+3q+1
        38: 2q^3+5q^2+4q+1
        39: 2q^3+5q^2+4q+1
        40: q^3+5q^2+4q+1
        41: q^3+5q^2+4q+1
        42: 3q^2+4q+1
        43: 2q^3+5q^2+4q+1
        44: 2q^2+3q+1
        45: 2q^3+5q^2+4q+1
        46: 2q^3+5q^2+4q+1
        47: 3q^3+6q^2+4q+1
        48: q^3+5q^2+4q+1
        49: q^3+4q^2+4q+1
        50: 4q^2+4q+1
        51: 4q^2+4q+1
        52: 4q^2+4q+1
        53: 2q^2+3q+1
        54: 4q^2+4q+1
        55: 4q^2+4q+1
        56: 4q^2+4q+1
        57: 4q^2+4q+1
        58: q^3+5q^2+4q+1
        59: 4q^2+4q+1
        60: 4q^2+4q+1
        61: 4q^2+4q+1
        62: q^3+5q^2+4q+1
        63: q^3+5q^2+4q+1
        64: 3q^2+4q+1
        65: q^3+5q^2+4q+1
        66: q^3+5q^2+4q+1
        67: 3q^2+4q+1
        68: 3q^3+6q^2+4q+1
        69: q^3+5q^2+4q+1
        70: q^3+4q^2+4q+1
        71: 3q^2+4q+1
        72: q^3+5q^2+4q+1
        73: 3q^2+4q+1
        74: 3q^2+4q+1
        75: 3q^2+4q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: q^2+3q+1
        79: 2q^3+5q^2+4q+1
        80: 2q^2+3q+1
        81: 2q^3+5q^2+4q+1
        82: 2q^2+3q+1
        83: 2q^3+5q^2+4q+1
        84: 3q^2+4q+1
        85: q^3+5q^2+4q+1
        86: 3q^2+4q+1
        87: 3q^2+4q+1
        88: 3q^2+4q+1
        89: 2q^2+3q+1
        90: 2q^2+3q+1
        91: q^2+3q+1
        92: 2q^3+5q^2+4q+1
        93: 2q^2+3q+1
        94: 2q^3+5q^2+4q+1
        95: 2q^2+3q+1
        96: 2q^3+5q^2+4q+1
        97: q^3+5q^2+4q+1
        98: q^3+5q^2+4q+1
        99: 2q^2+4q+1
       100: q^3+4q^2+4q+1
       101: q^2+3q+1
       102: q^3+4q^2+4q+1
       103: q^3+4q^2+4q+1
       104: 4q^2+4q+1
       105: 4q^2+4q+1
       106: 4q^2+4q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: 4q^2+4q+1
       111: q^2+3q+1
       112: 4q^2+4q+1
       113: 4q^2+4q+1
       114: 4q^2+4q+1
       115: 2q^2+3q+1
       116: 4q^2+4q+1
       117: 4q^2+4q+1
       118: 4q^2+4q+1
       119: 3q^2+4q+1
       120: q^3+5q^2+4q+1
       121: 3q^2+4q+1
       122: 3q^2+4q+1
       123: 3q^2+4q+1
       124: 3q^2+4q+1
       125: q^3+5q^2+4q+1
       126: 3q^2+4q+1
       127: 3q^2+4q+1
       128: 3q^2+4q+1
       129: q^3+5q^2+4q+1
       130: q^3+5q^2+4q+1
       131: 2q^2+4q+1
       132: q^3+4q^2+4q+1
       133: q^2+3q+1
       134: 3q^2+4q+1
       135: 3q^2+4q+1
       136: 3q^2+4q+1
       137: 2q+1
       138: 3q^2+4q+1
       139: 3q^2+4q+1
       140: 3q^2+4q+1
       141: q^2+3q+1
       142: 2q^2+3q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+3q+1
       152: 2q^3+5q^2+4q+1
       153: 2q^2+3q+1
       154: q^3+4q^2+4q+1
       155: 3q^2+4q+1
       156: 3q^2+4q+1
       157: 3q^2+4q+1
       158: 2q+1
       159: 3q^2+4q+1
       160: 3q^2+4q+1
       161: 3q^2+4q+1
       162: q^2+3q+1
       163: 2q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: q^2+3q+1
       170: 2q^2+3q+1
       171: 2q^2+3q+1
       172: 2q+1
       173: 2q^3+5q^2+4q+1
       174: 2q^2+3q+1
       175: q^3+4q^2+4q+1
       176: 2q^2+4q+1
       177: q^3+5q^2+4q+1
       178: 2q^2+4q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: q^2+3q+1
       182: q^2+3q+1
       183: 3q+1
       184: q^3+4q^2+4q+1
       185: q^2+3q+1
       186: q^3+4q^2+4q+1
       187: q^2+3q+1
       188: q^3+4q^2+4q+1
       189: q^2+3q+1
       190: 4q^2+4q+1
       191: 2q^2+3q+1
       192: 2q^2+3q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: 2q^2+3q+1
       196: q^2+3q+1
       197: 2q+1
       198: 4q^2+4q+1
       199: 4q^2+4q+1
       200: 4q^2+4q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q^2+3q+1
       204: 4q^2+4q+1
       205: q^2+3q+1
       206: 3q^2+4q+1
       207: 3q^2+4q+1
       208: 3q^2+4q+1
       209: 2q+1
       210: 3q^2+4q+1
       211: 3q^2+4q+1
       212: 3q^2+4q+1
       213: 3q^2+4q+1
       214: 3q^2+4q+1
       215: 3q^2+4q+1
       216: 2q+1
       217: 3q^2+4q+1
       218: 3q^2+4q+1
       219: 3q^2+4q+1
       220: 2q^2+4q+1
       221: q^3+5q^2+4q+1
       222: 2q^2+4q+1
       223: 2q^2+4q+1
       224: 2q^2+4q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: 3q+1
       228: 3q^2+4q+1
       229: 3q^2+4q+1
       230: 3q^2+4q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 3q^2+4q+1
       235: q^2+3q+1
       236: q^2+3q+1
       237: q^2+3q+1
       238: q^2+3q+1
       239: 2q+1
       240: q^2+3q+1
       241: q^2+3q+1
       242: q^2+3q+1
       243: 2q+1
       244: 2q^2+3q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q^2+3q+1
       249: 2q^2+3q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q+1
       256: q^3+4q^2+4q+1
       257: q^2+3q+1
       258: 3q^2+4q+1
       259: 3q^2+4q+1
       260: 3q^2+4q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 3q^2+4q+1
       265: q^2+3q+1
       266: q^2+3q+1
       267: q^2+3q+1
       268: q^2+3q+1
       269: 2q+1
       270: q^2+3q+1
       271: q^2+3q+1
       272: q^2+3q+1
       273: q^2+3q+1
       274: 2q^2+3q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: q^2+3q+1
       278: 2q+1
       279: 2q^2+3q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: 2q+1
       286: q^3+4q^2+4q+1
       287: q^2+3q+1
       288: 2q^2+4q+1
       289: 2q^2+4q+1
       290: 2q^2+4q+1
       291: 2q+1
       292: 2q^2+4q+1
       293: 2q^2+4q+1
       294: 2q^2+4q+1
       295: 3q+1
       296: q^2+3q+1
       297: 3q+1
       298: 3q+1
       299: 3q+1
       300: q^2+3q+1
       301: q^2+3q+1
       302: 2q+1
       303: q^2+3q+1
       304: q^2+3q+1
       305: 2q+1
       306: q^3+4q^2+4q+1
       307: q^2+3q+1
       308: q^3+4q^2+4q+1
       309: 2q+1
       310: q^2+3q+1
       311: 2q^2+3q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: q+1
       317: q+1
       318: 2q+1
       319: q^2+3q+1
       320: 4q^2+4q+1
       321: 2q^2+3q+1
       322: 2q^2+3q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: 2q^2+3q+1
       326: q^2+3q+1
       327: 2q+1
       328: 3q^2+4q+1
       329: 3q^2+4q+1
       330: 3q^2+4q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 3q^2+4q+1
       335: q^2+3q+1
       336: 3q^2+4q+1
       337: 3q^2+4q+1
       338: 3q^2+4q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 3q^2+4q+1
       343: q^2+3q+1
       344: 2q^2+4q+1
       345: 2q^2+4q+1
       346: 2q^2+4q+1
       347: 2q+1
       348: 2q^2+4q+1
       349: 2q^2+4q+1
       350: 2q^2+4q+1
       351: 3q+1
       352: q^2+3q+1
       353: 3q+1
       354: 3q+1
       355: 3q+1
       356: q^2+3q+1
       357: 3q^2+4q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q^2+3q+1
       364: 2q+1
       365: q^2+3q+1
       366: q^2+3q+1
       367: q^2+3q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: q^2+3q+1
       372: q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q^2+3q+1
       381: q^2+3q+1
       382: q^2+3q+1
       383: 2q+1
       384: q^2+3q+1
       385: q^2+3q+1
       386: q^2+3q+1
       387: 2q+1
       388: 2q^2+3q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q^2+3q+1
       393: q^2+3q+1
       394: 2q+1
       395: q^2+3q+1
       396: 3q^2+4q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q^2+3q+1
       403: 2q+1
       404: q^2+3q+1
       405: q^2+3q+1
       406: q^2+3q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: q^2+3q+1
       411: q+1
       412: q^2+3q+1
       413: q^2+3q+1
       414: q^2+3q+1
       415: 2q+1
       416: q^2+3q+1
       417: q^2+3q+1
       418: q^2+3q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: 2q^2+3q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q^2+3q+1
       432: q^2+3q+1
       433: 2q+1
       434: 2q^2+4q+1
       435: 2q^2+4q+1
       436: 2q^2+4q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+4q+1
       441: q^2+3q+1
       442: 3q+1
       443: 3q+1
       444: 3q+1
       445: 2q+1
       446: 3q+1
       447: 3q+1
       448: 3q+1
       449: 2q+1
       450: q^2+3q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: q^2+3q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: q^2+3q+1
       460: q^2+3q+1
       461: q+1
       462: q^3+4q^2+4q+1
       463: q^2+3q+1
       464: 2q+1
       465: q+1
       466: q+1
       467: q^2+2q+1
       468: q^2+2q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       473: 2q+1
       474: q^2+3q+1
       475: 2q^2+3q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: q+1
       481: q+1
       482: 2q+1
       483: q^2+3q+1
       484: 3q^2+4q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q^2+3q+1
       491: 2q+1
       492: q^2+3q+1
       493: 3q^2+4q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q^2+3q+1
       500: 2q+1
       501: 2q^2+4q+1
       502: 2q^2+4q+1
       503: 2q^2+4q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q^2+4q+1
       508: q^2+3q+1
       509: 3q+1
       510: 3q+1
       511: 3q+1
       512: 2q+1
       513: 3q+1
       514: 3q+1
       515: 3q+1
       516: 2q+1
       517: q^2+3q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: 2q+1
       526: q+1
       527: q^2+3q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       541: 2q+1
       542: q+1
       543: q^2+3q+1
       544: q^2+3q+1
       545: q^2+3q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: q^2+3q+1
       550: q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 2q+1
       559: q^2+3q+1
       560: 2q+1
       561: 2q+1
       562: 2q+1
       563: 2q+1
       564: q^2+3q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: 2q+1
       573: q+1
       574: q^2+3q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: q+1
       581: q+1
       582: q^2+3q+1
       583: q^2+3q+1
       584: q^2+3q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: q^2+3q+1
       589: q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       596: 2q+1
       597: q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 2q+1
       606: q^2+3q+1
       607: 2q+1
       608: 2q+1
       609: 2q+1
       610: q^2+3q+1
       611: 2q^2+4q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q^2+3q+1
       618: 2q+1
       619: 3q+1
       620: 3q+1
       621: 3q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 3q+1
       626: 1
       627: 2q+1
       628: 2q+1
       629: 2q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: 2q+1
       635: 2q+1
       636: 2q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: q+1
       642: q^2+3q+1
       643: q+1
       644: q+1
       645: q+1
       646: q^2+3q+1
       647: q^2+3q+1
       648: q+1
       649: q+1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 2q+1
       658: q+1
       659: q+1
       660: q^2+2q+1
       661: q^2+2q+1
       662: q+1
       663: q+1
       664: 1
       665: q+1
       666: 2q+1
       667: q^2+3q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       675: 2q+1
       676: 2q+1
       677: q^2+3q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       685: 2q+1
       686: q^2+3q+1
       687: 2q^2+4q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q^2+3q+1
       694: 2q+1
       695: 3q+1
       696: 3q+1
       697: 3q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: 3q+1
       702: 1
       703: 2q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: q+1
       713: q+1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       721: q+1
       722: q+1
       723: 2q+1
       729: q+1
       730: q+1
       731: q+1
       732: q^2+3q+1
       733: 2q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       746: 2q+1
       747: q+1
       748: 2q+1
       749: 2q+1
       750: 2q+1
       752: 2q+1
       753: 2q+1
       754: 2q+1
       755: 2q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       773: q+1
       774: q+1
       775: q^2+3q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: q+1
       782: q+1
       783: q+1
       784: 2q+1
       790: q+1
       791: q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       798: 2q+1
       799: q+1
       800: 2q+1
       801: 2q+1
       802: 2q+1
       804: 2q+1
       805: 2q+1
       806: 2q+1
       807: 2q+1
       808: q^2+3q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: 2q+1
       817: 1
       818: 3q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: 2q+1
       827: 2q+1
       828: 2q+1
       832: 2q+1
       833: 1
       834: 2q+1
       835: 2q+1
       836: 2q+1
       840: 2q+1
       841: 1
       842: q+1
       843: q+1
       844: q+1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       850: q^2+3q+1
       851: q+1
       852: q+1
       853: q+1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 2q+1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 2q+1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: q+1
       887: 2q+1
       888: q^2+3q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       896: 2q+1
       897: 1
       898: 3q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: q+1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       923: q+1
       924: q+1
       932: q+1
       933: q+1
       934: q+1
       935: 2q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: 1
       942: q+1
       943: q+1
       944: 2q+1
       950: q+1
       951: q+1
       952: 2q+1
       953: 2q+1
       954: 2q+1
       958: 2q+1
       959: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: q+1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       977: q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: 1
       986: q+1
       987: q+1
       988: q+1
       996: q+1
       997: q+1
       998: 2q+1
      1004: q+1
      1005: q+1
      1006: 2q+1
      1007: 2q+1
      1008: 2q+1
      1012: 2q+1
      1013: 1
      1014: 2q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: 2q+1
      1040: 1
      1041: 1
      1042: 1
      1043: 2q+1
      1049: 1
      1050: 1
      1051: q+1
      1052: q+1
      1053: q+1
      1057: q+1
      1058: 1
      1059: q+1
      1060: q+1
      1061: q+1
      1063: q+1
      1064: q+1
      1065: q+1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 2q+1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: 2q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: q+1
      1137: q+1
      1139: 1
      1140: q+1
      1141: q+1
      1142: 1
      1143: 1
      1146: q+1
      1147: q+1
      1155: q+1
      1156: 1
      1157: 2q+1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: q+1
      1182: 1
      1183: q+1
      1184: q+1
      1185: 1
      1186: 1
      1189: q+1
      1198: q+1
      1199: q+1
      1207: q+1
      1208: 1
      1209: 2q+1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: q+1
      1261: 1
      1262: 1
      1263: q+1
      1264: q+1
      1265: q+1
      1269: q+1
      1270: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1338: q+1
      1347: 1
      1348: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1385: q+1
      1394: 1
      1395: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: q+1
      1454: 1
      1455: 1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1486: 1
      1504: 1
      1516: 1
      1525: 1
      1536: 1
      1555: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1572: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1614: 1
      1617: 1
      1620: 1
      1621: 1
      1622: 1
      1624: 1
      1628: 1
      1692: 1
      1722: 1
      1736: 1

1737:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1156: 1
      1164: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1208: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1312: 1
      1313: 1
      1347: 1
      1359: 1
      1360: 1
      1394: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1447: 1
      1455: 1
      1459: 1
      1463: 1
      1464: 1
      1468: 1
      1469: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1487: 1
      1526: 1
      1566: 1
      1567: 1
      1601: 1
      1615: 1
      1618: 1
      1622: 1
      1623: 1
      1693: 1
      1737: 1

1738:    0: 2q^2+q+1
         1: 2q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: 2q^2+q+1
         5: 2q^2+q+1
         6: q+1
         7: 2q^2+q+1
         8: 2q^2+q+1
         9: 2q^2+q+1
        10: 2q^2+q+1
        11: 2q^2+q+1
        12: 2q^2+q+1
        13: 2q^2+q+1
        14: 2q^2+q+1
        15: 2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: 2q^2+q+1
        19: 2q^2+q+1
        20: q+1
        21: q+1
        22: 2q^2+q+1
        23: 2q^2+q+1
        24: 2q^2+q+1
        25: q+1
        26: 2q^2+q+1
        27: 2q^2+q+1
        28: 2q^2+q+1
        29: 2q^2+q+1
        30: 2q^2+q+1
        31: 2q^2+q+1
        32: 2q^2+q+1
        33: q+1
        34: 2q^2+q+1
        35: 2q^2+q+1
        36: 2q^2+q+1
        37: q^2+1
        38: 2q^2+q+1
        39: 2q^2+q+1
        40: q+1
        41: 2q^2+q+1
        42: 2q^2+q+1
        43: 2q^2+q+1
        44: q^2+1
        45: 2q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: 2q^2+q+1
        49: 2q^2+q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q^2+q+1
        55: 2q^2+q+1
        56: 2q^2+q+1
        57: q+1
        58: q+1
        59: 2q^2+q+1
        60: 2q^2+q+1
        61: 2q^2+q+1
        62: q+1
        63: 2q^2+q+1
        64: 2q^2+q+1
        65: q+1
        66: 2q^2+q+1
        67: 2q^2+q+1
        68: 2q^2+q+1
        69: 2q^2+q+1
        70: 2q^2+q+1
        71: q+1
        72: q+1
        73: 2q^2+q+1
        74: 2q^2+q+1
        75: 2q^2+q+1
        76: 1
        77: q^2+1
        78: q^2+1
        79: 2q^2+q+1
        80: q^2+1
        81: 2q^2+q+1
        82: q^2+1
        83: 2q^2+q+1
        84: q+1
        85: q+1
        86: 2q^2+q+1
        87: 2q^2+q+1
        88: 2q^2+q+1
        89: 1
        90: q^2+1
        91: q^2+1
        92: 2q^2+q+1
        93: q^2+1
        94: 2q^2+q+1
        95: q^2+1
        96: 2q^2+q+1
        97: q+1
        98: 2q^2+q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: 1
       102: 2q^2+q+1
       103: 2q^2+q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: 2q^2+q+1
       111: 2q^2+q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 2q^2+q+1
       117: 2q^2+q+1
       118: 2q^2+q+1
       119: q+1
       120: q+1
       121: 2q^2+q+1
       122: 2q^2+q+1
       123: 2q^2+q+1
       124: q+1
       125: q+1
       126: 2q^2+q+1
       127: 2q^2+q+1
       128: 2q^2+q+1
       129: q+1
       130: 2q^2+q+1
       131: 2q^2+q+1
       132: 2q^2+q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: 2q^2+q+1
       139: 2q^2+q+1
       140: 2q^2+q+1
       141: 1
       142: 1
       143: q^2+1
       144: q^2+1
       145: q^2+1
       146: 1
       147: q^2+1
       148: q^2+1
       149: 1
       150: q^2+1
       151: q^2+1
       152: 2q^2+q+1
       153: q^2+1
       154: 2q^2+q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: 2q^2+q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: 1
       163: 1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: 1
       168: q^2+1
       169: q^2+1
       170: 1
       171: q^2+1
       172: q^2+1
       173: 2q^2+q+1
       174: q^2+1
       175: 2q^2+q+1
       176: q+1
       177: q+1
       178: 2q^2+q+1
       179: 2q^2+q+1
       180: 2q^2+q+1
       181: 1
       182: 1
       183: 1
       184: 2q^2+q+1
       185: 1
       186: 2q^2+q+1
       187: 1
       188: 2q^2+q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: 2q^2+q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: 2q^2+q+1
       205: 2q^2+q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: 2q^2+q+1
       211: 2q^2+q+1
       212: 2q^2+q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: 2q^2+q+1
       218: 2q^2+q+1
       219: 2q^2+q+1
       220: q+1
       221: q+1
       222: 2q^2+q+1
       223: 2q^2+q+1
       224: 2q^2+q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: q^2+1
       241: q^2+1
       242: q^2+1
       243: 1
       244: 1
       245: q^2+1
       246: q^2+1
       247: q^2+1
       248: 1
       249: 1
       250: q^2+1
       251: q^2+1
       252: q^2+1
       253: 1
       254: q^2+1
       255: q^2+1
       256: 2q^2+q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 2q^2+q+1
       265: 2q^2+q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: q^2+1
       271: q^2+1
       272: q^2+1
       273: 1
       274: 1
       275: q^2+1
       276: q^2+1
       277: q^2+1
       278: 1
       279: 1
       280: q^2+1
       281: q^2+1
       282: q^2+1
       283: 1
       284: q^2+1
       285: q^2+1
       286: 2q^2+q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: 2q^2+q+1
       293: 2q^2+q+1
       294: 2q^2+q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 2q^2+q+1
       307: 1
       308: 2q^2+q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: 2q^2+q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 2q^2+q+1
       335: 2q^2+q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 2q^2+q+1
       343: 2q^2+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: 2q^2+q+1
       349: 2q^2+q+1
       350: 2q^2+q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 2q^2+q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q^2+1
       372: q^2+1
       373: 1
       374: 1
       375: 1
       377: q^2+1
       378: q^2+1
       379: q^2+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: q^2+1
       385: q^2+1
       386: q^2+1
       387: 1
       388: 1
       389: q^2+1
       390: q^2+1
       391: q^2+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 2q^2+q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q^2+1
       411: q^2+1
       412: 1
       413: 1
       414: 1
       415: 1
       416: q^2+1
       417: q^2+1
       418: q^2+1
       419: 1
       420: 1
       421: 1
       423: q^2+1
       424: q^2+1
       425: q^2+1
       426: 1
       427: 1
       428: q^2+1
       429: q^2+1
       430: q^2+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 2q^2+q+1
       441: 2q^2+q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 2q^2+q+1
       463: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 2q^2+q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 2q^2+q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 2q^2+q+1
       508: 2q^2+q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q^2+1
       534: 1
       535: 1
       536: 1
       537: 1
       541: q^2+1
       542: q^2+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: q^2+1
       550: q^2+1
       551: 1
       552: 1
       553: 1
       555: q^2+1
       556: q^2+1
       557: q^2+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q^2+1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: q^2+1
       589: q^2+1
       590: 1
       591: 1
       592: 1
       596: q^2+1
       597: q^2+1
       598: 1
       599: 1
       600: 1
       602: q^2+1
       603: q^2+1
       604: q^2+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 2q^2+q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 2q^2+q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       722: 1
       723: 1
       729: q^2+1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q^2+1
       739: 1
       740: 1
       741: 1
       742: 1
       746: q^2+1
       747: q^2+1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q^2+1
       782: 1
       783: 1
       784: 1
       790: q^2+1
       791: 1
       792: 1
       793: 1
       794: 1
       798: q^2+1
       799: q^2+1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       932: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       942: 1
       943: 1
       944: 1
       950: q^2+1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       986: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: q^2+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1069: 1
      1070: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1243: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1273: 1
      1277: 1
      1278: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1313: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1348: 1
      1356: 1
      1360: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1395: 1
      1403: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1460: 1
      1464: 1
      1465: 1
      1469: 1
      1470: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1488: 1
      1504: 1
      1527: 1
      1536: 1
      1567: 1
      1568: 1
      1572: 1
      1602: 1
      1610: 1
      1616: 1
      1619: 1
      1623: 1
      1624: 1
      1628: 1
      1694: 1
      1738: 1

1739:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: 2q^3+4q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: 2q^3+4q^2+3q+1
         8: q^3+3q^2+3q+1
         9: 2q^3+4q^2+3q+1
        10: 2q^3+4q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: 2q^3+4q^2+3q+1
        15: q^3+3q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^3+4q^2+3q+1
        22: q^3+3q^2+3q+1
        23: q^2+2q+1
        24: q^3+3q^2+3q+1
        25: 2q^3+4q^2+3q+1
        26: 2q^3+4q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^3+3q^2+3q+1
        29: q^3+3q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 2q^3+4q^2+3q+1
        32: q^3+3q^2+3q+1
        33: 2q^3+4q^2+3q+1
        34: 2q^3+4q^2+3q+1
        35: 2q^2+3q+1
        36: q^3+3q^2+3q+1
        37: q^3+3q^2+3q+1
        38: q^2+2q+1
        39: q^3+3q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+2q+1
        51: q^3+3q^2+3q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^2+2q+1
        55: q^3+3q^2+3q+1
        56: q^2+2q+1
        57: q^3+3q^2+3q+1
        58: 2q^3+4q^2+3q+1
        59: q^3+3q^2+3q+1
        60: q^2+2q+1
        61: q^3+3q^2+3q+1
        62: q^3+3q^2+3q+1
        63: q^3+3q^2+3q+1
        64: q^2+3q+1
        65: 2q^3+4q^2+3q+1
        66: 2q^3+4q^2+3q+1
        67: 2q^2+3q+1
        68: q^3+3q^2+3q+1
        69: q^3+3q^2+3q+1
        70: 2q^2+3q+1
        71: 2q^2+3q+1
        72: 2q^3+4q^2+3q+1
        73: 2q^2+3q+1
        74: q+1
        75: 2q^2+3q+1
        76: q^3+3q^2+3q+1
        77: q^3+3q^2+3q+1
        78: 2q^2+3q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^3+3q^2+3q+1
        82: q^3+3q^2+3q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q^2+3q+1
        89: 2q^2+3q+1
        90: 2q^2+3q+1
        91: q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: q^2+2q+1
       103: 2q^2+3q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^3+3q^2+3q+1
       107: q^3+3q^2+3q+1
       108: q^2+2q+1
       109: q^3+3q^2+3q+1
       110: q^2+2q+1
       111: 2q+1
       112: q^2+2q+1
       113: q^3+3q^2+3q+1
       114: q^3+3q^2+3q+1
       115: q^3+3q^2+3q+1
       116: q^2+2q+1
       117: q^3+3q^2+3q+1
       118: q^2+2q+1
       119: q^2+3q+1
       120: q^3+3q^2+3q+1
       121: q^2+3q+1
       122: 2q+1
       123: q^2+3q+1
       124: 2q^2+3q+1
       125: 2q^3+4q^2+3q+1
       126: 2q^2+3q+1
       127: q+1
       128: 2q^2+3q+1
       129: q^3+3q^2+3q+1
       130: q^3+3q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^2+3q+1
       134: q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: q+1
       139: 2q^2+3q+1
       140: q+1
       141: 2q^2+3q+1
       142: q^3+3q^2+3q+1
       143: 2q^2+3q+1
       144: q+1
       145: 2q^2+3q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: q^3+3q^2+3q+1
       150: q^3+3q^2+3q+1
       151: 2q^2+3q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: 2q+1
       160: q^2+3q+1
       161: 2q+1
       162: q^2+3q+1
       163: 2q^2+3q+1
       164: q^2+3q+1
       165: 2q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: q^2+3q+1
       170: 2q^2+3q+1
       171: 2q^2+3q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: 2q^2+3q+1
       176: q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q^2+3q+1
       181: 2q^2+3q+1
       182: 2q^2+3q+1
       183: q^2+3q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: q^2+2q+1
       189: 2q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^3+3q^2+3q+1
       193: q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: 2q+1
       197: 2q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^3+3q^2+3q+1
       201: q^3+3q^2+3q+1
       202: q^2+2q+1
       203: q^3+3q^2+3q+1
       204: q^2+2q+1
       205: 2q+1
       206: 2q+1
       207: q^2+3q+1
       208: q^2+3q+1
       209: q^2+3q+1
       210: 2q+1
       211: q^2+3q+1
       212: 2q+1
       213: q+1
       214: 2q^2+3q+1
       215: 2q^2+3q+1
       216: 2q^2+3q+1
       217: q+1
       218: 2q^2+3q+1
       219: q+1
       220: q^2+3q+1
       221: q^3+3q^2+3q+1
       222: q^2+3q+1
       223: q+1
       224: q^2+3q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: q^2+3q+1
       228: q+1
       229: q+1
       230: 2q^2+3q+1
       231: 2q^2+3q+1
       232: q+1
       233: 2q^2+3q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q^2+3q+1
       238: 2q^2+3q+1
       239: 2q^2+3q+1
       240: q+1
       241: 2q^2+3q+1
       242: q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: 1
       247: q+1
       248: 2q^2+3q+1
       249: q^3+3q^2+3q+1
       250: 2q^2+3q+1
       251: q+1
       252: 2q^2+3q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q^2+3q+1
       262: 2q+1
       263: q^2+3q+1
       264: 2q+1
       265: 2q+1
       266: 2q+1
       267: q^2+3q+1
       268: q^2+3q+1
       269: q^2+3q+1
       270: 2q+1
       271: q^2+3q+1
       272: 2q+1
       273: q^2+3q+1
       274: 2q^2+3q+1
       275: q^2+3q+1
       276: 2q+1
       277: q^2+3q+1
       278: 2q+1
       279: 2q^2+3q+1
       280: 2q+1
       282: 2q+1
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: 2q+1
       286: 2q^2+3q+1
       287: 2q^2+3q+1
       288: q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: q+1
       293: q^2+3q+1
       294: q+1
       295: q^2+3q+1
       296: 2q^2+3q+1
       297: q^2+3q+1
       298: q+1
       299: q^2+3q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q+1
       303: 2q^2+3q+1
       304: 2q^2+3q+1
       305: 2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: 2q+1
       310: 2q+1
       311: q^2+2q+1
       312: q+1
       313: q+1
       315: q^2+2q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 2q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^3+3q^2+3q+1
       323: q+1
       324: q^2+2q+1
       325: q^2+2q+1
       326: 2q+1
       327: 2q+1
       328: 2q+1
       329: 2q+1
       330: q^2+3q+1
       331: q^2+3q+1
       332: 2q+1
       333: q^2+3q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: 2q^2+3q+1
       339: 2q^2+3q+1
       340: q+1
       341: 2q^2+3q+1
       342: q+1
       343: q+1
       344: q+1
       345: q^2+3q+1
       346: q^2+3q+1
       347: q^2+3q+1
       348: q+1
       349: q^2+3q+1
       350: q+1
       351: q^2+3q+1
       352: 2q^2+3q+1
       353: q^2+3q+1
       354: q+1
       355: q^2+3q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q^2+3q+1
       360: 1
       361: q^2+2q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: 2q^2+3q+1
       368: 2q^2+3q+1
       369: q+1
       370: 2q^2+3q+1
       371: q+1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       380: q+1
       381: 2q^2+3q+1
       382: 2q^2+3q+1
       383: 2q^2+3q+1
       384: q+1
       385: 2q^2+3q+1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: 1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q+1
       395: 2q+1
       396: 2q+1
       397: 2q+1
       398: q^2+3q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: 2q+1
       403: 2q+1
       404: 2q+1
       405: 2q+1
       406: q^2+3q+1
       407: q^2+3q+1
       408: 2q+1
       409: q^2+3q+1
       410: 2q+1
       411: q+1
       412: 2q+1
       413: q^2+3q+1
       414: q^2+3q+1
       415: q^2+3q+1
       416: 2q+1
       417: q^2+3q+1
       418: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       424: 2q+1
       426: 2q+1
       427: 2q^2+3q+1
       428: 2q+1
       430: 2q+1
       431: 2q^2+3q+1
       432: 2q^2+3q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: q+1
       439: q^2+3q+1
       440: q+1
       441: q+1
       442: q+1
       443: q^2+3q+1
       444: q^2+3q+1
       445: q^2+3q+1
       446: q+1
       447: q^2+3q+1
       448: q+1
       449: q+1
       450: q^2+2q+1
       451: q+1
       452: 1
       453: q+1
       454: 2q+1
       455: 2q^2+3q+1
       456: 2q+1
       458: 2q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: 2q+1
       465: 2q+1
       466: q+1
       467: q+1
       470: q+1
       471: q+1
       472: 2q+1
       473: 2q+1
       474: 2q+1
       475: q^2+2q+1
       476: q+1
       477: q+1
       479: q^2+2q+1
       480: q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: 2q+1
       485: 2q+1
       486: q^2+3q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: 2q+1
       491: 2q+1
       492: q+1
       493: q+1
       494: q+1
       495: 2q^2+3q+1
       496: 1
       497: q^2+2q+1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q^2+3q+1
       504: q^2+3q+1
       505: q+1
       506: q^2+3q+1
       507: q+1
       508: q+1
       509: q+1
       510: q^2+3q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: q+1
       514: q^2+3q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       520: 1
       522: q^2+2q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: 2q^2+3q+1
       530: 1
       531: q^2+2q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 2q^2+3q+1
       546: 2q^2+3q+1
       547: q+1
       548: 2q^2+3q+1
       549: q+1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q^2+2q+1
       560: q+1
       561: 1
       562: q+1
       563: 2q+1
       564: 2q+1
       565: 2q+1
       566: q+1
       567: q+1
       569: q+1
       570: 1
       571: 2q+1
       572: 2q+1
       573: q+1
       574: 2q+1
       575: 2q+1
       576: q^2+3q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: q+1
       581: q+1
       582: 2q+1
       583: 2q+1
       584: q^2+3q+1
       585: q^2+3q+1
       586: 2q+1
       587: q^2+3q+1
       588: 2q+1
       589: q+1
       592: 2q+1
       593: 2q+1
       595: 2q+1
       599: 2q+1
       600: 2q+1
       601: 2q+1
       603: 2q+1
       605: 2q+1
       606: 2q^2+3q+1
       607: 2q+1
       609: 2q+1
       610: q+1
       611: q+1
       612: q+1
       613: q^2+3q+1
       614: 1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q^2+3q+1
       622: q^2+3q+1
       623: q+1
       624: q^2+3q+1
       625: q+1
       626: 1
       627: 1
       628: q+1
       629: q+1
       630: q+1
       631: 1
       632: q+1
       633: 1
       635: 2q+1
       636: 2q+1
       637: 2q+1
       639: 2q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: 2q+1
       650: q+1
       651: q+1
       655: q+1
       656: q+1
       657: 2q+1
       658: 2q+1
       659: q+1
       660: q+1
       663: q+1
       664: q+1
       665: 2q+1
       666: 2q+1
       667: 2q+1
       668: 2q+1
       669: q+1
       670: q+1
       672: q+1
       673: 1
       674: 2q+1
       675: 2q+1
       676: q+1
       677: q+1
       678: q+1
       679: 1
       680: 1
       682: q^2+2q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: q^2+3q+1
       690: 1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q+1
       697: q^2+3q+1
       698: q^2+3q+1
       699: q+1
       700: q^2+3q+1
       701: q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q^2+2q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q^2+3q+1
       735: 1
       736: q^2+2q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 1
       755: 2q+1
       756: 2q+1
       757: 1
       758: q+1
       761: 1
       762: 1
       763: 2q+1
       764: q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       770: q+1
       771: 1
       772: q+1
       773: q+1
       774: q+1
       775: 2q+1
       776: 2q+1
       777: q^2+3q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: q+1
       782: q+1
       786: 2q+1
       788: q+1
       794: 2q+1
       795: 2q+1
       797: 2q+1
       801: 2q+1
       802: 2q+1
       803: 2q+1
       805: 2q+1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q^2+3q+1
       821: 1
       822: q+1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: q+1
       829: q+1
       830: 1
       831: q+1
       832: 1
       833: 1
       836: 2q+1
       837: 2q+1
       839: 2q+1
       843: q+1
       844: q+1
       845: q+1
       847: q+1
       849: q+1
       850: q^2+2q+1
       851: q+1
       853: q+1
       854: q+1
       855: q+1
       860: q+1
       861: 2q+1
       862: q+1
       863: q+1
       867: q+1
       868: q+1
       869: 2q+1
       870: 2q+1
       871: 1
       872: q+1
       875: 1
       876: 1
       877: 2q+1
       878: q+1
       879: q+1
       880: 1
       881: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q^2+3q+1
       901: 1
       902: q+1
       903: q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q^2+2q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: 1
       960: 2q+1
       961: 1
       962: 1
       966: 1
       967: 1
       968: q+1
       969: q+1
       970: 1
       971: q+1
       974: 1
       975: 1
       976: q+1
       977: q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       983: q+1
       984: 1
       985: q+1
       986: q+1
       993: q+1
      1000: 2q+1
      1002: q+1
      1008: 2q+1
      1009: 2q+1
      1011: 2q+1
      1014: q+1
      1015: q+1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: q+1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 2q+1
      1047: q+1
      1053: q+1
      1054: q+1
      1056: q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1064: q+1
      1066: q+1
      1071: q+1
      1072: q+1
      1077: q+1
      1078: 2q+1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1172: q+1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: q+1
      1181: q+1
      1182: 1
      1183: q+1
      1186: 1
      1187: 1
      1188: q+1
      1204: q+1
      1211: 2q+1
      1213: q+1
      1217: q+1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1250: q+1
      1257: q+1
      1265: q+1
      1266: q+1
      1268: q+1
      1274: q+1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: q+1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: q+1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: 1
      1427: 1
      1450: q+1
      1461: 1
      1466: 1
      1471: 1
      1472: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1489: 1
      1501: 1
      1502: 1
      1507: 1
      1508: 1
      1516: 1
      1517: 1
      1519: 1
      1524: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1620: 1
      1625: 1
      1626: 1
      1631: 1
      1642: 1
      1654: 1
      1667: 1
      1695: 1
      1739: 1

1740:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: 2q^3+4q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: q^3+3q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: 2q^3+4q^2+3q+1
         8: q^3+3q^2+3q+1
         9: 2q^3+4q^2+3q+1
        10: 2q^3+4q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: q^3+3q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: q^3+3q^2+3q+1
        19: q^3+3q^2+3q+1
        20: q^3+3q^2+3q+1
        21: 2q^3+4q^2+3q+1
        22: q^3+3q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^2+2q+1
        25: 2q^3+4q^2+3q+1
        26: 2q^3+4q^2+3q+1
        27: q^3+3q^2+3q+1
        28: 2q^3+4q^2+3q+1
        29: 2q^3+4q^2+3q+1
        30: q^3+3q^2+3q+1
        31: q^3+3q^2+3q+1
        32: q^3+3q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^3+4q^2+3q+1
        41: 2q^3+4q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: q^2+2q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+3q^2+3q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^3+3q^2+3q+1
        58: 2q^3+4q^2+3q+1
        59: q^3+3q^2+3q+1
        60: q^3+3q^2+3q+1
        61: q^2+2q+1
        62: 2q^3+4q^2+3q+1
        63: 2q^3+4q^2+3q+1
        64: 2q^2+3q+1
        65: q^3+3q^2+3q+1
        66: q^3+3q^2+3q+1
        67: q^2+3q+1
        68: q^3+3q^2+3q+1
        69: q^3+3q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: 2q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: 2q^3+4q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: q+1
        89: q^3+3q^2+3q+1
        90: q^3+3q^2+3q+1
        91: 2q^2+3q+1
        92: q^3+3q^2+3q+1
        93: q^3+3q^2+3q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: q^3+3q^2+3q+1
       106: q^2+2q+1
       107: q^3+3q^2+3q+1
       108: q^3+3q^2+3q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: 2q+1
       112: q^3+3q^2+3q+1
       113: q^2+2q+1
       114: q^3+3q^2+3q+1
       115: q^3+3q^2+3q+1
       116: q^3+3q^2+3q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: 2q^2+3q+1
       120: 2q^3+4q^2+3q+1
       121: 2q^2+3q+1
       122: 2q^2+3q+1
       123: q+1
       124: q^2+3q+1
       125: q^3+3q^2+3q+1
       126: q^2+3q+1
       127: q^2+3q+1
       128: 2q+1
       129: q^3+3q^2+3q+1
       130: q^3+3q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^2+3q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: 2q+1
       140: 2q+1
       141: q^2+3q+1
       142: 2q^2+3q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: 2q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: 2q^2+3q+1
       156: q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+3q+1
       160: q+1
       161: q+1
       162: 2q^2+3q+1
       163: q^3+3q^2+3q+1
       164: 2q^2+3q+1
       165: 2q^2+3q+1
       166: q+1
       167: q^3+3q^2+3q+1
       168: q^3+3q^2+3q+1
       169: 2q^2+3q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: q+1
       181: 2q^2+3q+1
       182: 2q^2+3q+1
       183: q^2+3q+1
       184: 2q^2+3q+1
       185: 2q^2+3q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: 2q+1
       190: q^2+2q+1
       191: q^3+3q^2+3q+1
       192: q^2+2q+1
       193: q^2+2q+1
       194: q+1
       195: q^2+2q+1
       196: 2q+1
       197: 2q+1
       198: q^2+2q+1
       199: q^3+3q^2+3q+1
       200: q^2+2q+1
       201: q^3+3q^2+3q+1
       202: q^3+3q^2+3q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: 2q+1
       206: 2q^2+3q+1
       207: q+1
       208: 2q^2+3q+1
       209: 2q^2+3q+1
       210: 2q^2+3q+1
       211: q+1
       212: q+1
       213: q^2+3q+1
       214: 2q+1
       215: q^2+3q+1
       216: q^2+3q+1
       217: q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: q^2+3q+1
       221: q^3+3q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q+1
       225: 2q^2+3q+1
       226: 2q^2+3q+1
       227: q^2+3q+1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q^2+3q+1
       232: q^2+3q+1
       233: 2q+1
       234: 2q+1
       235: 2q+1
       236: q^2+3q+1
       237: 2q+1
       238: q^2+3q+1
       239: q^2+3q+1
       240: q^2+3q+1
       241: 2q+1
       242: 2q+1
       243: 2q+1
       244: 2q^2+3q+1
       245: 2q+1
       246: 2q+1
       248: q^2+3q+1
       249: 2q^2+3q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: 2q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: q+1
       259: 2q^2+3q+1
       260: q+1
       261: 2q^2+3q+1
       262: 2q^2+3q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q^2+3q+1
       267: q+1
       268: 2q^2+3q+1
       269: 2q^2+3q+1
       270: 2q^2+3q+1
       271: q+1
       272: q+1
       273: 2q^2+3q+1
       274: q^3+3q^2+3q+1
       275: 2q^2+3q+1
       276: 2q^2+3q+1
       277: q+1
       278: q+1
       279: q^2+2q+1
       280: q+1
       281: q+1
       282: 1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q^2+3q+1
       289: q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: q^2+3q+1
       293: q+1
       294: q+1
       295: q^2+3q+1
       296: 2q^2+3q+1
       297: q^2+3q+1
       298: q^2+3q+1
       299: q+1
       300: 2q^2+3q+1
       301: 2q^2+3q+1
       302: 2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: 2q+1
       310: 2q+1
       311: q^2+2q+1
       312: q^2+2q+1
       314: q+1
       315: q+1
       316: q+1
       317: 2q+1
       318: 2q+1
       319: 2q+1
       320: q^2+2q+1
       321: q^3+3q^2+3q+1
       322: q^2+2q+1
       323: q^2+2q+1
       324: q+1
       325: q^2+2q+1
       326: 2q+1
       327: 2q+1
       328: q+1
       329: 2q^2+3q+1
       330: q+1
       331: 2q^2+3q+1
       332: 2q^2+3q+1
       333: q+1
       334: q+1
       335: q+1
       336: 2q+1
       337: q^2+3q+1
       338: 2q+1
       339: q^2+3q+1
       340: q^2+3q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: q^2+3q+1
       345: q+1
       346: q^2+3q+1
       347: q^2+3q+1
       348: q^2+3q+1
       349: q+1
       350: q+1
       351: q^2+3q+1
       352: 2q^2+3q+1
       353: q^2+3q+1
       354: q^2+3q+1
       355: q+1
       356: 2q+1
       357: 2q+1
       358: q^2+3q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: 2q+1
       364: 2q+1
       365: 2q+1
       366: q^2+3q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+3q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: 2q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       380: q^2+3q+1
       381: 2q+1
       382: q^2+3q+1
       383: q^2+3q+1
       384: q^2+3q+1
       385: 2q+1
       386: 2q+1
       387: 2q+1
       388: 2q^2+3q+1
       389: 2q+1
       390: 2q+1
       392: 2q^2+3q+1
       393: 2q^2+3q+1
       394: 2q+1
       395: q+1
       396: q+1
       397: 2q^2+3q+1
       398: q+1
       399: q^2+2q+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: 2q^2+3q+1
       406: q+1
       407: 2q^2+3q+1
       408: 2q^2+3q+1
       409: q+1
       410: q+1
       411: 1
       412: 2q^2+3q+1
       413: q+1
       414: 2q^2+3q+1
       415: 2q^2+3q+1
       416: 2q^2+3q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: 1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q+1
       434: q+1
       435: q^2+3q+1
       436: q+1
       437: q^2+3q+1
       438: q^2+3q+1
       439: q+1
       440: q+1
       441: q+1
       442: q^2+3q+1
       443: q+1
       444: q^2+3q+1
       445: q^2+3q+1
       446: q^2+3q+1
       447: q+1
       448: q+1
       449: 2q+1
       450: 2q^2+3q+1
       451: 2q+1
       452: 2q+1
       454: q+1
       455: q^2+2q+1
       456: q+1
       457: q+1
       458: 1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: 2q+1
       465: 2q+1
       466: q+1
       468: q+1
       469: q+1
       471: q+1
       472: 2q+1
       473: 2q+1
       474: 2q+1
       475: q^2+2q+1
       476: q^2+2q+1
       478: q+1
       479: q+1
       480: q+1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: q+1
       485: 2q^2+3q+1
       486: q+1
       487: q^2+2q+1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       492: 2q+1
       493: 2q+1
       494: q^2+3q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       502: q^2+3q+1
       503: q+1
       504: q^2+3q+1
       505: q^2+3q+1
       506: q+1
       507: q+1
       508: q+1
       509: q^2+3q+1
       510: q+1
       511: q^2+3q+1
       512: q^2+3q+1
       513: q^2+3q+1
       514: q+1
       515: q+1
       516: 2q+1
       517: 2q+1
       518: 2q+1
       519: q+1
       521: q+1
       522: q+1
       523: 1
       524: 2q+1
       525: 2q+1
       526: q+1
       527: 2q+1
       528: q^2+3q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       536: 2q+1
       538: 2q+1
       539: 2q+1
       543: 2q+1
       544: q^2+3q+1
       545: 2q+1
       546: q^2+3q+1
       547: q^2+3q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: 2q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       558: 2q+1
       559: 2q^2+3q+1
       560: 2q+1
       561: 2q+1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+2q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: 2q^2+3q+1
       576: q+1
       577: q^2+2q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 2q^2+3q+1
       584: q+1
       585: 2q^2+3q+1
       586: 2q^2+3q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q^2+2q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: q^2+3q+1
       613: q+1
       614: q+1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q^2+3q+1
       621: q+1
       622: q^2+3q+1
       623: q^2+3q+1
       624: q+1
       625: q+1
       626: 1
       627: 2q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       634: q+1
       635: 1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: 2q+1
       650: q+1
       652: q+1
       654: q+1
       656: q+1
       657: 2q+1
       658: 2q+1
       659: q+1
       661: q+1
       662: q+1
       664: q+1
       665: 2q+1
       666: q+1
       667: q+1
       668: q+1
       669: q^2+2q+1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       676: 2q+1
       677: 2q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: q+1
       683: 1
       684: 2q+1
       685: 2q+1
       686: q+1
       687: q+1
       688: q^2+3q+1
       689: q+1
       690: q+1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q^2+3q+1
       697: q+1
       698: q^2+3q+1
       699: q^2+3q+1
       700: q+1
       701: q+1
       702: 1
       703: 2q+1
       704: 2q+1
       705: 1
       707: q+1
       708: 1
       710: 1
       711: 2q+1
       712: q+1
       713: q+1
       714: 2q+1
       715: q+1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       721: q+1
       724: 2q+1
       726: q+1
       731: q+1
       732: 2q+1
       733: q^2+3q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       741: 2q+1
       743: 2q+1
       744: 2q+1
       748: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       755: q+1
       756: q+1
       757: 1
       759: 1
       760: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q^2+2q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: 2q^2+3q+1
       777: q+1
       778: q^2+2q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q^2+3q+1
       820: q+1
       821: q+1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 2q+1
       829: 2q+1
       830: 2q+1
       834: 1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: q+1
       845: q+1
       846: q+1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       854: q+1
       856: q+1
       859: q+1
       861: 2q+1
       862: q+1
       864: q+1
       866: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       873: 1
       874: 1
       876: 1
       877: q+1
       878: 2q+1
       879: 2q+1
       880: 1
       882: q+1
       883: 1
       885: 1
       886: 2q+1
       887: q+1
       888: q+1
       889: q+1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: q^2+3q+1
       900: q+1
       901: q+1
       902: 1
       903: q+1
       904: 1
       905: 1
       906: 2q+1
       907: 1
       909: 1
       911: 1
       913: 1
       914: q+1
       915: q+1
       916: 1
       918: q+1
       919: 1
       921: 1
       922: q+1
       926: q+1
       933: q+1
       934: q+1
       935: 2q+1
       936: q+1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       942: q+1
       945: 2q+1
       947: q+1
       953: 2q+1
       955: 2q+1
       956: 2q+1
       960: q+1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q^2+2q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 2q+1
      1037: q+1
      1042: 1
      1043: 1
      1044: q+1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: q+1
      1054: q+1
      1055: q+1
      1059: q+1
      1061: q+1
      1062: q+1
      1063: q+1
      1067: q+1
      1071: q+1
      1073: q+1
      1076: q+1
      1078: q+1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: 2q+1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: q+1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: q+1
      1138: q+1
      1139: 1
      1141: q+1
      1142: 1
      1144: 1
      1145: q+1
      1149: q+1
      1158: 2q+1
      1160: q+1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: 1
      1177: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: q+1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1256: q+1
      1264: q+1
      1266: q+1
      1267: q+1
      1275: q+1
      1279: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1291: 1
      1293: q+1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: q+1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: q+1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1369: 1
      1370: 1
      1372: 1
      1374: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1428: 1
      1429: 1
      1432: 1
      1436: 1
      1449: q+1
      1462: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1478: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1490: 1
      1501: 1
      1503: 1
      1506: 1
      1529: 1
      1533: 1
      1535: 1
      1538: 1
      1547: 1
      1555: 1
      1556: 1
      1559: 1
      1563: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1584: 1
      1621: 1
      1625: 1
      1627: 1
      1630: 1
      1643: 1
      1668: 1
      1684: 1
      1696: 1
      1740: 1

1741:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 5q^2+4q+1
         3: 5q^2+4q+1
         4: 5q^2+4q+1
         5: 5q^2+4q+1
         6: 5q^2+4q+1
         7: 3q^2+4q+1
         8: 3q^2+4q+1
         9: 5q^2+4q+1
        10: 5q^2+4q+1
        11: 5q^2+4q+1
        12: 5q^2+4q+1
        13: 5q^2+4q+1
        14: 5q^2+4q+1
        15: 3q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 3q^2+4q+1
        19: 5q^2+4q+1
        20: 3q^2+4q+1
        21: 3q^2+4q+1
        22: q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: 5q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: 5q^2+4q+1
        29: 5q^2+4q+1
        30: 5q^2+4q+1
        31: 5q^2+4q+1
        32: 5q^2+4q+1
        33: 5q^2+4q+1
        34: 3q^2+4q+1
        35: q^2+4q+1
        36: 3q^2+4q+1
        37: 3q^2+4q+1
        38: 3q^2+4q+1
        39: 3q^2+4q+1
        40: 5q^2+4q+1
        41: 3q^2+4q+1
        42: q^2+4q+1
        43: 3q^2+4q+1
        44: 3q^2+4q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 5q^2+4q+1
        48: 5q^2+4q+1
        49: 2q^2+4q+1
        50: 3q^2+4q+1
        51: 3q^2+4q+1
        52: q^2+4q+1
        53: q^2+4q+1
        54: q^2+4q+1
        55: q^2+4q+1
        56: 3q^2+4q+1
        57: 3q^2+4q+1
        58: 3q^2+4q+1
        59: q^2+4q+1
        60: 3q^2+4q+1
        61: 3q^2+4q+1
        62: 5q^2+4q+1
        63: 3q^2+4q+1
        64: q^2+4q+1
        65: 5q^2+4q+1
        66: 3q^2+4q+1
        67: q^2+4q+1
        68: 5q^2+4q+1
        69: 5q^2+4q+1
        70: 2q^2+4q+1
        71: q^2+4q+1
        72: 3q^2+4q+1
        73: 4q+1
        74: q^2+4q+1
        75: q^2+4q+1
        76: 3q^2+4q+1
        77: q^2+2q+1
        78: q^2+4q+1
        79: 3q^2+4q+1
        80: 3q^2+4q+1
        81: 3q^2+4q+1
        82: 3q^2+4q+1
        83: 3q^2+4q+1
        84: q^2+4q+1
        85: 3q^2+4q+1
        86: 4q+1
        87: q^2+4q+1
        88: q^2+4q+1
        89: 3q^2+4q+1
        90: q^2+2q+1
        91: q^2+4q+1
        92: 3q^2+4q+1
        93: 3q^2+4q+1
        94: 3q^2+4q+1
        95: 3q^2+4q+1
        96: 3q^2+4q+1
        97: 5q^2+4q+1
        98: 3q^2+4q+1
        99: 4q+1
       100: 2q^2+4q+1
       101: 2q^2+4q+1
       102: 2q^2+4q+1
       103: 2q^2+4q+1
       104: 3q^2+4q+1
       105: q^2+4q+1
       106: q^2+4q+1
       107: q^2+4q+1
       108: q^2+4q+1
       109: q^2+4q+1
       110: q^2+4q+1
       111: 3q+1
       112: 3q^2+4q+1
       113: 3q^2+4q+1
       114: q^2+4q+1
       115: q^2+4q+1
       116: q^2+4q+1
       117: q^2+4q+1
       118: 3q^2+4q+1
       119: q^2+4q+1
       120: 3q^2+4q+1
       121: 4q+1
       122: q^2+4q+1
       123: q^2+4q+1
       124: q^2+4q+1
       125: 3q^2+4q+1
       126: 4q+1
       127: q^2+4q+1
       128: q^2+4q+1
       129: 5q^2+4q+1
       130: 3q^2+4q+1
       131: 4q+1
       132: 2q^2+4q+1
       133: 2q^2+4q+1
       134: q^2+4q+1
       135: q^2+4q+1
       136: 4q+1
       137: 4q+1
       138: 4q+1
       139: 4q+1
       140: q^2+4q+1
       141: q^2+4q+1
       142: q^2+2q+1
       143: 2q+1
       144: q^2+4q+1
       145: q^2+4q+1
       146: 3q^2+4q+1
       147: q^2+2q+1
       148: 2q+1
       149: 3q^2+4q+1
       150: q^2+2q+1
       151: q^2+4q+1
       152: 3q^2+4q+1
       153: 3q^2+4q+1
       154: 2q^2+4q+1
       155: q^2+4q+1
       156: q^2+4q+1
       157: 4q+1
       158: 4q+1
       159: 4q+1
       160: 4q+1
       161: q^2+4q+1
       162: q^2+4q+1
       163: q^2+2q+1
       164: 2q+1
       165: q^2+4q+1
       166: q^2+4q+1
       167: 3q^2+4q+1
       168: q^2+2q+1
       169: q^2+4q+1
       170: 3q^2+4q+1
       171: q^2+2q+1
       172: 2q+1
       173: 3q^2+4q+1
       174: 3q^2+4q+1
       175: 2q^2+4q+1
       176: 4q+1
       177: 3q^2+4q+1
       178: 4q+1
       179: 4q+1
       180: 4q+1
       181: 2q^2+4q+1
       182: q+1
       183: 4q+1
       184: 2q^2+4q+1
       185: 2q^2+4q+1
       186: 2q^2+4q+1
       187: 2q^2+4q+1
       188: 2q^2+4q+1
       189: 3q+1
       190: q^2+4q+1
       191: q^2+4q+1
       192: q^2+4q+1
       193: 2q+1
       194: 2q+1
       195: q^2+4q+1
       196: 3q+1
       197: 3q+1
       198: 3q^2+4q+1
       199: q^2+4q+1
       200: q^2+4q+1
       201: q^2+4q+1
       202: q^2+4q+1
       203: q^2+4q+1
       204: q^2+4q+1
       205: 3q+1
       206: q^2+4q+1
       207: q^2+4q+1
       208: 4q+1
       209: 4q+1
       210: 4q+1
       211: 4q+1
       212: q^2+4q+1
       213: q^2+4q+1
       214: q^2+4q+1
       215: 4q+1
       216: 4q+1
       217: 4q+1
       218: 4q+1
       219: q^2+4q+1
       220: 4q+1
       221: 3q^2+4q+1
       222: 4q+1
       223: 4q+1
       224: 4q+1
       225: 2q^2+4q+1
       226: q+1
       227: 4q+1
       228: q^2+4q+1
       229: 4q+1
       230: 4q+1
       231: 4q+1
       232: 4q+1
       233: 4q+1
       234: 4q+1
       235: 3q+1
       236: q^2+4q+1
       237: q^2+4q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: q^2+4q+1
       243: 2q+1
       244: q^2+2q+1
       245: q+1
       246: 2q+1
       247: 2q+1
       248: q^2+4q+1
       249: q^2+2q+1
       250: 2q+1
       251: q^2+4q+1
       252: q^2+4q+1
       253: 3q^2+4q+1
       254: q^2+2q+1
       255: 2q+1
       256: 2q^2+4q+1
       257: 2q^2+4q+1
       258: q^2+4q+1
       259: 4q+1
       260: 4q+1
       261: 4q+1
       262: 4q+1
       263: 4q+1
       264: 4q+1
       265: 3q+1
       266: q^2+4q+1
       267: q^2+4q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: q^2+4q+1
       273: q^2+4q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+4q+1
       277: q^2+4q+1
       278: 2q+1
       279: q^2+2q+1
       280: q+1
       281: 2q+1
       282: 2q+1
       283: 3q^2+4q+1
       284: q^2+2q+1
       285: 2q+1
       286: 2q^2+4q+1
       287: 2q^2+4q+1
       288: 4q+1
       289: 4q+1
       290: 4q+1
       291: 4q+1
       292: 4q+1
       293: 4q+1
       294: 4q+1
       295: 4q+1
       296: q+1
       297: q+1
       298: 4q+1
       299: 4q+1
       300: 2q^2+4q+1
       301: q+1
       302: 2q+1
       303: 2q^2+4q+1
       304: q+1
       305: 2q+1
       306: 2q^2+4q+1
       307: 2q^2+4q+1
       308: 2q^2+4q+1
       309: 3q+1
       310: 3q+1
       311: q^2+4q+1
       312: 2q+1
       313: 2q+1
       314: 2q+1
       315: 2q+1
       316: q+1
       317: 3q+1
       319: 3q+1
       320: q^2+4q+1
       321: q^2+4q+1
       322: q^2+4q+1
       323: 2q+1
       324: 2q+1
       325: q^2+4q+1
       326: 3q+1
       327: 3q+1
       328: q^2+4q+1
       329: 4q+1
       330: 4q+1
       331: 4q+1
       332: 4q+1
       333: 4q+1
       334: 4q+1
       335: 3q+1
       336: q^2+4q+1
       337: 4q+1
       338: 4q+1
       339: 4q+1
       340: 4q+1
       341: 4q+1
       342: 4q+1
       343: 3q+1
       344: 4q+1
       345: 4q+1
       346: 4q+1
       347: 4q+1
       348: 4q+1
       349: 4q+1
       350: 4q+1
       351: 4q+1
       352: q+1
       353: q+1
       354: 4q+1
       355: 4q+1
       356: 3q+1
       357: 4q+1
       358: 4q+1
       359: 4q+1
       360: q+1
       361: 2q+1
       362: 4q+1
       363: 3q+1
       364: 3q+1
       365: q^2+4q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: 2q+1
       374: 2q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: 2q+1
       380: q^2+4q+1
       381: q^2+4q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: q^2+4q+1
       387: 2q+1
       388: q^2+2q+1
       389: q+1
       390: 2q+1
       391: 2q+1
       392: 2q^2+4q+1
       393: q+1
       394: 2q+1
       395: 3q+1
       396: 4q+1
       397: 4q+1
       398: 4q+1
       399: 2q+1
       400: q+1
       401: 4q+1
       402: 3q+1
       403: 3q+1
       404: q^2+4q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q+1
       412: q^2+4q+1
       413: q^2+4q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: q^2+4q+1
       419: 2q+1
       420: 2q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: 2q+1
       426: 2q+1
       427: q^2+2q+1
       428: q+1
       429: 2q+1
       430: 2q+1
       431: 2q^2+4q+1
       432: q+1
       433: 2q+1
       434: 4q+1
       435: 4q+1
       436: 4q+1
       437: 4q+1
       438: 4q+1
       439: 4q+1
       440: 4q+1
       441: 3q+1
       442: 4q+1
       443: 4q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 4q+1
       449: 2q+1
       450: q+1
       451: 1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: q+1
       456: 1
       457: 2q+1
       458: 2q+1
       459: 2q^2+4q+1
       460: q+1
       461: q+1
       462: 2q^2+4q+1
       463: 2q^2+4q+1
       465: 3q+1
       466: q+1
       467: 2q+1
       468: 2q+1
       469: q+1
       470: q+1
       471: q+1
       473: 3q+1
       474: 3q+1
       475: q^2+4q+1
       476: 2q+1
       477: 2q+1
       478: 2q+1
       479: 2q+1
       480: q+1
       481: 3q+1
       483: 3q+1
       484: 4q+1
       485: 4q+1
       486: 4q+1
       487: 2q+1
       488: q+1
       489: 4q+1
       490: 3q+1
       491: 3q+1
       492: 3q+1
       493: 4q+1
       494: 4q+1
       495: 4q+1
       496: q+1
       497: 2q+1
       498: 4q+1
       499: 3q+1
       500: 3q+1
       501: 4q+1
       502: 4q+1
       503: 4q+1
       504: 4q+1
       505: 4q+1
       506: 4q+1
       507: 4q+1
       508: 3q+1
       509: 4q+1
       510: 4q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 4q+1
       516: 3q+1
       517: 3q+1
       518: 4q+1
       519: q+1
       520: q+1
       521: 2q+1
       522: 2q+1
       523: 1
       524: 3q+1
       526: q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: 1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       535: 2q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: q^2+4q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: 2q+1
       552: 2q+1
       553: q+1
       554: q+1
       555: q+1
       556: q+1
       557: 2q+1
       558: 2q+1
       559: q+1
       560: 1
       561: 2q+1
       562: 2q+1
       563: 3q+1
       564: 3q+1
       565: 4q+1
       566: 2q+1
       567: 2q+1
       568: q+1
       569: q+1
       570: 1
       571: 3q+1
       573: q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: 1
       579: 2q+1
       580: q+1
       581: q+1
       582: q^2+4q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: 2q+1
       599: 2q+1
       600: q+1
       601: q+1
       602: q+1
       603: q+1
       604: 2q+1
       605: 2q+1
       606: q+1
       607: 1
       608: 2q+1
       609: 2q+1
       610: 3q+1
       611: 4q+1
       612: 4q+1
       613: 4q+1
       614: q+1
       615: q+1
       616: 4q+1
       617: 3q+1
       618: 3q+1
       619: 4q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 2q+1
       628: 2q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 2q+1
       634: 2q+1
       635: 2q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 2q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: 2q^2+4q+1
       647: q+1
       648: q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       658: 3q+1
       659: q+1
       660: 2q+1
       661: 2q+1
       662: q+1
       663: q+1
       664: q+1
       666: 3q+1
       667: 3q+1
       668: 4q+1
       669: 2q+1
       670: 2q+1
       671: q+1
       672: q+1
       673: 1
       674: 3q+1
       676: 3q+1
       677: 3q+1
       678: 4q+1
       679: q+1
       680: q+1
       681: 2q+1
       682: 2q+1
       683: 1
       684: 3q+1
       686: 3q+1
       687: 4q+1
       688: 4q+1
       689: 4q+1
       690: q+1
       691: q+1
       692: 4q+1
       693: 3q+1
       694: 3q+1
       695: 4q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       704: 3q+1
       705: 1
       706: q+1
       707: 2q+1
       708: 1
       709: 1
       710: 1
       712: q+1
       713: q+1
       714: 2q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       722: q+1
       723: q+1
       724: q+1
       725: q+1
       726: 1
       728: q+1
       729: q+1
       730: q+1
       731: q+1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: 1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       740: 2q+1
       741: q+1
       742: q+1
       743: q+1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: 2q+1
       749: 2q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 2q+1
       756: 3q+1
       757: 1
       758: 2q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: q+1
       774: q+1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: 1
       780: 2q+1
       781: q+1
       782: q+1
       783: q+1
       784: q+1
       785: q+1
       786: q+1
       788: 1
       789: q+1
       790: q+1
       791: q+1
       792: 2q+1
       793: q+1
       794: q+1
       795: q+1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       800: 2q+1
       801: 2q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 2q+1
       807: 3q+1
       808: 3q+1
       809: 4q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: 3q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 2q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 2q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       862: q+1
       863: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       870: 3q+1
       871: 1
       872: 2q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       879: 3q+1
       880: 1
       881: q+1
       882: 2q+1
       883: 1
       884: 1
       885: 1
       887: 3q+1
       888: 3q+1
       889: 4q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: 3q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: q+1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       923: q+1
       924: q+1
       925: q+1
       926: 1
       927: 1
       931: q+1
       933: q+1
       934: q+1
       935: 2q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       943: q+1
       944: q+1
       945: q+1
       946: q+1
       947: 1
       949: q+1
       950: q+1
       951: q+1
       952: 2q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: q+1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       977: q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: q+1
       987: q+1
       988: q+1
       989: q+1
       992: 1
       993: 1
       995: q+1
       997: q+1
       998: q+1
       999: q+1
      1000: q+1
      1002: 1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 2q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1015: 3q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1068: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 3q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: q+1
      1131: 1
      1138: q+1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1146: q+1
      1147: q+1
      1148: q+1
      1149: 1
      1150: 1
      1154: q+1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: q+1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1190: q+1
      1193: 1
      1198: q+1
      1199: q+1
      1200: q+1
      1203: 1
      1204: 1
      1206: q+1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1276: q+1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: q+1
      1341: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1386: q+1
      1389: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1422: 1
      1429: 1
      1432: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1454: 1
      1455: 1
      1463: 1
      1468: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1491: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1517: 1
      1519: 1
      1530: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1556: 1
      1559: 1
      1566: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1593: 1
      1601: 1
      1602: 1
      1603: 1
      1609: 1
      1622: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1644: 1
      1669: 1
      1697: 1
      1723: 1
      1741: 1

1742:    0: q^5+5q^4+15q^3+17q^2+7q+1
         1: 2q^4+12q^3+16q^2+7q+1
         2: 3q^4+11q^3+17q^2+7q+1
         3: q^5+5q^4+15q^3+17q^2+7q+1
         4: 3q^4+11q^3+17q^2+7q+1
         5: 3q^4+11q^3+17q^2+7q+1
         6: 5q^3+14q^2+7q+1
         7: 5q^3+14q^2+7q+1
         8: 3q^4+11q^3+17q^2+7q+1
         9: 2q^4+12q^3+16q^2+7q+1
        10: 3q^4+11q^3+17q^2+7q+1
        11: 3q^4+11q^3+17q^2+7q+1
        12: 3q^4+11q^3+17q^2+7q+1
        13: q^4+8q^3+16q^2+7q+1
        14: 2q^4+8q^3+17q^2+7q+1
        15: 3q^4+11q^3+17q^2+7q+1
        16: q^4+8q^3+16q^2+7q+1
        17: 2q^4+8q^3+17q^2+7q+1
        18: 3q^4+11q^3+17q^2+7q+1
        19: q^4+8q^3+17q^2+7q+1
        20: 5q^3+14q^2+7q+1
        21: 2q^3+12q^2+7q+1
        22: 5q^3+14q^2+7q+1
        23: q^4+6q^3+13q^2+7q+1
        24: q^4+6q^3+13q^2+7q+1
        25: 5q^3+14q^2+7q+1
        26: 5q^3+14q^2+7q+1
        27: 3q^4+11q^3+17q^2+7q+1
        28: q^4+8q^3+16q^2+7q+1
        29: 2q^4+8q^3+17q^2+7q+1
        30: q^4+8q^3+16q^2+7q+1
        31: 2q^4+8q^3+17q^2+7q+1
        32: q^4+8q^3+17q^2+7q+1
        33: 3q^3+14q^2+7q+1
        34: 3q^3+14q^2+7q+1
        35: 2q^4+8q^3+17q^2+7q+1
        36: q^4+8q^3+16q^2+7q+1
        37: q^4+6q^3+13q^2+7q+1
        38: 6q^3+13q^2+7q+1
        39: 3q^4+11q^3+17q^2+7q+1
        40: 3q^3+14q^2+7q+1
        41: 3q^3+14q^2+7q+1
        42: 2q^4+8q^3+17q^2+7q+1
        43: q^4+8q^3+16q^2+7q+1
        44: q^4+6q^3+13q^2+7q+1
        45: 3q^4+11q^3+17q^2+7q+1
        46: 6q^3+13q^2+7q+1
        47: 5q^3+16q^2+7q+1
        48: q^4+6q^3+17q^2+7q+1
        49: q^4+8q^3+17q^2+7q+1
        50: q^3+7q^2+5q+1
        51: q^3+7q^2+5q+1
        52: 2q^3+12q^2+7q+1
        53: q^3+8q^2+7q+1
        54: 2q^3+10q^2+7q+1
        55: 2q^3+10q^2+7q+1
        56: 2q^3+10q^2+7q+1
        57: 5q^3+14q^2+7q+1
        58: 2q^3+12q^2+7q+1
        59: 5q^3+14q^2+7q+1
        60: q^4+6q^3+13q^2+7q+1
        61: q^4+6q^3+13q^2+7q+1
        62: 3q^3+14q^2+7q+1
        63: 3q^3+14q^2+7q+1
        64: 2q^4+8q^3+17q^2+7q+1
        65: 3q^3+14q^2+7q+1
        66: 3q^3+14q^2+7q+1
        67: 2q^4+8q^3+17q^2+7q+1
        68: 5q^3+16q^2+7q+1
        69: q^4+6q^3+17q^2+7q+1
        70: q^4+8q^3+17q^2+7q+1
        71: 3q^3+14q^2+7q+1
        72: q^3+12q^2+7q+1
        73: 3q^3+14q^2+7q+1
        74: 3q^3+10q^2+7q+1
        75: q^4+6q^3+13q^2+7q+1
        76: 2q^3+10q^2+7q+1
        77: q^3+7q^2+5q+1
        78: q^4+6q^3+13q^2+7q+1
        79: 4q^3+12q^2+7q+1
        80: 3q^3+10q^2+7q+1
        81: q^4+8q^3+16q^2+7q+1
        82: q^4+6q^3+13q^2+7q+1
        83: 6q^3+13q^2+7q+1
        84: 3q^3+14q^2+7q+1
        85: q^3+12q^2+7q+1
        86: 3q^3+14q^2+7q+1
        87: q^4+6q^3+13q^2+7q+1
        88: 3q^3+10q^2+7q+1
        89: 2q^3+10q^2+7q+1
        90: q^3+7q^2+5q+1
        91: q^4+6q^3+13q^2+7q+1
        92: q^4+8q^3+16q^2+7q+1
        93: q^4+6q^3+13q^2+7q+1
        94: 4q^3+12q^2+7q+1
        95: 3q^3+10q^2+7q+1
        96: 6q^3+13q^2+7q+1
        97: 2q^3+14q^2+7q+1
        98: 2q^3+14q^2+7q+1
        99: q^4+6q^3+17q^2+7q+1
       100: 5q^3+16q^2+7q+1
       101: 2q^3+10q^2+7q+1
       102: 6q^3+13q^2+7q+1
       103: 6q^3+13q^2+7q+1
       104: 3q^2+4q+1
       105: 5q^2+5q+1
       106: 5q^2+5q+1
       107: q^3+8q^2+7q+1
       108: 6q^2+7q+1
       109: 6q^2+7q+1
       110: 7q^2+7q+1
       111: 2q^3+10q^2+7q+1
       112: q^3+7q^2+5q+1
       113: q^3+7q^2+5q+1
       114: 2q^3+12q^2+7q+1
       115: q^3+8q^2+7q+1
       116: 2q^3+10q^2+7q+1
       117: 2q^3+10q^2+7q+1
       118: 2q^3+10q^2+7q+1
       119: 3q^3+14q^2+7q+1
       120: q^3+12q^2+7q+1
       121: 3q^3+14q^2+7q+1
       122: q^4+6q^3+13q^2+7q+1
       123: 3q^3+10q^2+7q+1
       124: 3q^3+14q^2+7q+1
       125: q^3+12q^2+7q+1
       126: 3q^3+14q^2+7q+1
       127: 3q^3+10q^2+7q+1
       128: q^4+6q^3+13q^2+7q+1
       129: 2q^3+14q^2+7q+1
       130: 2q^3+14q^2+7q+1
       131: q^4+6q^3+17q^2+7q+1
       132: 5q^3+16q^2+7q+1
       133: 2q^3+10q^2+7q+1
       134: 5q^2+5q+1
       135: q^3+7q^2+5q+1
       136: q^3+12q^2+7q+1
       137: 6q^2+7q+1
       138: q^3+8q^2+7q+1
       139: 2q^3+10q^2+7q+1
       140: q^3+7q^2+7q+1
       141: 2q^3+10q^2+7q+1
       142: 5q^2+5q+1
       143: q^3+7q^2+5q+1
       144: 2q^3+7q^2+7q+1
       145: q^4+5q^3+10q^2+7q+1
       146: q^3+8q^2+7q+1
       147: 5q^2+5q+1
       148: 3q^3+10q^2+7q+1
       149: 2q^3+10q^2+7q+1
       150: q^3+7q^2+5q+1
       151: q^4+6q^3+13q^2+7q+1
       152: 4q^3+12q^2+7q+1
       153: 3q^3+10q^2+7q+1
       154: 6q^3+13q^2+7q+1
       155: q^3+7q^2+5q+1
       156: 5q^2+5q+1
       157: q^3+12q^2+7q+1
       158: 6q^2+7q+1
       159: 2q^3+10q^2+7q+1
       160: q^3+8q^2+7q+1
       161: q^3+7q^2+7q+1
       162: 2q^3+10q^2+7q+1
       163: 5q^2+5q+1
       164: q^3+7q^2+5q+1
       165: q^4+5q^3+10q^2+7q+1
       166: 2q^3+7q^2+7q+1
       167: 2q^3+10q^2+7q+1
       168: q^3+7q^2+5q+1
       169: q^4+6q^3+13q^2+7q+1
       170: q^3+8q^2+7q+1
       171: 5q^2+5q+1
       172: 3q^3+10q^2+7q+1
       173: 4q^3+12q^2+7q+1
       174: 3q^3+10q^2+7q+1
       175: 6q^3+13q^2+7q+1
       176: 2q^3+14q^2+7q+1
       177: q^3+12q^2+7q+1
       178: 2q^3+14q^2+7q+1
       179: 3q^3+10q^2+7q+1
       180: 3q^3+10q^2+7q+1
       181: 7q^2+7q+1
       182: 3q^2+4q+1
       183: 2q^3+10q^2+7q+1
       184: 4q^3+12q^2+7q+1
       185: q^3+7q^2+7q+1
       186: 4q^3+12q^2+7q+1
       187: q^3+7q^2+7q+1
       188: 4q^3+10q^2+7q+1
       189: 3q^2+4q+1
       190: q^2+4q+1
       191: 3q^2+5q+1
       192: 3q^2+5q+1
       193: 6q^2+7q+1
       194: 6q^2+7q+1
       195: 5q^2+7q+1
       196: 7q^2+7q+1
       197: 3q^2+4q+1
       198: 3q^2+4q+1
       199: 5q^2+5q+1
       200: 5q^2+5q+1
       201: q^3+8q^2+7q+1
       202: 6q^2+7q+1
       203: 6q^2+7q+1
       204: 7q^2+7q+1
       205: 2q^3+10q^2+7q+1
       206: q^3+7q^2+5q+1
       207: 5q^2+5q+1
       208: q^3+12q^2+7q+1
       209: 6q^2+7q+1
       210: 2q^3+10q^2+7q+1
       211: q^3+8q^2+7q+1
       212: q^3+7q^2+7q+1
       213: 5q^2+5q+1
       214: q^3+7q^2+5q+1
       215: q^3+12q^2+7q+1
       216: 6q^2+7q+1
       217: q^3+8q^2+7q+1
       218: 2q^3+10q^2+7q+1
       219: q^3+7q^2+7q+1
       220: 2q^3+14q^2+7q+1
       221: q^3+12q^2+7q+1
       222: 2q^3+14q^2+7q+1
       223: 3q^3+10q^2+7q+1
       224: 3q^3+10q^2+7q+1
       225: 7q^2+7q+1
       226: 3q^2+4q+1
       227: 2q^3+10q^2+7q+1
       228: q^2+4q+1
       229: 4q^2+5q+1
       230: 5q^2+5q+1
       231: 6q^2+7q+1
       232: 3q^2+7q+1
       233: 4q^2+7q+1
       234: 5q^2+7q+1
       235: q^3+7q^2+7q+1
       236: 3q^2+5q+1
       237: q^3+5q^2+5q+1
       238: 5q^2+5q+1
       239: 3q^2+5q+1
       240: 3q^2+5q+1
       241: q^3+5q^2+5q+1
       242: q^3+5q^2+7q+1
       243: q^3+8q^2+7q+1
       244: 4q^2+5q+1
       245: 5q^2+5q+1
       246: 2q^3+7q^2+7q+1
       247: q^3+4q^2+4q+1
       248: 2q^3+10q^2+7q+1
       249: 5q^2+5q+1
       250: q^3+7q^2+5q+1
       251: 2q^3+7q^2+7q+1
       252: q^4+5q^3+10q^2+7q+1
       253: q^3+8q^2+7q+1
       254: 5q^2+5q+1
       255: 3q^3+10q^2+7q+1
       256: 4q^3+12q^2+7q+1
       257: q^3+7q^2+7q+1
       258: q^2+4q+1
       259: 5q^2+5q+1
       260: 4q^2+5q+1
       261: 6q^2+7q+1
       262: 4q^2+7q+1
       263: 3q^2+7q+1
       264: 5q^2+7q+1
       265: q^3+7q^2+7q+1
       266: q^3+5q^2+5q+1
       267: 3q^2+5q+1
       268: 5q^2+5q+1
       269: 3q^2+5q+1
       270: q^3+5q^2+5q+1
       271: 3q^2+5q+1
       272: q^3+5q^2+7q+1
       273: 2q^3+10q^2+7q+1
       274: 5q^2+5q+1
       275: q^3+7q^2+5q+1
       276: q^4+5q^3+10q^2+7q+1
       277: 2q^3+7q^2+7q+1
       278: q^3+8q^2+7q+1
       279: 4q^2+5q+1
       280: 5q^2+5q+1
       281: q^3+4q^2+4q+1
       282: 2q^3+7q^2+7q+1
       283: q^3+8q^2+7q+1
       284: 5q^2+5q+1
       285: 3q^3+10q^2+7q+1
       286: 4q^3+12q^2+7q+1
       287: q^3+7q^2+7q+1
       288: 5q^2+5q+1
       289: 5q^2+5q+1
       290: q^3+12q^2+7q+1
       291: 5q^2+7q+1
       292: q^3+8q^2+7q+1
       293: q^3+8q^2+7q+1
       294: 5q^2+7q+1
       295: 7q^2+7q+1
       296: q^2+4q+1
       297: 3q^2+4q+1
       298: q^3+5q^2+7q+1
       299: q^3+5q^2+7q+1
       300: 5q^2+7q+1
       301: q^2+4q+1
       302: q^3+7q^2+7q+1
       303: 5q^2+7q+1
       304: q^2+4q+1
       305: q^3+7q^2+7q+1
       306: 3q^3+9q^2+7q+1
       307: 5q^2+7q+1
       308: 4q^3+10q^2+7q+1
       310: q^2+4q+1
       311: q^2+4q+1
       312: 3q^2+5q+1
       313: q^2+3q+1
       314: q^2+3q+1
       315: 3q^2+5q+1
       316: 5q^2+7q+1
       317: q^2+4q+1
       319: 3q^2+4q+1
       320: q^2+4q+1
       321: 3q^2+5q+1
       322: 3q^2+5q+1
       323: 6q^2+7q+1
       324: 6q^2+7q+1
       325: 5q^2+7q+1
       326: 7q^2+7q+1
       327: 3q^2+4q+1
       328: q^2+4q+1
       329: 5q^2+5q+1
       330: 4q^2+5q+1
       331: 6q^2+7q+1
       332: 4q^2+7q+1
       333: 3q^2+7q+1
       334: 5q^2+7q+1
       335: q^3+7q^2+7q+1
       336: q^2+4q+1
       337: 4q^2+5q+1
       338: 5q^2+5q+1
       339: 6q^2+7q+1
       340: 3q^2+7q+1
       341: 4q^2+7q+1
       342: 5q^2+7q+1
       343: q^3+7q^2+7q+1
       344: 5q^2+5q+1
       345: 5q^2+5q+1
       346: q^3+12q^2+7q+1
       347: 5q^2+7q+1
       348: q^3+8q^2+7q+1
       349: q^3+8q^2+7q+1
       350: 5q^2+7q+1
       351: 7q^2+7q+1
       352: q^2+4q+1
       353: 3q^2+4q+1
       354: q^3+5q^2+7q+1
       355: q^3+5q^2+7q+1
       356: q^2+4q+1
       357: 4q+1
       358: q^2+5q+1
       359: 2q^2+5q+1
       360: 3q^2+7q+1
       361: 4q^2+7q+1
       362: 2q^2+7q+1
       363: 5q^2+7q+1
       364: q^2+4q+1
       365: q^2+4q+1
       366: q^2+3q+1
       367: 2q^2+3q+1
       368: 3q^2+5q+1
       369: q^2+5q+1
       370: 2q^2+5q+1
       371: 2q^2+5q+1
       372: q^3+5q^2+7q+1
       373: 3q^2+5q+1
       374: 2q^2+3q+1
       375: 4q^2+5q+1
       376: q^2+3q+1
       377: 3q^2+5q+1
       378: 2q^2+3q+1
       379: 2q^2+4q+1
       380: 3q^2+5q+1
       381: q^3+5q^2+5q+1
       382: 5q^2+5q+1
       383: 3q^2+5q+1
       384: 3q^2+5q+1
       385: q^3+5q^2+5q+1
       386: q^3+5q^2+7q+1
       387: q^3+8q^2+7q+1
       388: 4q^2+5q+1
       389: 5q^2+5q+1
       390: 2q^3+7q^2+7q+1
       391: q^3+4q^2+4q+1
       392: 5q^2+7q+1
       393: q^2+4q+1
       394: q^3+7q^2+7q+1
       395: q^2+4q+1
       396: 4q+1
       397: 2q^2+5q+1
       398: q^2+5q+1
       399: 4q^2+7q+1
       400: 3q^2+7q+1
       401: 2q^2+7q+1
       402: 5q^2+7q+1
       403: q^2+4q+1
       404: q^2+4q+1
       405: 2q^2+3q+1
       406: q^2+3q+1
       407: 3q^2+5q+1
       408: 2q^2+5q+1
       409: q^2+5q+1
       410: 2q^2+5q+1
       411: q^3+5q^2+7q+1
       412: q^3+5q^2+5q+1
       413: 3q^2+5q+1
       414: 5q^2+5q+1
       415: 3q^2+5q+1
       416: q^3+5q^2+5q+1
       417: 3q^2+5q+1
       418: q^3+5q^2+7q+1
       419: 2q^2+3q+1
       420: 3q^2+5q+1
       421: 4q^2+5q+1
       422: q^2+3q+1
       423: 2q^2+3q+1
       424: 3q^2+5q+1
       425: 2q^2+4q+1
       426: q^3+8q^2+7q+1
       427: 4q^2+5q+1
       428: 5q^2+5q+1
       429: q^3+4q^2+4q+1
       430: 2q^3+7q^2+7q+1
       431: 5q^2+7q+1
       432: q^2+4q+1
       433: q^3+7q^2+7q+1
       434: 4q+1
       435: 4q^2+5q+1
       436: 4q^2+5q+1
       437: 5q^2+7q+1
       438: 2q^2+7q+1
       439: 2q^2+7q+1
       440: 4q^2+7q+1
       441: 5q^2+7q+1
       442: 2q^2+5q+1
       443: 2q^2+5q+1
       444: q^2+4q+1
       445: q^2+4q+1
       446: q^2+4q+1
       447: q^2+4q+1
       448: 2q^2+7q+1
       449: 5q^2+7q+1
       450: 4q+1
       451: q^2+4q+1
       452: q^3+5q^2+7q+1
       453: 2q^2+4q+1
       454: 5q^2+7q+1
       455: 4q+1
       456: q^2+4q+1
       457: 2q^2+4q+1
       458: q^3+5q^2+7q+1
       459: 4q^2+7q+1
       460: 4q+1
       461: 5q^2+7q+1
       462: 3q^3+9q^2+7q+1
       463: 5q^2+7q+1
       466: q^2+4q+1
       467: 2q+1
       468: 2q+1
       469: q^2+3q+1
       470: q^2+3q+1
       471: q^2+4q+1
       474: q^2+4q+1
       475: q^2+4q+1
       476: 3q^2+5q+1
       477: q^2+3q+1
       478: q^2+3q+1
       479: 3q^2+5q+1
       480: 5q^2+7q+1
       481: q^2+4q+1
       483: q^2+4q+1
       484: 4q+1
       485: 2q^2+5q+1
       486: q^2+5q+1
       487: 4q^2+7q+1
       488: 3q^2+7q+1
       489: 2q^2+7q+1
       490: 5q^2+7q+1
       491: q^2+4q+1
       492: q^2+4q+1
       493: 4q+1
       494: q^2+5q+1
       495: 2q^2+5q+1
       496: 3q^2+7q+1
       497: 4q^2+7q+1
       498: 2q^2+7q+1
       499: 5q^2+7q+1
       500: q^2+4q+1
       501: 4q+1
       502: 4q^2+5q+1
       503: 4q^2+5q+1
       504: 5q^2+7q+1
       505: 2q^2+7q+1
       506: 2q^2+7q+1
       507: 4q^2+7q+1
       508: 5q^2+7q+1
       509: 2q^2+5q+1
       510: 2q^2+5q+1
       511: q^2+4q+1
       512: q^2+4q+1
       513: q^2+4q+1
       514: q^2+4q+1
       515: 2q^2+7q+1
       517: 4q+1
       518: 4q+1
       519: q^2+5q+1
       520: 2q+1
       521: 3q+1
       522: 2q^2+5q+1
       523: 2q^2+7q+1
       524: 4q+1
       526: q^2+4q+1
       527: 2q+1
       528: 3q+1
       529: q^2+3q+1
       530: q^2+5q+1
       531: 2q^2+5q+1
       532: q^2+5q+1
       533: 2q^2+5q+1
       534: q^2+4q+1
       535: 2q+1
       536: q^2+3q+1
       537: q^2+2q+1
       538: q^2+3q+1
       539: 3q+1
       540: 2q+1
       541: q^2+3q+1
       542: 2q^2+4q+1
       543: q^2+4q+1
       544: q^2+3q+1
       545: 2q^2+3q+1
       546: 3q^2+5q+1
       547: q^2+5q+1
       548: 2q^2+5q+1
       549: 2q^2+5q+1
       550: q^3+5q^2+7q+1
       551: 3q^2+5q+1
       552: 2q^2+3q+1
       553: 4q^2+5q+1
       554: q^2+3q+1
       555: 3q^2+5q+1
       556: 2q^2+3q+1
       557: 2q^2+4q+1
       558: 5q^2+7q+1
       559: 4q+1
       560: q^2+4q+1
       561: q^3+5q^2+7q+1
       562: 2q^2+4q+1
       564: 4q+1
       565: 4q+1
       566: 2q^2+5q+1
       567: 3q+1
       568: 2q+1
       569: q^2+5q+1
       570: 2q^2+7q+1
       571: 4q+1
       573: q^2+4q+1
       574: 2q+1
       575: q^2+3q+1
       576: 3q+1
       577: 2q^2+5q+1
       578: q^2+5q+1
       579: q^2+5q+1
       580: 2q^2+5q+1
       581: q^2+4q+1
       582: q^2+4q+1
       583: 2q^2+3q+1
       584: q^2+3q+1
       585: 3q^2+5q+1
       586: 2q^2+5q+1
       587: q^2+5q+1
       588: 2q^2+5q+1
       589: q^3+5q^2+7q+1
       590: 2q+1
       591: q^2+2q+1
       592: q^2+3q+1
       593: q^2+3q+1
       594: 2q+1
       595: 3q+1
       596: q^2+3q+1
       597: 2q^2+4q+1
       598: 2q^2+3q+1
       599: 3q^2+5q+1
       600: 4q^2+5q+1
       601: q^2+3q+1
       602: 2q^2+3q+1
       603: 3q^2+5q+1
       604: 2q^2+4q+1
       605: 5q^2+7q+1
       606: 4q+1
       607: q^2+4q+1
       608: 2q^2+4q+1
       609: q^3+5q^2+7q+1
       610: 4q+1
       611: 4q+1
       612: q^2+5q+1
       613: q^2+5q+1
       614: 2q^2+7q+1
       615: 2q^2+7q+1
       616: q^2+7q+1
       617: 4q^2+7q+1
       618: 4q+1
       619: 4q+1
       620: 2q+1
       621: 2q+1
       622: q^2+4q+1
       623: 4q+1
       624: 4q+1
       625: 4q+1
       626: 2q^2+7q+1
       627: 2q^2+5q+1
       628: q^2+3q+1
       629: 4q+1
       630: 2q+1
       631: q^2+4q+1
       632: 2q+1
       633: q^2+4q+1
       634: q^2+3q+1
       635: 2q^2+5q+1
       636: 4q+1
       637: 2q+1
       638: 2q+1
       639: q^2+4q+1
       640: q^2+4q+1
       641: 4q^2+7q+1
       642: 4q+1
       643: 4q+1
       644: 2q^2+4q+1
       645: 2q^2+4q+1
       646: 4q^2+7q+1
       647: 4q+1
       648: 5q^2+7q+1
       651: 2q+1
       652: 2q+1
       653: q+1
       654: 2q+1
       655: 2q+1
       659: q^2+4q+1
       660: 2q+1
       661: 2q+1
       662: q^2+3q+1
       663: q^2+3q+1
       664: q^2+4q+1
       667: 4q+1
       668: 4q+1
       669: 2q^2+5q+1
       670: 3q+1
       671: 2q+1
       672: q^2+5q+1
       673: 2q^2+7q+1
       674: 4q+1
       677: 4q+1
       678: 4q+1
       679: q^2+5q+1
       680: 2q+1
       681: 3q+1
       682: 2q^2+5q+1
       683: 2q^2+7q+1
       684: 4q+1
       686: 4q+1
       687: 4q+1
       688: q^2+5q+1
       689: q^2+5q+1
       690: 2q^2+7q+1
       691: 2q^2+7q+1
       692: q^2+7q+1
       693: 4q^2+7q+1
       694: 4q+1
       695: 4q+1
       696: 2q+1
       697: 2q+1
       698: q^2+4q+1
       699: 4q+1
       700: 4q+1
       701: 4q+1
       702: 2q^2+7q+1
       705: 4q+1
       706: q+1
       707: 2q+1
       708: 3q+1
       709: 2q+1
       710: 4q+1
       713: 2q+1
       714: 2q+1
       715: 3q+1
       716: q+1
       717: 2q+1
       718: q^2+3q+1
       719: q^2+5q+1
       720: 2q+1
       722: 2q+1
       723: q+1
       724: 2q+1
       725: q+1
       726: 3q+1
       727: 2q+1
       728: 2q+1
       729: q^2+3q+1
       730: 2q+1
       731: q^2+4q+1
       732: 2q+1
       733: 3q+1
       734: q^2+3q+1
       735: q^2+5q+1
       736: 2q^2+5q+1
       737: q^2+5q+1
       738: 2q^2+5q+1
       739: q^2+4q+1
       740: 2q+1
       741: q^2+3q+1
       742: q^2+2q+1
       743: q^2+3q+1
       744: 3q+1
       745: 2q+1
       746: q^2+3q+1
       747: 2q^2+4q+1
       748: 2q^2+5q+1
       749: q^2+3q+1
       750: 4q+1
       751: 2q+1
       752: q^2+4q+1
       753: 2q+1
       754: q^2+4q+1
       757: 4q+1
       758: 2q+1
       759: q+1
       760: 2q+1
       761: 3q+1
       762: 4q+1
       765: 2q+1
       766: 2q+1
       767: q^2+3q+1
       768: 2q+1
       769: q+1
       770: 3q+1
       771: q^2+5q+1
       772: 2q+1
       774: q^2+4q+1
       775: 2q+1
       776: q^2+3q+1
       777: 3q+1
       778: 2q^2+5q+1
       779: q^2+5q+1
       780: q^2+5q+1
       781: 2q^2+5q+1
       782: q^2+4q+1
       783: 2q+1
       784: q+1
       785: q+1
       786: 2q+1
       787: 2q+1
       788: 3q+1
       789: 2q+1
       790: q^2+3q+1
       791: 2q+1
       792: 2q+1
       793: q^2+2q+1
       794: q^2+3q+1
       795: q^2+3q+1
       796: 2q+1
       797: 3q+1
       798: q^2+3q+1
       799: 2q^2+4q+1
       800: q^2+3q+1
       801: 2q^2+5q+1
       802: 4q+1
       803: 2q+1
       804: 2q+1
       805: q^2+4q+1
       806: q^2+4q+1
       808: 4q+1
       809: 4q+1
       810: q^2+5q+1
       811: 2q+1
       812: 2q+1
       813: q^2+5q+1
       814: q^2+7q+1
       815: 4q+1
       817: 4q+1
       818: q+1
       819: 2q+1
       820: 2q+1
       821: 4q+1
       822: 4q+1
       823: 4q+1
       824: 4q+1
       825: 4q+1
       826: 2q+1
       827: 2q+1
       828: q+1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: 2q+1
       833: q^2+4q+1
       834: 2q+1
       835: q+1
       836: 2q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: 2q+1
       841: q^2+4q+1
       842: q^2+3q+1
       843: q^2+3q+1
       844: 4q+1
       845: q+1
       846: 2q+1
       847: 2q+1
       848: 2q+1
       849: 4q^2+7q+1
       850: 4q+1
       851: 4q+1
       852: 2q^2+4q+1
       853: 2q^2+4q+1
       857: q+1
       858: q+1
       863: 2q+1
       864: 2q+1
       865: q+1
       866: 2q+1
       867: 2q+1
       871: 4q+1
       872: 2q+1
       873: q+1
       874: 2q+1
       875: 3q+1
       876: 4q+1
       880: 4q+1
       881: q+1
       882: 2q+1
       883: 3q+1
       884: 2q+1
       885: 4q+1
       888: 4q+1
       889: 4q+1
       890: q^2+5q+1
       891: 2q+1
       892: 2q+1
       893: q^2+5q+1
       894: q^2+7q+1
       895: 4q+1
       897: 4q+1
       898: q+1
       899: 2q+1
       900: 2q+1
       901: 4q+1
       902: 4q+1
       903: 4q+1
       904: 4q+1
       905: 4q+1
       908: q+1
       909: 2q+1
       910: 1
       911: 2q+1
       912: q+1
       916: 2q+1
       917: 1
       918: q+1
       919: 2q+1
       920: q+1
       921: 2q+1
       924: q+1
       925: q+1
       926: 2q+1
       927: 1
       929: q+1
       930: 2q+1
       931: q+1
       934: 2q+1
       935: 2q+1
       936: 3q+1
       937: q+1
       938: 2q+1
       939: q^2+3q+1
       940: q^2+5q+1
       941: 2q+1
       943: 2q+1
       944: q+1
       945: 2q+1
       946: q+1
       947: 3q+1
       948: 2q+1
       949: 2q+1
       950: q^2+3q+1
       951: 2q+1
       952: 2q+1
       953: 2q+1
       954: q+1
       955: 2q+1
       956: 2q+1
       957: q+1
       958: 2q+1
       959: q^2+4q+1
       962: 2q+1
       963: q+1
       964: 1
       965: q+1
       966: 2q+1
       970: 2q+1
       971: q+1
       972: 1
       973: q+1
       974: 2q+1
       975: 2q+1
       978: 2q+1
       979: 2q+1
       980: q^2+3q+1
       981: 2q+1
       982: q+1
       983: 3q+1
       984: q^2+5q+1
       985: 2q+1
       988: q+1
       989: q+1
       990: q+1
       992: 1
       993: 2q+1
       994: 2q+1
       995: q+1
       997: 2q+1
       998: q+1
       999: q+1
      1000: 2q+1
      1001: 2q+1
      1002: 3q+1
      1003: 2q+1
      1004: q^2+3q+1
      1005: 2q+1
      1006: 2q+1
      1007: q+1
      1008: 2q+1
      1009: 2q+1
      1010: q+1
      1011: 2q+1
      1012: 2q+1
      1013: q^2+4q+1
      1016: 4q+1
      1017: q+1
      1018: q+1
      1019: 2q+1
      1020: 2q+1
      1021: 4q+1
      1024: q+1
      1025: q+1
      1026: 2q+1
      1027: q+1
      1028: q+1
      1029: 2q+1
      1030: 4q+1
      1031: q+1
      1033: 2q+1
      1034: 1
      1035: q+1
      1036: 1
      1037: 2q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: 2q+1
      1042: 2q+1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: 2q+1
      1048: q+1
      1049: 2q+1
      1050: 2q+1
      1051: q+1
      1052: q+1
      1053: q+1
      1054: q+1
      1055: 1
      1056: 1
      1057: q+1
      1058: 2q+1
      1059: q^2+3q+1
      1060: q^2+3q+1
      1061: 4q+1
      1062: q+1
      1063: 2q+1
      1064: 2q+1
      1065: 2q+1
      1069: q+1
      1074: q+1
      1075: q+1
      1080: 2q+1
      1081: q+1
      1082: 1
      1083: q+1
      1084: 2q+1
      1088: q+1
      1089: 2q+1
      1090: 1
      1091: 2q+1
      1092: q+1
      1096: 4q+1
      1097: q+1
      1098: q+1
      1099: 2q+1
      1100: 2q+1
      1101: 4q+1
      1104: q+1
      1105: q+1
      1106: 2q+1
      1107: q+1
      1108: q+1
      1109: 2q+1
      1110: 4q+1
      1111: q+1
      1116: 1
      1117: 1
      1122: 1
      1123: q+1
      1124: 1
      1125: q+1
      1126: 1
      1130: q+1
      1131: 1
      1134: 1
      1135: q+1
      1139: 2q+1
      1140: 1
      1141: q+1
      1142: 2q+1
      1143: q+1
      1144: 2q+1
      1147: q+1
      1148: q+1
      1149: 2q+1
      1150: 1
      1152: q+1
      1153: 2q+1
      1154: q+1
      1156: 2q+1
      1157: 1
      1158: q+1
      1159: 1
      1160: 2q+1
      1161: q+1
      1162: q+1
      1163: 2q+1
      1164: 2q+1
      1168: 1
      1169: 1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: q+1
      1182: 2q+1
      1183: q+1
      1184: 1
      1185: q+1
      1186: 2q+1
      1187: 2q+1
      1191: q+1
      1193: 1
      1194: 1
      1196: q+1
      1199: q+1
      1200: q+1
      1201: q+1
      1203: 1
      1204: 2q+1
      1205: 2q+1
      1206: q+1
      1208: 2q+1
      1209: 1
      1210: 1
      1211: q+1
      1212: q+1
      1213: 2q+1
      1214: q+1
      1215: 2q+1
      1216: 2q+1
      1219: q+1
      1220: q+1
      1221: 1
      1222: q+1
      1223: q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: q+1
      1231: q+1
      1232: q+1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: q+1
      1242: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: q+1
      1252: 1
      1254: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: q+1
      1263: q+1
      1264: q+1
      1265: q+1
      1266: q+1
      1267: 1
      1268: 1
      1269: q+1
      1270: 2q+1
      1277: q+1
      1282: 1
      1283: 1
      1289: 1
      1290: 1
      1295: q+1
      1296: q+1
      1297: 1
      1298: q+1
      1299: q+1
      1303: q+1
      1304: 1
      1305: 1
      1306: q+1
      1307: q+1
      1308: q+1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1328: 1
      1332: 1
      1333: q+1
      1334: 1
      1335: q+1
      1336: 1
      1340: q+1
      1341: 1
      1344: 1
      1345: q+1
      1348: 1
      1349: 1
      1350: q+1
      1351: 1
      1353: 1
      1354: q+1
      1355: 1
      1360: 1
      1365: 1
      1366: 1
      1371: q+1
      1372: 1
      1373: 1
      1374: 1
      1375: q+1
      1380: 1
      1382: 1
      1387: q+1
      1389: 1
      1390: 1
      1392: q+1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: q+1
      1401: q+1
      1402: 1
      1407: 1
      1408: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q+1
      1455: q+1
      1464: 1
      1469: 1
      1474: 1
      1475: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1492: 1
      1504: 1
      1505: 1
      1510: 1
      1514: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1531: 1
      1536: 1
      1537: 1
      1550: 1
      1552: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1567: 1
      1572: 1
      1573: 1
      1578: 1
      1582: 1
      1587: 1
      1589: 1
      1594: 1
      1599: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1609: 1
      1623: 1
      1628: 1
      1629: 1
      1645: 1
      1656: 1
      1660: 1
      1670: 1
      1687: 1
      1689: 1
      1698: 1
      1724: 1
      1729: 1
      1742: 1

1743:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: 3q^2+3q+1
         7: 3q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: 3q^2+3q+1
        12: 3q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: q^2+3q+1
        19: 3q^2+3q+1
        20: q^2+q+1
        21: 3q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: 3q^2+3q+1
        29: 3q^2+3q+1
        30: 3q^2+3q+1
        31: 3q^2+3q+1
        32: 3q^2+3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: 3q^2+3q+1
        41: 3q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 3q^2+3q+1
        48: 3q^2+3q+1
        49: 3q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: 3q^2+3q+1
        54: 3q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: q^2+q+1
        58: 3q^2+3q+1
        59: 3q^2+3q+1
        60: 3q^2+3q+1
        61: 3q^2+3q+1
        62: 3q^2+3q+1
        63: 3q^2+3q+1
        64: q^2+3q+1
        65: 3q^2+3q+1
        66: 3q^2+3q+1
        67: q^2+3q+1
        68: 3q^2+3q+1
        69: 3q^2+3q+1
        70: 3q+1
        71: q+1
        72: 3q^2+3q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: q^2+3q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: q+1
        85: 3q^2+3q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: 3q+1
       100: 3q+1
       101: 3q+1
       102: 3q+1
       103: 3q+1
       104: q^2+q+1
       105: q^2+q+1
       106: q^2+q+1
       107: q^2+q+1
       108: 3q^2+3q+1
       109: 3q^2+3q+1
       110: 3q^2+3q+1
       111: 3q+1
       112: q^2+q+1
       113: q^2+q+1
       114: q^2+q+1
       115: 3q^2+3q+1
       116: 3q^2+3q+1
       117: 3q^2+3q+1
       118: 3q^2+3q+1
       119: q+1
       120: 3q^2+3q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: q^2+3q+1
       124: q+1
       125: 3q^2+3q+1
       126: q^2+3q+1
       127: q^2+3q+1
       128: q^2+3q+1
       129: 3q^2+3q+1
       130: 3q^2+3q+1
       131: 3q+1
       132: 3q+1
       133: 3q+1
       134: q+1
       135: q+1
       136: q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: q+1
       142: q^2+3q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: q+1
       149: q^2+3q+1
       150: q^2+3q+1
       151: q^2+3q+1
       152: q^2+3q+1
       153: q^2+3q+1
       154: 3q+1
       155: q+1
       156: q+1
       157: q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+3q+1
       169: q^2+3q+1
       170: q^2+3q+1
       171: q^2+3q+1
       172: q+1
       173: q^2+3q+1
       174: q^2+3q+1
       175: 3q+1
       176: q+1
       177: 3q^2+3q+1
       178: 3q+1
       179: 3q+1
       180: 3q+1
       181: 3q+1
       182: 3q+1
       183: 3q+1
       184: 3q+1
       185: 3q+1
       186: 3q+1
       187: 3q+1
       188: 3q+1
       190: q^2+q+1
       191: q^2+q+1
       192: q^2+q+1
       193: q+1
       194: q+1
       195: 3q^2+3q+1
       196: 3q+1
       197: 3q+1
       198: q^2+q+1
       199: q^2+q+1
       200: q^2+q+1
       201: q^2+q+1
       202: 3q^2+3q+1
       203: 3q^2+3q+1
       204: 3q^2+3q+1
       205: 3q+1
       206: q+1
       207: q+1
       208: q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: q^2+3q+1
       212: q^2+3q+1
       213: q+1
       214: q+1
       215: q+1
       216: q^2+3q+1
       217: q^2+3q+1
       218: q^2+3q+1
       219: q^2+3q+1
       220: q+1
       221: 3q^2+3q+1
       222: 3q+1
       223: 3q+1
       224: 3q+1
       225: 3q+1
       226: 3q+1
       227: 3q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q^2+3q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: 3q+1
       236: q+1
       237: q+1
       238: q+1
       239: q^2+3q+1
       240: q^2+3q+1
       241: q^2+3q+1
       242: q^2+3q+1
       243: 1
       244: q^2+3q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q^2+3q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q+1
       256: 3q+1
       257: 3q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q^2+3q+1
       263: q^2+3q+1
       264: q^2+3q+1
       265: 3q+1
       266: q+1
       267: q+1
       268: q+1
       269: q^2+3q+1
       270: q^2+3q+1
       271: q^2+3q+1
       272: q^2+3q+1
       273: q+1
       274: q^2+3q+1
       275: q^2+3q+1
       276: q^2+3q+1
       277: q^2+3q+1
       278: 1
       279: q^2+3q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+3q+1
       284: q^2+3q+1
       285: q+1
       286: 3q+1
       287: 3q+1
       288: q+1
       289: q+1
       290: q+1
       291: 3q+1
       292: 3q+1
       293: 3q+1
       294: 3q+1
       295: q+1
       296: 3q+1
       297: 3q+1
       298: 3q+1
       299: 3q+1
       300: 3q+1
       301: 3q+1
       302: q+1
       303: 3q+1
       304: 3q+1
       305: q+1
       306: 3q+1
       307: 3q+1
       308: 3q+1
       311: q^2+q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 3q+1
       318: 3q+1
       320: q^2+q+1
       321: q^2+q+1
       322: q^2+q+1
       323: q+1
       324: q+1
       325: 3q^2+3q+1
       326: 3q+1
       327: 3q+1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q^2+3q+1
       333: q^2+3q+1
       334: q^2+3q+1
       335: 3q+1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q^2+3q+1
       341: q^2+3q+1
       342: q^2+3q+1
       343: 3q+1
       344: q+1
       345: q+1
       346: q+1
       347: 3q+1
       348: 3q+1
       349: 3q+1
       350: 3q+1
       351: q+1
       352: 3q+1
       353: 3q+1
       354: 3q+1
       355: 3q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q^2+3q+1
       363: 3q+1
       364: 3q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q+1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: q^2+3q+1
       384: q^2+3q+1
       385: q^2+3q+1
       386: q^2+3q+1
       387: 1
       388: q^2+3q+1
       389: q+1
       390: q+1
       391: q+1
       392: 3q+1
       393: 3q+1
       394: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q^2+3q+1
       402: 3q+1
       403: 3q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q^2+3q+1
       409: q^2+3q+1
       410: q^2+3q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: q^2+3q+1
       416: q^2+3q+1
       417: q^2+3q+1
       418: q^2+3q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q^2+3q+1
       428: q+1
       429: q+1
       430: q+1
       431: 3q+1
       432: 3q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 3q+1
       439: 3q+1
       440: 3q+1
       441: 3q+1
       442: q+1
       443: q+1
       444: q+1
       445: 3q+1
       446: 3q+1
       447: 3q+1
       448: 3q+1
       449: 1
       450: 3q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: 3q+1
       456: q+1
       457: q+1
       458: q+1
       459: 3q+1
       460: 3q+1
       461: 1
       462: 3q+1
       463: 3q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       472: 3q+1
       475: q^2+q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 3q+1
       482: 3q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q^2+3q+1
       490: 3q+1
       491: 3q+1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q^2+3q+1
       499: 3q+1
       500: 3q+1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: 3q+1
       506: 3q+1
       507: 3q+1
       508: 3q+1
       509: q+1
       510: q+1
       511: q+1
       512: 3q+1
       513: 3q+1
       514: 3q+1
       515: 3q+1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: 3q+1
       525: 3q+1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q^2+3q+1
       533: q+1
       534: q+1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q^2+3q+1
       548: q^2+3q+1
       549: q^2+3q+1
       550: q+1
       551: 1
       552: 1
       553: 1
       554: q+1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: 3q+1
       560: q+1
       561: q+1
       562: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: 3q+1
       572: 3q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q^2+3q+1
       580: q+1
       581: q+1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q^2+3q+1
       587: q^2+3q+1
       588: q^2+3q+1
       589: q+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: 1
       599: 1
       600: 1
       601: q+1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: 3q+1
       607: q+1
       608: q+1
       609: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: 1
       616: 3q+1
       617: 3q+1
       618: 3q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: 3q+1
       624: 3q+1
       625: 3q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 3q+1
       643: 1
       644: 1
       645: 1
       646: 3q+1
       647: 3q+1
       648: 1
       653: q+1
       654: q+1
       655: q+1
       656: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: q+1
       665: 3q+1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: 3q+1
       675: 3q+1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: 3q+1
       685: 3q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: 1
       692: 3q+1
       693: 3q+1
       694: 3q+1
       695: q+1
       696: q+1
       697: q+1
       698: q+1
       699: 3q+1
       700: 3q+1
       701: 3q+1
       702: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: 3q+1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       721: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       728: q+1
       729: q+1
       730: q+1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q^2+3q+1
       738: q+1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: 1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: q+1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 3q+1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: q+1
       773: q+1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q^2+3q+1
       781: q+1
       782: q+1
       784: 1
       785: 1
       786: 1
       788: 1
       789: q+1
       790: q+1
       791: q+1
       792: 1
       793: 1
       794: 1
       795: 1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: q+1
       809: q+1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 3q+1
       816: 3q+1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: 3q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 3q+1
       851: 1
       852: 1
       853: 1
       858: q+1
       859: q+1
       860: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 3q+1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: 3q+1
       889: q+1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 3q+1
       896: 3q+1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: 3q+1
       904: 1
       905: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: q+1
       925: 1
       926: 1
       927: 1
       931: q+1
       932: q+1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       942: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       949: q+1
       950: q+1
       951: q+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: q+1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: q+1
       986: q+1
       989: 1
       992: 1
       993: 1
       995: q+1
       996: q+1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 3q+1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1070: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 3q+1
      1105: q+1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1136: q+1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: q+1
      1148: 1
      1149: 1
      1150: 1
      1154: q+1
      1155: q+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: q+1
      1163: 1
      1164: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: q+1
      1193: 1
      1197: q+1
      1200: 1
      1203: 1
      1204: 1
      1206: q+1
      1207: q+1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: q+1
      1215: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1278: q+1
      1283: 1
      1284: 1
      1285: 1
      1290: 1
      1291: 1
      1292: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1341: 1
      1346: q+1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1389: 1
      1393: q+1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1422: 1
      1427: 1
      1432: 1
      1436: 1
      1439: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1454: 1
      1455: 1
      1465: 1
      1470: 1
      1475: 1
      1476: 1
      1477: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1493: 1
      1505: 1
      1506: 1
      1507: 1
      1519: 1
      1524: 1
      1532: 1
      1537: 1
      1538: 1
      1539: 1
      1559: 1
      1563: 1
      1568: 1
      1573: 1
      1574: 1
      1575: 1
      1600: 1
      1603: 1
      1609: 1
      1610: 1
      1624: 1
      1629: 1
      1630: 1
      1631: 1
      1646: 1
      1671: 1
      1699: 1
      1730: 1
      1743: 1

1744:    0: q^4+q^3+2q^2+q+1
         1: q^4+q^3+2q^2+q+1
         2: q^4+q^3+2q^2+q+1
         3: q^3+q^2+q+1
         4: q^4+q^3+2q^2+q+1
         5: q^2+q+1
         6: q^4+q^3+2q^2+q+1
         7: q^4+q^3+2q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q+1
        12: q^3+q^2+q+1
        13: q^4+q^3+2q^2+q+1
        14: q^4+q^3+2q^2+q+1
        15: q^3+q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: q^3+q^2+q+1
        21: q^4+q^3+2q^2+q+1
        22: q^3+q^2+q+1
        23: q+1
        24: q^3+q^2+q+1
        25: q^3+q^2+q+1
        26: q^3+q^2+q+1
        27: q^3+q^2+q+1
        28: q+1
        29: q+1
        30: q^3+q^2+q+1
        31: q^3+q^2+q+1
        32: q+1
        33: q^4+q^3+2q^2+q+1
        34: q^4+q^3+2q^2+q+1
        35: q^3+q^2+q+1
        36: q^3+q^2+q+1
        37: q^3+q^2+q+1
        38: q+1
        39: q^3+q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q^3+q^2+q+1
        52: q^3+q^2+q+1
        53: q^3+q^2+q+1
        54: q+1
        55: q^3+q^2+q+1
        56: q+1
        57: q^3+q^2+q+1
        58: q^3+q^2+q+1
        59: q^3+q^2+q+1
        60: q+1
        61: q^3+q^2+q+1
        62: q+1
        63: q+1
        64: 1
        65: q^3+q^2+q+1
        66: q^3+q^2+q+1
        67: q^2+1
        68: q+1
        69: q+1
        70: q+1
        71: q^3+q^2+q+1
        72: q^4+q^3+2q^2+q+1
        73: q^3+q^2+q+1
        74: q+1
        75: q^3+q^2+q+1
        76: q^3+q^2+q+1
        77: q^3+q^2+q+1
        78: q^3+q^2+q+1
        79: q+1
        80: q+1
        81: q^3+q^2+q+1
        82: q^3+q^2+q+1
        83: q+1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q^3+q^2+q+1
       107: q^3+q^2+q+1
       108: q+1
       109: q^3+q^2+q+1
       110: q+1
       111: q+1
       112: q+1
       113: q^3+q^2+q+1
       114: q^3+q^2+q+1
       115: q^3+q^2+q+1
       116: q+1
       117: q^3+q^2+q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q^2+1
       125: q^3+q^2+q+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q^3+q^2+q+1
       136: q^3+q^2+q+1
       137: q^3+q^2+q+1
       138: q+1
       139: q^3+q^2+q+1
       140: q+1
       141: q^3+q^2+q+1
       142: q^3+q^2+q+1
       143: q^3+q^2+q+1
       144: q+1
       145: q^3+q^2+q+1
       146: q+1
       147: q+1
       148: 1
       149: q^3+q^2+q+1
       150: q^3+q^2+q+1
       151: q^2+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^3+q^2+q+1
       193: 1
       194: q^2+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q^3+q^2+q+1
       201: q^3+q^2+q+1
       202: q+1
       203: q^3+q^2+q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: q^2+1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q^3+q^2+q+1
       231: q^3+q^2+q+1
       232: q+1
       233: q^3+q^2+q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^3+q^2+q+1
       238: q^3+q^2+q+1
       239: q^3+q^2+q+1
       240: q+1
       241: q^3+q^2+q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^3+q^2+q+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: q^2+1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: q+1
       321: q+1
       322: q^3+q^2+q+1
       323: 1
       324: q^2+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q^3+q^2+q+1
       360: 1
       361: q^2+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q^3+q^2+q+1
       368: q^3+q^2+q+1
       369: q+1
       370: q^3+q^2+q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: q^2+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: q^2+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       520: 1
       521: 1
       522: q^2+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q^3+q^2+q+1
       530: 1
       531: q^2+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: 1
       567: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: q^2+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: 1
       718: q^2+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 1
       758: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: q+1
       851: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: q^2+1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1008: 1
      1009: 1
      1011: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1141: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: 1
      1188: 1
      1211: 1
      1217: q+1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1250: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1293: 1
      1301: 1
      1302: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1338: 1
      1339: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1355: 1
      1356: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: 1
      1427: 1
      1450: 1
      1456: 1
      1457: 1
      1458: 1
      1478: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1508: 1
      1516: 1
      1517: 1
      1524: 1
      1528: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1611: 1
      1632: 1
      1633: 1
      1634: 1
      1654: 1
      1695: 1
      1744: 1

1745:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: 2q^3+4q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: 2q^3+4q^2+3q+1
         8: 2q^3+4q^2+3q+1
         9: 2q^3+4q^2+3q+1
        10: q^3+3q^2+3q+1
        11: 2q^2+3q+1
        12: q^3+3q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: 2q^3+4q^2+3q+1
        15: 2q^3+4q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: q^3+3q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: 2q^3+4q^2+3q+1
        22: 2q^3+4q^2+3q+1
        23: 2q^2+3q+1
        24: q^3+3q^2+3q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^3+4q^2+3q+1
        34: 2q^3+4q^2+3q+1
        35: 2q^3+4q^2+3q+1
        36: 2q^3+4q^2+3q+1
        37: q^3+3q^2+3q+1
        38: 2q^2+3q+1
        39: q^3+3q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q^3+3q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^2+2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: q^3+3q^2+3q+1
        50: 2q^2+3q+1
        51: q^3+3q^2+3q+1
        52: 2q^3+4q^2+3q+1
        53: q^3+3q^2+3q+1
        54: 2q^2+3q+1
        55: q^3+3q^2+3q+1
        56: 2q^2+3q+1
        57: q^3+3q^2+3q+1
        58: q^3+3q^2+3q+1
        59: q^3+3q^2+3q+1
        60: q^2+3q+1
        61: 2q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: 2q^3+4q^2+3q+1
        72: 2q^3+4q^2+3q+1
        73: 2q^3+4q^2+3q+1
        74: 2q^2+3q+1
        75: q^3+3q^2+3q+1
        76: q^3+3q^2+3q+1
        77: q^3+3q^2+3q+1
        78: q^3+3q^2+3q+1
        79: 2q^2+3q+1
        80: q^2+3q+1
        81: q^3+3q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^3+3q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^3+3q^2+3q+1
        87: 2q^2+3q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^3+3q^2+3q+1
       100: q^3+3q^2+3q+1
       101: q^2+2q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       104: 2q^2+3q+1
       105: 2q^2+3q+1
       106: q^3+3q^2+3q+1
       107: q^3+3q^2+3q+1
       108: q^2+3q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       111: 2q^2+3q+1
       112: q^2+3q+1
       113: 2q^2+3q+1
       114: q^3+3q^2+3q+1
       115: q^3+3q^2+3q+1
       116: q^2+3q+1
       117: 2q^2+3q+1
       118: q^2+3q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: q+1
       124: 2q^2+3q+1
       125: 2q^2+3q+1
       126: 2q^2+3q+1
       127: 2q+1
       128: 2q^2+3q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: 2q^2+3q+1
       135: q^3+3q^2+3q+1
       136: 2q^3+4q^2+3q+1
       137: q^3+3q^2+3q+1
       138: 2q^2+3q+1
       139: q^3+3q^2+3q+1
       140: 2q^2+3q+1
       141: q^3+3q^2+3q+1
       142: q^3+3q^2+3q+1
       143: q^3+3q^2+3q+1
       144: q^2+3q+1
       145: 2q^2+3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 2q^2+3q+1
       152: 2q^2+3q+1
       153: q^2+3q+1
       154: 2q^2+3q+1
       155: 2q^2+3q+1
       156: q^2+2q+1
       157: q^3+3q^2+3q+1
       158: q^2+2q+1
       159: 2q^2+3q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: 2q+1
       166: q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^3+3q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^3+3q^2+3q+1
       179: 2q^2+3q+1
       180: q^2+2q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: 2q^2+3q+1
       190: 2q^2+3q+1
       191: q^2+3q+1
       192: 2q^2+3q+1
       193: q^2+3q+1
       194: 2q^2+3q+1
       195: q^2+3q+1
       196: 2q^2+3q+1
       197: 2q+1
       198: q^2+3q+1
       199: q^2+3q+1
       200: 2q^2+3q+1
       201: q^3+3q^2+3q+1
       202: q^2+3q+1
       203: 2q^2+3q+1
       204: q^2+3q+1
       205: q^2+3q+1
       206: q^2+3q+1
       207: q+1
       208: q^2+3q+1
       209: q+1
       210: q^2+3q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: 2q^2+3q+1
       215: 2q^2+3q+1
       216: q^2+2q+1
       217: 2q+1
       218: 2q^2+3q+1
       219: 2q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: 2q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: 2q^2+3q+1
       230: q^3+3q^2+3q+1
       231: q^3+3q^2+3q+1
       232: q^2+3q+1
       233: 2q^2+3q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+3q+1
       237: 2q^2+3q+1
       238: q^3+3q^2+3q+1
       239: q^3+3q^2+3q+1
       240: q^2+3q+1
       241: 2q^2+3q+1
       242: q^2+3q+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: q^2+3q+1
       247: q+1
       248: 2q^2+3q+1
       249: 2q^2+3q+1
       250: 2q^2+3q+1
       251: 2q+1
       252: 2q^2+3q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 2q^2+3q+1
       257: 2q+1
       258: q^2+2q+1
       259: 2q^2+3q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: 2q+1
       263: q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: 2q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: 2q^2+3q+1
       289: q^2+2q+1
       290: q^3+3q^2+3q+1
       291: q^2+2q+1
       292: 2q^2+3q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: 2q+1
       299: q+1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: 2q+1
       310: 2q^2+3q+1
       311: q^2+3q+1
       312: q^2+3q+1
       313: q+1
       314: 2q+1
       315: 2q^2+3q+1
       316: q^2+3q+1
       317: 2q+1
       318: 2q+1
       319: q^2+3q+1
       320: q^2+3q+1
       321: q^2+3q+1
       322: 2q^2+3q+1
       323: q^2+3q+1
       324: 2q^2+3q+1
       325: q^2+3q+1
       326: q^2+3q+1
       327: 2q+1
       328: q+1
       329: q^2+3q+1
       330: q+1
       331: q+1
       332: q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: 2q^2+3q+1
       339: q^2+2q+1
       340: q+1
       341: q^2+2q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       348: 2q+1
       349: q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: q+1
       355: 1
       356: 2q^2+3q+1
       357: 2q^2+3q+1
       358: q^2+3q+1
       359: 2q^2+3q+1
       360: q^2+3q+1
       361: 2q^2+3q+1
       362: q^2+3q+1
       363: 2q^2+3q+1
       364: 2q+1
       365: q^2+3q+1
       366: q^2+3q+1
       367: 2q^2+3q+1
       368: q^3+3q^2+3q+1
       369: q^2+3q+1
       370: 2q^2+3q+1
       371: q^2+3q+1
       372: q^2+3q+1
       373: q^2+3q+1
       374: q+1
       375: q^2+3q+1
       376: q+1
       377: q^2+3q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: 2q^2+3q+1
       382: 2q^2+3q+1
       383: q^2+2q+1
       384: 2q+1
       385: 2q^2+3q+1
       386: 2q+1
       387: q^2+3q+1
       388: q^2+3q+1
       389: q^2+3q+1
       390: 2q+1
       391: q+1
       392: 2q+1
       393: 2q+1
       394: 2q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: q+1
       401: q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: 2q+1
       406: q+1
       407: q^2+2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: q+1
       412: 2q+1
       413: 1
       414: 2q+1
       415: q+1
       416: 2q+1
       417: 1
       418: 1
       420: q+1
       421: q+1
       424: q+1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q^2+2q+1
       435: 2q^2+3q+1
       436: q^2+2q+1
       437: q^2+2q+1
       438: 2q+1
       439: q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: 2q+1
       447: q+1
       448: q+1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: 2q+1
       465: 2q+1
       466: q^2+3q+1
       467: q+1
       468: 2q+1
       469: 2q+1
       470: q+1
       471: 2q+1
       472: 2q+1
       473: 2q+1
       474: q^2+3q+1
       475: q^2+3q+1
       476: q^2+3q+1
       477: q+1
       478: 2q+1
       479: 2q^2+3q+1
       480: q^2+3q+1
       481: q+1
       482: 2q+1
       483: q+1
       484: q+1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: q^2+2q+1
       496: q+1
       497: q^2+2q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: 2q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       511: 2q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       516: 2q+1
       517: 2q^2+3q+1
       518: q^2+3q+1
       519: q^2+3q+1
       520: q+1
       521: 2q+1
       522: 2q^2+3q+1
       523: q^2+3q+1
       524: 2q+1
       525: 2q+1
       526: q^2+3q+1
       527: q^2+3q+1
       528: q^2+3q+1
       529: 2q^2+3q+1
       530: q^2+3q+1
       531: 2q^2+3q+1
       532: q^2+3q+1
       533: q^2+3q+1
       534: 2q+1
       535: q+1
       536: q^2+3q+1
       537: q+1
       538: q+1
       539: q+1
       540: 1
       541: q+1
       542: q+1
       543: 2q+1
       544: 2q+1
       545: 2q^2+3q+1
       546: q^2+2q+1
       547: q+1
       548: q^2+2q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: q+1
       553: q^2+3q+1
       554: q+1
       555: 2q+1
       556: q+1
       557: q+1
       558: 2q+1
       559: 2q+1
       560: 2q+1
       561: q+1
       562: 1
       563: q+1
       564: q^2+2q+1
       565: q+1
       566: 2q+1
       567: 1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: 2q+1
       576: q+1
       577: 2q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: 2q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       592: q+1
       599: 1
       600: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: q^2+2q+1
       611: q^2+2q+1
       612: 2q+1
       613: q+1
       614: 2q+1
       615: q+1
       616: q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: 2q+1
       621: q+1
       622: q^2+2q+1
       623: 2q+1
       624: q+1
       625: q+1
       626: q+1
       627: 2q+1
       628: 1
       629: 2q+1
       630: q+1
       631: 2q+1
       632: 1
       633: 1
       635: q+1
       636: q+1
       639: q+1
       641: q+1
       642: q+1
       643: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: 2q+1
       650: 2q+1
       651: q+1
       652: 2q+1
       653: q+1
       654: q+1
       655: 1
       656: 2q+1
       657: 2q+1
       658: q+1
       659: q^2+3q+1
       660: q+1
       661: 2q+1
       662: 2q+1
       663: q+1
       664: q+1
       665: q+1
       666: 1
       667: q+1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       681: q+1
       682: q^2+2q+1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 2q+1
       704: 2q+1
       705: q^2+3q+1
       706: q+1
       707: 2q+1
       708: 2q+1
       709: q+1
       710: 2q+1
       711: 2q+1
       712: 2q+1
       713: q^2+3q+1
       714: q^2+3q+1
       715: q^2+3q+1
       716: q+1
       717: 2q+1
       718: 2q^2+3q+1
       719: q^2+3q+1
       720: q+1
       721: 2q+1
       722: q+1
       723: q+1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: q+1
       730: 1
       731: 2q+1
       732: 2q+1
       733: q+1
       734: q^2+2q+1
       735: q+1
       736: q^2+2q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: q+1
       741: 2q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       750: 2q+1
       751: q+1
       752: q+1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: q+1
       758: 1
       761: 1
       762: q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: 2q+1
       768: 1
       770: q+1
       771: q+1
       773: q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: q+1
       805: 1
       807: q+1
       808: q^2+2q+1
       809: q+1
       810: 2q+1
       811: 1
       813: q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: 2q+1
       820: q+1
       821: 2q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: 2q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 1
       836: q+1
       843: 1
       844: q+1
       847: 1
       849: q+1
       850: q+1
       851: q+1
       853: 1
       854: 2q+1
       855: 1
       856: q+1
       857: q+1
       858: 1
       859: q+1
       860: 1
       861: q+1
       862: q+1
       863: q+1
       864: 2q+1
       865: q+1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: q+1
       882: q+1
       883: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 2q+1
       907: 2q+1
       908: q+1
       909: 2q+1
       910: q+1
       911: q+1
       912: 1
       913: 2q+1
       914: 2q+1
       915: q+1
       916: q^2+3q+1
       917: q+1
       918: 2q+1
       919: 2q+1
       920: q+1
       921: q+1
       922: q+1
       923: 1
       924: q+1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: q+1
       934: 2q+1
       935: q+1
       936: q+1
       938: q+1
       939: q^2+2q+1
       940: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: 1
       966: 1
       967: q+1
       968: q+1
       970: q+1
       971: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1017: 1
      1020: 1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: 2q+1
      1027: 1
      1029: q+1
      1030: q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: q+1
      1064: 1
      1066: 1
      1067: q+1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: q+1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 2q+1
      1114: 1
      1115: q+1
      1116: q+1
      1117: 1
      1118: q+1
      1119: 1
      1120: q+1
      1121: q+1
      1122: q+1
      1123: 2q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: q+1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: q+1
      1141: q+1
      1142: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1182: 1
      1183: 1
      1186: 1
      1217: q+1
      1218: q+1
      1219: 1
      1223: 1
      1224: q+1
      1225: q+1
      1227: q+1
      1228: 1
      1231: 1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: 1
      1243: 1
      1265: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1303: 1
      1310: 1
      1311: q+1
      1312: 1
      1313: 1
      1314: 1
      1315: q+1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1333: q+1
      1335: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1356: 1
      1357: 1
      1371: 1
      1404: q+1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1421: 1
      1422: 1
      1425: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1467: 1
      1471: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1503: 1
      1506: 1
      1508: 1
      1509: 1
      1515: 1
      1516: 1
      1518: 1
      1564: 1
      1578: 1
      1612: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1643: 1
      1647: 1
      1745: 1

1746:    0: q^4+4q^3+5q^2+3q+1
         1: 2q^3+5q^2+3q+1
         2: q^4+4q^3+5q^2+3q+1
         3: q^4+4q^3+5q^2+3q+1
         4: q^4+4q^3+5q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: 2q^3+5q^2+3q+1
         7: 2q^3+5q^2+3q+1
         8: q^4+4q^3+5q^2+3q+1
         9: 2q^3+5q^2+3q+1
        10: q^4+4q^3+5q^2+3q+1
        11: q^3+2q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: 2q^3+5q^2+3q+1
        14: q^4+4q^3+5q^2+3q+1
        15: q^4+4q^3+5q^2+3q+1
        16: q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: 2q^3+4q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+5q^2+3q+1
        21: 2q^3+5q^2+3q+1
        22: 2q^3+5q^2+3q+1
        23: q^3+2q^2+3q+1
        24: 2q^3+4q^2+3q+1
        25: 2q^3+5q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^4+4q^3+5q^2+3q+1
        28: 2q^2+3q+1
        29: q^3+2q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^3+4q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^3+5q^2+3q+1
        34: 2q^3+5q^2+3q+1
        35: q^4+4q^3+5q^2+3q+1
        36: 2q^3+5q^2+3q+1
        37: q^4+4q^3+5q^2+3q+1
        38: q^3+2q^2+3q+1
        39: 2q^3+4q^2+3q+1
        40: q^3+4q^2+3q+1
        41: q^3+4q^2+3q+1
        42: 2q^3+4q^2+3q+1
        43: q^3+4q^2+3q+1
        44: 2q^3+4q^2+3q+1
        45: q^3+2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+4q^2+3q+1
        48: 2q^3+4q^2+3q+1
        49: 2q^3+4q^2+3q+1
        50: q^2+q+1
        51: 2q^2+2q+1
        52: 2q^3+5q^2+3q+1
        53: 2q^3+5q^2+3q+1
        54: 2q^2+3q+1
        55: q^3+4q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^3+5q^2+3q+1
        58: q^3+3q^2+3q+1
        59: q^3+3q^2+3q+1
        60: q^3+2q^2+3q+1
        61: 2q^3+4q^2+3q+1
        62: 2q^2+3q+1
        63: q^2+3q+1
        64: q^3+2q^2+3q+1
        65: q^3+4q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^3+4q^2+3q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: 2q^3+5q^2+3q+1
        72: 2q^3+5q^2+3q+1
        73: 2q^3+5q^2+3q+1
        74: q^3+2q^2+3q+1
        75: 2q^3+4q^2+3q+1
        76: 2q^3+5q^2+3q+1
        77: q^3+3q^2+3q+1
        78: q^4+4q^3+5q^2+3q+1
        79: 2q^2+3q+1
        80: q^3+2q^2+3q+1
        81: q^3+4q^2+3q+1
        82: 2q^3+4q^2+3q+1
        83: 2q^2+3q+1
        84: q^3+4q^2+3q+1
        85: q^3+4q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+2q^2+3q+1
        88: 2q^2+3q+1
        89: q^3+4q^2+3q+1
        90: q^2+2q+1
        91: 2q^3+4q^2+3q+1
        92: 2q^2+3q+1
        93: q^3+2q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^3+4q^2+3q+1
       100: q^3+4q^2+3q+1
       101: 2q^3+4q^2+3q+1
       102: q^3+2q^2+3q+1
       103: 2q^2+3q+1
       104: q+1
       105: q^2+q+1
       106: 2q^2+2q+1
       107: 2q^3+5q^2+3q+1
       108: 2q^2+3q+1
       109: q^3+4q^2+3q+1
       110: 2q^2+3q+1
       111: 2q^2+3q+1
       112: q^2+q+1
       113: 2q^2+2q+1
       114: q^3+3q^2+3q+1
       115: q^3+3q^2+3q+1
       116: q^2+3q+1
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: 2q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: q^3+2q^2+3q+1
       123: 2q+1
       124: q^3+4q^2+3q+1
       125: 2q^2+3q+1
       126: 2q^2+3q+1
       127: q^2+q+1
       128: 2q^3+4q^2+3q+1
       129: 2q^2+3q+1
       130: q^2+3q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^2+3q+1
       134: q^2+q+1
       135: 2q^2+2q+1
       136: 2q^3+5q^2+3q+1
       137: 2q^3+5q^2+3q+1
       138: 2q^2+3q+1
       139: q^3+4q^2+3q+1
       140: 2q^2+3q+1
       141: 2q^3+5q^2+3q+1
       142: q^3+3q^2+3q+1
       143: q^3+3q^2+3q+1
       144: q^3+2q^2+3q+1
       145: 2q^3+4q^2+3q+1
       146: 2q^2+3q+1
       147: q^2+3q+1
       148: q^3+2q^2+3q+1
       149: q^3+4q^2+3q+1
       150: 2q^2+3q+1
       151: 2q^3+4q^2+3q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: 2q^2+3q+1
       155: q^2+q+1
       156: q^2+2q+1
       157: q^3+4q^2+3q+1
       158: q^3+4q^2+3q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: q^2+3q+1
       162: q^3+4q^2+3q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^3+2q^2+3q+1
       166: 2q^2+3q+1
       167: 2q^2+3q+1
       168: 2q+1
       169: q^3+2q^2+3q+1
       170: 2q^2+3q+1
       171: 2q+1
       172: 2q^2+3q+1
       173: q^2+3q+1
       174: q^2+3q+1
       175: q^2+3q+1
       176: q^3+4q^2+3q+1
       177: q^3+4q^2+3q+1
       178: q^3+4q^2+3q+1
       179: q^3+2q^2+3q+1
       180: 2q^2+3q+1
       181: q^3+4q^2+3q+1
       182: q^2+2q+1
       183: 2q^3+4q^2+3q+1
       184: 2q^2+3q+1
       185: q^3+2q^2+3q+1
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: q^2+3q+1
       189: q+1
       190: q+1
       191: q^2+q+1
       192: 2q^2+2q+1
       193: 2q^2+3q+1
       194: q^3+4q^2+3q+1
       195: 2q^2+3q+1
       196: 2q^2+3q+1
       197: 2q^2+3q+1
       198: q+1
       199: q+1
       200: q^2+2q+1
       201: q^3+3q^2+3q+1
       202: q^2+3q+1
       203: 2q^2+3q+1
       204: q^2+3q+1
       205: 2q^2+3q+1
       206: q^2+q+1
       207: q+1
       208: q^2+3q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q+1
       212: 2q+1
       213: q^2+1
       214: 2q^2+2q+1
       215: 2q^2+3q+1
       216: 2q^2+3q+1
       217: q+1
       218: 2q^2+3q+1
       219: q^2+q+1
       220: 2q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q^2+q+1
       224: 2q+1
       225: 2q^2+3q+1
       226: q+1
       227: 2q^2+3q+1
       228: q+1
       229: q^2+q+1
       230: 2q^2+2q+1
       231: 2q^3+5q^2+3q+1
       232: 2q^2+3q+1
       233: q^3+4q^2+3q+1
       234: 2q^2+3q+1
       235: 2q^2+3q+1
       236: q^2+q+1
       237: 2q^2+2q+1
       238: q^3+3q^2+3q+1
       239: q^3+3q^2+3q+1
       240: q^2+3q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: 2q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: q^3+2q^2+3q+1
       247: 2q+1
       248: q^3+4q^2+3q+1
       249: 2q^2+3q+1
       250: 2q^2+3q+1
       251: q^2+q+1
       252: 2q^3+4q^2+3q+1
       253: 2q^2+3q+1
       254: q^2+3q+1
       255: 2q^2+3q+1
       256: 2q^2+3q+1
       257: 2q^2+3q+1
       258: q+1
       259: q^2+q+1
       260: q^2+2q+1
       261: q^3+4q^2+3q+1
       262: 2q^2+3q+1
       263: 2q^2+3q+1
       264: q^2+3q+1
       265: q^2+3q+1
       266: q^2+q+1
       267: q^2+2q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: 2q+1
       271: 2q+1
       272: q^2+3q+1
       273: 2q^2+3q+1
       274: 2q+1
       275: 2q+1
       276: q^3+2q^2+3q+1
       277: 2q+1
       278: 2q^2+3q+1
       279: 2q+1
       280: 2q+1
       282: 2q^2+3q+1
       283: q^2+3q+1
       284: 2q+1
       285: q^2+3q+1
       286: q^2+3q+1
       287: q^2+3q+1
       288: q^2+q+1
       289: q^2+2q+1
       290: q^3+4q^2+3q+1
       291: q^3+4q^2+3q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: q^2+3q+1
       295: q^3+4q^2+3q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q^3+2q^2+3q+1
       299: 2q^2+3q+1
       300: 2q^2+3q+1
       301: 2q+1
       302: q^3+2q^2+3q+1
       303: 2q^2+3q+1
       304: 2q+1
       305: 2q^2+3q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: q+1
       310: q+1
       311: q+1
       312: q^2+q+1
       313: q+1
       314: q^2+1
       315: 2q^2+2q+1
       316: 2q^2+3q+1
       317: 2q^2+3q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q^2+2q+1
       323: q^2+3q+1
       324: 2q^2+3q+1
       325: q^2+3q+1
       326: q^2+3q+1
       327: 2q^2+3q+1
       328: 1
       329: q+1
       330: q+1
       331: q^2+3q+1
       332: q^2+3q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: 1
       338: q^2+2q+1
       339: 2q^2+3q+1
       340: q+1
       341: 2q^2+3q+1
       342: q+1
       343: q^2+q+1
       344: q^2+1
       345: q+1
       346: q^2+3q+1
       347: q^2+3q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2q^2+3q+1
       352: q+1
       353: q+1
       354: q^2+q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: 2q^2+2q+1
       360: 2q^2+3q+1
       361: q^3+4q^2+3q+1
       362: 2q^2+3q+1
       363: 2q^2+3q+1
       364: 2q^2+3q+1
       365: q+1
       366: q+1
       367: q^2+2q+1
       368: q^3+3q^2+3q+1
       369: q^2+3q+1
       370: 2q^2+3q+1
       371: q^2+3q+1
       372: 2q^2+3q+1
       373: q^2+q+1
       374: q+1
       375: q^2+3q+1
       376: q^2+3q+1
       377: q^2+3q+1
       378: 2q+1
       379: 2q+1
       380: q^2+1
       381: 2q^2+2q+1
       382: 2q^2+3q+1
       383: 2q^2+3q+1
       384: q+1
       385: 2q^2+3q+1
       386: q^2+q+1
       387: 2q^2+3q+1
       388: q^2+3q+1
       389: q^2+3q+1
       390: q^2+q+1
       391: 2q+1
       392: 2q^2+3q+1
       393: q+1
       394: 2q^2+3q+1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q^2+2q+1
       399: 2q^2+3q+1
       400: 2q^2+3q+1
       401: q^2+3q+1
       402: q^2+3q+1
       403: q^2+3q+1
       404: q+1
       405: q+1
       406: q+1
       407: q^2+2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q^2+3q+1
       412: q^2+q+1
       413: q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: 2q+1
       420: q^2+2q+1
       421: 2q+1
       422: 2q+1
       424: 2q+1
       426: q^2+3q+1
       427: 2q+1
       428: 2q+1
       430: 2q+1
       431: q^2+3q+1
       432: q+1
       433: q^2+3q+1
       434: q+1
       435: q^2+q+1
       436: q^2+2q+1
       437: q^3+4q^2+3q+1
       438: 2q^2+3q+1
       439: 2q^2+3q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: q^2+q+1
       443: q^2+2q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: 2q+1
       447: 2q+1
       448: q^2+3q+1
       449: 2q^2+3q+1
       450: 2q+1
       451: 2q+1
       452: q^3+2q^2+3q+1
       453: 2q+1
       454: 2q^2+3q+1
       455: 2q+1
       456: 2q+1
       458: 2q^2+3q+1
       459: q^2+3q+1
       460: 2q+1
       461: q^2+3q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: q^2+1
       470: q+1
       471: 2q^2+3q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: q^2+2q+1
       480: q^2+3q+1
       481: q^2+3q+1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: q+1
       487: q^2+3q+1
       488: 2q+1
       489: 2q+1
       490: 2q+1
       491: 2q+1
       492: 1
       493: 1
       494: 1
       495: q^2+2q+1
       496: q+1
       497: 2q^2+3q+1
       498: q+1
       499: q+1
       500: q^2+q+1
       501: 1
       502: 1
       503: q+1
       504: q^2+3q+1
       505: q+1
       506: 2q+1
       507: q+1
       508: q+1
       509: q^2+1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q^2+q+1
       520: q+1
       521: q^2+1
       522: 2q^2+2q+1
       523: 2q^2+3q+1
       524: 2q^2+3q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q^2+2q+1
       530: q^2+3q+1
       531: 2q^2+3q+1
       532: q^2+3q+1
       533: q^2+3q+1
       534: 2q^2+3q+1
       535: 1
       536: q+1
       537: q+1
       538: q^2+3q+1
       539: q^2+3q+1
       540: 2q+1
       541: 2q+1
       542: 2q+1
       543: 1
       544: 1
       545: q^2+2q+1
       546: 2q^2+3q+1
       547: q+1
       548: 2q^2+3q+1
       549: q+1
       550: q^2+q+1
       551: q^2+1
       552: q+1
       553: q^2+3q+1
       554: q^2+3q+1
       555: q+1
       556: 2q+1
       557: q+1
       558: 2q^2+3q+1
       559: q+1
       560: q+1
       561: q^2+q+1
       562: 2q+1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: q+1
       569: q^2+2q+1
       570: q^2+3q+1
       571: q^2+3q+1
       572: q+1
       573: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q^2+3q+1
       582: 1
       583: q+1
       584: 1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 2q+1
       592: q+1
       593: 2q+1
       595: 2q+1
       599: q+1
       600: 2q+1
       601: 2q+1
       603: q+1
       605: q^2+3q+1
       606: q+1
       607: q+1
       609: 2q+1
       610: q+1
       611: q+1
       612: q^2+q+1
       613: q^2+2q+1
       614: 2q^2+3q+1
       615: 2q^2+3q+1
       616: q^2+3q+1
       617: q^2+3q+1
       618: q^2+3q+1
       619: q+1
       620: q+1
       621: q+1
       622: q^2+2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: q^2+3q+1
       627: q^2+q+1
       628: q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: q+1
       633: 2q+1
       635: q^2+2q+1
       636: 2q+1
       637: 2q+1
       639: 2q+1
       641: q^2+3q+1
       642: 2q+1
       643: 2q+1
       645: 2q+1
       646: q^2+3q+1
       647: q+1
       648: q^2+3q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: q^2+1
       655: q+1
       656: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: q+1
       664: q^2+3q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q+1
       670: q+1
       672: q+1
       673: 2q+1
       674: 2q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q^2+2q+1
       683: q+1
       684: q+1
       685: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: q+1
       691: 2q+1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: q+1
       705: q+1
       706: 1
       707: 1
       708: q^2+1
       709: q+1
       710: 2q^2+3q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       716: q+1
       717: 1
       718: q^2+2q+1
       719: q^2+3q+1
       720: q^2+3q+1
       721: q+1
       722: 1
       723: 1
       724: q+1
       725: q+1
       726: q^2+3q+1
       727: 2q+1
       728: 2q+1
       729: 2q+1
       730: 2q+1
       731: 1
       732: 1
       733: 1
       734: q^2+2q+1
       735: q+1
       736: 2q^2+3q+1
       737: q+1
       738: q+1
       739: q^2+q+1
       740: 1
       741: 1
       742: q+1
       743: q^2+3q+1
       744: q+1
       745: 2q+1
       746: q+1
       747: q+1
       748: q^2+1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: 1
       754: q+1
       756: q+1
       757: q+1
       758: 1
       761: q+1
       762: q^2+3q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q+1
       768: 1
       770: q+1
       771: 2q+1
       772: 2q+1
       773: q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       779: q+1
       780: q+1
       781: q+1
       782: 2q+1
       786: q+1
       788: 2q+1
       794: 1
       795: 2q+1
       797: q+1
       801: q+1
       802: q+1
       803: q+1
       805: 1
       807: q+1
       808: q+1
       809: q+1
       810: q^2+q+1
       811: q+1
       813: q^2+2q+1
       814: q^2+3q+1
       815: q^2+3q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q^2+3q+1
       826: 1
       827: q+1
       828: 1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: q+1
       833: 2q+1
       836: q+1
       837: 2q+1
       839: 2q+1
       843: q+1
       844: 2q+1
       845: 2q+1
       847: q+1
       849: q^2+3q+1
       850: q+1
       851: q+1
       853: 2q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: q+1
       868: q+1
       870: 1
       871: 1
       872: 1
       875: q+1
       876: 2q+1
       877: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: q+1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: q+1
       894: q+1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: q+1
       907: q+1
       908: 1
       909: 1
       910: 1
       911: q^2+1
       912: q+1
       913: q+1
       915: q+1
       916: q+1
       917: 1
       918: 1
       919: 1
       920: q+1
       921: q^2+3q+1
       922: q+1
       923: 1
       924: 1
       925: 1
       926: q+1
       927: q+1
       929: q+1
       930: 2q+1
       931: 2q+1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q^2+2q+1
       940: q+1
       941: q+1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: q+1
       948: 2q+1
       949: q+1
       950: q+1
       951: q+1
       952: 1
       953: 1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: q+1
       961: q+1
       962: 1
       966: q+1
       967: q+1
       969: q+1
       970: q+1
       971: 1
       974: 1
       975: 2q+1
       976: q+1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: q+1
       985: q+1
       986: 1
       993: q+1
      1000: 1
      1002: q+1
      1008: 1
      1009: q+1
      1011: 1
      1015: q+1
      1016: q+1
      1017: 1
      1020: q+1
      1021: q^2+3q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 1
      1029: q+1
      1030: 2q+1
      1031: 2q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: 2q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: 2q+1
      1045: q+1
      1047: 2q+1
      1053: 1
      1054: 2q+1
      1056: q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1064: 1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1079: 1
      1080: 1
      1084: q+1
      1085: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1095: 1
      1096: 1
      1101: q+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1121: q+1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: q+1
      1127: q+1
      1129: 1
      1130: 1
      1131: 1
      1134: q+1
      1135: 2q+1
      1136: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: q+1
      1153: q+1
      1154: q+1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 1
      1171: 1
      1173: q+1
      1174: 1
      1178: 1
      1179: q+1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: q+1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1218: q+1
      1219: 1
      1223: q+1
      1224: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1231: 1
      1232: 2q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: q+1
      1242: q+1
      1243: 1
      1250: q+1
      1257: 1
      1259: q+1
      1265: 1
      1266: q+1
      1268: 1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: 1
      1285: 1
      1288: 1
      1291: 1
      1294: 1
      1300: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1323: 1
      1324: 1
      1328: q+1
      1329: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1339: 1
      1340: 1
      1345: q+1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1363: 1
      1368: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1405: 1
      1410: 1
      1412: q+1
      1413: 1
      1417: 1
      1418: q+1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: q+1
      1427: 1
      1443: 1
      1450: 1
      1452: 1
      1457: 1
      1459: 1
      1460: 1
      1479: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1492: 1
      1493: 1
      1495: 1
      1500: 1
      1503: 1
      1506: 1
      1509: 1
      1515: 1
      1517: 1
      1518: 1
      1523: 1
      1524: 1
      1534: 1
      1539: 1
      1570: 1
      1575: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1607: 1
      1613: 1
      1633: 1
      1635: 1
      1636: 1
      1655: 1
      1661: 1
      1701: 1
      1706: 1
      1746: 1

1747:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q^2+3q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+2q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: 2q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+3q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: q^2+3q+1
        79: 2q^2+3q+1
        80: q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+3q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^3+3q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: 2q^2+3q+1
        95: 2q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 2q^2+3q+1
       105: 2q^2+3q+1
       106: 2q^2+3q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: 2q^2+3q+1
       111: q^2+2q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q^2+3q+1
       118: q^2+3q+1
       119: q^2+2q+1
       120: q^2+3q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 2q+1
       125: q^2+3q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q+1
       132: q^2+2q+1
       133: q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: q^2+3q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: 2q^2+3q+1
       141: q^2+3q+1
       142: q^2+3q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: q^2+2q+1
       149: q^2+3q+1
       150: q^2+3q+1
       151: 2q+1
       152: 2q^2+3q+1
       153: q^2+3q+1
       154: q^2+2q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 2q^2+3q+1
       158: 2q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q^2+3q+1
       174: 2q+1
       175: q^2+2q+1
       176: 2q^2+3q+1
       177: q^3+3q^2+3q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: 2q^2+3q+1
       189: q^2+2q+1
       190: 2q^2+3q+1
       191: q^2+3q+1
       192: q^2+3q+1
       193: q^2+2q+1
       194: 2q+1
       195: q^2+3q+1
       196: q^2+2q+1
       197: q+1
       198: q^2+3q+1
       199: q^2+3q+1
       200: q^2+3q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: q+1
       206: q^2+2q+1
       207: q^2+2q+1
       208: q^2+2q+1
       209: q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+3q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: 2q^2+3q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: q^2+3q+1
       232: q^2+3q+1
       233: q^2+3q+1
       234: 2q^2+3q+1
       235: q^2+2q+1
       236: q^2+3q+1
       237: q^2+3q+1
       238: q^2+3q+1
       239: q^2+3q+1
       240: q^2+3q+1
       241: q^2+3q+1
       242: q^2+3q+1
       243: q^2+2q+1
       244: q^2+3q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: 2q+1
       249: q^2+3q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: 2q^2+3q+1
       259: 2q^2+3q+1
       260: 2q^2+3q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q^2+3q+1
       265: q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: 2q^2+3q+1
       289: 2q^2+3q+1
       290: 2q^2+3q+1
       291: 2q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: 2q^2+3q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q^2+3q+1
       307: 2q+1
       308: q^2+2q+1
       309: q+1
       310: q^2+2q+1
       311: q^2+3q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: 2q+1
       315: 2q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+3q+1
       321: q^2+3q+1
       322: q^2+3q+1
       323: q^2+2q+1
       324: 2q+1
       325: q^2+3q+1
       326: q+1
       327: 1
       328: q^2+2q+1
       329: q^2+2q+1
       330: q^2+2q+1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+2q+1
       357: 2q^2+3q+1
       358: q^2+3q+1
       359: q^2+3q+1
       360: q^2+2q+1
       361: 2q+1
       362: q^2+3q+1
       363: q^2+2q+1
       364: q+1
       365: q^2+3q+1
       366: q^2+3q+1
       367: q^2+3q+1
       368: q^2+3q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: q+1
       373: q^2+2q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q+1
       377: q^2+2q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: q+1
       388: q^2+3q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: q+1
       394: 1
       395: q^2+2q+1
       396: 2q^2+3q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 2q^2+3q+1
       435: 2q^2+3q+1
       436: 2q^2+3q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: q^2+2q+1
       468: 2q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       473: 1
       474: q+1
       475: q^2+3q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: 2q+1
       479: 2q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q^2+2q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: q+1
       491: 1
       492: q+1
       493: 2q+1
       494: q+1
       495: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: q^2+3q+1
       519: q^2+2q+1
       520: q^2+2q+1
       521: 2q+1
       522: 2q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q^2+3q+1
       528: q^2+3q+1
       529: q^2+3q+1
       530: q^2+2q+1
       531: 2q+1
       532: q^2+3q+1
       533: q+1
       534: 1
       535: q^2+2q+1
       536: q^2+2q+1
       537: q^2+2q+1
       538: q+1
       539: q+1
       540: q+1
       541: q^2+2q+1
       542: q+1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q^2+2q+1
       661: 2q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: q+1
       681: q+1
       682: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: q+1
       704: q+1
       705: q+1
       706: q^2+2q+1
       707: 2q+1
       708: q+1
       709: q+1
       710: 1
       711: q+1
       712: 1
       713: q+1
       714: q^2+3q+1
       715: q^2+2q+1
       716: q^2+2q+1
       717: 2q+1
       718: 2q+1
       719: q+1
       720: 1
       721: 1
       722: q+1
       723: q^2+2q+1
       724: q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: q+1
       730: 1
       731: q+1
       732: 2q+1
       733: q+1
       734: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       882: q+1
       886: 1
       887: 1
       888: q+1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       906: q+1
       907: 1
       908: q+1
       909: q+1
       910: q+1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: q+1
       917: q^2+2q+1
       918: 2q+1
       919: q+1
       920: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: q+1
       926: q+1
       927: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: q+1
       935: q+1
       938: q+1
       939: q+1
       941: 1
       942: 1
       943: q+1
       944: q+1
       945: 1
       946: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1094: 1
      1095: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1113: 1
      1114: 1
      1115: 1
      1116: q+1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: q+1
      1123: q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: q+1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1141: q+1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1161: 1
      1162: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1209: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: 1
      1240: 1
      1241: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1293: 1
      1305: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1338: 1
      1339: 1
      1342: 1
      1346: 1
      1349: 1
      1352: 1
      1353: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1385: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1421: 1
      1422: q+1
      1423: 1
      1424: 1
      1425: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1448: 1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1508: 1
      1520: 1
      1525: 1
      1536: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1592: 1
      1614: 1
      1634: 1
      1637: 1
      1638: 1
      1639: 1
      1641: 1
      1692: 1
      1703: 1
      1747: 1

1748:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q+1
        25: q^2+q+1
        26: q^2+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^2+1
        59: q^2+1
        60: q^2+q+1
        61: q+1
        62: q^2+q+1
        63: q^2+1
        64: q^2+q+1
        65: q+1
        66: 1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q+1
        76: q^2+q+1
        77: q^2+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q^2+q+1
       103: q+1
       104: q+1
       105: q^2+q+1
       106: q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^2+q+1
       113: q+1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: 1
       118: q+1
       119: q^2+q+1
       120: q^2+1
       121: q^2+1
       122: q^2+q+1
       123: 1
       124: q+1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: q+1
       130: 1
       131: q+1
       132: q+1
       133: q+1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q+1
       140: q+1
       141: q^2+q+1
       142: q^2+1
       143: q^2+1
       144: q^2+q+1
       145: q+1
       146: q^2+q+1
       147: q^2+1
       148: q^2+q+1
       149: q+1
       150: 1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q^2+q+1
       169: q^2+q+1
       170: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q^2+q+1
       180: q+1
       181: q^2+q+1
       183: q^2+q+1
       184: q^2+q+1
       185: q^2+q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q^2+q+1
       192: q+1
       193: q^2+q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q^2+1
       200: 1
       201: q^2+1
       202: q^2+1
       203: 1
       204: 1
       205: q+1
       206: q^2+q+1
       207: 1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: q+1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       227: q+1
       228: q+1
       229: q^2+q+1
       230: q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q+1
       234: q+1
       235: q+1
       236: q^2+q+1
       237: q+1
       238: q^2+1
       239: q^2+1
       240: q^2+1
       241: 1
       242: q+1
       243: q^2+q+1
       244: q^2+1
       245: q^2+1
       246: q^2+q+1
       247: 1
       248: q+1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q+1
       260: q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+q+1
       267: q+1
       272: q+1
       273: q^2+q+1
       276: q^2+q+1
       277: 1
       278: q+1
       281: q+1
       282: q+1
       283: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q^2+q+1
       289: q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q^2+q+1
       293: q+1
       294: q+1
       295: q^2+q+1
       298: q^2+q+1
       299: q+1
       300: q^2+q+1
       302: q^2+q+1
       303: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q^2+q+1
       313: 1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       319: q+1
       320: 1
       321: q^2+1
       322: 1
       323: q^2+1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: 1
       329: q^2+1
       330: 1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: q+1
       360: q^2+q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q^2+1
       367: 1
       368: q^2+1
       369: q^2+1
       370: 1
       371: 1
       372: q+1
       373: q^2+q+1
       374: 1
       375: q^2+1
       376: q^2+1
       377: q^2+1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: q+1
       388: 1
       389: 1
       390: q+1
       391: 1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q+1
       399: q^2+q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       411: q+1
       412: q^2+q+1
       413: 1
       418: 1
       419: q+1
       420: q+1
       425: q+1
       426: q+1
       429: q+1
       430: 1
       431: q+1
       433: q+1
       434: q+1
       435: q^2+q+1
       436: q+1
       437: q^2+q+1
       438: q^2+q+1
       439: q+1
       440: q+1
       441: q+1
       442: q^2+q+1
       443: q+1
       448: q+1
       449: q^2+q+1
       452: q^2+q+1
       453: 1
       454: q+1
       457: q+1
       458: q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: q+1
       466: q+1
       467: 1
       468: q+1
       469: q+1
       470: 1
       471: q+1
       473: q+1
       474: 1
       475: 1
       476: q^2+1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q^2+1
       486: 1
       487: q^2+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q^2+q+1
       520: 1
       521: q+1
       522: q+1
       523: q+1
       524: q+1
       526: q+1
       527: 1
       528: q^2+1
       529: 1
       530: q^2+1
       531: 1
       532: 1
       533: 1
       534: q+1
       535: 1
       536: q^2+1
       537: 1
       538: q^2+1
       539: q^2+1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: q+1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: q+1
       561: q+1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: 1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       573: q+1
       581: q+1
       582: 1
       589: 1
       590: q+1
       597: q+1
       598: q+1
       599: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: q^2+q+1
       613: q+1
       614: q^2+q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       626: q+1
       627: q^2+q+1
       628: 1
       633: 1
       634: q+1
       635: q+1
       640: q+1
       641: q+1
       644: q+1
       645: 1
       646: q+1
       648: q+1
       650: q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q^2+1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: q+1
       705: q+1
       706: 1
       707: q+1
       708: q+1
       709: 1
       710: q+1
       712: q+1
       713: 1
       714: 1
       715: q^2+1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: q^2+1
       725: 1
       726: q^2+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       754: 1
       756: q+1
       757: q+1
       758: 1
       759: q+1
       760: q+1
       761: 1
       762: q+1
       764: q+1
       774: 1
       782: 1
       783: q+1
       791: q+1
       792: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q^2+q+1
       811: 1
       812: q+1
       813: q+1
       814: q+1
       815: q+1
       817: q+1
       825: q+1
       826: 1
       833: 1
       834: q+1
       841: q+1
       842: q+1
       843: 1
       848: 1
       849: q+1
       852: q+1
       853: 1
       855: 1
       856: q+1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: q+1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: q^2+1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: q+1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       977: 1
       987: q+1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1015: q+1
      1016: q+1
      1017: 1
      1018: q+1
      1019: q+1
      1020: 1
      1021: q+1
      1023: q+1
      1033: 1
      1041: 1
      1042: q+1
      1050: q+1
      1051: 1
      1058: 1
      1059: q+1
      1060: 1
      1065: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1114: 1
      1115: q+1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1166: 1
      1167: q+1
      1168: 1
      1169: 1
      1198: 1
      1208: 1
      1216: 1
      1218: q+1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1234: 1
      1244: q+1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1312: 1
      1313: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1331: 1
      1333: 1
      1335: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1347: 1
      1359: 1
      1360: 1
      1394: 1
      1405: 1
      1406: q+1
      1407: 1
      1408: 1
      1437: 1
      1447: 1
      1455: 1
      1459: 1
      1463: 1
      1464: 1
      1473: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1503: 1
      1509: 1
      1511: 1
      1513: 1
      1526: 1
      1566: 1
      1567: 1
      1601: 1
      1615: 1
      1635: 1
      1639: 1
      1640: 1
      1649: 1
      1693: 1
      1748: 1

1749:    0: 2q^3+5q^2+3q+1
         1: 2q^3+5q^2+3q+1
         2: 2q^3+5q^2+3q+1
         3: 2q^3+5q^2+3q+1
         4: 2q^3+5q^2+3q+1
         5: 2q^3+5q^2+3q+1
         6: q^3+3q^2+3q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: 2q^3+5q^2+3q+1
        10: q^3+3q^2+3q+1
        11: 2q^3+5q^2+3q+1
        12: q^3+4q^2+3q+1
        13: 2q^3+5q^2+3q+1
        14: 2q^3+5q^2+3q+1
        15: 2q^3+5q^2+3q+1
        16: 2q^3+5q^2+3q+1
        17: 2q^3+5q^2+3q+1
        18: 2q^3+5q^2+3q+1
        19: 2q^3+5q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^3+5q^2+3q+1
        23: 2q^3+5q^2+3q+1
        24: q^3+4q^2+3q+1
        25: q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: 2q^3+5q^2+3q+1
        29: q^3+3q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+4q^2+3q+1
        33: q^3+3q^2+3q+1
        34: 2q^3+5q^2+3q+1
        35: 2q^3+5q^2+3q+1
        36: 2q^3+5q^2+3q+1
        37: q^3+3q^2+3q+1
        38: 2q^3+5q^2+3q+1
        39: q^3+4q^2+3q+1
        40: q^3+3q^2+3q+1
        41: 2q^3+5q^2+3q+1
        42: 2q^3+5q^2+3q+1
        43: 2q^3+5q^2+3q+1
        44: q^2+2q+1
        45: 2q^3+5q^2+3q+1
        46: q^3+3q^2+3q+1
        47: 2q^3+5q^2+3q+1
        48: 2q^3+5q^2+3q+1
        49: 2q^3+5q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^2+2q+1
        52: q^3+3q^2+3q+1
        53: q^2+3q+1
        54: 2q^3+5q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^3+3q^2+3q+1
        60: q^3+3q^2+3q+1
        61: 2q^2+3q+1
        62: q^2+3q+1
        63: q^3+3q^2+3q+1
        64: q^3+3q^2+3q+1
        65: q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^2+3q+1
        70: q^3+4q^2+3q+1
        71: q^3+3q^2+3q+1
        72: q^3+3q^2+3q+1
        73: 2q^3+5q^2+3q+1
        74: 2q^3+5q^2+3q+1
        75: q^3+4q^2+3q+1
        76: q^2+3q+1
        77: q^3+3q^2+3q+1
        78: q^3+3q^2+3q+1
        79: 2q^3+5q^2+3q+1
        80: q^3+3q^2+3q+1
        81: q^3+4q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^3+3q^2+3q+1
        85: q^3+3q^2+3q+1
        86: 2q^3+5q^2+3q+1
        87: 2q^3+5q^2+3q+1
        88: q^3+3q^2+3q+1
        89: 2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^3+5q^2+3q+1
        93: q^2+2q+1
        94: q^3+3q^2+3q+1
        95: 2q+1
        96: q^3+3q^2+3q+1
        97: q^3+3q^2+3q+1
        98: 2q^3+5q^2+3q+1
        99: 2q^3+5q^2+3q+1
       100: 2q^3+5q^2+3q+1
       101: q^2+2q+1
       102: 2q^3+5q^2+3q+1
       103: q^3+3q^2+3q+1
       104: q^2+2q+1
       105: q^3+3q^2+3q+1
       106: q^2+2q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^3+4q^2+3q+1
       111: q^3+4q^2+3q+1
       112: q^2+3q+1
       113: 2q+1
       114: q^2+3q+1
       115: q^2+3q+1
       116: q^3+3q^2+3q+1
       117: 2q^2+3q+1
       118: 2q^2+3q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^3+3q^2+3q+1
       122: q^3+3q^2+3q+1
       123: q^2+2q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: 2q^2+3q+1
       127: 2q^2+3q+1
       128: 2q^2+3q+1
       129: q^2+3q+1
       130: 2q^2+3q+1
       131: 2q^2+3q+1
       132: q^3+4q^2+3q+1
       133: q+1
       134: q^3+3q^2+3q+1
       135: q^2+2q+1
       136: q^3+3q^2+3q+1
       137: q^2+3q+1
       138: 2q^3+5q^2+3q+1
       139: q^3+4q^2+3q+1
       140: q^3+4q^2+3q+1
       141: q^2+3q+1
       142: q^2+3q+1
       143: q^3+3q^2+3q+1
       144: q^3+3q^2+3q+1
       145: 2q^2+3q+1
       146: q^2+3q+1
       147: q^3+3q^2+3q+1
       148: q^3+3q^2+3q+1
       149: q^2+3q+1
       150: 2q^2+3q+1
       151: 2q^2+3q+1
       152: q^3+4q^2+3q+1
       153: 2q^2+3q+1
       154: q^3+4q^2+3q+1
       155: q^3+3q^2+3q+1
       156: q^2+2q+1
       157: q^3+3q^2+3q+1
       158: 2q+1
       159: 2q^3+5q^2+3q+1
       160: q^3+3q^2+3q+1
       161: q^3+3q^2+3q+1
       162: 2q+1
       163: 2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q+1
       171: 2q+1
       172: 2q+1
       173: q^3+3q^2+3q+1
       174: 2q+1
       175: q^3+3q^2+3q+1
       176: q^3+3q^2+3q+1
       177: q^3+3q^2+3q+1
       178: 2q^3+5q^2+3q+1
       179: 2q^3+5q^2+3q+1
       180: q^3+3q^2+3q+1
       181: 2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: 2q^3+5q^2+3q+1
       185: q^2+2q+1
       186: q^3+3q^2+3q+1
       187: 2q+1
       188: q^3+3q^2+3q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: q^2+3q+1
       192: 2q+1
       193: q^2+3q+1
       194: q^2+3q+1
       195: q^2+3q+1
       196: q^3+4q^2+3q+1
       197: q+1
       198: 2q+1
       199: q^2+3q+1
       200: 2q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: 2q^2+3q+1
       205: 2q^2+3q+1
       206: q^2+3q+1
       207: q+1
       208: q^2+3q+1
       209: q+1
       210: q^3+3q^2+3q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q^2+3q+1
       214: 2q+1
       215: q^2+3q+1
       216: q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 2q^2+3q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^3+3q^2+3q+1
       230: q^2+2q+1
       231: q^2+3q+1
       232: q^2+3q+1
       233: q^2+3q+1
       234: q^3+4q^2+3q+1
       235: q^3+4q^2+3q+1
       236: q^2+3q+1
       237: 2q+1
       238: q^2+3q+1
       239: q^2+3q+1
       240: q^3+3q^2+3q+1
       241: 2q^2+3q+1
       242: 2q^2+3q+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^3+3q^2+3q+1
       246: q^3+3q^2+3q+1
       247: q^2+2q+1
       248: q^2+3q+1
       249: q^2+3q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+4q^2+3q+1
       257: q+1
       258: q^2+2q+1
       259: q^3+3q^2+3q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^3+3q^2+3q+1
       265: q^3+3q^2+3q+1
       266: 2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: q^2+2q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       279: 2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^3+3q^2+3q+1
       287: q+1
       288: q^3+3q^2+3q+1
       289: q^2+2q+1
       290: q^3+3q^2+3q+1
       291: 2q+1
       292: 2q^3+5q^2+3q+1
       293: q^3+3q^2+3q+1
       294: q^3+3q^2+3q+1
       295: 2q+1
       296: 2q+1
       297: q^2+2q+1
       298: q^2+2q+1
       299: 2q+1
       300: 2q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^3+3q^2+3q+1
       307: 2q+1
       308: q^3+3q^2+3q+1
       310: q^2+2q+1
       311: 2q+1
       312: q^2+3q+1
       313: q+1
       314: q^2+3q+1
       315: 2q+1
       316: q^2+3q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q^2+3q+1
       322: 2q+1
       323: q^2+3q+1
       324: q^2+3q+1
       325: q^2+3q+1
       326: 2q^2+3q+1
       327: q+1
       328: q+1
       329: q^2+3q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: q^2+3q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q^2+3q+1
       343: 2q^2+3q+1
       344: q^2+3q+1
       345: q+1
       346: q^2+3q+1
       347: 1
       348: 2q^2+3q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q^2+3q+1
       359: 2q+1
       360: q^2+3q+1
       361: q^2+3q+1
       362: q^2+3q+1
       363: q^3+4q^2+3q+1
       364: q+1
       365: 2q+1
       366: q^2+3q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: 2q^2+3q+1
       372: 2q^2+3q+1
       373: q^2+3q+1
       374: q+1
       375: q^2+3q+1
       376: q+1
       377: q^3+3q^2+3q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: q^2+3q+1
       381: 2q+1
       382: q^2+3q+1
       383: q+1
       384: 2q^2+3q+1
       385: 2q^2+3q+1
       386: 2q^2+3q+1
       387: q^2+3q+1
       388: q^2+3q+1
       389: 2q^2+3q+1
       390: 2q^2+3q+1
       391: q^2+2q+1
       392: q+1
       393: q+1
       394: q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^3+3q^2+3q+1
       403: q+1
       404: q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: 2q+1
       420: q+1
       421: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       429: 2q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q^2+2q+1
       435: q^3+3q^2+3q+1
       436: q^2+2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^3+3q^2+3q+1
       441: q^3+3q^2+3q+1
       442: 2q+1
       443: q+1
       444: 2q+1
       445: 2q+1
       446: q^2+2q+1
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: q^2+2q+1
       452: q^2+2q+1
       453: q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^3+3q^2+3q+1
       463: q+1
       466: 2q+1
       467: q+1
       468: 2q+1
       469: q^2+3q+1
       470: q+1
       471: q+1
       472: q+1
       474: 2q+1
       475: 2q+1
       476: q^2+3q+1
       477: q+1
       478: q^2+3q+1
       479: 2q+1
       480: q^2+3q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: 1
       487: q+1
       488: q+1
       489: q+1
       490: q^2+2q+1
       491: 1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q^2+3q+1
       500: q+1
       501: q+1
       502: q^2+3q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q^2+2q+1
       508: q^2+2q+1
       509: q+1
       510: 1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       517: q^2+2q+1
       518: 2q+1
       519: q^2+3q+1
       520: q+1
       521: q^2+3q+1
       522: 2q+1
       523: q^2+3q+1
       524: q+1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: q^2+3q+1
       529: 2q+1
       530: q^2+3q+1
       531: q^2+3q+1
       532: q^2+3q+1
       533: 2q^2+3q+1
       534: q+1
       535: q+1
       536: q^2+3q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q^2+2q+1
       542: q^2+2q+1
       543: 2q+1
       544: q^2+3q+1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q^2+3q+1
       550: 2q^2+3q+1
       551: q^2+3q+1
       552: q+1
       553: q^2+3q+1
       554: 1
       555: 2q^2+3q+1
       556: q^2+2q+1
       557: q^2+2q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       564: q^2+2q+1
       565: q+1
       566: 2q+1
       567: 1
       568: 2q+1
       569: q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: 2q+1
       576: q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: 1
       583: 2q+1
       584: 1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: q+1
       591: 2q+1
       592: q+1
       596: 2q+1
       597: 2q+1
       598: 2q+1
       599: 1
       600: 2q+1
       602: 2q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q^2+2q+1
       611: q^2+2q+1
       612: 2q+1
       613: q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^3+3q^2+3q+1
       618: q+1
       619: q+1
       620: 2q+1
       621: q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: 2q+1
       628: 1
       629: 2q+1
       630: q+1
       631: q^2+2q+1
       632: q+1
       633: q+1
       634: 2q+1
       635: q+1
       636: 2q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       651: q+1
       652: 2q+1
       653: q+1
       654: q+1
       655: 1
       656: q+1
       659: 2q+1
       660: q+1
       661: 2q+1
       662: q^2+3q+1
       663: q+1
       664: 1
       665: 1
       667: q+1
       668: 1
       669: q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: 1
       675: 1
       677: 2q+1
       678: q+1
       679: q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+2q+1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 2q+1
       706: q+1
       707: 2q+1
       708: q^2+3q+1
       709: q+1
       710: q+1
       711: q+1
       713: 2q+1
       714: 2q+1
       715: q^2+3q+1
       716: q+1
       717: q^2+3q+1
       718: 2q+1
       719: q^2+3q+1
       720: 1
       721: q+1
       722: q+1
       723: q+1
       724: q+1
       725: 1
       726: q+1
       727: q+1
       728: q+1
       729: q^2+2q+1
       730: 1
       731: 2q+1
       732: 2q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q^2+3q+1
       739: q+1
       740: q+1
       741: q^2+3q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q^2+2q+1
       747: q^2+2q+1
       748: q+1
       749: 1
       750: q+1
       751: 1
       752: q+1
       753: 1
       754: 1
       757: q+1
       758: 1
       759: q+1
       760: 2q+1
       761: 1
       762: q+1
       763: q+1
       765: q+1
       766: q+1
       767: 2q+1
       768: 1
       769: 2q+1
       770: q+1
       771: 2q+1
       773: q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: q+1
       784: q+1
       790: 2q+1
       791: q+1
       792: 1
       793: 2q+1
       794: 1
       798: q+1
       799: q+1
       800: q+1
       801: 1
       802: q+1
       804: q+1
       805: 1
       806: 1
       808: q^2+2q+1
       809: q+1
       810: 2q+1
       811: 1
       812: 2q+1
       813: q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: 2q+1
       820: q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: 1
       827: 2q+1
       828: 1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       834: q+1
       835: 2q+1
       836: q+1
       840: 2q+1
       841: 2q+1
       842: 2q+1
       843: 1
       844: 2q+1
       846: 2q+1
       847: q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       857: q+1
       858: 1
       859: q+1
       860: 1
       863: q+1
       864: 2q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       880: q+1
       882: q+1
       883: q+1
       885: 1
       886: 1
       888: q+1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: q+1
       909: 2q+1
       910: q+1
       911: q+1
       912: 1
       913: q+1
       916: 2q+1
       917: q+1
       918: 2q+1
       919: q^2+3q+1
       920: q+1
       921: 1
       922: 1
       924: q+1
       925: 1
       926: q+1
       927: 1
       928: q+1
       929: 1
       930: q+1
       931: 1
       932: 1
       934: 2q+1
       935: q+1
       936: q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q^2+2q+1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       967: q+1
       970: q+1
       971: 1
       972: q+1
       973: 2q+1
       974: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       986: 1
       988: q+1
       996: q+1
       997: 1
       998: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1012: 1
      1013: 1
      1016: q+1
      1017: 1
      1018: q+1
      1019: 2q+1
      1020: 1
      1021: q+1
      1022: q+1
      1024: q+1
      1025: q+1
      1026: 2q+1
      1027: 1
      1028: 2q+1
      1029: q+1
      1030: 2q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: 1
      1042: q+1
      1043: q+1
      1049: 2q+1
      1050: q+1
      1051: 1
      1052: 2q+1
      1053: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: 1
      1061: q+1
      1063: q+1
      1064: 1
      1065: 1
      1069: 1
      1070: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1089: q+1
      1091: 1
      1093: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1116: q+1
      1117: 1
      1118: q+1
      1119: 1
      1122: q+1
      1123: 2q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1130: 1
      1131: 1
      1132: 1
      1133: q+1
      1134: 1
      1135: 1
      1136: 1
      1139: q+1
      1141: q+1
      1142: q+1
      1144: 1
      1145: 1
      1147: q+1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1168: 1
      1169: 1
      1170: q+1
      1171: 1
      1174: 1
      1175: q+1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1224: q+1
      1227: q+1
      1228: 1
      1229: q+1
      1230: 2q+1
      1231: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1239: q+1
      1240: 1
      1241: q+1
      1243: 1
      1245: q+1
      1253: q+1
      1254: 1
      1255: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1269: 1
      1270: 1
      1273: 1
      1277: 1
      1278: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1291: 1
      1296: 1
      1298: 1
      1300: 1
      1303: 1
      1305: 1
      1306: 1
      1313: 1
      1314: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1333: q+1
      1335: 1
      1337: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: 1
      1348: 1
      1349: 1
      1350: 1
      1352: 1
      1353: 1
      1354: 1
      1356: 1
      1360: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1395: 1
      1403: 1
      1407: 1
      1408: 1
      1409: q+1
      1410: 1
      1413: 1
      1414: q+1
      1415: 1
      1421: 1
      1422: 1
      1423: 1
      1424: q+1
      1425: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1460: 1
      1464: 1
      1465: 1
      1476: 1
      1481: 1
      1488: 1
      1492: 1
      1493: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1506: 1
      1511: 1
      1513: 1
      1515: 1
      1518: 1
      1520: 1
      1521: 1
      1527: 1
      1536: 1
      1567: 1
      1568: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1602: 1
      1610: 1
      1616: 1
      1636: 1
      1640: 1
      1641: 1
      1652: 1
      1657: 1
      1694: 1
      1703: 1
      1749: 1

1750:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: 1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: q+1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: 1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       279: 1
       283: 1
       284: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: 1
       364: 1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       427: 1
       431: 1
       432: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       455: 1
       459: 1
       460: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: q+1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       571: 1
       572: 1
       574: 1
       575: 1
       576: 1
       577: 1
       579: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       606: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       661: q+1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       758: 1
       763: 1
       766: 1
       767: 1
       768: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       821: 1
       823: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       850: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       960: 1
       971: 1
       979: 1
       980: 1
       981: 1
      1014: 1
      1015: 1
      1017: 1
      1022: 1
      1025: 1
      1026: 1
      1027: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1183: 1
      1217: 1
      1228: 1
      1236: 1
      1237: 1
      1238: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1304: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1349: 1
      1350: 1
      1351: 1
      1422: 1
      1458: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1519: 1
      1617: 1
      1634: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1750: 1

1751:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: 1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: q^2+1
        32: 1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: 1
        55: q^2+1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q^2+1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: q^2+1
       107: q^2+1
       108: 1
       109: q^2+1
       110: 1
       111: 1
       112: 1
       113: q^2+1
       114: q^2+1
       115: q^2+1
       116: 1
       117: q^2+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q^2+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q^2+1
       136: q^2+1
       137: q^2+1
       138: 1
       139: q^2+1
       140: 1
       141: q^2+1
       142: q^2+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: q^2+1
       193: 1
       194: q^2+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q^2+1
       201: q^2+1
       202: 1
       203: q^2+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: q^2+1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: q^2+1
       231: q^2+1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       236: 1
       237: q^2+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q^2+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: q^2+1
       323: 1
       324: q^2+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q^2+1
       360: 1
       361: q^2+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: q^2+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       420: 1
       426: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: q^2+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: q^2+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       599: 1
       605: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       635: 1
       641: 1
       645: 1
       646: 1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: q^2+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: q^2+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       801: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       843: 1
       849: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: q^2+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       966: 1
       977: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1060: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1166: 1
      1218: 1
      1219: 1
      1223: 1
      1234: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1299: 1
      1312: 1
      1313: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1347: 1
      1405: 1
      1459: 1
      1468: 1
      1469: 1
      1472: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1514: 1
      1618: 1
      1635: 1
      1644: 1
      1645: 1
      1648: 1
      1751: 1

1752:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q+1
        24: q^2+q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q^2+q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q^2+q+1
       127: q+1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: 1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: 1
       313: q+1
       314: 1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: 1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: q+1
       471: 1
       472: 1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: 1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: q+1
       521: 1
       522: q+1
       523: q+1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: 1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: q+1
       664: 1
       665: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: q+1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       716: q+1
       717: 1
       718: q+1
       719: q+1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: 1
       886: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       921: 1
       922: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q+1
       940: q+1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       962: 1
       966: 1
       967: 1
       970: 1
       971: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1084: 1
      1085: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1144: 1
      1145: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1171: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1219: 1
      1223: 1
      1224: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1243: 1
      1265: 1
      1273: 1
      1277: 1
      1278: 1
      1285: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1295: 1
      1299: 1
      1300: 1
      1303: 1
      1304: 1
      1307: 1
      1313: 1
      1314: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1324: 1
      1328: 1
      1329: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1356: 1
      1371: 1
      1410: 1
      1413: 1
      1421: 1
      1422: 1
      1425: 1
      1460: 1
      1469: 1
      1470: 1
      1477: 1
      1480: 1
      1488: 1
      1492: 1
      1493: 1
      1500: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1510: 1
      1514: 1
      1515: 1
      1518: 1
      1519: 1
      1522: 1
      1578: 1
      1619: 1
      1636: 1
      1645: 1
      1646: 1
      1653: 1
      1656: 1
      1752: 1

1753:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: 2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: 2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 2q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: q+1
        24: 2q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: 2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: q^3+2q^2+2q+1
        37: 2q^2+2q+1
        38: q^2+2q+1
        39: q^3+2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: 2q^2+2q+1
        52: 2q^2+2q+1
        53: q^2+2q+1
        54: q+1
        55: 2q^2+2q+1
        56: q+1
        57: 2q^2+2q+1
        58: 2q^2+2q+1
        59: 2q^2+2q+1
        60: q+1
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: 2q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: 2q^2+2q+1
        74: q+1
        75: 2q^2+2q+1
        76: 2q^2+2q+1
        77: 2q^2+2q+1
        78: 2q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^3+2q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: 2q^2+2q+1
       107: q^2+2q+1
       108: q+1
       109: q^2+2q+1
       110: q+1
       111: q+1
       112: q+1
       113: 2q^2+2q+1
       114: 2q^2+2q+1
       115: q^2+2q+1
       116: q+1
       117: 2q^2+2q+1
       118: q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q+1
       123: q^2+2q+1
       124: 2q^2+2q+1
       125: 2q^2+2q+1
       126: 2q^2+2q+1
       127: q+1
       128: 2q^2+2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: 2q^2+2q+1
       136: 2q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: 2q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: 2q^2+2q+1
       143: 2q^2+2q+1
       144: q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: q^2+2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^2+2q+1
       193: q+1
       194: q^2+2q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: 2q^2+2q+1
       201: q^2+2q+1
       202: q+1
       203: q^2+2q+1
       204: q+1
       205: q+1
       206: q+1
       207: q^2+2q+1
       208: q^2+2q+1
       209: q+1
       210: q+1
       211: q^2+2q+1
       212: q+1
       213: q+1
       214: 2q^2+2q+1
       215: 2q^2+2q+1
       216: q^2+2q+1
       217: q+1
       218: 2q^2+2q+1
       219: q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: 2q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: q^2+2q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q^2+2q+1
       238: 2q^2+2q+1
       239: q^2+2q+1
       240: q+1
       241: 2q^2+2q+1
       242: q+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q+1
       247: q^2+2q+1
       248: 2q^2+2q+1
       249: 2q^2+2q+1
       250: 2q^2+2q+1
       251: q+1
       252: 2q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: q+1
       262: 1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       315: q^2+2q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q^2+2q+1
       323: q+1
       324: q^2+2q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q^2+2q+1
       331: q+1
       332: 1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: 2q^2+2q+1
       339: q^2+2q+1
       340: q+1
       341: q^2+2q+1
       342: q+1
       343: q+1
       344: q+1
       345: q^2+2q+1
       346: q^2+2q+1
       347: q+1
       348: q+1
       349: q^2+2q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+2q+1
       360: q+1
       361: q^2+2q+1
       362: q+1
       363: q+1
       364: 1
       365: q+1
       366: q+1
       367: 2q^2+2q+1
       368: q^2+2q+1
       369: q+1
       370: q^2+2q+1
       371: q+1
       372: q+1
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q+1
       377: q+1
       378: q^2+2q+1
       379: q+1
       380: q+1
       381: 2q^2+2q+1
       382: 2q^2+2q+1
       383: q^2+2q+1
       384: q+1
       385: 2q^2+2q+1
       386: q+1
       387: q^2+2q+1
       388: q^2+2q+1
       389: q^2+2q+1
       390: q+1
       391: q^2+2q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       412: 1
       413: q+1
       414: q+1
       415: q+1
       416: 1
       417: q+1
       418: 1
       420: q+1
       421: q+1
       424: q+1
       426: q+1
       427: q+1
       428: q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: 1
       465: 1
       466: q+1
       467: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       479: q^2+2q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q^2+2q+1
       496: q+1
       497: q^2+2q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q^2+2q+1
       504: q+1
       505: 1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       516: 1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q^2+2q+1
       523: q+1
       524: 1
       525: 1
       526: q+1
       527: q+1
       528: q+1
       529: q^2+2q+1
       530: q+1
       531: q^2+2q+1
       532: q+1
       533: q+1
       534: 1
       535: q+1
       536: q+1
       537: q^2+2q+1
       538: q+1
       539: 1
       540: q+1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: 2q^2+2q+1
       546: q^2+2q+1
       547: q+1
       548: q^2+2q+1
       549: q+1
       550: q+1
       551: q+1
       552: q^2+2q+1
       553: q^2+2q+1
       554: q+1
       555: q+1
       556: q^2+2q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: q+1
       585: q+1
       586: 1
       587: q+1
       588: 1
       589: 1
       592: q+1
       599: q+1
       600: q+1
       603: q+1
       605: q+1
       606: q+1
       607: q+1
       609: q+1
       610: q+1
       611: q+1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: q+1
       629: q+1
       630: q+1
       631: 1
       632: q+1
       633: 1
       635: q+1
       636: q+1
       639: q+1
       641: q+1
       642: q+1
       643: q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       651: q+1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       682: q^2+2q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       702: 1
       703: 1
       704: 1
       705: q+1
       706: q+1
       709: q+1
       710: 1
       711: 1
       712: 1
       713: q+1
       714: q+1
       715: q+1
       716: q+1
       718: q^2+2q+1
       719: q+1
       720: 1
       721: 1
       722: q+1
       723: q+1
       724: 1
       725: q+1
       726: 1
       727: q+1
       728: 1
       729: q+1
       730: 1
       731: q+1
       732: q+1
       733: q+1
       734: q^2+2q+1
       735: q+1
       736: q^2+2q+1
       737: q+1
       738: q+1
       739: 1
       740: q+1
       741: q+1
       742: q^2+2q+1
       743: q+1
       744: 1
       745: q+1
       746: q+1
       747: q+1
       748: 1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: q+1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: q+1
       778: 1
       779: q+1
       780: 1
       781: 1
       782: 1
       794: q+1
       801: q+1
       802: q+1
       805: q+1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: q+1
       829: q+1
       830: 1
       831: q+1
       832: 1
       833: 1
       836: q+1
       843: q+1
       844: q+1
       847: q+1
       849: q+1
       850: q+1
       851: q+1
       853: q+1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       881: q+1
       884: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       902: q+1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: q+1
       912: 1
       913: 1
       914: 1
       915: 1
       916: q+1
       917: q+1
       920: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: 1
       926: 1
       927: 1
       929: q+1
       930: 1
       931: 1
       932: 1
       933: 1
       934: q+1
       935: q+1
       936: q+1
       937: q+1
       939: q^2+2q+1
       940: q+1
       941: 1
       942: 1
       943: q+1
       944: q+1
       945: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: q+1
       984: 1
       986: 1
      1008: q+1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: q+1
      1037: 1
      1038: q+1
      1039: 1
      1040: 1
      1041: 1
      1053: q+1
      1060: q+1
      1061: q+1
      1064: q+1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: q+1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: q+1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: q+1
      1140: q+1
      1143: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1152: q+1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1161: q+1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1182: 1
      1183: 1
      1186: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: q+1
      1241: 1
      1243: 1
      1265: q+1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1307: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: q+1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: q+1
      1354: 1
      1356: 1
      1357: 1
      1371: 1
      1404: 1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1421: 1
      1422: 1
      1425: 1
      1461: 1
      1466: 1
      1471: 1
      1472: 1
      1477: 1
      1480: 1
      1489: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1502: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1518: 1
      1519: 1
      1522: 1
      1564: 1
      1578: 1
      1620: 1
      1637: 1
      1642: 1
      1647: 1
      1648: 1
      1653: 1
      1656: 1
      1753: 1

1754:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: 2q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q+1
        45: 2q^2+3q+1
        46: q^2+2q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+3q+1
        51: 2q+1
        52: q^2+3q+1
        53: q^2+2q+1
        54: q^2+3q+1
        55: 2q+1
        56: 2q+1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: 2q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: 2q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: q^2+3q+1
        79: 2q^2+3q+1
        80: q^2+3q+1
        81: 2q^2+3q+1
        82: q^2+3q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q^2+3q+1
        93: 2q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: q^2+2q+1
       104: 2q+1
       105: q^2+3q+1
       106: 2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q+1
       110: 2q+1
       111: 2q+1
       112: q^2+3q+1
       113: 2q+1
       114: q^2+3q+1
       115: q^2+2q+1
       116: q^2+3q+1
       117: 2q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: q^2+3q+1
       123: q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q^2+3q+1
       128: 2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: q^2+2q+1
       138: q^2+3q+1
       139: 2q+1
       140: 2q+1
       141: q^2+3q+1
       142: q^2+3q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: 2q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: q^2+3q+1
       149: q^2+3q+1
       150: q^2+3q+1
       151: q^2+3q+1
       152: 2q^2+3q+1
       153: q^2+3q+1
       154: 2q^2+3q+1
       155: q^2+3q+1
       156: q+1
       157: q^2+3q+1
       158: q+1
       159: q^2+3q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q^2+2q+1
       192: q+1
       193: q^2+2q+1
       194: q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: q^2+3q+1
       200: 2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q+1
       204: 2q+1
       205: 2q+1
       206: q^2+3q+1
       207: q+1
       208: q^2+3q+1
       209: q+1
       210: q^2+3q+1
       211: q+1
       212: q+1
       213: q^2+3q+1
       214: 2q+1
       215: q^2+3q+1
       216: q^2+2q+1
       217: q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q+1
       234: 2q+1
       235: 2q+1
       236: q^2+3q+1
       237: 2q+1
       238: q^2+3q+1
       239: q^2+2q+1
       240: q^2+3q+1
       241: 2q+1
       242: 2q+1
       243: q^2+3q+1
       244: q^2+3q+1
       245: q^2+3q+1
       246: q^2+3q+1
       247: q+1
       248: q^2+3q+1
       249: q^2+3q+1
       250: q^2+3q+1
       251: q^2+3q+1
       252: 2q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: q^2+3q+1
       256: 2q^2+3q+1
       257: 2q+1
       258: q+1
       259: q^2+3q+1
       260: q+1
       261: q+1
       262: q+1
       263: 1
       264: q+1
       265: q+1
       266: 2q+1
       267: 1
       268: 2q+1
       269: q+1
       270: 2q+1
       271: 1
       272: 1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: 2q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+3q+1
       289: q+1
       290: q^2+3q+1
       291: q+1
       292: q^2+3q+1
       293: q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q^2+2q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q^2+2q+1
       322: q+1
       323: q^2+2q+1
       324: q+1
       325: q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: q^2+3q+1
       330: q+1
       331: q+1
       332: q+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: q^2+3q+1
       338: 2q+1
       339: q^2+2q+1
       340: q^2+2q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: q^2+3q+1
       345: q+1
       346: q^2+3q+1
       347: q+1
       348: q^2+3q+1
       349: q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 2q+1
       355: 1
       356: 2q+1
       357: 2q+1
       358: q^2+2q+1
       359: q+1
       360: q^2+2q+1
       361: q+1
       362: q+1
       363: 2q+1
       364: q+1
       365: 2q+1
       366: q^2+3q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q+1
       371: 2q+1
       372: 2q+1
       373: q^2+3q+1
       374: q+1
       375: q^2+3q+1
       376: q+1
       377: q^2+3q+1
       378: q+1
       379: q+1
       380: q^2+3q+1
       381: 2q+1
       382: q^2+3q+1
       383: q^2+2q+1
       384: q^2+3q+1
       385: 2q+1
       386: 2q+1
       387: q^2+3q+1
       388: q^2+3q+1
       389: q^2+3q+1
       390: q^2+3q+1
       391: q+1
       392: 2q+1
       393: 2q+1
       394: 2q+1
       395: q+1
       396: q+1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 2q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: 2q+1
       413: 1
       414: 2q+1
       415: q+1
       416: 2q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q^2+3q+1
       436: q+1
       437: q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       442: 2q+1
       443: 1
       444: 2q+1
       445: q+1
       446: 2q+1
       447: 1
       448: 1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       468: q+1
       469: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q^2+2q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: 2q+1
       493: 2q+1
       494: q^2+2q+1
       495: q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: q^2+3q+1
       503: q+1
       504: q+1
       505: q+1
       506: 1
       507: q+1
       508: q+1
       509: 2q+1
       510: 1
       511: 2q+1
       512: q+1
       513: 2q+1
       514: 1
       515: 1
       516: q+1
       517: 2q+1
       518: q+1
       519: q^2+2q+1
       521: q+1
       522: q+1
       523: q+1
       524: 1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: q^2+2q+1
       529: q+1
       530: q^2+2q+1
       531: q+1
       532: q+1
       533: 2q+1
       534: q+1
       535: q+1
       536: q^2+3q+1
       537: q+1
       538: q+1
       539: q+1
       540: 1
       541: q+1
       542: q+1
       543: 2q+1
       544: q^2+3q+1
       545: 2q+1
       546: q^2+2q+1
       547: q^2+2q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: q^2+3q+1
       552: q+1
       553: q^2+3q+1
       554: q+1
       555: q^2+3q+1
       556: q+1
       557: q+1
       558: 2q+1
       559: 2q+1
       560: 2q+1
       561: 2q+1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 2q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 2q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: 2q+1
       628: 1
       629: 2q+1
       630: q+1
       631: 2q+1
       632: 1
       633: 1
       634: q+1
       635: 1
       636: q+1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       652: q+1
       654: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       661: q+1
       662: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 2q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: 1
       705: q+1
       707: q+1
       708: q+1
       710: 1
       711: 1
       712: q+1
       713: 2q+1
       714: q+1
       715: q^2+2q+1
       717: q+1
       718: q+1
       719: q+1
       720: 1
       721: q+1
       722: q+1
       723: q+1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: q+1
       730: 1
       731: 2q+1
       732: 2q+1
       733: q^2+2q+1
       734: q+1
       735: q^2+2q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: q+1
       741: q^2+3q+1
       742: q+1
       743: q+1
       744: q+1
       745: 1
       746: q+1
       747: q+1
       748: 2q+1
       749: 1
       750: 2q+1
       751: q+1
       752: 2q+1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       804: q+1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 2q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 1
       834: 1
       835: q+1
       836: 1
       840: 1
       841: 1
       842: q+1
       843: 1
       844: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: q+1
       866: 1
       868: 1
       869: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: q+1
       882: q+1
       883: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: q+1
       911: 1
       913: 1
       914: q+1
       915: 1
       916: q+1
       918: q+1
       919: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: 1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: q+1
       934: 2q+1
       935: q+1
       936: q^2+2q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: q+1
       946: 1
       947: q+1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 2q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       959: 1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       970: 1
       972: 1
       973: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       982: 1
       983: 1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: q+1
      1053: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1063: q+1
      1064: 1
      1065: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: 1
      1087: 1
      1089: q+1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: q+1
      1125: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: q+1
      1141: q+1
      1142: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1167: 1
      1170: 1
      1175: 1
      1180: 1
      1182: 1
      1184: 1
      1185: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1227: 1
      1229: 1
      1230: 1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1239: 1
      1240: 1
      1241: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1269: 1
      1270: 1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1303: 1
      1305: 1
      1306: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1322: 1
      1323: 1
      1325: 1
      1327: 1
      1329: 1
      1330: 1
      1331: 1
      1333: q+1
      1335: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1356: 1
      1358: 1
      1372: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1414: 1
      1419: 1
      1421: 1
      1423: 1
      1424: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1462: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1481: 1
      1490: 1
      1494: 1
      1496: 1
      1499: 1
      1501: 1
      1503: 1
      1506: 1
      1508: 1
      1509: 1
      1511: 1
      1513: 1
      1515: 1
      1516: 1
      1518: 1
      1520: 1
      1521: 1
      1555: 1
      1565: 1
      1579: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1621: 1
      1638: 1
      1643: 1
      1647: 1
      1649: 1
      1652: 1
      1657: 1
      1722: 1
      1754: 1

1755:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 2q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: 2q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: 2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: 2q+1
       149: 2q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+2q+1
       153: 2q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       165: 2q+1
       166: 2q+1
       167: q^2+2q+1
       169: 2q+1
       170: q^2+2q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q^2+2q+1
       214: q^2+2q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: q^2+2q+1
       220: 2q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q^2+2q+1
       237: q^2+2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: q^2+2q+1
       243: 2q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: 2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 2q^2+2q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       272: 2q+1
       273: 2q+1
       276: 2q+1
       277: 2q+1
       278: q+1
       281: q+1
       282: q+1
       283: q^2+2q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       302: 2q+1
       303: q^2+2q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: q^2+2q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: q^2+2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q^2+2q+1
       381: q^2+2q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: q^2+2q+1
       387: 2q+1
       388: q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q^2+2q+1
       394: 2q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       411: 1
       412: 2q+1
       413: 2q+1
       418: 2q+1
       419: q+1
       420: q+1
       425: q+1
       426: q+1
       429: q+1
       430: q+1
       431: q^2+2q+1
       433: q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       448: 2q+1
       449: 2q+1
       452: 2q+1
       453: 2q+1
       454: q+1
       457: q+1
       458: q+1
       459: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: q+1
       474: q+1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: 2q+1
       510: 2q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       543: q^2+2q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 2q+1
       561: 2q+1
       562: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       581: 1
       582: 2q+1
       589: 1
       590: q+1
       597: 1
       598: q+1
       599: q+1
       604: q+1
       605: q+1
       608: q+1
       609: q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       626: 1
       627: 2q+1
       628: 2q+1
       633: 2q+1
       634: q+1
       635: q+1
       640: q+1
       641: q+1
       644: q+1
       645: q+1
       646: q^2+2q+1
       648: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: q+1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       702: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: q+1
       713: q+1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       722: q+1
       723: 2q+1
       724: 2q+1
       725: 2q+1
       726: q+1
       727: q+1
       728: 2q+1
       729: q+1
       730: q+1
       731: q+1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: 2q+1
       749: 2q+1
       754: 2q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: q+1
       799: 1
       800: q+1
       801: q+1
       806: q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       825: 1
       826: 2q+1
       833: 1
       834: q+1
       841: 1
       842: q+1
       843: q+1
       848: q+1
       849: q+1
       852: q+1
       853: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       897: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: q+1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       921: 1
       923: q+1
       924: q+1
       925: 2q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: 1
       931: q+1
       933: q+1
       934: q+1
       935: 2q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       943: q+1
       944: 2q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: q+1
       951: q+1
       952: 2q+1
       959: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: q+1
      1013: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: q+1
      1058: 1
      1059: q+1
      1060: q+1
      1065: q+1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: q+1
      1130: 1
      1131: q+1
      1132: q+1
      1133: 1
      1134: 1
      1135: 1
      1138: q+1
      1139: 1
      1140: q+1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1146: q+1
      1147: q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1156: 1
      1164: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1208: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: q+1
      1270: 1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: q+1
      1340: 1
      1341: q+1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1347: 1
      1359: 1
      1394: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1447: 1
      1455: 1
      1463: 1
      1468: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1491: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1566: 1
      1601: 1
      1622: 1
      1639: 1
      1644: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1755: 1

1756:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: 1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: 1
        21: 1
        22: q^2+1
        23: q^2+1
        24: q^2+1
        25: 1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: q^2+1
        31: q^2+1
        32: q^2+1
        33: 1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: q^2+1
        39: q^2+1
        40: 1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: 1
        45: q^2+1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: q^2+1
        55: q^2+1
        56: q^2+1
        57: 1
        58: 1
        59: q^2+1
        60: q^2+1
        61: q^2+1
        62: 1
        63: q^2+1
        64: q^2+1
        65: 1
        66: q^2+1
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: 1
        72: 1
        73: q^2+1
        74: q^2+1
        75: q^2+1
        76: 1
        77: q^2+1
        78: q^2+1
        79: q^2+1
        80: q^2+1
        81: q^2+1
        82: q^2+1
        83: q^2+1
        84: 1
        85: 1
        86: q^2+1
        87: q^2+1
        88: q^2+1
        89: 1
        91: 1
        92: q^2+1
        93: 1
        94: q^2+1
        95: 1
        96: q^2+1
        97: 1
        98: q^2+1
        99: q^2+1
       100: q^2+1
       101: 1
       102: q^2+1
       103: q^2+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: q^2+1
       111: q^2+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: q^2+1
       117: q^2+1
       118: q^2+1
       119: 1
       120: 1
       121: q^2+1
       122: q^2+1
       123: q^2+1
       124: 1
       125: 1
       126: q^2+1
       127: q^2+1
       128: q^2+1
       129: 1
       130: q^2+1
       131: q^2+1
       132: q^2+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: q^2+1
       139: q^2+1
       140: q^2+1
       141: 1
       142: 1
       143: q^2+1
       144: q^2+1
       145: q^2+1
       146: 1
       147: q^2+1
       148: q^2+1
       149: 1
       150: q^2+1
       151: q^2+1
       152: q^2+1
       153: q^2+1
       154: q^2+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: q^2+1
       160: q^2+1
       161: q^2+1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: q^2+1
       174: 1
       175: q^2+1
       176: 1
       177: 1
       178: q^2+1
       179: q^2+1
       180: q^2+1
       181: 1
       183: 1
       184: q^2+1
       185: 1
       186: q^2+1
       187: 1
       188: q^2+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q^2+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: q^2+1
       205: q^2+1
       206: 1
       207: 1
       208: 1
       209: 1
       210: q^2+1
       211: q^2+1
       212: q^2+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: q^2+1
       218: q^2+1
       219: q^2+1
       220: 1
       221: 1
       222: q^2+1
       223: q^2+1
       224: q^2+1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q^2+1
       235: q^2+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: q^2+1
       241: q^2+1
       242: q^2+1
       243: 1
       244: 1
       245: q^2+1
       246: q^2+1
       247: q^2+1
       248: 1
       249: 1
       250: q^2+1
       251: q^2+1
       252: q^2+1
       253: 1
       254: q^2+1
       255: q^2+1
       256: q^2+1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: q^2+1
       265: q^2+1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: q^2+1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: q^2+1
       293: q^2+1
       294: q^2+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q^2+1
       307: 1
       308: q^2+1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q^2+1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: q^2+1
       335: q^2+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q^2+1
       343: q^2+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: q^2+1
       350: q^2+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q^2+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q^2+1
       372: q^2+1
       373: 1
       374: 1
       375: 1
       376: 1
       377: q^2+1
       378: q^2+1
       379: q^2+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: q^2+1
       385: q^2+1
       386: q^2+1
       387: 1
       388: 1
       389: q^2+1
       390: q^2+1
       391: q^2+1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q^2+1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q^2+1
       441: q^2+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q^2+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q^2+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q^2+1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q^2+1
       508: q^2+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q^2+1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: q^2+1
       542: q^2+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: q^2+1
       550: q^2+1
       551: 1
       552: 1
       553: 1
       554: 1
       555: q^2+1
       556: q^2+1
       557: q^2+1
       558: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+1
       694: 1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q^2+1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q^2+1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: q^2+1
       747: q^2+1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q^2+1
       951: 1
       952: 1
       959: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1168: 1
      1169: 1
      1208: 1
      1216: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1277: 1
      1282: 1
      1283: 1
      1289: 1
      1290: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1360: 1
      1407: 1
      1408: 1
      1447: 1
      1455: 1
      1464: 1
      1469: 1
      1474: 1
      1475: 1
      1492: 1
      1497: 1
      1498: 1
      1504: 1
      1505: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1567: 1
      1623: 1
      1640: 1
      1645: 1
      1650: 1
      1651: 1
      1756: 1

1757:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: 2q^2+2q+1
        25: q^2+2q+1
        26: 2q^2+2q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: 2q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: 2q^2+2q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: 2q^2+2q+1
        67: 2q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: 2q^2+2q+1
        75: 2q^2+2q+1
        76: q^2+2q+1
        77: 2q^2+2q+1
        78: 2q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+2q+1
        93: q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+2q+1
       111: q^2+2q+1
       112: q+1
       113: q+1
       114: q+1
       115: q^2+2q+1
       116: 2q^2+2q+1
       117: 2q^2+2q+1
       118: 2q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: 2q^2+2q+1
       128: 2q^2+2q+1
       129: q^2+2q+1
       130: 2q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: 2q^2+2q+1
       141: q+1
       142: q^2+2q+1
       143: 2q^2+2q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+2q+1
       152: 2q^2+2q+1
       153: 2q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: q^2+2q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 2q^2+2q+1
       205: q^2+2q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q+1
       214: q+1
       215: q+1
       216: q^2+2q+1
       217: 2q^2+2q+1
       218: 2q^2+2q+1
       219: 2q^2+2q+1
       220: q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: q+1
       238: q+1
       239: q^2+2q+1
       240: 2q^2+2q+1
       241: 2q^2+2q+1
       242: 2q^2+2q+1
       243: q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q+1
       249: q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+2q+1
       252: 2q^2+2q+1
       253: q^2+2q+1
       254: 2q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: q^2+2q+1
       327: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q^2+2q+1
       341: q^2+2q+1
       342: 2q^2+2q+1
       343: q^2+2q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q^2+2q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: 2q^2+2q+1
       372: q^2+2q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q^2+2q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: q+1
       381: q+1
       382: q+1
       383: q^2+2q+1
       384: 2q^2+2q+1
       385: 2q^2+2q+1
       386: 2q^2+2q+1
       387: q+1
       388: q^2+2q+1
       389: q^2+2q+1
       390: q^2+2q+1
       391: q^2+2q+1
       392: q+1
       393: q+1
       394: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q^2+2q+1
       403: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q^2+2q+1
       491: q+1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: q^2+2q+1
       508: q^2+2q+1
       509: 1
       510: 1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       524: q+1
       525: q+1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q^2+2q+1
       533: q^2+2q+1
       534: q+1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: q+1
       540: q+1
       541: q^2+2q+1
       542: q^2+2q+1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q^2+2q+1
       548: q^2+2q+1
       549: 2q^2+2q+1
       550: q^2+2q+1
       551: q+1
       552: q+1
       553: q+1
       554: q+1
       555: q^2+2q+1
       556: q^2+2q+1
       557: q^2+2q+1
       558: 1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q^2+2q+1
       618: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: q+1
       654: 1
       655: 1
       656: 1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       678: q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q^2+2q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: 1
       711: q+1
       714: q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: q+1
       720: q+1
       721: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q^2+2q+1
       730: q+1
       732: q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q^2+2q+1
       738: q^2+2q+1
       739: q+1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: q+1
       745: q+1
       746: q^2+2q+1
       747: q^2+2q+1
       748: 1
       749: 1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: q+1
       866: 1
       867: 1
       868: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       885: 1
       886: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       910: q+1
       911: 1
       912: 1
       913: 1
       917: q+1
       918: q+1
       919: q+1
       920: q+1
       921: 1
       922: q+1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: q+1
       932: q+1
       935: q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: q+1
       941: q+1
       942: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q^2+2q+1
       951: q+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       986: 1
       996: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1117: 1
      1118: 1
      1119: 1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: q+1
      1140: q+1
      1141: q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1155: q+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1207: 1
      1209: 1
      1215: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1243: 1
      1253: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1290: 1
      1291: 1
      1292: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: q+1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1356: 1
      1361: 1
      1373: 1
      1403: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1446: 1
      1448: 1
      1454: 1
      1455: 1
      1465: 1
      1470: 1
      1475: 1
      1476: 1
      1477: 1
      1482: 1
      1493: 1
      1498: 1
      1499: 1
      1500: 1
      1505: 1
      1506: 1
      1507: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1568: 1
      1580: 1
      1610: 1
      1624: 1
      1641: 1
      1646: 1
      1651: 1
      1652: 1
      1653: 1
      1658: 1
      1757: 1

1758:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q+1
        12: q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^3+q^2+q+1
        21: q^3+q^2+q+1
        22: q^3+q^2+q+1
        23: 1
        24: q^2+1
        25: q^3+q^2+q+1
        26: q^3+q^2+q+1
        27: q^3+q^2+q+1
        28: q+1
        29: q+1
        30: q^3+q^2+q+1
        31: q^3+q^2+q+1
        32: q+1
        33: q^3+q^2+q+1
        34: q^3+q^2+q+1
        35: q^3+q^2+q+1
        36: q^3+q^2+q+1
        37: q^3+q^2+q+1
        38: q+1
        39: q^3+q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q^2+1
        52: q^3+q^2+q+1
        53: q^3+q^2+q+1
        54: 1
        55: q^2+1
        56: 1
        57: q^3+q^2+q+1
        58: q^3+q^2+q+1
        59: q^3+q^2+q+1
        60: 1
        61: q^2+1
        62: q+1
        63: q+1
        64: q+1
        65: q^3+q^2+q+1
        66: q^3+q^2+q+1
        67: q^3+q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^3+q^2+q+1
        72: q^3+q^2+q+1
        73: q^3+q^2+q+1
        74: 1
        75: q^2+1
        76: q^3+q^2+q+1
        77: q^3+q^2+q+1
        78: q^3+q^2+q+1
        79: q+1
        80: q+1
        81: q^3+q^2+q+1
        82: q^3+q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q^2+1
       107: q^3+q^2+q+1
       108: 1
       109: q^2+1
       110: 1
       111: 1
       112: 1
       113: q^2+1
       114: q^3+q^2+q+1
       115: q^3+q^2+q+1
       116: 1
       117: q^2+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: 1
       124: q^3+q^2+q+1
       125: q^3+q^2+q+1
       126: q^3+q^2+q+1
       127: 1
       128: q^2+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q^2+1
       136: q^3+q^2+q+1
       137: q^3+q^2+q+1
       138: 1
       139: q^2+1
       140: 1
       141: q^3+q^2+q+1
       142: q^3+q^2+q+1
       143: q^3+q^2+q+1
       144: 1
       145: q^2+1
       146: q+1
       147: q+1
       148: q+1
       149: q^3+q^2+q+1
       150: q^3+q^2+q+1
       151: q^3+q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q^2+1
       193: 1
       194: q^2+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q^2+1
       201: q^3+q^2+q+1
       202: 1
       203: q^2+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       213: 1
       214: q^2+1
       215: q^3+q^2+q+1
       216: q^3+q^2+q+1
       217: 1
       218: q^2+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: q^2+1
       231: q^3+q^2+q+1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       236: 1
       237: q^2+1
       238: q^3+q^2+q+1
       239: q^3+q^2+q+1
       240: 1
       241: q^2+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: 1
       248: q^3+q^2+q+1
       249: q^3+q^2+q+1
       250: q^3+q^2+q+1
       251: 1
       252: q^2+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: q^2+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q^2+1
       323: 1
       324: q^2+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+1
       339: q^3+q^2+q+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q^2+1
       360: 1
       361: q^2+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q^2+1
       368: q^3+q^2+q+1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: q+1
       376: q+1
       377: 1
       378: 1
       379: 1
       380: 1
       381: q^2+1
       382: q^3+q^2+q+1
       383: q^3+q^2+q+1
       384: 1
       385: q^2+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: 1
       420: 1
       421: q+1
       422: q+1
       424: 1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: q^2+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: q^2+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+1
       546: q^3+q^2+q+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: q+1
       554: q+1
       555: 1
       556: 1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: q+1
       595: 1
       599: 1
       600: q+1
       601: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: q+1
       630: q+1
       631: 1
       632: 1
       633: 1
       635: 1
       636: q+1
       637: q+1
       639: 1
       641: q+1
       642: q+1
       643: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: q^2+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: q+1
       751: q+1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: q+1
       797: 1
       801: 1
       802: q+1
       803: q+1
       805: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: q+1
       839: 1
       843: 1
       844: q+1
       845: q+1
       847: 1
       849: q+1
       850: q+1
       851: q+1
       853: 1
       854: 1
       861: 1
       862: 1
       868: 1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       913: 1
       914: 1
       915: 1
       916: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: q^2+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       960: 1
       961: 1
       967: 1
       968: 1
       969: 1
       970: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: q+1
      1011: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: q+1
      1056: 1
      1060: 1
      1061: q+1
      1062: q+1
      1064: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1086: 1
      1087: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1250: 1
      1257: 1
      1259: 1
      1265: 1
      1266: q+1
      1268: 1
      1279: 1
      1286: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1315: 1
      1322: 1
      1323: 1
      1329: 1
      1330: 1
      1331: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1362: 1
      1369: 1
      1370: 1
      1376: 1
      1400: 1
      1404: 1
      1411: 1
      1412: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1426: 1
      1427: 1
      1443: 1
      1450: 1
      1452: 1
      1471: 1
      1478: 1
      1479: 1
      1485: 1
      1494: 1
      1501: 1
      1508: 1
      1509: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1523: 1
      1524: 1
      1533: 1
      1569: 1
      1576: 1
      1577: 1
      1583: 1
      1607: 1
      1625: 1
      1647: 1
      1654: 1
      1655: 1
      1661: 1
      1700: 1
      1758: 1

1759:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: 1
        24: q^2+q+1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: 1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+q+1
        66: q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q+1
        73: q+1
        74: 1
        75: q^2+q+1
        76: q^2+q+1
        77: q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q^2+q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q^2+q+1
       125: q+1
       126: q+1
       127: 1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q^2+q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q^2+q+1
       142: q+1
       143: q+1
       144: 1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: 1
       164: 1
       165: 1
       166: q+1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q^2+q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: q+1
       226: 1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q^2+q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q^2+q+1
       249: q+1
       250: q+1
       251: 1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: 1
       275: 1
       276: 1
       277: q+1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: 1
       299: q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: 1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q^2+q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: 1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: q+1
       427: 1
       428: 1
       430: q+1
       431: q+1
       432: 1
       433: q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: 1
       453: q+1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: 1
       560: 1
       561: 1
       562: q+1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: q+1
       600: 1
       601: 1
       603: 1
       605: q+1
       606: 1
       607: 1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: 1
       643: 1
       645: q+1
       646: q+1
       647: 1
       648: q+1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       727: q+1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: q+1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: q+1
       844: 1
       845: 1
       847: 1
       849: q+1
       850: 1
       851: 1
       853: q+1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: q+1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       961: 1
       962: 1
       966: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: q+1
      1061: 1
      1062: 1
      1064: 1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: q+1
      1153: 1
      1154: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1204: 1
      1211: 1
      1213: 1
      1218: 1
      1219: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1250: 1
      1257: 1
      1259: 1
      1265: 1
      1266: 1
      1268: 1
      1280: 1
      1287: 1
      1294: 1
      1295: 1
      1299: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1316: 1
      1323: 1
      1324: 1
      1328: 1
      1331: 1
      1332: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1363: 1
      1370: 1
      1371: 1
      1375: 1
      1400: 1
      1405: 1
      1412: 1
      1413: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1443: 1
      1450: 1
      1452: 1
      1472: 1
      1479: 1
      1480: 1
      1484: 1
      1495: 1
      1502: 1
      1509: 1
      1510: 1
      1514: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1534: 1
      1570: 1
      1577: 1
      1578: 1
      1582: 1
      1607: 1
      1626: 1
      1648: 1
      1655: 1
      1656: 1
      1660: 1
      1701: 1
      1759: 1

1760:    0: 2q^3+5q^2+3q+1
         1: 2q^3+5q^2+3q+1
         2: 2q^3+5q^2+3q+1
         3: 2q^3+5q^2+3q+1
         4: 2q^3+5q^2+3q+1
         5: 2q^3+5q^2+3q+1
         6: 2q^3+5q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: 2q^3+5q^2+3q+1
        10: 2q^3+5q^2+3q+1
        11: 2q^3+5q^2+3q+1
        12: 2q^3+5q^2+3q+1
        13: 2q^3+5q^2+3q+1
        14: 2q^3+5q^2+3q+1
        15: 2q^3+5q^2+3q+1
        16: 2q^3+5q^2+3q+1
        17: 2q^3+5q^2+3q+1
        18: q^3+4q^2+3q+1
        19: 2q^3+5q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: q^3+3q^2+3q+1
        24: q^2+2q+1
        25: 2q^3+5q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: 2q^3+5q^2+3q+1
        29: 2q^3+5q^2+3q+1
        30: 2q^3+5q^2+3q+1
        31: 2q^3+5q^2+3q+1
        32: 2q^3+5q^2+3q+1
        33: 2q^3+5q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q^3+3q^2+3q+1
        36: 2q^3+5q^2+3q+1
        37: 2q^3+5q^2+3q+1
        38: 2q^3+5q^2+3q+1
        39: 2q^3+5q^2+3q+1
        40: 2q^3+5q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: q^3+3q^2+3q+1
        47: 2q^3+5q^2+3q+1
        48: 2q^3+5q^2+3q+1
        49: q^3+4q^2+3q+1
        50: q^3+3q^2+3q+1
        51: q^2+2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^3+3q^2+3q+1
        58: q^3+3q^2+3q+1
        59: q^2+3q+1
        60: q^3+3q^2+3q+1
        61: q^2+2q+1
        62: 2q^3+5q^2+3q+1
        63: q^3+3q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^3+5q^2+3q+1
        66: q^3+3q^2+3q+1
        67: q^3+3q^2+3q+1
        68: 2q^3+5q^2+3q+1
        69: 2q^3+5q^2+3q+1
        70: q^3+4q^2+3q+1
        71: q^3+3q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q^3+3q^2+3q+1
        75: q^2+2q+1
        76: 2q^3+5q^2+3q+1
        77: q^3+3q^2+3q+1
        78: q^3+3q^2+3q+1
        79: 2q^3+5q^2+3q+1
        80: 2q^3+5q^2+3q+1
        81: 2q^3+5q^2+3q+1
        82: 2q^3+5q^2+3q+1
        83: 2q^3+5q^2+3q+1
        84: 2q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: 2q^2+3q+1
        88: 2q+1
        89: q^3+4q^2+3q+1
        90: q^2+2q+1
        91: 2q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: q^3+3q^2+3q+1
        95: q^3+3q^2+3q+1
        96: q^3+3q^2+3q+1
        97: 2q^3+5q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: q^3+4q^2+3q+1
       103: q^3+3q^2+3q+1
       104: q^2+2q+1
       105: q^2+3q+1
       106: 2q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^3+3q^2+3q+1
       113: q^2+2q+1
       114: q^2+3q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: 2q+1
       118: q^2+2q+1
       119: 2q^2+3q+1
       120: q^3+3q^2+3q+1
       121: q^2+3q+1
       122: 2q^2+3q+1
       123: 2q+1
       124: q^3+3q^2+3q+1
       125: q^3+3q^2+3q+1
       126: q^2+3q+1
       127: q^3+3q^2+3q+1
       128: q^2+2q+1
       129: 2q^3+5q^2+3q+1
       130: q^3+3q^2+3q+1
       131: 2q^2+3q+1
       132: q^3+4q^2+3q+1
       133: q^3+4q^2+3q+1
       134: q^3+3q^2+3q+1
       135: q^2+2q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: 2q+1
       140: q^2+2q+1
       141: q^3+3q^2+3q+1
       142: q^3+3q^2+3q+1
       143: q^2+3q+1
       144: q^3+3q^2+3q+1
       145: q^2+2q+1
       146: 2q^3+5q^2+3q+1
       147: q^3+3q^2+3q+1
       148: 2q^2+3q+1
       149: 2q^3+5q^2+3q+1
       150: q^3+3q^2+3q+1
       151: q^3+3q^2+3q+1
       152: 2q^3+5q^2+3q+1
       153: 2q^3+5q^2+3q+1
       154: q^3+4q^2+3q+1
       155: 2q^2+3q+1
       156: 2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: 2q^2+3q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q^2+3q+1
       166: 2q+1
       167: q^3+4q^2+3q+1
       168: q^2+2q+1
       169: 2q^2+3q+1
       170: q^3+3q^2+3q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^3+3q^2+3q+1
       174: q^3+3q^2+3q+1
       175: q^3+3q^2+3q+1
       176: 2q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+3q+1
       180: 2q+1
       181: q^3+4q^2+3q+1
       182: q^2+2q+1
       183: 2q^2+3q+1
       184: q^3+4q^2+3q+1
       185: q^3+4q^2+3q+1
       186: q^3+3q^2+3q+1
       187: q^3+3q^2+3q+1
       188: q^3+3q^2+3q+1
       189: q+1
       190: 2q+1
       191: q^2+3q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: q^2+3q+1
       200: 2q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: 2q^2+3q+1
       207: 2q+1
       208: q^2+3q+1
       209: q^2+3q+1
       210: q^2+3q+1
       211: 2q+1
       212: 2q+1
       213: q^3+3q^2+3q+1
       214: q^2+2q+1
       215: q^2+3q+1
       216: q^2+3q+1
       217: q^2+3q+1
       218: 2q+1
       219: q^2+2q+1
       220: 2q^2+3q+1
       221: q^3+3q^2+3q+1
       222: q^2+3q+1
       223: 2q^2+3q+1
       224: 2q+1
       225: q^3+4q^2+3q+1
       226: q^2+2q+1
       227: 2q^2+3q+1
       228: q^2+2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q^2+3q+1
       232: q^2+3q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q^3+3q^2+3q+1
       237: q^2+2q+1
       238: q^2+3q+1
       239: q^2+3q+1
       240: q^2+3q+1
       241: 2q+1
       242: q^2+2q+1
       243: 2q^2+3q+1
       244: q^3+3q^2+3q+1
       245: q^2+3q+1
       246: 2q^2+3q+1
       247: 2q+1
       248: q^3+3q^2+3q+1
       249: q^3+3q^2+3q+1
       250: q^2+3q+1
       251: q^3+3q^2+3q+1
       252: q^2+2q+1
       253: 2q^3+5q^2+3q+1
       254: q^3+3q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+4q^2+3q+1
       257: q^3+4q^2+3q+1
       258: 2q+1
       259: q^2+3q+1
       260: 2q+1
       261: q^2+3q+1
       262: q^2+3q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q^2+3q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: 2q+1
       273: 2q^2+3q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q^2+3q+1
       277: 2q+1
       278: q^2+2q+1
       279: q^2+2q+1
       280: q+1
       281: q^2+2q+1
       282: q+1
       283: q^3+3q^2+3q+1
       284: q^2+2q+1
       285: q^2+2q+1
       286: q^3+3q^2+3q+1
       287: q^3+3q^2+3q+1
       288: 2q^2+3q+1
       289: 2q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: q^2+3q+1
       293: 2q+1
       294: 2q+1
       295: 2q^2+3q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q^2+3q+1
       299: 2q+1
       300: q^3+4q^2+3q+1
       301: q^2+2q+1
       302: 2q^2+3q+1
       303: q^3+3q^2+3q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^3+3q^2+3q+1
       307: q^3+3q^2+3q+1
       308: q^3+3q^2+3q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: q+1
       320: 2q+1
       321: q^2+3q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       328: 2q+1
       329: q^2+3q+1
       330: 2q+1
       331: q^2+3q+1
       332: q^2+3q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: q^2+2q+1
       337: q^2+3q+1
       338: 2q+1
       339: q^2+3q+1
       340: q^2+3q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: 2q^2+3q+1
       345: 2q+1
       346: q^2+3q+1
       347: q^2+3q+1
       348: q^2+3q+1
       349: 2q+1
       350: 2q+1
       351: 2q^2+3q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q^2+3q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: q^2+3q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: q^2+2q+1
       366: q^2+3q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+3q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: 2q^2+3q+1
       374: 2q+1
       375: q^2+3q+1
       376: q^2+3q+1
       377: q^2+3q+1
       378: 2q+1
       379: 2q+1
       380: q^3+3q^2+3q+1
       381: q^2+2q+1
       382: q^2+3q+1
       383: q^2+3q+1
       384: q^2+3q+1
       385: 2q+1
       386: q^2+2q+1
       387: 2q^2+3q+1
       388: q^3+3q^2+3q+1
       389: q^2+3q+1
       390: 2q^2+3q+1
       391: 2q+1
       392: q^3+4q^2+3q+1
       393: q^2+2q+1
       394: 2q^2+3q+1
       395: q+1
       396: 2q+1
       397: q^2+3q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: 2q^2+3q+1
       413: 2q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: 2q+1
       419: q^2+2q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: q+1
       426: q^2+2q+1
       427: q^2+2q+1
       428: q+1
       429: q^2+2q+1
       430: q+1
       431: q^3+3q^2+3q+1
       432: q^2+2q+1
       433: q^2+2q+1
       434: 2q+1
       435: q^2+3q+1
       436: 2q+1
       437: q^2+3q+1
       438: q^2+3q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q^2+3q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: q+1
       448: 2q+1
       449: 2q^2+3q+1
       450: q^2+2q+1
       451: 2q+1
       452: 2q^2+3q+1
       453: 2q+1
       454: q^2+2q+1
       455: q^2+2q+1
       456: q+1
       457: q^2+2q+1
       458: q+1
       459: q^3+3q^2+3q+1
       460: q^2+2q+1
       461: q^2+2q+1
       462: q^3+3q^2+3q+1
       463: q^3+3q^2+3q+1
       465: q+1
       466: 1
       468: q+1
       469: 1
       471: 1
       473: q+1
       474: q+1
       475: 2q+1
       476: q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       483: q+1
       484: 2q+1
       485: q^2+3q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: q^2+3q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: q^2+3q+1
       503: 2q+1
       504: q^2+3q+1
       505: q^2+3q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: 2q^2+3q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: q+1
       527: 2q+1
       528: q^2+3q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       535: 2q+1
       536: q^2+3q+1
       537: 2q+1
       538: q^2+3q+1
       539: q^2+3q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       543: q^2+2q+1
       544: q^2+3q+1
       545: 2q+1
       546: q^2+3q+1
       547: q^2+3q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: 2q^2+3q+1
       552: 2q+1
       553: q^2+3q+1
       554: q^2+3q+1
       555: q^2+3q+1
       556: 2q+1
       557: 2q+1
       558: 2q^2+3q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q^2+3q+1
       562: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 2q+1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q^2+2q+1
       599: q+1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: q+1
       605: q^2+2q+1
       606: q^2+2q+1
       607: q+1
       608: q^2+2q+1
       609: q+1
       610: q+1
       611: 2q+1
       612: q^2+3q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: q+1
       622: 2q+1
       623: 2q+1
       624: q+1
       625: q+1
       626: 1
       627: 2q^2+3q+1
       628: 2q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: q+1
       633: 2q+1
       634: q^2+2q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: q+1
       641: q^2+2q+1
       642: q^2+2q+1
       643: q+1
       644: q^2+2q+1
       645: q+1
       646: q^3+3q^2+3q+1
       647: q^2+2q+1
       648: q^2+2q+1
       650: 1
       652: 1
       654: 1
       658: q+1
       659: 1
       661: q+1
       662: 1
       664: 1
       666: q+1
       667: q+1
       668: 2q+1
       669: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       686: q+1
       687: 2q+1
       688: q^2+3q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       696: 2q+1
       697: q+1
       698: 2q+1
       699: 2q+1
       700: q+1
       701: q+1
       702: 1
       704: q+1
       705: 1
       707: q+1
       708: 1
       710: 1
       712: q+1
       713: q+1
       714: 2q+1
       715: q+1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       722: q+1
       723: 2q+1
       724: q^2+3q+1
       725: 2q+1
       726: q+1
       727: q+1
       728: 2q+1
       729: q+1
       730: q+1
       731: q+1
       732: 2q+1
       733: q^2+3q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       740: 2q+1
       741: q^2+3q+1
       742: 2q+1
       743: q^2+3q+1
       744: q^2+3q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: 2q^2+3q+1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: q+1
       754: 2q+1
       756: q+1
       757: 1
       759: q+1
       760: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: q+1
       776: 2q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: q+1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q^2+2q+1
       801: q+1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: 2q+1
       820: q+1
       821: q+1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 2q+1
       827: 2q+1
       828: q+1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       841: 1
       842: q^2+2q+1
       843: q+1
       844: q+1
       845: q+1
       846: q+1
       847: 1
       848: q+1
       849: q^2+2q+1
       850: q^2+2q+1
       851: q+1
       852: q^2+2q+1
       853: q+1
       856: 1
       862: 1
       864: 1
       866: 1
       870: q+1
       871: 1
       873: q+1
       874: 1
       876: 1
       879: q+1
       880: 1
       882: q+1
       883: 1
       885: 1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       897: 1
       898: q+1
       899: 2q+1
       900: q+1
       901: q+1
       902: 1
       903: q+1
       904: 1
       905: 1
       907: 1
       909: 1
       911: 1
       915: q+1
       916: 1
       918: q+1
       919: 1
       921: 1
       923: q+1
       924: q+1
       925: 2q+1
       926: q+1
       928: q+1
       929: q+1
       930: 1
       931: q+1
       933: q+1
       934: q+1
       935: 2q+1
       936: q+1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       943: q+1
       944: 2q+1
       945: q^2+3q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: q+1
       951: q+1
       952: 2q+1
       953: 2q+1
       954: q+1
       955: 2q+1
       956: 2q+1
       957: q+1
       958: q+1
       959: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: q+1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1015: q+1
      1016: 1
      1018: q+1
      1019: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: q+1
      1035: 2q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: q+1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: q+1
      1052: q+1
      1053: 1
      1054: q+1
      1055: q+1
      1056: 1
      1057: 1
      1058: 1
      1059: q^2+2q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: 1
      1065: q+1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1087: 1
      1089: 1
      1091: 1
      1095: q+1
      1096: 1
      1098: q+1
      1099: 1
      1101: 1
      1103: 1
      1104: 1
      1105: q+1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1129: q+1
      1130: 1
      1132: q+1
      1133: 1
      1135: 1
      1138: q+1
      1139: 1
      1141: q+1
      1142: 1
      1144: 1
      1146: q+1
      1147: q+1
      1148: 2q+1
      1149: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1156: 1
      1157: q+1
      1158: 2q+1
      1159: q+1
      1160: q+1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1190: 1
      1193: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1254: 1
      1255: 1
      1256: q+1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: q+1
      1264: q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1270: 1
      1281: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1317: 1
      1323: 1
      1325: 1
      1327: 1
      1331: 1
      1333: 1
      1335: 1
      1339: q+1
      1340: 1
      1342: q+1
      1343: 1
      1345: 1
      1347: 1
      1348: 1
      1349: q+1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1364: 1
      1370: 1
      1372: 1
      1374: 1
      1386: 1
      1389: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1406: 1
      1412: 1
      1414: 1
      1416: 1
      1420: 1
      1421: 1
      1423: 1
      1424: 1
      1426: 1
      1429: 1
      1432: 1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1447: 1
      1448: 1
      1449: q+1
      1450: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1473: 1
      1479: 1
      1481: 1
      1483: 1
      1496: 1
      1503: 1
      1509: 1
      1511: 1
      1513: 1
      1517: 1
      1518: 1
      1520: 1
      1521: 1
      1523: 1
      1535: 1
      1556: 1
      1559: 1
      1571: 1
      1577: 1
      1579: 1
      1581: 1
      1593: 1
      1596: 1
      1601: 1
      1602: 1
      1603: 1
      1606: 1
      1607: 1
      1609: 1
      1627: 1
      1649: 1
      1655: 1
      1657: 1
      1659: 1
      1702: 1
      1723: 1
      1726: 1
      1760: 1

1761:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: 1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q+1
        49: q^2+q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+q+1
        69: q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q^2+q+1
        93: 1
        94: q^2+q+1
        95: 1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: 1
       102: q^2+q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+q+1
       153: q+1
       154: q^2+q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q^2+q+1
       174: 1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q^2+q+1
       185: 1
       186: q^2+q+1
       187: 1
       188: q^2+q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q^2+q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+q+1
       307: 1
       308: q^2+q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       731: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       790: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: q+1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       934: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       988: 1
       997: 1
       998: 1
      1004: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: 1
      1043: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1088: 1
      1089: 1
      1090: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1199: 1
      1208: 1
      1209: 1
      1215: 1
      1219: 1
      1220: 1
      1221: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1245: 1
      1254: 1
      1255: 1
      1261: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1282: 1
      1289: 1
      1295: 1
      1296: 1
      1297: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1318: 1
      1324: 1
      1325: 1
      1326: 1
      1332: 1
      1333: 1
      1334: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1395: 1
      1407: 1
      1413: 1
      1414: 1
      1415: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1438: 1
      1447: 1
      1448: 1
      1454: 1
      1474: 1
      1480: 1
      1481: 1
      1482: 1
      1497: 1
      1504: 1
      1510: 1
      1511: 1
      1512: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1536: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1602: 1
      1628: 1
      1650: 1
      1656: 1
      1657: 1
      1658: 1
      1703: 1
      1761: 1

1762:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^2+q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q^2+q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 2q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+q+1
       105: q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+q+1
       113: q^2+q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q^2+q+1
       125: q^2+2q+1
       126: 2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q^2+q+1
       135: q^2+q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q^2+2q+1
       141: q^2+q+1
       142: q^2+2q+1
       143: 2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: 2q+1
       149: 2q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+2q+1
       153: 2q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q+1
       169: 2q+1
       170: q^2+2q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       182: q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q^2+q+1
       199: q+1
       200: q+1
       201: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q^2+q+1
       214: q^2+q+1
       215: q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q+1
       227: 2q+1
       228: q^2+q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q^2+q+1
       237: q^2+q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: q^2+2q+1
       243: q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q^2+q+1
       249: q^2+2q+1
       250: 2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 2q^2+2q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: q+1
       276: 2q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: q^2+2q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q+1
       302: 2q+1
       303: q^2+2q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       311: q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: q^2+q+1
       337: q+1
       338: q+1
       339: q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: q+1
       352: q+1
       353: q+1
       354: 2q+1
       355: 2q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: q^2+q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q^2+q+1
       381: q^2+q+1
       382: q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: q^2+2q+1
       387: q+1
       388: q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q^2+2q+1
       393: q+1
       394: 2q+1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: 2q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q+1
       427: q+1
       428: 1
       429: q+1
       430: q+1
       431: q^2+2q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: q+1
       452: 2q+1
       453: 2q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: q^2+2q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       475: q+1
       476: 1
       477: 1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       484: q+1
       485: q+1
       486: q+1
       487: 1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: 2q+1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       543: q^2+q+1
       544: q+1
       545: q+1
       546: q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: q+1
       559: q+1
       560: q+1
       561: 2q+1
       562: 2q+1
       565: q+1
       566: 1
       567: 1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q+1
       605: q+1
       606: q+1
       607: 1
       608: q+1
       609: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: 2q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q+1
       653: 1
       654: 1
       655: 1
       660: 1
       661: q+1
       662: 1
       663: 1
       664: 1
       668: q+1
       669: 1
       670: 1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: q+1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       723: q+1
       724: q+1
       725: q+1
       726: 1
       727: q+1
       728: 2q+1
       729: q+1
       730: q+1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       740: q+1
       741: q+1
       742: q+1
       743: q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: q+1
       749: q+1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: 2q+1
       758: 1
       759: q+1
       760: 1
       761: 1
       762: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       809: q+1
       810: 1
       811: 1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       873: q+1
       874: 1
       875: 1
       876: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       889: q+1
       890: 1
       891: 1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       925: q+1
       926: 1
       927: 1
       928: q+1
       929: q+1
       930: 1
       931: q+1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       944: q+1
       945: q+1
       946: q+1
       947: 1
       948: q+1
       949: 2q+1
       950: q+1
       951: q+1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       964: 1
       965: 1
       966: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       989: 1
       992: 1
       993: 1
       995: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1017: 1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1132: q+1
      1133: 1
      1134: 1
      1135: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1148: q+1
      1149: 1
      1150: 1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1193: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1283: 1
      1290: 1
      1297: 1
      1298: 1
      1299: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1319: 1
      1326: 1
      1327: 1
      1328: 1
      1334: 1
      1335: 1
      1336: 1
      1341: 1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1366: 1
      1373: 1
      1374: 1
      1375: 1
      1389: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1408: 1
      1415: 1
      1416: 1
      1417: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1432: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1448: 1
      1449: 1
      1450: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1475: 1
      1482: 1
      1483: 1
      1484: 1
      1498: 1
      1505: 1
      1512: 1
      1513: 1
      1514: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1537: 1
      1559: 1
      1573: 1
      1580: 1
      1581: 1
      1582: 1
      1596: 1
      1603: 1
      1606: 1
      1607: 1
      1609: 1
      1629: 1
      1651: 1
      1658: 1
      1659: 1
      1660: 1
      1704: 1
      1726: 1
      1762: 1

1763:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: q^2+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q^2+1
        52: q^2+1
        53: q^2+q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q+1
        71: q^2+1
        72: q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: 1
        85: q^2+q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       105: q^2+1
       107: q^2+1
       108: q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q+1
       112: q^2+1
       114: q^2+1
       115: q^2+q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: 1
       120: q^2+q+1
       121: q+1
       122: q+1
       123: q+1
       124: q^2+1
       125: q^2+q+1
       126: q^2+q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q+1
       132: q+1
       133: q+1
       134: q^2+1
       136: q^2+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: q^2+q+1
       141: q^2+1
       142: q^2+q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q^2+q+1
       153: q^2+q+1
       154: q+1
       155: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       191: q^2+1
       193: 1
       194: q^2+1
       195: q^2+q+1
       196: q+1
       197: q+1
       199: q^2+1
       201: q^2+1
       202: q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q+1
       206: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q^2+1
       215: q^2+1
       216: q^2+q+1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+q+1
       220: 1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       229: q^2+1
       231: q^2+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q^2+1
       238: q^2+1
       239: q^2+q+1
       240: q^2+q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 1
       244: q^2+q+1
       245: q+1
       246: q+1
       247: q+1
       248: q^2+1
       249: q^2+q+1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q^2+q+1
       254: q^2+q+1
       255: q+1
       256: q+1
       257: q+1
       259: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       312: 1
       314: q^2+1
       316: 1
       317: q+1
       318: q+1
       321: q^2+1
       323: 1
       324: q^2+1
       325: q^2+q+1
       326: q+1
       327: q+1
       329: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       337: q^2+1
       339: q^2+1
       340: q^2+q+1
       341: q^2+q+1
       342: q^2+q+1
       343: q+1
       344: 1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       358: q^2+1
       360: 1
       361: q^2+1
       362: q^2+q+1
       363: q+1
       364: q+1
       366: q^2+1
       368: q^2+1
       369: q^2+q+1
       370: q^2+q+1
       371: q^2+q+1
       372: q+1
       373: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q^2+1
       382: q^2+1
       383: q^2+q+1
       384: q^2+q+1
       385: q^2+q+1
       386: q^2+q+1
       387: 1
       388: q^2+q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       397: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       405: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       435: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       469: 1
       471: 1
       472: q+1
       476: 1
       478: q^2+1
       480: 1
       481: q+1
       482: q+1
       485: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       494: q^2+1
       496: 1
       497: q^2+1
       498: q^2+q+1
       499: q+1
       500: q+1
       502: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       519: 1
       521: q^2+1
       523: 1
       524: q+1
       525: q+1
       528: q^2+1
       530: 1
       531: q^2+1
       532: q^2+q+1
       533: q+1
       534: q+1
       536: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       544: q^2+1
       546: q^2+1
       547: q^2+q+1
       548: q^2+q+1
       549: q^2+q+1
       550: q+1
       551: 1
       553: 1
       554: q+1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       566: 1
       568: 1
       570: 1
       571: q+1
       572: q+1
       575: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       583: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       620: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       654: 1
       656: 1
       662: 1
       664: 1
       665: q+1
       669: 1
       671: 1
       673: 1
       674: q+1
       675: q+1
       679: 1
       681: q^2+1
       683: 1
       684: q+1
       685: q+1
       688: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       696: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       708: 1
       710: 1
       711: q+1
       715: 1
       717: q^2+1
       719: 1
       720: q+1
       721: q+1
       724: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       730: q+1
       733: q^2+1
       735: 1
       736: q^2+1
       737: q^2+q+1
       738: q+1
       739: q+1
       741: 1
       743: 1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: 1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: q+1
       760: 1
       762: 1
       763: q+1
       767: 1
       769: 1
       771: 1
       772: 1
       773: 1
       776: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       785: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: q+1
       816: q+1
       819: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       859: 1
       866: 1
       868: 1
       874: 1
       876: 1
       877: q+1
       883: 1
       885: 1
       886: q+1
       890: 1
       892: 1
       894: 1
       895: q+1
       896: q+1
       899: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       911: 1
       913: 1
       919: 1
       921: 1
       922: q+1
       926: 1
       928: 1
       930: 1
       931: q+1
       932: q+1
       936: 1
       938: q^2+1
       940: 1
       941: q+1
       942: q+1
       945: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       951: q+1
       953: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       965: 1
       967: 1
       973: 1
       975: 1
       976: 1
       980: 1
       982: 1
       984: 1
       985: 1
       986: 1
       992: 1
       995: 1
       996: 1
       999: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1022: q+1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1044: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1076: 1
      1083: 1
      1085: 1
      1091: 1
      1093: 1
      1099: 1
      1101: 1
      1102: q+1
      1106: 1
      1108: 1
      1110: 1
      1111: 1
      1112: 1
      1118: 1
      1125: 1
      1127: 1
      1133: 1
      1135: 1
      1136: q+1
      1142: 1
      1144: 1
      1145: q+1
      1149: 1
      1151: 1
      1153: 1
      1154: q+1
      1155: q+1
      1158: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1170: 1
      1177: 1
      1179: 1
      1185: 1
      1187: 1
      1188: 1
      1197: 1
      1203: 1
      1206: 1
      1207: 1
      1210: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1222: 1
      1224: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1239: 1
      1241: 1
      1242: 1
      1243: 1
      1249: 1
      1252: 1
      1253: 1
      1256: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1264: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1284: 1
      1291: 1
      1298: 1
      1300: 1
      1306: 1
      1308: 1
      1309: 1
      1320: 1
      1327: 1
      1329: 1
      1335: 1
      1337: 1
      1343: 1
      1345: 1
      1346: q+1
      1350: 1
      1352: 1
      1354: 1
      1355: 1
      1356: 1
      1367: 1
      1374: 1
      1376: 1
      1393: 1
      1399: 1
      1402: 1
      1403: 1
      1409: 1
      1416: 1
      1418: 1
      1424: 1
      1426: 1
      1427: 1
      1436: 1
      1442: 1
      1445: 1
      1446: 1
      1449: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1476: 1
      1483: 1
      1485: 1
      1499: 1
      1506: 1
      1513: 1
      1515: 1
      1521: 1
      1523: 1
      1524: 1
      1538: 1
      1563: 1
      1574: 1
      1581: 1
      1583: 1
      1600: 1
      1606: 1
      1609: 1
      1610: 1
      1630: 1
      1652: 1
      1659: 1
      1661: 1
      1705: 1
      1730: 1
      1763: 1

1764:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: 1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: q^2+1
        32: 1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: 1
        55: q^2+1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q^2+1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       106: q^2+1
       107: q^2+1
       108: 1
       109: q^2+1
       110: 1
       111: 1
       113: q^2+1
       114: q^2+1
       115: q^2+1
       116: 1
       117: q^2+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q^2+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       135: q^2+1
       136: q^2+1
       137: q^2+1
       138: 1
       139: q^2+1
       140: 1
       141: q^2+1
       142: q^2+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       192: q^2+1
       193: 1
       194: q^2+1
       195: 1
       196: 1
       197: 1
       200: q^2+1
       201: q^2+1
       202: 1
       203: q^2+1
       204: 1
       205: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q^2+1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       230: q^2+1
       231: q^2+1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       237: q^2+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       313: 1
       315: q^2+1
       316: 1
       317: 1
       318: 1
       322: q^2+1
       323: 1
       324: q^2+1
       325: 1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q^2+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       359: q^2+1
       360: 1
       361: q^2+1
       362: 1
       363: 1
       364: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q^2+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       470: 1
       471: 1
       472: 1
       477: 1
       479: q^2+1
       480: 1
       481: 1
       482: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       520: 1
       522: q^2+1
       523: 1
       524: 1
       525: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       655: 1
       656: 1
       663: 1
       664: 1
       665: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       680: 1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 1
       710: 1
       711: 1
       716: 1
       718: q^2+1
       719: 1
       720: 1
       721: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       761: 1
       762: 1
       763: 1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       860: 1
       867: 1
       868: 1
       875: 1
       876: 1
       877: 1
       884: 1
       885: 1
       886: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       912: 1
       913: 1
       920: 1
       921: 1
       922: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       937: 1
       939: q^2+1
       940: 1
       941: 1
       942: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1077: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1100: 1
      1101: 1
      1102: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1119: 1
      1126: 1
      1127: 1
      1134: 1
      1135: 1
      1136: 1
      1143: 1
      1144: 1
      1145: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1171: 1
      1178: 1
      1179: 1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1223: 1
      1224: 1
      1231: 1
      1232: 1
      1233: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1250: 1
      1257: 1
      1259: 1
      1265: 1
      1266: 1
      1268: 1
      1285: 1
      1292: 1
      1299: 1
      1300: 1
      1307: 1
      1308: 1
      1309: 1
      1321: 1
      1328: 1
      1329: 1
      1336: 1
      1337: 1
      1344: 1
      1345: 1
      1346: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1368: 1
      1375: 1
      1376: 1
      1400: 1
      1410: 1
      1417: 1
      1418: 1
      1425: 1
      1426: 1
      1427: 1
      1443: 1
      1450: 1
      1452: 1
      1477: 1
      1484: 1
      1485: 1
      1500: 1
      1507: 1
      1514: 1
      1515: 1
      1522: 1
      1523: 1
      1524: 1
      1539: 1
      1575: 1
      1582: 1
      1583: 1
      1607: 1
      1631: 1
      1653: 1
      1660: 1
      1661: 1
      1706: 1
      1764: 1

1765:    0: q^4+q^3+2q^2+q+1
         1: q^4+q^3+2q^2+q+1
         2: q^4+q^3+2q^2+q+1
         3: q^3+q^2+q+1
         4: q^2+q+1
         5: q^4+q^3+2q^2+q+1
         6: q^4+q^3+2q^2+q+1
         7: q^4+q^3+2q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q^3+q^2+q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q+1
        16: q^4+q^3+2q^2+q+1
        17: q^4+q^3+2q^2+q+1
        18: q^3+q^2+q+1
        19: q^2+q+1
        20: q^3+q^2+q+1
        21: q^4+q^3+2q^2+q+1
        22: q^3+q^2+q+1
        23: q^3+q^2+q+1
        24: q+1
        25: q^3+q^2+q+1
        26: q^3+q^2+q+1
        27: q^3+q^2+q+1
        28: q^3+q^2+q+1
        29: q^3+q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^4+q^3+2q^2+q+1
        41: q^4+q^3+2q^2+q+1
        42: q^3+q^2+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q^3+q^2+q+1
        51: q+1
        52: q^3+q^2+q+1
        53: q^3+q^2+q+1
        54: q^3+q^2+q+1
        55: q+1
        56: q+1
        57: q^3+q^2+q+1
        58: q^3+q^2+q+1
        59: q^3+q^2+q+1
        60: q^3+q^2+q+1
        61: q+1
        62: q^3+q^2+q+1
        63: q^3+q^2+q+1
        64: q^2+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^3+q^2+q+1
        85: q^4+q^3+2q^2+q+1
        86: q^3+q^2+q+1
        87: q^3+q^2+q+1
        88: q+1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q^3+q^2+q+1
       106: q+1
       107: q^3+q^2+q+1
       108: q^3+q^2+q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^3+q^2+q+1
       113: q+1
       114: q^3+q^2+q+1
       115: q^3+q^2+q+1
       116: q^3+q^2+q+1
       117: q+1
       118: q+1
       119: q^2+1
       120: q^3+q^2+q+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q^3+q^2+q+1
       156: q+1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^3+q^2+q+1
       160: q+1
       161: q+1
       162: q^3+q^2+q+1
       163: q^3+q^2+q+1
       164: q^3+q^2+q+1
       165: q^3+q^2+q+1
       166: q+1
       167: q^3+q^2+q+1
       168: q^3+q^2+q+1
       169: q^2+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q^3+q^2+q+1
       192: q+1
       193: q^2+1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q^3+q^2+q+1
       200: q+1
       201: q^3+q^2+q+1
       202: q^3+q^2+q+1
       203: q+1
       204: q+1
       205: 1
       206: q^2+1
       207: 1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q^3+q^2+q+1
       260: q+1
       261: q^3+q^2+q+1
       262: q^3+q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^3+q^2+q+1
       267: q+1
       268: q^3+q^2+q+1
       269: q^3+q^2+q+1
       270: q^3+q^2+q+1
       271: q+1
       272: q+1
       273: q^2+1
       274: q^3+q^2+q+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q^2+1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: q+1
       321: q^3+q^2+q+1
       322: q+1
       323: q^2+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: q^2+1
       330: 1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q^3+q^2+q+1
       398: q+1
       399: q^2+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q^3+q^2+q+1
       406: q+1
       407: q^3+q^2+q+1
       408: q^3+q^2+q+1
       409: q+1
       410: q+1
       411: 1
       412: q^2+1
       413: 1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: q^2+1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q^2+1
       486: 1
       487: q^2+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q^3+q^2+q+1
       576: q+1
       577: q^2+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: q^2+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: q^2+1
       670: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: 1
       707: 1
       708: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: q+1
       756: q+1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q^2+1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       942: 1
       945: 1
       953: 1
       955: 1
       956: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q^2+1
       981: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1141: 1
      1145: 1
      1158: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: 1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1293: 1
      1301: 1
      1302: 1
      1309: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1377: 1
      1385: 1
      1386: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1402: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1428: 1
      1429: 1
      1432: 1
      1436: 1
      1449: 1
      1456: 1
      1457: 1
      1458: 1
      1478: 1
      1490: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1547: 1
      1555: 1
      1556: 1
      1563: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1584: 1
      1611: 1
      1662: 1
      1663: 1
      1664: 1
      1684: 1
      1696: 1
      1765: 1

1766:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: 2q^3+4q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: q^3+3q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: 2q^3+4q^2+3q+1
         8: 2q^3+4q^2+3q+1
         9: 2q^3+4q^2+3q+1
        10: q^3+3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: 2q^3+4q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q^3+4q^2+3q+1
        21: 2q^3+4q^2+3q+1
        22: 2q^3+4q^2+3q+1
        23: q^3+3q^2+3q+1
        24: 2q^2+3q+1
        25: q^3+3q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^3+3q^2+3q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q^3+3q^2+3q+1
        36: q^3+3q^2+3q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: 2q^3+4q^2+3q+1
        41: 2q^3+4q^2+3q+1
        42: 2q^3+4q^2+3q+1
        43: 2q^3+4q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: q^3+3q^2+3q+1
        50: q^3+3q^2+3q+1
        51: 2q^2+3q+1
        52: 2q^3+4q^2+3q+1
        53: q^3+3q^2+3q+1
        54: q^3+3q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^3+3q^2+3q+1
        58: q^3+3q^2+3q+1
        59: q^3+3q^2+3q+1
        60: 2q^2+3q+1
        61: q^2+3q+1
        62: 2q^2+3q+1
        63: 2q^2+3q+1
        64: 2q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+3q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^3+3q^2+3q+1
        74: q^2+2q+1
        75: 2q^2+3q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: 2q^3+4q^2+3q+1
        85: 2q^3+4q^2+3q+1
        86: 2q^3+4q^2+3q+1
        87: q^3+3q^2+3q+1
        88: 2q^2+3q+1
        89: q^3+3q^2+3q+1
        90: q^3+3q^2+3q+1
        91: q^3+3q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^3+3q^2+3q+1
       100: q^3+3q^2+3q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+3q+1
       104: 2q^2+3q+1
       105: q^3+3q^2+3q+1
       106: 2q^2+3q+1
       107: q^3+3q^2+3q+1
       108: 2q^2+3q+1
       109: q^2+3q+1
       110: 2q^2+3q+1
       111: 2q^2+3q+1
       112: 2q^2+3q+1
       113: q^2+3q+1
       114: q^3+3q^2+3q+1
       115: q^3+3q^2+3q+1
       116: 2q^2+3q+1
       117: q^2+3q+1
       118: q^2+3q+1
       119: 2q^2+3q+1
       120: 2q^2+3q+1
       121: 2q^2+3q+1
       122: 2q^2+3q+1
       123: 2q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q+1
       128: q^2+3q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q^2+2q+1
       135: 2q^2+3q+1
       136: q^3+3q^2+3q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+3q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q+1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q^3+3q^2+3q+1
       156: 2q^2+3q+1
       157: 2q^3+4q^2+3q+1
       158: q^3+3q^2+3q+1
       159: q^3+3q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: q^3+3q^2+3q+1
       163: q^3+3q^2+3q+1
       164: q^3+3q^2+3q+1
       165: 2q^2+3q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: 2q^2+3q+1
       170: q^2+3q+1
       171: q^2+3q+1
       172: q^2+3q+1
       173: 2q^2+3q+1
       174: q^2+3q+1
       175: 2q^2+3q+1
       176: q^3+3q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^3+3q^2+3q+1
       179: q^2+2q+1
       180: 2q^2+3q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: q^2+2q+1
       189: 2q^2+3q+1
       190: 2q^2+3q+1
       191: 2q^2+3q+1
       192: q^2+3q+1
       193: 2q^2+3q+1
       194: q^2+3q+1
       195: q^2+3q+1
       196: 2q^2+3q+1
       197: 2q+1
       198: q^2+3q+1
       199: 2q^2+3q+1
       200: q^2+3q+1
       201: q^3+3q^2+3q+1
       202: 2q^2+3q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: q^2+3q+1
       206: 2q^2+3q+1
       207: 2q+1
       208: 2q^2+3q+1
       209: q^2+2q+1
       210: 2q^2+3q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: q^2+3q+1
       215: q^2+3q+1
       216: q+1
       217: q+1
       218: q^2+3q+1
       219: q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       224: 2q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+3q+1
       231: q^2+2q+1
       232: q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: 2q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: 2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: 2q^2+3q+1
       259: q^3+3q^2+3q+1
       260: 2q^2+3q+1
       261: q^3+3q^2+3q+1
       262: 2q^2+3q+1
       263: q^2+3q+1
       264: 2q^2+3q+1
       265: 2q^2+3q+1
       266: 2q^2+3q+1
       267: q^2+3q+1
       268: q^3+3q^2+3q+1
       269: q^3+3q^2+3q+1
       270: 2q^2+3q+1
       271: q^2+3q+1
       272: q^2+3q+1
       273: 2q^2+3q+1
       274: 2q^2+3q+1
       275: 2q^2+3q+1
       276: 2q^2+3q+1
       277: 2q+1
       278: q^2+3q+1
       279: q^2+3q+1
       280: q^2+3q+1
       281: q+1
       282: q^2+3q+1
       283: q^2+3q+1
       284: q^2+3q+1
       285: q^2+3q+1
       286: 2q^2+3q+1
       287: 2q+1
       288: q^2+2q+1
       289: 2q^2+3q+1
       290: q^3+3q^2+3q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: 2q^2+3q+1
       294: q^2+2q+1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q+1
       299: 2q+1
       300: q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: 2q+1
       310: 2q^2+3q+1
       311: q^2+3q+1
       312: 2q^2+3q+1
       313: 2q+1
       314: q+1
       315: q^2+3q+1
       316: q^2+3q+1
       317: 2q+1
       318: 2q+1
       319: q^2+3q+1
       320: q^2+3q+1
       321: 2q^2+3q+1
       322: q^2+3q+1
       323: 2q^2+3q+1
       324: q^2+3q+1
       325: q^2+3q+1
       326: q^2+3q+1
       327: 2q+1
       328: 2q+1
       329: 2q^2+3q+1
       330: 2q+1
       331: q^2+2q+1
       332: q^2+2q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: q^2+3q+1
       339: q+1
       340: 1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: 2q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       355: q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: q^2+2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: q+1
       373: q+1
       375: q+1
       377: q+1
       380: 1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: 1
       385: 2q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       395: 2q^2+3q+1
       396: 2q^2+3q+1
       397: 2q^2+3q+1
       398: q^2+3q+1
       399: 2q^2+3q+1
       400: q^2+3q+1
       401: q^2+3q+1
       402: 2q^2+3q+1
       403: 2q+1
       404: q^2+3q+1
       405: 2q^2+3q+1
       406: q^2+3q+1
       407: q^3+3q^2+3q+1
       408: 2q^2+3q+1
       409: q^2+3q+1
       410: q^2+3q+1
       411: q^2+3q+1
       412: 2q^2+3q+1
       413: 2q+1
       414: 2q^2+3q+1
       415: q^2+2q+1
       416: 2q^2+3q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: q^2+3q+1
       421: q^2+3q+1
       422: q+1
       423: q+1
       424: q^2+3q+1
       425: q+1
       426: q^2+3q+1
       427: q^2+3q+1
       428: q^2+3q+1
       429: q+1
       430: 2q+1
       431: 2q+1
       432: 2q+1
       433: 2q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: 2q^2+3q+1
       437: q^2+2q+1
       438: q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q+1
       443: 2q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: q+1
       447: 2q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 1
       458: 2q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: 2q+1
       465: 2q+1
       466: q^2+3q+1
       467: 2q+1
       468: q+1
       469: q+1
       470: 2q+1
       471: 2q+1
       472: 2q+1
       473: 2q+1
       474: q^2+3q+1
       475: q^2+3q+1
       476: 2q^2+3q+1
       477: 2q+1
       478: q+1
       479: q^2+3q+1
       480: q^2+3q+1
       481: q+1
       482: 2q+1
       483: 2q+1
       484: 2q+1
       485: q^2+2q+1
       486: q+1
       487: q^2+2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: q+1
       493: q+1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: 2q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       511: 2q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       521: 1
       522: 2q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: 2q+1
       530: q+1
       531: 2q+1
       532: q+1
       533: q+1
       534: q+1
       536: q+1
       543: 1
       544: 1
       545: 2q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       553: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       563: 2q+1
       564: 2q^2+3q+1
       565: q^2+3q+1
       566: 2q^2+3q+1
       567: 2q+1
       568: q+1
       569: q^2+3q+1
       570: q^2+3q+1
       571: 2q+1
       572: 2q+1
       573: q^2+3q+1
       574: q^2+3q+1
       575: 2q^2+3q+1
       576: q^2+3q+1
       577: 2q^2+3q+1
       578: q^2+3q+1
       579: q^2+3q+1
       580: q^2+3q+1
       581: 2q+1
       582: 2q+1
       583: 2q^2+3q+1
       584: 2q+1
       585: q^2+2q+1
       586: q^2+2q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: q^2+3q+1
       593: q+1
       594: 1
       595: q+1
       596: q+1
       597: q+1
       598: q+1
       599: 2q+1
       600: q^2+3q+1
       601: q+1
       602: q+1
       603: 2q+1
       604: q+1
       605: 2q+1
       606: 2q+1
       607: 2q+1
       608: 1
       609: q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: q+1
       613: 2q+1
       614: q+1
       615: 2q+1
       616: q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: q+1
       621: 2q+1
       622: q^2+2q+1
       623: q+1
       624: 2q+1
       625: q+1
       626: q+1
       627: q+1
       629: q+1
       631: q+1
       634: 1
       635: 2q+1
       636: 2q+1
       637: q+1
       638: 1
       639: 2q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       646: q+1
       647: q+1
       648: q+1
       649: 2q+1
       650: 2q+1
       651: 2q+1
       652: q+1
       653: q+1
       654: 1
       655: q+1
       656: 2q+1
       657: 2q+1
       658: q+1
       659: q^2+3q+1
       660: 2q+1
       661: q+1
       662: q+1
       663: 2q+1
       664: q+1
       665: q+1
       666: q+1
       667: 2q+1
       668: q+1
       669: q^2+2q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       676: 1
       677: q+1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: q+1
       707: 1
       708: 1
       710: q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       717: 1
       718: 2q+1
       719: q+1
       721: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: q+1
       752: 1
       755: 2q+1
       756: 2q+1
       757: q^2+3q+1
       758: 2q+1
       759: q+1
       760: q+1
       761: 2q+1
       762: 2q+1
       763: 2q+1
       764: 2q+1
       765: q^2+3q+1
       766: q^2+3q+1
       767: 2q^2+3q+1
       768: 2q+1
       769: q+1
       770: q^2+3q+1
       771: q^2+3q+1
       772: q+1
       773: 2q+1
       774: 2q+1
       775: 2q+1
       776: q^2+2q+1
       777: q+1
       778: q^2+2q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: q+1
       784: q+1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: 2q+1
       795: q+1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       802: 2q+1
       803: q+1
       804: 1
       805: q+1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: q+1
       810: q+1
       812: 1
       813: 2q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: 2q+1
       821: q+1
       822: 2q+1
       823: q+1
       824: q+1
       825: q+1
       827: q+1
       834: 1
       835: 1
       836: 2q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: 1
       842: 1
       844: q+1
       846: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       854: 2q+1
       855: q+1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: q+1
       861: q+1
       862: q+1
       863: 2q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: q+1
       869: q+1
       870: 1
       871: q+1
       872: q+1
       875: q+1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       909: 1
       911: 1
       913: q+1
       914: q+1
       916: q+1
       918: 1
       919: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: 1
       942: 1
       953: 1
       960: 2q+1
       961: 2q+1
       962: 2q+1
       963: q+1
       964: q+1
       965: 1
       966: q+1
       967: 2q+1
       968: 2q+1
       969: q+1
       970: q^2+3q+1
       971: 2q+1
       972: q+1
       973: q+1
       974: 2q+1
       975: q+1
       976: q+1
       977: q+1
       978: 2q+1
       979: q+1
       980: q^2+2q+1
       981: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       987: 1
       988: q+1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1018: 1
      1019: 1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1028: 1
      1029: 2q+1
      1030: q+1
      1032: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: q+1
      1063: 1
      1066: q+1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1113: q+1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1139: 1
      1141: 1
      1142: 1
      1165: 2q+1
      1166: q+1
      1167: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: q+1
      1172: q+1
      1173: q+1
      1174: 2q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: q+1
      1180: q+1
      1181: 1
      1182: q+1
      1183: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1220: 1
      1222: 1
      1224: q+1
      1225: q+1
      1227: q+1
      1229: 1
      1230: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: 1
      1253: 1
      1264: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1303: 1
      1311: 1
      1333: 1
      1357: q+1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: q+1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1403: 1
      1404: q+1
      1406: 1
      1409: 1
      1414: 1
      1428: 1
      1430: 1
      1432: 1
      1433: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1467: 1
      1471: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1554: 1
      1555: 1
      1557: 1
      1565: 1
      1587: 1
      1612: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1673: 1
      1677: 1
      1766: 1

1767:    0: q^4+4q^3+5q^2+3q+1
         1: 2q^3+5q^2+3q+1
         2: q^4+4q^3+5q^2+3q+1
         3: q^4+4q^3+5q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: q^4+4q^3+5q^2+3q+1
         6: 2q^3+5q^2+3q+1
         7: 2q^3+5q^2+3q+1
         8: q^4+4q^3+5q^2+3q+1
         9: 2q^3+5q^2+3q+1
        10: q^4+4q^3+5q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: q^3+2q^2+3q+1
        13: q^3+4q^2+3q+1
        14: 2q^3+4q^2+3q+1
        15: 2q^3+4q^2+3q+1
        16: 2q^3+5q^2+3q+1
        17: q^4+4q^3+5q^2+3q+1
        18: q^4+4q^3+5q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: 2q^3+5q^2+3q+1
        21: 2q^3+5q^2+3q+1
        22: 2q^3+5q^2+3q+1
        23: 2q^3+4q^2+3q+1
        24: q^3+2q^2+3q+1
        25: 2q^3+5q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^4+4q^3+5q^2+3q+1
        28: q^3+4q^2+3q+1
        29: 2q^3+4q^2+3q+1
        30: 2q^2+3q+1
        31: q^3+2q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+4q^2+3q+1
        34: q^3+4q^2+3q+1
        35: 2q^3+4q^2+3q+1
        36: q^3+4q^2+3q+1
        37: 2q^3+4q^2+3q+1
        38: 2q^2+3q+1
        39: q^3+2q^2+3q+1
        40: 2q^3+5q^2+3q+1
        41: 2q^3+5q^2+3q+1
        42: q^4+4q^3+5q^2+3q+1
        43: 2q^3+5q^2+3q+1
        44: q^4+4q^3+5q^2+3q+1
        45: 2q^3+4q^2+3q+1
        46: q^3+2q^2+3q+1
        47: q^3+4q^2+3q+1
        48: 2q^3+4q^2+3q+1
        49: 2q^3+4q^2+3q+1
        50: 2q^2+2q+1
        51: q^2+q+1
        52: 2q^3+5q^2+3q+1
        53: 2q^3+5q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: 2q^3+5q^2+3q+1
        58: q^3+3q^2+3q+1
        59: q^3+3q^2+3q+1
        60: 2q^3+4q^2+3q+1
        61: q^3+2q^2+3q+1
        62: q^3+4q^2+3q+1
        63: 2q^2+3q+1
        64: 2q^3+4q^2+3q+1
        65: 2q^2+3q+1
        66: q^2+3q+1
        67: q^3+2q^2+3q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: 2q^2+3q+1
        71: q^3+4q^2+3q+1
        72: q^3+4q^2+3q+1
        73: q^3+4q^2+3q+1
        74: 2q^2+3q+1
        75: q^3+2q^2+3q+1
        76: q^3+4q^2+3q+1
        77: q^2+2q+1
        78: 2q^3+4q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: q^3+2q^2+3q+1
        83: q^2+3q+1
        84: 2q^3+5q^2+3q+1
        85: 2q^3+5q^2+3q+1
        86: 2q^3+5q^2+3q+1
        87: 2q^3+4q^2+3q+1
        88: q^3+2q^2+3q+1
        89: 2q^3+5q^2+3q+1
        90: q^3+3q^2+3q+1
        91: q^4+4q^3+5q^2+3q+1
        92: q^3+4q^2+3q+1
        93: 2q^3+4q^2+3q+1
        94: 2q^2+3q+1
        95: q^3+2q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^3+4q^2+3q+1
       100: q^3+4q^2+3q+1
       101: 2q^3+4q^2+3q+1
       102: 2q^2+3q+1
       103: q^3+2q^2+3q+1
       104: q+1
       105: 2q^2+2q+1
       106: q^2+q+1
       107: 2q^3+5q^2+3q+1
       108: q^3+4q^2+3q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       111: 2q^2+3q+1
       112: 2q^2+2q+1
       113: q^2+q+1
       114: q^3+3q^2+3q+1
       115: q^3+3q^2+3q+1
       116: 2q^2+3q+1
       117: q^2+3q+1
       118: 2q^2+3q+1
       119: q^3+4q^2+3q+1
       120: 2q^2+3q+1
       121: 2q^2+3q+1
       122: 2q^3+4q^2+3q+1
       123: q^2+q+1
       124: 2q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: 2q+1
       128: q^3+2q^2+3q+1
       129: 2q^2+3q+1
       130: q^2+3q+1
       131: 2q^2+3q+1
       132: 2q^2+3q+1
       133: 2q^2+3q+1
       134: q^2+2q+1
       135: q^2+q+1
       136: q^3+4q^2+3q+1
       137: q^3+4q^2+3q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: q^2+3q+1
       141: q^3+4q^2+3q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: 2q^2+3q+1
       145: q^3+2q^2+3q+1
       146: 2q^2+3q+1
       147: 2q+1
       148: 2q^2+3q+1
       149: 2q^2+3q+1
       150: 2q+1
       151: q^3+2q^2+3q+1
       152: q^2+3q+1
       153: q^2+3q+1
       154: q^2+3q+1
       155: 2q^2+2q+1
       156: q^2+q+1
       157: 2q^3+5q^2+3q+1
       158: 2q^3+5q^2+3q+1
       159: q^3+4q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q^3+5q^2+3q+1
       163: q^3+3q^2+3q+1
       164: q^3+3q^2+3q+1
       165: 2q^3+4q^2+3q+1
       166: q^3+2q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 2q^2+3q+1
       169: 2q^3+4q^2+3q+1
       170: 2q^2+3q+1
       171: q^2+3q+1
       172: q^3+2q^2+3q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: 2q^2+3q+1
       176: q^3+4q^2+3q+1
       177: q^3+4q^2+3q+1
       178: q^3+4q^2+3q+1
       179: 2q^2+3q+1
       180: q^3+2q^2+3q+1
       181: q^3+4q^2+3q+1
       182: q^2+2q+1
       183: 2q^3+4q^2+3q+1
       184: 2q^2+3q+1
       185: 2q^2+3q+1
       186: 2q^2+3q+1
       187: q^3+2q^2+3q+1
       188: q^2+3q+1
       189: q+1
       190: q+1
       191: 2q^2+2q+1
       192: q^2+q+1
       193: q^3+4q^2+3q+1
       194: 2q^2+3q+1
       195: 2q^2+3q+1
       196: 2q^2+3q+1
       197: 2q^2+3q+1
       198: q+1
       199: q^2+2q+1
       200: q+1
       201: q^3+3q^2+3q+1
       202: 2q^2+3q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: 2q^2+3q+1
       206: 2q^2+2q+1
       207: q^2+1
       208: 2q^2+3q+1
       209: 2q^2+3q+1
       210: 2q^2+3q+1
       211: q+1
       212: q^2+q+1
       213: q+1
       214: q^2+q+1
       215: q^2+3q+1
       216: q^2+3q+1
       217: 2q+1
       218: q^2+3q+1
       219: 2q+1
       220: 2q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: 2q+1
       224: q^2+q+1
       225: 2q^2+3q+1
       226: q+1
       227: 2q^2+3q+1
       228: q+1
       229: q^2+2q+1
       230: q^2+q+1
       231: q^3+4q^2+3q+1
       232: 2q^2+3q+1
       233: 2q^2+3q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: q^2+2q+1
       237: q^2+q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: 2q+1
       241: 2q+1
       242: q^2+3q+1
       243: 2q^2+3q+1
       244: 2q+1
       245: 2q+1
       246: 2q^2+3q+1
       248: 2q^2+3q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: q^3+2q^2+3q+1
       253: q^2+3q+1
       254: 2q+1
       255: q^2+3q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: q+1
       259: 2q^2+2q+1
       260: q^2+q+1
       261: 2q^3+5q^2+3q+1
       262: q^3+4q^2+3q+1
       263: 2q^2+3q+1
       264: 2q^2+3q+1
       265: 2q^2+3q+1
       266: 2q^2+2q+1
       267: q^2+q+1
       268: q^3+3q^2+3q+1
       269: q^3+3q^2+3q+1
       270: 2q^2+3q+1
       271: q^2+3q+1
       272: 2q^2+3q+1
       273: q^3+4q^2+3q+1
       274: 2q^2+3q+1
       275: 2q^2+3q+1
       276: 2q^3+4q^2+3q+1
       277: q^2+q+1
       278: 2q^2+3q+1
       279: q^2+3q+1
       280: q^2+3q+1
       281: 2q+1
       282: q^3+2q^2+3q+1
       283: 2q^2+3q+1
       284: q^2+3q+1
       285: 2q^2+3q+1
       286: 2q^2+3q+1
       287: 2q^2+3q+1
       288: q^2+2q+1
       289: q^2+q+1
       290: q^3+4q^2+3q+1
       291: q^3+4q^2+3q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: q^2+3q+1
       295: q^3+4q^2+3q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: 2q^2+3q+1
       299: q^3+2q^2+3q+1
       300: 2q^2+3q+1
       301: 2q+1
       302: 2q^2+3q+1
       303: 2q^2+3q+1
       304: 2q+1
       305: q^3+2q^2+3q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: q^2+3q+1
       309: q+1
       310: q+1
       311: q+1
       312: 2q^2+2q+1
       313: q^2+1
       314: q+1
       315: q^2+q+1
       316: 2q^2+3q+1
       317: 2q^2+3q+1
       318: q+1
       319: q+1
       320: q+1
       321: q^2+2q+1
       322: q+1
       323: 2q^2+3q+1
       324: q^2+3q+1
       325: q^2+3q+1
       326: q^2+3q+1
       327: 2q^2+3q+1
       328: 1
       329: q^2+2q+1
       330: 1
       331: 2q^2+3q+1
       332: 2q^2+3q+1
       333: q+1
       334: q+1
       335: q^2+q+1
       336: 1
       337: q+1
       338: q+1
       339: q^2+3q+1
       340: 2q+1
       341: q^2+3q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: q^2+1
       346: q^2+3q+1
       347: q^2+3q+1
       348: 2q+1
       349: q+1
       350: q+1
       351: 2q^2+3q+1
       352: q+1
       353: q+1
       354: 2q+1
       355: q^2+q+1
       356: q+1
       357: q+1
       358: q^2+2q+1
       359: q^2+q+1
       360: 2q^2+3q+1
       361: 2q^2+3q+1
       362: q^2+3q+1
       363: q^2+3q+1
       364: q^2+3q+1
       365: q+1
       366: q+1
       367: q+1
       368: q^2+2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q^2+3q+1
       373: q^2+2q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       380: q+1
       381: q^2+q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: 2q+1
       387: q^2+3q+1
       388: 2q+1
       389: 2q+1
       390: 2q+1
       392: q^2+3q+1
       393: q+1
       394: q^2+3q+1
       395: q+1
       396: q+1
       397: 2q^2+2q+1
       398: q^2+q+1
       399: q^3+4q^2+3q+1
       400: 2q^2+3q+1
       401: 2q^2+3q+1
       402: 2q^2+3q+1
       403: 2q^2+3q+1
       404: q+1
       405: q^2+2q+1
       406: q+1
       407: q^3+3q^2+3q+1
       408: 2q^2+3q+1
       409: q^2+3q+1
       410: q^2+3q+1
       411: 2q^2+3q+1
       412: 2q^2+2q+1
       413: q^2+1
       414: 2q^2+3q+1
       415: 2q^2+3q+1
       416: 2q^2+3q+1
       417: q+1
       418: q^2+q+1
       419: q+1
       420: q^2+q+1
       421: q^2+3q+1
       422: q^2+3q+1
       423: 2q+1
       424: q^2+3q+1
       425: 2q+1
       426: 2q^2+3q+1
       427: q^2+3q+1
       428: q^2+3q+1
       429: 2q+1
       430: q^2+q+1
       431: 2q^2+3q+1
       432: q+1
       433: 2q^2+3q+1
       434: q+1
       435: q^2+2q+1
       436: q^2+q+1
       437: q^3+4q^2+3q+1
       438: 2q^2+3q+1
       439: 2q^2+3q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: q^2+2q+1
       443: q^2+q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: 2q+1
       447: 2q+1
       448: q^2+3q+1
       449: 2q^2+3q+1
       450: 2q+1
       451: 2q+1
       452: 2q^2+3q+1
       454: 2q^2+3q+1
       455: 2q+1
       456: 2q+1
       457: 2q+1
       458: q^3+2q^2+3q+1
       459: q^2+3q+1
       460: 2q+1
       461: q^2+3q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: q+1
       470: q^2+1
       471: 2q^2+3q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q^2+2q+1
       477: 1
       478: q+1
       479: q+1
       480: q^2+3q+1
       481: q^2+3q+1
       482: q+1
       483: 1
       484: 1
       485: q^2+2q+1
       486: 1
       487: 2q^2+3q+1
       488: q+1
       489: q+1
       490: q+1
       491: q^2+q+1
       492: 1
       493: 1
       494: q+1
       495: q+1
       496: 2q+1
       497: q^2+3q+1
       498: 2q+1
       499: 2q+1
       500: 2q+1
       501: 1
       502: q+1
       503: 1
       504: q^2+3q+1
       505: 2q+1
       506: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q^2+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q^2+2q+1
       521: q+1
       522: q^2+q+1
       523: q^2+3q+1
       524: q^2+3q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q^2+3q+1
       536: q+1
       538: 2q+1
       539: 2q+1
       543: 1
       544: 1
       545: q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 2q+1
       551: q+1
       553: 2q+1
       554: 2q+1
       555: q+1
       558: q^2+3q+1
       559: q+1
       560: q+1
       561: 2q+1
       563: q+1
       564: q+1
       565: q+1
       566: 2q^2+2q+1
       567: q^2+1
       568: q+1
       569: q^2+q+1
       570: 2q^2+3q+1
       571: 2q^2+3q+1
       572: q+1
       573: q+1
       574: q+1
       575: q^2+2q+1
       576: q+1
       577: 2q^2+3q+1
       578: q^2+3q+1
       579: q^2+3q+1
       580: q^2+3q+1
       581: 2q^2+3q+1
       582: 1
       583: q^2+2q+1
       584: 1
       585: 2q^2+3q+1
       586: 2q^2+3q+1
       587: q+1
       588: q+1
       589: q^2+q+1
       590: 1
       591: q+1
       592: q+1
       593: q^2+3q+1
       594: 2q+1
       595: q^2+3q+1
       596: 2q+1
       597: 2q+1
       598: q+1
       599: q^2+1
       600: q^2+3q+1
       601: q^2+3q+1
       602: 2q+1
       603: q+1
       604: q+1
       605: 2q^2+3q+1
       606: q+1
       607: q+1
       608: 2q+1
       609: q^2+q+1
       610: q+1
       611: q+1
       612: q^2+2q+1
       613: q^2+q+1
       614: 2q^2+3q+1
       615: 2q^2+3q+1
       616: q^2+3q+1
       617: q^2+3q+1
       618: q^2+3q+1
       619: q+1
       620: q+1
       621: q+1
       622: q^2+2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: q^2+3q+1
       627: q^2+2q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       634: q+1
       635: q^2+q+1
       636: 2q+1
       637: 2q+1
       638: q+1
       639: 2q+1
       640: 2q+1
       641: q^2+3q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       646: q^2+3q+1
       647: q+1
       648: q^2+3q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: q+1
       655: q^2+1
       656: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: 1
       664: q^2+3q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q^2+2q+1
       670: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       681: q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: 2q+1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: q+1
       705: q+1
       707: 1
       708: q+1
       710: q^2+3q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       717: 1
       718: q+1
       719: 2q+1
       720: 2q+1
       721: q+1
       724: q+1
       726: 2q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: 2q+1
       737: q+1
       738: q+1
       739: 2q+1
       741: 1
       743: 2q+1
       744: q+1
       748: q+1
       750: q+1
       751: q+1
       752: 1
       756: q+1
       757: q+1
       758: 1
       759: 1
       760: q+1
       761: q^2+1
       762: 2q^2+3q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q^2+2q+1
       768: 1
       769: q+1
       770: q+1
       771: q^2+3q+1
       772: q^2+3q+1
       773: q+1
       774: 1
       775: 1
       776: q^2+2q+1
       777: 1
       778: 2q^2+3q+1
       779: q+1
       780: q+1
       781: q+1
       782: q^2+q+1
       783: 1
       784: 1
       785: q+1
       786: q+1
       787: 2q+1
       788: q^2+3q+1
       789: 2q+1
       790: 2q+1
       791: 2q+1
       792: 1
       793: q+1
       794: 1
       795: q^2+3q+1
       796: 2q+1
       797: q+1
       798: q+1
       799: q+1
       800: q+1
       801: q^2+1
       802: q+1
       803: q+1
       804: 1
       805: 1
       806: q+1
       807: q+1
       808: q+1
       809: q+1
       810: q^2+2q+1
       812: q+1
       813: q^2+q+1
       814: q^2+3q+1
       815: q^2+3q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q^2+3q+1
       827: q+1
       829: 2q+1
       830: 2q+1
       834: 1
       835: 1
       836: q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: q+1
       841: 2q+1
       842: q+1
       844: 2q+1
       845: 2q+1
       846: q+1
       849: q^2+3q+1
       850: q+1
       851: q+1
       852: 2q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: q+1
       867: 1
       868: q+1
       870: 1
       871: 1
       872: 1
       875: 1
       876: q+1
       877: 1
       879: 1
       880: 1
       882: 1
       883: q+1
       885: 2q+1
       886: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       893: 1
       894: q+1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: q+1
       907: q+1
       909: 1
       911: q+1
       913: q+1
       915: q+1
       916: q+1
       918: 1
       919: 1
       921: 2q+1
       922: q+1
       926: q+1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: q+1
       941: q+1
       942: 1
       945: 1
       947: q+1
       953: 1
       955: q+1
       956: 1
       961: q+1
       962: 1
       963: 1
       964: 1
       965: q+1
       966: q^2+1
       967: q+1
       969: q+1
       970: q+1
       971: 1
       972: 1
       973: q+1
       974: 1
       975: q^2+3q+1
       976: q+1
       977: 1
       978: 1
       979: 1
       980: q^2+2q+1
       981: 1
       983: 1
       984: q+1
       985: q+1
       986: 1
       987: 1
       988: 1
       989: 1
       990: q+1
       992: q+1
       993: q+1
       994: 2q+1
       995: 2q+1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: 2q+1
      1002: q+1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: 1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: q+1
      1015: q+1
      1016: q+1
      1018: 1
      1019: q+1
      1021: q^2+3q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1028: 1
      1029: q+1
      1030: 2q+1
      1031: 2q+1
      1032: q+1
      1035: q+1
      1037: 2q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: 2q+1
      1048: q+1
      1049: q+1
      1050: 2q+1
      1052: 1
      1054: 2q+1
      1055: q+1
      1059: q+1
      1061: q+1
      1062: q+1
      1063: 1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1087: 1
      1089: 1
      1091: q+1
      1093: 1
      1095: 1
      1096: 1
      1101: q+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1115: 1
      1118: 1
      1121: q+1
      1123: 1
      1125: 1
      1127: q+1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: q+1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1173: q+1
      1174: 1
      1175: 1
      1176: 1
      1177: q+1
      1178: 1
      1179: q+1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: q+1
      1188: 1
      1190: 1
      1191: 1
      1193: 1
      1194: q+1
      1196: 2q+1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1204: 1
      1205: q+1
      1206: q+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: q+1
      1220: 1
      1222: q+1
      1224: q+1
      1226: q+1
      1227: q+1
      1229: 1
      1230: 1
      1232: 2q+1
      1233: q+1
      1237: q+1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: q+1
      1252: q+1
      1253: 1
      1256: 1
      1258: q+1
      1264: 1
      1266: q+1
      1267: 1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: 1
      1285: 1
      1288: 1
      1291: 1
      1294: 1
      1300: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1317: 1
      1320: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1378: 1
      1380: 1
      1382: q+1
      1384: 1
      1386: 1
      1387: 1
      1392: q+1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1406: 1
      1409: 1
      1412: q+1
      1414: 1
      1416: 1
      1418: q+1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: q+1
      1436: 1
      1440: 1
      1449: 1
      1451: 1
      1457: 1
      1459: 1
      1460: 1
      1479: 1
      1485: 1
      1503: 1
      1506: 1
      1526: 1
      1527: 1
      1530: 1
      1531: 1
      1532: 1
      1534: 1
      1539: 1
      1542: 1
      1545: 1
      1548: 1
      1554: 1
      1556: 1
      1557: 1
      1562: 1
      1563: 1
      1571: 1
      1574: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1604: 1
      1613: 1
      1663: 1
      1665: 1
      1666: 1
      1685: 1
      1691: 1
      1709: 1
      1712: 1
      1767: 1

1768:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: 1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: 1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: 1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: 1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: 1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: 1
       195: q+1
       196: 1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       244: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       256: 1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: 1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       388: 1
       392: 1
       393: 1
       395: 1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: 1
       403: 1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       450: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       521: 1
       522: 1
       524: 1
       525: 1
       527: 1
       528: 1
       529: 1
       531: 1
       532: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       559: 1
       563: 1
       564: 1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       642: 1
       646: 1
       647: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: q+1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: 1
       704: 1
       707: 1
       711: 1
       714: 1
       717: 1
       718: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       755: 1
       756: 1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       812: 1
       813: 1
       815: 1
       816: 1
       818: 1
       819: 1
       820: 1
       822: 1
       823: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       850: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       906: 1
       918: 1
       935: 1
       938: 1
       939: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1014: 1
      1015: 1
      1018: 1
      1022: 1
      1025: 1
      1028: 1
      1029: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1094: 1
      1095: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1141: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1217: 1
      1229: 1
      1246: 1
      1249: 1
      1250: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1293: 1
      1305: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1396: 1
      1399: 1
      1400: 1
      1432: 1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1547: 1
      1559: 1
      1614: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1768: 1

1769:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: 1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: q^2+1
        51: 1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: 1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: q^2+1
       106: 1
       107: q^2+1
       108: q^2+1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       113: 1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: 1
       118: 1
       119: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q^2+1
       156: 1
       157: q^2+1
       158: q^2+1
       159: q^2+1
       160: 1
       161: 1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q^2+1
       192: 1
       193: q^2+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q^2+1
       200: 1
       201: q^2+1
       202: q^2+1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       207: 1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q^2+1
       260: 1
       261: q^2+1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       267: 1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: 1
       273: q^2+1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: q^2+1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: q^2+1
       322: 1
       323: q^2+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q^2+1
       330: 1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       372: 1
       373: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: q^2+1
       398: 1
       399: q^2+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q^2+1
       406: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: q^2+1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q^2+1
       486: 1
       487: q^2+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       543: 1
       550: 1
       551: 1
       558: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q^2+1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: q^2+1
       576: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q^2+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       646: 1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q^2+1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       731: 1
       739: 1
       748: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: q^2+1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       834: 1
       841: 1
       842: 1
       849: 1
       852: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       909: 1
       911: 1
       933: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: q^2+1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1042: 1
      1050: 1
      1059: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1115: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1244: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1359: 1
      1360: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1394: 1
      1406: 1
      1459: 1
      1463: 1
      1464: 1
      1473: 1
      1526: 1
      1530: 1
      1531: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1542: 1
      1548: 1
      1550: 1
      1552: 1
      1615: 1
      1665: 1
      1669: 1
      1670: 1
      1679: 1
      1769: 1

1770:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q+1
        62: q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: 1
       114: q+1
       115: q+1
       116: q^2+q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: q+1
       214: 1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       310: 1
       311: 1
       312: q+1
       313: 1
       314: q+1
       315: 1
       316: q+1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: q+1
       470: 1
       471: 1
       472: 1
       474: 1
       475: 1
       476: q+1
       477: 1
       478: q+1
       479: 1
       480: q+1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       564: 1
       565: 1
       566: q+1
       567: 1
       568: q+1
       569: 1
       570: q+1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: 1
       591: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: 1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       659: 1
       660: 1
       661: 1
       662: q+1
       663: 1
       664: 1
       665: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: 1
       675: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       757: 1
       758: 1
       759: 1
       760: q+1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: q+1
       768: 1
       769: q+1
       770: 1
       771: q+1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       909: 1
       911: 1
       913: 1
       916: 1
       918: 1
       919: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       942: 1
       953: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       970: 1
       971: 1
       972: 1
       973: q+1
       974: 1
       975: 1
       976: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       985: 1
       986: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1093: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1118: 1
      1123: 1
      1139: 1
      1141: 1
      1142: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1187: 1
      1188: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1220: 1
      1222: 1
      1224: 1
      1227: 1
      1229: 1
      1230: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1253: 1
      1264: 1
      1273: 1
      1277: 1
      1278: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1291: 1
      1296: 1
      1298: 1
      1300: 1
      1303: 1
      1305: 1
      1306: 1
      1333: 1
      1360: 1
      1361: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1380: 1
      1382: 1
      1384: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1403: 1
      1409: 1
      1414: 1
      1430: 1
      1432: 1
      1433: 1
      1460: 1
      1464: 1
      1465: 1
      1476: 1
      1481: 1
      1527: 1
      1531: 1
      1532: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1545: 1
      1550: 1
      1552: 1
      1554: 1
      1557: 1
      1559: 1
      1560: 1
      1587: 1
      1616: 1
      1666: 1
      1670: 1
      1671: 1
      1682: 1
      1687: 1
      1770: 1

1771:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 2q^2+3q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 2q^2+3q+1
        43: 2q^2+3q+1
        44: q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: 2q^2+3q+1
        51: 2q^2+3q+1
        52: 2q^2+3q+1
        53: q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 2q^2+3q+1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: 2q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+2q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: q^2+2q+1
        71: 2q^2+3q+1
        72: q^3+3q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q^2+3q+1
        80: 2q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: 2q^2+3q+1
        84: 2q^2+3q+1
        85: q^3+3q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: 2q^2+3q+1
        93: q^2+3q+1
        94: 2q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 2q^2+3q+1
       105: 2q^2+3q+1
       106: 2q^2+3q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: 2q^2+3q+1
       111: q^2+2q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q^2+3q+1
       118: q^2+3q+1
       119: 2q+1
       120: q^2+3q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q^2+2q+1
       125: q^2+3q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q+1
       132: q^2+2q+1
       133: q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: 2q^2+3q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q^2+3q+1
       153: 2q+1
       154: q^2+2q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 2q^2+3q+1
       158: q^2+3q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+3q+1
       169: 2q+1
       170: q^2+3q+1
       171: q^2+3q+1
       172: q^2+2q+1
       173: 2q^2+3q+1
       174: q^2+3q+1
       175: q^2+2q+1
       176: 2q^2+3q+1
       177: q^3+3q^2+3q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q^2+3q+1
       185: 2q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: 2q^2+3q+1
       189: q^2+2q+1
       190: 2q^2+3q+1
       191: q^2+3q+1
       192: q^2+3q+1
       193: 2q+1
       194: q^2+2q+1
       195: q^2+3q+1
       196: q^2+2q+1
       197: q+1
       198: q^2+3q+1
       199: q^2+3q+1
       200: q^2+3q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q^2+2q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+3q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: 1
       228: 2q^2+3q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q^2+3q+1
       235: q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: 2q^2+3q+1
       259: 2q^2+3q+1
       260: 2q^2+3q+1
       261: q^2+3q+1
       262: q^2+3q+1
       263: q^2+3q+1
       264: 2q^2+3q+1
       265: q^2+2q+1
       266: q^2+3q+1
       267: q^2+3q+1
       268: q^2+3q+1
       269: q^2+3q+1
       270: q^2+3q+1
       271: q^2+3q+1
       272: q^2+3q+1
       273: 2q+1
       274: q^2+3q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: q^2+2q+1
       279: q^2+3q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: q^2+3q+1
       284: q^2+3q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: 2q^2+3q+1
       289: 2q^2+3q+1
       290: 2q^2+3q+1
       291: 2q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: 2q^2+3q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q^2+3q+1
       307: 2q+1
       308: q^2+2q+1
       309: q+1
       310: q^2+2q+1
       311: q^2+3q+1
       312: 2q+1
       313: 2q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+3q+1
       321: q^2+3q+1
       322: q^2+3q+1
       323: 2q+1
       324: q^2+2q+1
       325: q^2+3q+1
       326: q+1
       327: 1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: q^2+2q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q^2+2q+1
       357: 2q^2+3q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q^2+2q+1
       396: 2q^2+3q+1
       397: q^2+3q+1
       398: q^2+3q+1
       399: 2q+1
       400: q^2+2q+1
       401: q^2+3q+1
       402: q^2+2q+1
       403: q+1
       404: q^2+3q+1
       405: q^2+3q+1
       406: q^2+3q+1
       407: q^2+3q+1
       408: q^2+3q+1
       409: q^2+3q+1
       410: q^2+3q+1
       411: q+1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: q^2+2q+1
       420: q^2+2q+1
       421: q^2+2q+1
       422: q+1
       423: q^2+2q+1
       424: q^2+2q+1
       425: q^2+2q+1
       426: q+1
       427: q^2+3q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: 1
       434: 2q^2+3q+1
       435: 2q^2+3q+1
       436: 2q^2+3q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: 2q+1
       468: q^2+2q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       473: 1
       474: q+1
       475: q^2+3q+1
       476: 2q+1
       477: 2q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       489: q+1
       490: q+1
       491: 1
       492: q+1
       493: q^2+2q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q^2+2q+1
       565: q^2+3q+1
       566: 2q+1
       567: 2q+1
       568: q^2+2q+1
       569: q^2+2q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q^2+3q+1
       575: q^2+3q+1
       576: q^2+3q+1
       577: 2q+1
       578: q^2+2q+1
       579: q^2+3q+1
       580: q+1
       581: 1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: q+1
       590: q^2+2q+1
       591: q^2+2q+1
       592: q^2+2q+1
       593: q+1
       594: q+1
       595: q+1
       596: q^2+2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: 2q+1
       661: q^2+2q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: q+1
       758: 2q+1
       759: q^2+2q+1
       760: q+1
       761: q+1
       762: 1
       763: q+1
       764: 1
       765: q+1
       766: q^2+3q+1
       767: 2q+1
       768: 2q+1
       769: q^2+2q+1
       770: q^2+2q+1
       771: q+1
       772: 1
       773: 1
       774: q+1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       780: q+1
       781: q+1
       782: 1
       783: q+1
       784: q^2+2q+1
       785: q+1
       786: q+1
       787: 1
       788: q+1
       789: q+1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: q+1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       960: q+1
       961: 1
       962: q+1
       963: q+1
       964: q+1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: q+1
       971: 2q+1
       972: q^2+2q+1
       973: q+1
       974: q+1
       975: 1
       976: 1
       977: 1
       978: q+1
       979: q+1
       980: q+1
       981: q+1
       985: 1
       986: 1
       987: 1
       988: q+1
       989: q+1
       990: 1
       991: 1
       992: q+1
       993: q+1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1157: 1
      1165: 1
      1166: 1
      1167: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: q+1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1214: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1249: q+1
      1250: q+1
      1251: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1304: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1338: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1377: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1388: 1
      1393: 1
      1396: 1
      1397: 1
      1398: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1428: 1
      1430: 1
      1431: 1
      1432: q+1
      1433: 1
      1434: 1
      1437: 1
      1438: 1
      1446: 1
      1448: 1
      1458: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1486: 1
      1504: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1558: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1572: 1
      1586: 1
      1587: 1
      1588: 1
      1592: 1
      1617: 1
      1664: 1
      1672: 1
      1673: 1
      1674: 1
      1676: 1
      1692: 1
      1710: 1
      1771: 1

1772:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q^2+q+1
        58: q^2+1
        59: q^2+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: 1
        64: q+1
        65: q^2+q+1
        66: q^2+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+1
        91: q^2+q+1
        92: q+1
        93: q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q+1
       109: q^2+q+1
       110: q+1
       111: q+1
       112: q+1
       113: q^2+q+1
       114: q^2+1
       115: q^2+1
       116: 1
       117: q^2+1
       118: q+1
       119: q+1
       120: 1
       121: 1
       122: q+1
       123: q+1
       124: q^2+q+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+q+1
       129: q+1
       130: 1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       148: q+1
       149: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q^2+q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q+1
       160: q^2+q+1
       161: q+1
       162: q^2+q+1
       163: q^2+1
       164: q^2+1
       165: q+1
       166: q^2+q+1
       167: q+1
       168: 1
       169: q+1
       170: q^2+q+1
       171: q^2+1
       172: q^2+q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q+1
       180: q^2+q+1
       181: q^2+q+1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: q^2+q+1
       187: q^2+q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^2+q+1
       193: q+1
       194: q^2+q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: 1
       200: q^2+1
       201: q^2+1
       202: 1
       203: q^2+1
       204: 1
       205: q+1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: q^2+q+1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: q+1
       221: 1
       222: 1
       223: 1
       224: q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+q+1
       231: q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+q+1
       242: q+1
       243: q+1
       246: q+1
       247: q+1
       248: q^2+q+1
       251: 1
       252: q^2+q+1
       253: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+q+1
       261: q^2+q+1
       262: q+1
       263: q^2+q+1
       264: q+1
       265: q+1
       266: q+1
       267: q^2+q+1
       268: q^2+1
       269: q^2+1
       270: 1
       271: q^2+1
       272: q+1
       273: q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       278: q^2+q+1
       279: q^2+1
       280: q^2+1
       281: 1
       282: q^2+q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q^2+q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q+1
       293: q^2+q+1
       294: q+1
       295: q^2+q+1
       298: q+1
       299: q^2+q+1
       300: q+1
       302: q+1
       303: q^2+q+1
       305: q^2+q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: q^2+q+1
       316: q+1
       317: q+1
       319: q+1
       320: 1
       321: 1
       322: q^2+1
       323: 1
       324: q^2+1
       325: 1
       326: 1
       327: q+1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q^2+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       372: q+1
       373: q+1
       374: q+1
       379: q+1
       380: 1
       381: q^2+q+1
       386: 1
       387: q+1
       390: 1
       391: q+1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q^2+q+1
       399: q+1
       400: q^2+q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: 1
       406: q^2+1
       407: q^2+1
       408: 1
       409: q^2+1
       410: 1
       411: q+1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: q^2+q+1
       421: q^2+1
       422: q^2+1
       423: 1
       424: q^2+1
       425: 1
       426: q+1
       427: 1
       428: 1
       429: 1
       430: q+1
       431: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q^2+q+1
       437: q^2+q+1
       438: q+1
       439: q^2+q+1
       440: q+1
       441: q+1
       442: q+1
       443: q^2+q+1
       448: q+1
       449: q+1
       452: q+1
       453: q+1
       454: q^2+q+1
       457: 1
       458: q^2+q+1
       459: q+1
       461: q+1
       462: q+1
       463: q+1
       465: q+1
       466: q+1
       467: q+1
       468: 1
       469: 1
       470: q+1
       471: q+1
       473: q+1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: q^2+1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: q^2+q+1
       523: q+1
       524: q+1
       526: q+1
       534: q+1
       535: q+1
       542: q+1
       543: 1
       550: 1
       551: 1
       552: q+1
       557: 1
       558: q+1
       561: 1
       562: q+1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: q^2+q+1
       570: q+1
       571: q+1
       573: q+1
       574: 1
       575: 1
       576: q^2+1
       577: 1
       578: q^2+1
       579: 1
       580: 1
       581: q+1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       590: 1
       591: 1
       592: q^2+1
       593: q^2+1
       594: 1
       595: q^2+1
       596: 1
       597: 1
       598: 1
       599: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: q^2+q+1
       614: q+1
       615: q^2+q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       626: q+1
       627: q+1
       628: q+1
       633: q+1
       634: 1
       635: q^2+q+1
       640: 1
       641: q+1
       644: 1
       645: q+1
       646: q+1
       648: q+1
       650: q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: q^2+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: q+1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: q+1
       710: q+1
       712: q+1
       722: q+1
       730: q+1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       756: q+1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: q+1
       762: q+1
       764: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: q^2+1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q^2+1
       787: 1
       788: q^2+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: q+1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: q^2+q+1
       814: q+1
       815: q+1
       817: q+1
       825: q+1
       826: q+1
       833: q+1
       834: 1
       841: 1
       842: 1
       843: q+1
       848: 1
       849: q+1
       852: 1
       853: q+1
       855: q+1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: q+1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       923: q+1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       961: q+1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: q+1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: q^2+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: q+1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: q+1
      1021: q+1
      1023: q+1
      1033: q+1
      1041: q+1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: q+1
      1065: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1114: q+1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1156: 1
      1164: 1
      1166: q+1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: q+1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1234: q+1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1299: 1
      1312: 1
      1313: 1
      1347: 1
      1359: 1
      1360: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1375: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1394: 1
      1405: q+1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1447: 1
      1455: 1
      1459: 1
      1468: 1
      1469: 1
      1472: 1
      1487: 1
      1526: 1
      1530: 1
      1531: 1
      1534: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1548: 1
      1549: 1
      1553: 1
      1566: 1
      1567: 1
      1601: 1
      1618: 1
      1665: 1
      1674: 1
      1675: 1
      1678: 1
      1693: 1
      1772: 1

1773:    0: 2q^3+5q^2+3q+1
         1: 2q^3+5q^2+3q+1
         2: 2q^3+5q^2+3q+1
         3: 2q^3+5q^2+3q+1
         4: 2q^3+5q^2+3q+1
         5: 2q^3+5q^2+3q+1
         6: q^3+3q^2+3q+1
         7: 2q^3+5q^2+3q+1
         8: 2q^3+5q^2+3q+1
         9: 2q^3+5q^2+3q+1
        10: q^3+3q^2+3q+1
        11: q^3+4q^2+3q+1
        12: 2q^3+5q^2+3q+1
        13: 2q^3+5q^2+3q+1
        14: 2q^3+5q^2+3q+1
        15: 2q^3+5q^2+3q+1
        16: 2q^3+5q^2+3q+1
        17: 2q^3+5q^2+3q+1
        18: 2q^3+5q^2+3q+1
        19: 2q^3+5q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^3+5q^2+3q+1
        23: q^3+4q^2+3q+1
        24: 2q^3+5q^2+3q+1
        25: q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: q^3+4q^2+3q+1
        29: 2q^2+3q+1
        30: 2q^3+5q^2+3q+1
        31: q^3+3q^2+3q+1
        32: q^3+4q^2+3q+1
        33: q^3+3q^2+3q+1
        34: 2q^3+5q^2+3q+1
        35: 2q^3+5q^2+3q+1
        36: 2q^3+5q^2+3q+1
        37: q^2+2q+1
        38: q^3+3q^2+3q+1
        39: 2q^3+5q^2+3q+1
        40: q^3+3q^2+3q+1
        41: 2q^3+5q^2+3q+1
        42: 2q^3+5q^2+3q+1
        43: 2q^3+5q^2+3q+1
        44: q^3+3q^2+3q+1
        45: q^3+4q^2+3q+1
        46: 2q^3+5q^2+3q+1
        47: 2q^3+5q^2+3q+1
        48: 2q^3+5q^2+3q+1
        49: 2q^3+5q^2+3q+1
        50: q^2+2q+1
        51: q^3+3q^2+3q+1
        52: q^3+3q^2+3q+1
        53: q^2+3q+1
        54: q^3+4q^2+3q+1
        55: 2q^3+5q^2+3q+1
        56: q^3+4q^2+3q+1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^3+3q^2+3q+1
        60: 2q^2+3q+1
        61: q^3+3q^2+3q+1
        62: q^2+3q+1
        63: 2q^2+3q+1
        64: 2q^2+3q+1
        65: q^2+3q+1
        66: q^3+3q^2+3q+1
        67: q^3+3q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^2+3q+1
        70: q^3+4q^2+3q+1
        71: q^3+3q^2+3q+1
        72: q^3+3q^2+3q+1
        73: 2q^3+5q^2+3q+1
        74: q^3+3q^2+3q+1
        75: 2q^3+5q^2+3q+1
        76: 2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^3+3q^2+3q+1
        80: 2q+1
        81: 2q^3+5q^2+3q+1
        82: q^2+2q+1
        83: q^3+3q^2+3q+1
        84: q^3+3q^2+3q+1
        85: q^3+3q^2+3q+1
        86: 2q^3+5q^2+3q+1
        87: q^3+4q^2+3q+1
        88: 2q^3+5q^2+3q+1
        89: q^2+3q+1
        90: q^3+3q^2+3q+1
        91: q^3+3q^2+3q+1
        92: q^3+4q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^3+5q^2+3q+1
        95: q^3+3q^2+3q+1
        96: q^3+4q^2+3q+1
        97: q^3+3q^2+3q+1
        98: 2q^3+5q^2+3q+1
        99: 2q^3+5q^2+3q+1
       100: 2q^3+5q^2+3q+1
       101: q^2+2q+1
       102: q^3+3q^2+3q+1
       103: 2q^3+5q^2+3q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^3+3q^2+3q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^3+4q^2+3q+1
       111: q^3+4q^2+3q+1
       112: 2q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: q^2+3q+1
       116: 2q^2+3q+1
       117: q^3+3q^2+3q+1
       118: 2q^2+3q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: 2q^2+3q+1
       122: 2q^2+3q+1
       123: 2q^2+3q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^3+3q^2+3q+1
       127: q^2+2q+1
       128: q^3+3q^2+3q+1
       129: q^2+3q+1
       130: 2q^2+3q+1
       131: 2q^2+3q+1
       132: q^3+4q^2+3q+1
       133: q+1
       134: q^2+2q+1
       135: q^3+3q^2+3q+1
       136: q^3+3q^2+3q+1
       137: 2q+1
       138: q^3+3q^2+3q+1
       139: 2q^3+5q^2+3q+1
       140: q^3+3q^2+3q+1
       141: 2q+1
       142: 2q+1
       143: q^2+2q+1
       144: 2q+1
       145: q^2+2q+1
       146: 2q+1
       147: 2q+1
       148: 2q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^3+3q^2+3q+1
       153: 2q+1
       154: q^3+3q^2+3q+1
       155: q^2+2q+1
       156: q^3+3q^2+3q+1
       157: q^3+3q^2+3q+1
       158: q^2+3q+1
       159: q^3+4q^2+3q+1
       160: 2q^3+5q^2+3q+1
       161: q^3+4q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^3+3q^2+3q+1
       165: 2q^2+3q+1
       166: q^3+3q^2+3q+1
       167: q^2+3q+1
       168: 2q^2+3q+1
       169: 2q^2+3q+1
       170: q^2+3q+1
       171: q^3+3q^2+3q+1
       172: q^3+3q^2+3q+1
       173: q^3+4q^2+3q+1
       174: 2q^2+3q+1
       175: q^3+4q^2+3q+1
       176: q^3+3q^2+3q+1
       177: q^3+3q^2+3q+1
       178: 2q^3+5q^2+3q+1
       179: q^3+3q^2+3q+1
       180: 2q^3+5q^2+3q+1
       181: 2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^3+3q^2+3q+1
       185: 2q+1
       186: 2q^3+5q^2+3q+1
       187: q^2+2q+1
       188: q^3+3q^2+3q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: 2q+1
       192: q^2+3q+1
       193: q^2+3q+1
       194: q^2+3q+1
       195: q^2+3q+1
       196: q^3+4q^2+3q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: q^2+3q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: 2q^2+3q+1
       205: 2q^2+3q+1
       206: 2q+1
       207: q^2+3q+1
       208: q^2+3q+1
       209: q+1
       210: 2q^2+3q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: q+1
       214: q^2+3q+1
       215: q^2+3q+1
       216: q+1
       217: q^2+2q+1
       218: q^3+3q^2+3q+1
       219: q^2+2q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: 2q^2+3q+1
       223: q^2+2q+1
       224: 2q^2+3q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^3+3q^2+3q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^3+3q^2+3q+1
       235: q^3+3q^2+3q+1
       236: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+2q+1
       242: 2q+1
       243: 2q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: 2q+1
       249: 2q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^3+3q^2+3q+1
       257: q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^3+3q^2+3q+1
       261: q^2+3q+1
       262: q^2+3q+1
       263: q^2+3q+1
       264: q^3+4q^2+3q+1
       265: q^3+4q^2+3q+1
       266: 2q+1
       267: q^2+3q+1
       268: q^2+3q+1
       269: q^2+3q+1
       270: 2q^2+3q+1
       271: q^3+3q^2+3q+1
       272: 2q^2+3q+1
       273: q^2+3q+1
       274: q^2+3q+1
       275: 2q^2+3q+1
       276: 2q^2+3q+1
       277: 2q^2+3q+1
       278: q^2+3q+1
       279: q^2+3q+1
       280: q^3+3q^2+3q+1
       281: q^2+2q+1
       282: q^3+3q^2+3q+1
       283: q^2+3q+1
       284: 2q^2+3q+1
       285: 2q^2+3q+1
       286: q^3+4q^2+3q+1
       287: q+1
       288: q^2+2q+1
       289: q^3+3q^2+3q+1
       290: q^3+3q^2+3q+1
       291: 2q+1
       292: q^3+3q^2+3q+1
       293: 2q^3+5q^2+3q+1
       294: q^3+3q^2+3q+1
       295: 2q+1
       296: 2q+1
       297: q^2+2q+1
       298: 2q+1
       299: q^2+2q+1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: 2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^3+3q^2+3q+1
       307: 2q+1
       308: q^3+3q^2+3q+1
       310: q^2+2q+1
       311: 2q+1
       312: 2q+1
       313: q^2+3q+1
       314: q+1
       315: q^2+3q+1
       316: q^2+3q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: q^2+3q+1
       323: q^2+3q+1
       324: q^2+3q+1
       325: q^2+3q+1
       326: 2q^2+3q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: q^2+3q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: q+1
       337: q+1
       338: q^2+3q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q^2+2q+1
       344: q+1
       345: q^2+3q+1
       346: q^2+3q+1
       347: 1
       348: q^2+2q+1
       349: 2q^2+3q+1
       350: q^2+2q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^3+3q^2+3q+1
       364: q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: 1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: q+1
       391: 2q+1
       392: q+1
       393: q+1
       394: q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q+1
       398: q^2+3q+1
       399: q^2+3q+1
       400: q^2+3q+1
       401: q^2+3q+1
       402: q^3+4q^2+3q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: q^2+3q+1
       407: q^2+3q+1
       408: q^2+3q+1
       409: q^2+3q+1
       410: 2q^2+3q+1
       411: 2q^2+3q+1
       412: 2q+1
       413: q^2+3q+1
       414: q^2+3q+1
       415: q+1
       416: 2q^2+3q+1
       417: 2q^2+3q+1
       418: 2q^2+3q+1
       419: q+1
       420: q^2+3q+1
       421: q^2+3q+1
       422: q+1
       423: q^2+2q+1
       424: q^3+3q^2+3q+1
       425: q^2+2q+1
       426: q^2+3q+1
       427: q^2+3q+1
       428: 2q^2+3q+1
       429: q^2+2q+1
       430: 2q^2+3q+1
       431: q+1
       432: q+1
       433: q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^3+3q^2+3q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^3+3q^2+3q+1
       441: q^3+3q^2+3q+1
       442: q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: q^2+2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: 2q+1
       456: q^2+2q+1
       457: q+1
       458: q^2+2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^3+3q^2+3q+1
       463: q+1
       466: 2q+1
       467: 2q+1
       468: q+1
       469: q+1
       470: q^2+3q+1
       471: q+1
       472: q+1
       474: 2q+1
       475: 2q+1
       476: 2q+1
       477: q^2+3q+1
       478: q+1
       479: q^2+3q+1
       480: q^2+3q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q^2+3q+1
       491: q+1
       492: q+1
       493: q+1
       494: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q^2+2q+1
       500: 1
       501: q+1
       502: q+1
       503: q^2+3q+1
       504: 1
       505: 1
       506: 1
       507: q^2+2q+1
       508: q^2+2q+1
       509: 1
       510: q+1
       511: q+1
       512: 1
       513: 1
       514: q+1
       515: 1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: 2q+1
       521: 1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: 2q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: q+1
       536: q+1
       537: 2q+1
       541: 2q+1
       542: 2q+1
       543: 1
       544: 1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: 1
       552: 2q+1
       553: 2q+1
       555: q+1
       556: 2q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       564: q^2+2q+1
       565: 2q+1
       566: 2q+1
       567: q^2+3q+1
       568: q+1
       569: q^2+3q+1
       570: q^2+3q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: q^2+3q+1
       577: q^2+3q+1
       578: q^2+3q+1
       579: q^2+3q+1
       580: 2q^2+3q+1
       581: q+1
       582: 2q+1
       583: 2q+1
       584: q^2+3q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q^2+3q+1
       589: 2q^2+3q+1
       590: q+1
       591: q+1
       592: q^2+3q+1
       593: q+1
       594: q+1
       595: q+1
       596: q^2+2q+1
       597: q^2+2q+1
       598: q+1
       599: q^2+3q+1
       600: q^2+3q+1
       601: 1
       602: q^2+2q+1
       603: 2q^2+3q+1
       604: q^2+2q+1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^3+3q^2+3q+1
       618: q+1
       619: q+1
       620: q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: q+1
       628: 2q+1
       629: 2q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: 1
       635: 2q+1
       636: 2q+1
       637: q+1
       638: q+1
       639: q^2+2q+1
       640: q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: q+1
       645: 2q+1
       646: q+1
       647: q+1
       648: q+1
       651: 2q+1
       652: q+1
       653: q+1
       654: 1
       655: q+1
       656: q+1
       659: 2q+1
       660: 2q+1
       661: q+1
       662: q+1
       663: q^2+3q+1
       664: 1
       665: 1
       667: 2q+1
       668: q+1
       669: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       677: q+1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+2q+1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: 2q+1
       710: q+1
       711: q+1
       713: q+1
       714: q+1
       715: q+1
       716: 2q+1
       717: 1
       718: 2q+1
       719: 2q+1
       721: q+1
       722: q+1
       723: q+1
       729: 2q+1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       740: 1
       741: 1
       742: 2q+1
       746: q+1
       747: q+1
       748: 1
       749: q+1
       750: q+1
       752: 1
       753: q+1
       754: 1
       757: 2q+1
       758: 2q+1
       759: q+1
       760: q+1
       761: q^2+3q+1
       762: q+1
       763: q+1
       765: 2q+1
       766: 2q+1
       767: 2q+1
       768: q^2+3q+1
       769: q+1
       770: q^2+3q+1
       771: q^2+3q+1
       772: 1
       773: q+1
       774: 2q+1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q^2+3q+1
       782: q+1
       783: q+1
       784: q+1
       785: 1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: q^2+2q+1
       791: 1
       792: q+1
       793: q+1
       794: q^2+3q+1
       795: 1
       796: 1
       797: 1
       798: q^2+2q+1
       799: q^2+2q+1
       800: 1
       801: q+1
       802: q+1
       803: 1
       804: 1
       805: q+1
       806: 1
       808: q^2+2q+1
       809: q+1
       810: q+1
       811: 2q+1
       812: 1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: 2q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: q+1
       827: q+1
       828: 2q+1
       832: 2q+1
       833: 2q+1
       834: 1
       835: 1
       836: 2q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       842: 1
       843: 2q+1
       844: 2q+1
       846: q+1
       847: 2q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       857: q+1
       858: 1
       859: 1
       860: q+1
       863: 2q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       871: q+1
       872: q+1
       875: q+1
       876: 1
       877: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: 1
       886: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       913: q+1
       916: q+1
       917: q+1
       918: 1
       919: 1
       920: 2q+1
       924: q+1
       932: q+1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q+1
       940: q+1
       942: 1
       943: 1
       944: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: q+1
       958: 1
       959: 1
       962: 2q+1
       963: q+1
       964: q+1
       965: 1
       966: q+1
       967: q+1
       970: 2q+1
       971: 2q+1
       972: q+1
       973: q+1
       974: q^2+3q+1
       975: 1
       976: 1
       978: 2q+1
       979: q+1
       980: q+1
       981: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       988: q+1
       989: 1
       990: 1
       991: q+1
       992: 1
       993: q+1
       994: q+1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q^2+2q+1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: 2q+1
      1021: q+1
      1022: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 2q+1
      1028: 1
      1029: 2q+1
      1030: 2q+1
      1032: q+1
      1033: q+1
      1034: q+1
      1040: 2q+1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: q+1
      1050: 1
      1051: 1
      1052: 1
      1053: 2q+1
      1057: q+1
      1058: q+1
      1059: 1
      1060: q+1
      1061: q+1
      1063: 1
      1064: q+1
      1065: 1
      1069: 1
      1070: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1080: q+1
      1084: 1
      1085: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1116: 1
      1117: 1
      1118: 1
      1119: q+1
      1122: q+1
      1123: 1
      1124: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: q+1
      1174: 2q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1182: q+1
      1183: q+1
      1186: q+1
      1187: 1
      1188: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: q+1
      1196: 1
      1197: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1224: q+1
      1227: q+1
      1228: q+1
      1229: 1
      1230: 1
      1231: 2q+1
      1235: q+1
      1243: q+1
      1245: 1
      1246: 1
      1247: 1
      1248: q+1
      1249: 1
      1250: q+1
      1251: q+1
      1253: 1
      1254: 1
      1255: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1269: 1
      1270: 1
      1273: 1
      1277: 1
      1278: 1
      1285: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1295: 1
      1299: 1
      1300: 1
      1303: 1
      1304: 1
      1307: 1
      1313: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1348: 1
      1356: 1
      1360: 1
      1361: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1371: q+1
      1375: 1
      1376: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: 1
      1401: 1
      1403: 1
      1407: 1
      1408: 1
      1409: 1
      1410: q+1
      1413: q+1
      1414: 1
      1415: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: q+1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1460: 1
      1469: 1
      1470: 1
      1477: 1
      1480: 1
      1488: 1
      1504: 1
      1527: 1
      1531: 1
      1532: 1
      1539: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1549: 1
      1553: 1
      1554: 1
      1557: 1
      1558: 1
      1561: 1
      1567: 1
      1568: 1
      1572: 1
      1586: 1
      1587: 1
      1588: 1
      1602: 1
      1610: 1
      1619: 1
      1666: 1
      1675: 1
      1676: 1
      1683: 1
      1686: 1
      1694: 1
      1710: 1
      1773: 1

1774:    0: 2q^2+3q+1
         1: 2q^2+3q+1
         2: q^2+3q+1
         3: 2q^2+3q+1
         4: 2q^2+3q+1
         5: 2q^2+3q+1
         6: q^2+3q+1
         7: q^2+3q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: q^2+3q+1
        18: 2q^2+3q+1
        19: 2q^2+3q+1
        20: q^2+3q+1
        21: q^2+3q+1
        22: q^2+3q+1
        23: 2q+1
        24: q^2+3q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: q^2+3q+1
        30: 2q^2+3q+1
        31: q^2+3q+1
        32: 2q^2+3q+1
        33: q^2+3q+1
        34: q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q+1
        38: q^2+2q+1
        39: 2q^2+3q+1
        40: q^2+3q+1
        41: q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: q^2+3q+1
        52: q^2+3q+1
        53: q^2+2q+1
        54: 2q+1
        55: q^2+3q+1
        56: 2q+1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: 2q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q^2+3q+1
        68: 2q^2+3q+1
        69: q^2+3q+1
        70: 2q^2+3q+1
        71: q^2+3q+1
        72: q^2+3q+1
        73: q^2+3q+1
        74: q+1
        75: q^2+3q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q+1
        81: 2q^2+3q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+3q+1
        85: q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: 2q^2+3q+1
        93: q^2+3q+1
        94: 2q^2+3q+1
        95: q^2+3q+1
        96: 2q^2+3q+1
        97: q^2+3q+1
        98: q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q+1
       102: q^2+2q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: q^2+3q+1
       107: q^2+2q+1
       108: q+1
       109: q^2+2q+1
       110: 2q+1
       111: 2q+1
       112: 2q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: q^2+2q+1
       116: 2q+1
       117: q^2+3q+1
       118: 2q+1
       119: q^2+3q+1
       120: q^2+3q+1
       121: q^2+3q+1
       122: 2q+1
       123: q^2+3q+1
       124: q^2+3q+1
       125: q^2+3q+1
       126: q^2+3q+1
       127: q+1
       128: q^2+3q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: q^2+3q+1
       132: 2q^2+3q+1
       133: 2q+1
       134: q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q+1
       138: q+1
       139: q^2+3q+1
       140: q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 1
       145: 2q+1
       146: q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 2q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: q^2+2q+1
       159: 2q+1
       160: q^2+3q+1
       161: 2q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: 2q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+3q+1
       169: q^2+3q+1
       170: q^2+3q+1
       171: q^2+3q+1
       172: q^2+3q+1
       173: 2q^2+3q+1
       174: q^2+3q+1
       175: 2q^2+3q+1
       176: q^2+3q+1
       177: q^2+3q+1
       178: q^2+3q+1
       179: q+1
       180: q^2+3q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q+1
       186: 2q^2+3q+1
       187: 2q+1
       188: q^2+2q+1
       189: 2q+1
       190: 2q+1
       191: q+1
       192: q^2+2q+1
       193: q+1
       194: q^2+2q+1
       195: q+1
       196: 2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: q^2+3q+1
       201: q^2+2q+1
       202: q+1
       203: q^2+2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: q^2+3q+1
       208: q^2+3q+1
       209: q^2+2q+1
       210: 2q+1
       211: q^2+3q+1
       212: 2q+1
       213: q+1
       214: q^2+3q+1
       215: q^2+3q+1
       216: q+1
       217: q+1
       218: q^2+3q+1
       219: q+1
       220: q^2+3q+1
       221: q^2+3q+1
       222: q^2+3q+1
       223: q+1
       224: q^2+3q+1
       225: 2q+1
       226: 2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: q^2+3q+1
       231: q+1
       232: 1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: 2q+1
       238: 2q+1
       239: q+1
       240: 1
       241: 2q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 1
       252: 2q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q^2+2q+1
       262: q+1
       263: q^2+2q+1
       264: 2q+1
       265: 2q+1
       266: 2q+1
       267: q^2+3q+1
       268: q^2+3q+1
       269: q^2+2q+1
       270: 2q+1
       271: q^2+3q+1
       272: 2q+1
       273: q^2+3q+1
       274: q^2+3q+1
       275: q^2+3q+1
       276: 2q+1
       277: q^2+3q+1
       278: q^2+3q+1
       279: q^2+3q+1
       280: q^2+3q+1
       281: q+1
       282: q^2+3q+1
       283: q^2+3q+1
       284: q^2+3q+1
       285: q^2+3q+1
       286: 2q^2+3q+1
       287: 2q+1
       288: q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: q+1
       292: q+1
       293: q^2+3q+1
       294: q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 1
       299: 2q+1
       300: q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: 2q+1
       311: q+1
       312: q+1
       313: q+1
       315: q^2+2q+1
       316: q+1
       317: 1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q+1
       322: q^2+2q+1
       323: q+1
       324: q^2+2q+1
       325: q+1
       326: 2q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: q^2+3q+1
       331: q^2+2q+1
       332: q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: q^2+3q+1
       339: q+1
       340: 1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: q^2+3q+1
       346: q^2+3q+1
       347: q+1
       348: q+1
       349: q^2+3q+1
       350: q+1
       351: 2q+1
       352: 2q+1
       353: 2q+1
       354: 1
       355: 2q+1
       356: q+1
       357: q+1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 2q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: 1
       385: 2q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: 2q+1
       396: 2q+1
       397: q+1
       398: q^2+2q+1
       399: q+1
       400: q^2+2q+1
       401: q+1
       402: 2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: q^2+3q+1
       407: q^2+2q+1
       408: q+1
       409: q^2+2q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       413: q^2+3q+1
       414: q^2+3q+1
       415: q^2+2q+1
       416: 2q+1
       417: q^2+3q+1
       418: 2q+1
       419: q+1
       420: q^2+3q+1
       421: q^2+3q+1
       422: q+1
       423: q+1
       424: q^2+3q+1
       425: q+1
       426: q^2+3q+1
       427: q^2+3q+1
       428: q^2+3q+1
       429: q+1
       430: q^2+3q+1
       431: 2q+1
       432: 2q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: q^2+3q+1
       437: q+1
       438: 1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: 2q+1
       444: 2q+1
       445: q+1
       446: 1
       447: 2q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 1
       458: 2q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: 1
       466: q+1
       467: q+1
       470: q+1
       471: 1
       472: 1
       473: q+1
       474: 2q+1
       475: q+1
       476: q+1
       477: q+1
       479: q^2+2q+1
       480: q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q^2+2q+1
       487: q+1
       488: q^2+2q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: q+1
       493: q+1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q^2+3q+1
       504: q+1
       505: 1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: 2q+1
       511: 2q+1
       512: q+1
       513: 1
       514: 2q+1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 2q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       563: q+1
       564: 2q+1
       565: q+1
       566: q+1
       567: q+1
       569: q^2+2q+1
       570: q+1
       571: 1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: q+1
       576: q^2+2q+1
       577: q+1
       578: q^2+2q+1
       579: q+1
       580: 2q+1
       581: q+1
       582: 2q+1
       583: 2q+1
       584: q^2+3q+1
       585: q^2+2q+1
       586: q+1
       587: q^2+2q+1
       588: 2q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: q^2+3q+1
       593: q+1
       594: 1
       595: q+1
       596: q+1
       597: q+1
       598: q+1
       599: q^2+3q+1
       600: q^2+3q+1
       601: q+1
       602: q+1
       603: q^2+3q+1
       604: q+1
       605: 2q+1
       606: 2q+1
       607: 2q+1
       608: 1
       609: 2q+1
       610: q+1
       611: q+1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 2q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: q+1
       629: q+1
       631: 1
       632: q+1
       633: 1
       634: 1
       635: 2q+1
       636: 2q+1
       637: q+1
       638: 1
       639: 2q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       651: q+1
       655: 1
       656: 1
       657: q+1
       658: 1
       659: q+1
       660: q+1
       663: q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: q+1
       669: q+1
       670: q+1
       672: q^2+2q+1
       673: q+1
       674: 1
       675: q+1
       676: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 2q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       752: 1
       753: q+1
       754: 1
       755: q+1
       756: 1
       757: q+1
       758: q+1
       761: q+1
       762: 1
       763: 1
       764: q+1
       765: 2q+1
       766: q+1
       767: q+1
       768: q+1
       770: q^2+2q+1
       771: q+1
       772: 1
       773: q+1
       774: 2q+1
       775: 2q+1
       776: q+1
       777: q^2+2q+1
       778: q+1
       779: q^2+2q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: q+1
       784: q+1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: q^2+3q+1
       795: q+1
       796: 1
       797: q+1
       798: q+1
       799: q+1
       800: 1
       801: 2q+1
       802: 2q+1
       803: q+1
       804: 1
       805: 2q+1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: q+1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 2q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: 1
       842: 1
       843: q+1
       844: q+1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       867: 1
       868: 1
       869: q+1
       870: 1
       871: q+1
       872: q+1
       875: q+1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       902: q+1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: q+1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       958: 1
       959: 1
       960: 1
       961: 1
       962: q+1
       966: 1
       967: 1
       968: q+1
       969: 1
       970: q+1
       971: q+1
       974: q+1
       975: 1
       976: 1
       977: q+1
       978: 2q+1
       979: q+1
       980: q+1
       981: q+1
       983: q^2+2q+1
       984: q+1
       985: 1
       986: q+1
       987: 1
       988: q+1
       989: 1
       990: 1
       991: 1
       993: q+1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: q+1
      1001: 1
      1002: q+1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 2q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1061: q+1
      1063: 1
      1064: q+1
      1065: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1119: 1
      1122: 1
      1128: 1
      1137: 1
      1139: 1
      1140: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: q+1
      1178: 1
      1179: 1
      1180: q+1
      1181: 1
      1182: q+1
      1183: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1204: q+1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1213: q+1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1250: q+1
      1251: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1269: 1
      1270: 1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1307: 1
      1310: 1
      1332: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1379: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1403: 1
      1404: 1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1428: 1
      1430: 1
      1431: 1
      1434: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1461: 1
      1466: 1
      1471: 1
      1472: 1
      1477: 1
      1480: 1
      1516: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1541: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1553: 1
      1554: 1
      1555: 1
      1557: 1
      1558: 1
      1561: 1
      1564: 1
      1586: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1620: 1
      1667: 1
      1672: 1
      1677: 1
      1678: 1
      1683: 1
      1686: 1
      1722: 1
      1774: 1

1775:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: 2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^2+2q+1
         5: q^3+2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^3+2q^2+2q+1
        17: 2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^2+2q+1
        20: 2q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: 2q^2+2q+1
        28: q^3+2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: q^3+2q^2+2q+1
        44: 2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 2q^2+2q+1
        51: q+1
        52: 2q^2+2q+1
        53: q^2+2q+1
        54: 2q^2+2q+1
        55: q+1
        56: q+1
        57: 2q^2+2q+1
        58: 2q^2+2q+1
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: 2q^2+2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: 2q^2+2q+1
        92: q^3+2q^2+2q+1
        93: 2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: 2q^2+2q+1
       106: q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q+1
       110: q+1
       111: q+1
       112: 2q^2+2q+1
       113: q+1
       114: 2q^2+2q+1
       115: q^2+2q+1
       116: 2q^2+2q+1
       117: q+1
       118: q+1
       119: 2q^2+2q+1
       120: 2q^2+2q+1
       121: 2q^2+2q+1
       122: 2q^2+2q+1
       123: q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: 2q^2+2q+1
       156: q+1
       157: 2q^2+2q+1
       158: q^2+2q+1
       159: 2q^2+2q+1
       160: q+1
       161: q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: 2q^2+2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q^2+2q+1
       192: q+1
       193: q^2+2q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: 2q^2+2q+1
       200: q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q+1
       204: q+1
       205: q+1
       206: 2q^2+2q+1
       207: q+1
       208: 2q^2+2q+1
       209: q^2+2q+1
       210: 2q^2+2q+1
       211: q+1
       212: q+1
       213: q^2+2q+1
       214: q+1
       215: q^2+2q+1
       216: q+1
       217: q^2+2q+1
       218: q+1
       219: q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: q+1
       232: q+1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: 2q^2+2q+1
       260: q+1
       261: q^2+2q+1
       262: q^2+2q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q^2+2q+1
       267: q+1
       268: 2q^2+2q+1
       269: q^2+2q+1
       270: 2q^2+2q+1
       271: q+1
       272: q+1
       273: 2q^2+2q+1
       274: 2q^2+2q+1
       275: 2q^2+2q+1
       276: 2q^2+2q+1
       277: q+1
       278: q^2+2q+1
       279: q^2+2q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: 1
       310: q+1
       311: q+1
       312: q^2+2q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q^2+2q+1
       322: q+1
       323: q^2+2q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: 2q^2+2q+1
       330: q+1
       331: q^2+2q+1
       332: q^2+2q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q^2+2q+1
       338: q+1
       339: q+1
       340: q+1
       341: 1
       342: q+1
       343: q+1
       344: q^2+2q+1
       345: q+1
       346: q^2+2q+1
       347: q+1
       348: q^2+2q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       377: q+1
       380: q+1
       381: 1
       382: q+1
       383: q+1
       384: q+1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q^2+2q+1
       398: q+1
       399: q^2+2q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       404: q+1
       405: 2q^2+2q+1
       406: q+1
       407: q^2+2q+1
       408: q^2+2q+1
       409: q+1
       410: q+1
       411: q+1
       412: 2q^2+2q+1
       413: q+1
       414: 2q^2+2q+1
       415: q^2+2q+1
       416: 2q^2+2q+1
       417: q+1
       418: q+1
       419: q^2+2q+1
       420: q+1
       421: q^2+2q+1
       422: q+1
       423: q^2+2q+1
       424: q+1
       425: q+1
       426: q^2+2q+1
       427: q^2+2q+1
       428: q^2+2q+1
       429: q^2+2q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: q+1
       438: q+1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: 1
       465: 1
       466: q+1
       468: q+1
       469: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q^2+2q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: q^2+2q+1
       486: q+1
       487: q^2+2q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q^2+2q+1
       503: q+1
       504: q+1
       505: q+1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       511: q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       543: 1
       544: q+1
       545: 1
       546: q+1
       547: q+1
       548: 1
       549: 1
       550: 1
       551: q+1
       553: q+1
       555: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       563: 1
       564: q+1
       565: q+1
       566: q^2+2q+1
       568: q+1
       569: q+1
       570: q+1
       571: 1
       572: 1
       573: q+1
       574: q+1
       575: q^2+2q+1
       576: q+1
       577: q^2+2q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       582: q+1
       583: 2q^2+2q+1
       584: q+1
       585: q^2+2q+1
       586: q^2+2q+1
       587: q+1
       588: q+1
       589: q+1
       590: q+1
       591: q^2+2q+1
       592: q+1
       593: q+1
       594: q+1
       595: 1
       596: q+1
       597: q+1
       598: q^2+2q+1
       599: q+1
       600: q^2+2q+1
       601: q+1
       602: q^2+2q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       631: q+1
       634: q+1
       635: 1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       652: q+1
       654: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       661: q+1
       662: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q^2+2q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: q+1
       734: 1
       735: q+1
       736: 1
       737: 1
       738: 1
       739: 1
       741: q+1
       748: q+1
       750: q+1
       752: q+1
       755: 1
       756: 1
       757: q+1
       759: q+1
       760: q+1
       762: 1
       763: 1
       764: 1
       765: q+1
       766: q+1
       767: q^2+2q+1
       769: q+1
       770: q+1
       771: q+1
       772: 1
       773: 1
       774: q+1
       775: q+1
       776: q^2+2q+1
       777: q+1
       778: q^2+2q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: q+1
       784: q+1
       785: q+1
       786: 1
       787: q+1
       788: 1
       789: 1
       790: q+1
       791: 1
       792: q+1
       793: q^2+2q+1
       794: q+1
       795: q+1
       796: q+1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       834: 1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: q+1
       846: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: q+1
       866: 1
       868: 1
       869: 1
       870: 1
       871: q+1
       873: q+1
       874: q+1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       935: 1
       936: q+1
       938: 1
       939: 1
       940: 1
       942: 1
       953: q+1
       960: 1
       961: 1
       963: q+1
       965: 1
       967: 1
       968: 1
       969: 1
       970: q+1
       972: q+1
       973: q+1
       975: 1
       976: 1
       977: 1
       978: q+1
       979: q+1
       980: q^2+2q+1
       982: q+1
       983: q+1
       984: q+1
       985: 1
       986: 1
       987: 1
       988: q+1
       989: 1
       990: q+1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1044: q+1
      1045: 1
      1046: q+1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: q+1
      1059: q+1
      1061: q+1
      1063: q+1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: q+1
      1083: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1139: 1
      1141: 1
      1142: 1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: q+1
      1177: 1
      1179: 1
      1180: 1
      1181: 1
      1182: q+1
      1184: q+1
      1185: q+1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1212: q+1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1227: 1
      1229: 1
      1230: 1
      1244: 1
      1245: 1
      1246: 1
      1247: q+1
      1249: 1
      1250: 1
      1251: 1
      1253: 1
      1264: q+1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1303: 1
      1305: 1
      1306: 1
      1311: 1
      1333: 1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1369: 1
      1370: 1
      1372: q+1
      1374: 1
      1376: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: q+1
      1399: 1
      1400: 1
      1401: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1414: 1
      1428: 1
      1430: 1
      1432: 1
      1433: 1
      1462: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1481: 1
      1529: 1
      1533: 1
      1535: 1
      1538: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1557: 1
      1559: 1
      1560: 1
      1565: 1
      1587: 1
      1621: 1
      1668: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1687: 1
      1775: 1

1776:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 2q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       148: q+1
       149: q^2+2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: 2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: 2q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q^2+2q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: q^2+2q+1
       207: q^2+2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: q^2+2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       227: 2q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       242: 2q+1
       243: q+1
       246: q+1
       247: q+1
       248: 2q+1
       251: 2q+1
       252: 2q+1
       253: q^2+2q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q^2+2q+1
       267: q^2+2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: q^2+2q+1
       273: q^2+2q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 2q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q^2+2q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       302: q+1
       303: q^2+2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       328: q^2+2q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       372: 1
       373: q+1
       374: q+1
       379: q+1
       380: 2q+1
       381: 2q+1
       386: 2q+1
       387: q+1
       390: q+1
       391: q+1
       392: q^2+2q+1
       394: q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: q^2+2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q+1
       412: q^2+2q+1
       413: q^2+2q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: q^2+2q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q^2+2q+1
       433: 2q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       448: 2q+1
       449: q+1
       452: q+1
       453: q+1
       454: 2q+1
       457: 2q+1
       458: 2q+1
       459: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: q+1
       474: q+1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: 2q+1
       510: 2q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       534: 1
       535: q+1
       542: 1
       543: 2q+1
       550: 1
       551: q+1
       552: q+1
       557: q+1
       558: q+1
       561: q+1
       562: q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: q+1
       581: q+1
       582: q^2+2q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 2q+1
       608: 2q+1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       626: 1
       627: q+1
       628: q+1
       633: q+1
       634: 2q+1
       635: 2q+1
       640: 2q+1
       641: q+1
       644: q+1
       645: q+1
       646: q^2+2q+1
       648: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: q+1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       702: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: q+1
       747: 1
       748: q+1
       749: q+1
       754: q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       772: q+1
       774: q+1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: q+1
       782: q+1
       783: q+1
       784: 2q+1
       785: 2q+1
       786: 2q+1
       787: q+1
       788: q+1
       789: 2q+1
       790: q+1
       791: q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: q+1
       800: 2q+1
       801: 2q+1
       806: 2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       825: 1
       826: q+1
       833: 1
       834: 2q+1
       841: 1
       842: q+1
       843: q+1
       848: q+1
       849: q+1
       852: q+1
       853: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       897: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: q+1
       959: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: q+1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       977: q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: 1
       985: q+1
       987: q+1
       988: q+1
       989: 2q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: 1
       995: q+1
       997: q+1
       998: 2q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1006: 2q+1
      1013: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: q+1
      1058: 1
      1059: q+1
      1060: q+1
      1065: q+1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1146: 1
      1156: 1
      1164: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: q+1
      1182: 1
      1183: q+1
      1184: q+1
      1185: 1
      1186: 1
      1187: 1
      1190: q+1
      1191: 1
      1192: q+1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1198: q+1
      1199: q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1203: q+1
      1204: q+1
      1205: 1
      1206: q+1
      1208: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: q+1
      1270: 1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1312: 1
      1347: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: q+1
      1387: 1
      1388: q+1
      1389: q+1
      1390: 1
      1391: 1
      1392: 1
      1394: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1447: 1
      1455: 1
      1463: 1
      1468: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1530: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1566: 1
      1601: 1
      1622: 1
      1669: 1
      1674: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1776: 1

1777:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: 1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: 1
        21: 1
        22: q^2+1
        23: q^2+1
        24: q^2+1
        25: 1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: q^2+1
        31: q^2+1
        32: q^2+1
        33: 1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: 1
        38: q^2+1
        39: q^2+1
        40: 1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: q^2+1
        55: q^2+1
        56: q^2+1
        57: 1
        58: 1
        59: q^2+1
        60: q^2+1
        61: q^2+1
        62: 1
        63: q^2+1
        64: q^2+1
        65: 1
        66: q^2+1
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: 1
        72: 1
        73: q^2+1
        74: q^2+1
        75: q^2+1
        76: 1
        78: 1
        79: q^2+1
        80: 1
        81: q^2+1
        82: 1
        83: q^2+1
        84: 1
        85: 1
        86: q^2+1
        87: q^2+1
        88: q^2+1
        89: 1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: 1
        98: q^2+1
        99: q^2+1
       100: q^2+1
       101: 1
       102: q^2+1
       103: q^2+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: q^2+1
       111: q^2+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: q^2+1
       117: q^2+1
       118: q^2+1
       119: 1
       120: 1
       121: q^2+1
       122: q^2+1
       123: q^2+1
       124: 1
       125: 1
       126: q^2+1
       127: q^2+1
       128: q^2+1
       129: 1
       130: q^2+1
       131: q^2+1
       132: q^2+1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: q^2+1
       139: q^2+1
       140: q^2+1
       141: 1
       144: 1
       145: 1
       146: 1
       148: 1
       149: 1
       151: 1
       152: q^2+1
       153: 1
       154: q^2+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: q^2+1
       160: q^2+1
       161: q^2+1
       162: 1
       163: 1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: 1
       168: q^2+1
       169: q^2+1
       170: 1
       171: q^2+1
       172: q^2+1
       173: q^2+1
       174: q^2+1
       175: q^2+1
       176: 1
       177: 1
       178: q^2+1
       179: q^2+1
       180: q^2+1
       181: 1
       183: 1
       184: q^2+1
       185: 1
       186: q^2+1
       187: 1
       188: q^2+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q^2+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: q^2+1
       205: q^2+1
       206: 1
       207: 1
       208: 1
       209: 1
       210: q^2+1
       211: q^2+1
       212: q^2+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: q^2+1
       218: q^2+1
       219: q^2+1
       220: 1
       221: 1
       222: q^2+1
       223: q^2+1
       224: q^2+1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q^2+1
       235: q^2+1
       236: 1
       237: 1
       242: 1
       243: 1
       246: 1
       247: 1
       248: 1
       251: 1
       252: 1
       253: 1
       255: 1
       256: q^2+1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: q^2+1
       265: q^2+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: q^2+1
       271: q^2+1
       272: q^2+1
       273: 1
       274: 1
       275: q^2+1
       276: q^2+1
       277: q^2+1
       278: 1
       279: 1
       280: q^2+1
       281: q^2+1
       282: q^2+1
       283: 1
       284: q^2+1
       285: q^2+1
       286: q^2+1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: q^2+1
       293: q^2+1
       294: q^2+1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: q^2+1
       307: 1
       308: q^2+1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q^2+1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: q^2+1
       335: q^2+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q^2+1
       343: q^2+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: q^2+1
       350: q^2+1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q^2+1
       364: 1
       365: 1
       372: 1
       373: 1
       374: 1
       379: 1
       380: 1
       381: 1
       386: 1
       387: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q^2+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q^2+1
       411: q^2+1
       412: 1
       413: 1
       414: 1
       415: 1
       416: q^2+1
       417: q^2+1
       418: q^2+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: q^2+1
       424: q^2+1
       425: q^2+1
       426: 1
       427: 1
       428: q^2+1
       429: q^2+1
       430: q^2+1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q^2+1
       441: q^2+1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: q^2+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q^2+1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q^2+1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q^2+1
       508: q^2+1
       509: 1
       510: 1
       515: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       534: 1
       535: 1
       542: 1
       543: 1
       550: 1
       551: 1
       552: 1
       557: 1
       558: 1
       561: 1
       562: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q^2+1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: q^2+1
       589: q^2+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: q^2+1
       597: q^2+1
       598: 1
       599: 1
       600: 1
       601: 1
       602: q^2+1
       603: q^2+1
       604: q^2+1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+1
       694: 1
       695: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q^2+1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q^2+1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q^2+1
       799: q^2+1
       800: 1
       801: 1
       806: 1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       943: 1
       951: 1
       952: 1
       959: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q^2+1
      1005: 1
      1006: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1116: 1
      1117: 1
      1156: 1
      1164: 1
      1168: 1
      1169: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1277: 1
      1282: 1
      1283: 1
      1289: 1
      1290: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1313: 1
      1360: 1
      1365: 1
      1366: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1407: 1
      1408: 1
      1447: 1
      1455: 1
      1464: 1
      1469: 1
      1474: 1
      1475: 1
      1531: 1
      1536: 1
      1537: 1
      1543: 1
      1544: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1567: 1
      1623: 1
      1670: 1
      1675: 1
      1680: 1
      1681: 1
      1777: 1

1778:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: 2q^2+2q+1
        25: q^2+2q+1
        26: 2q^2+2q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: 2q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: 2q^2+2q+1
        64: 2q^2+2q+1
        65: q^2+2q+1
        66: 2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+2q+1
        80: q+1
        81: q^2+2q+1
        82: q+1
        83: q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^2+2q+1
        89: q^2+2q+1
        90: 2q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+2q+1
       111: q^2+2q+1
       112: q+1
       113: q+1
       114: q+1
       115: q^2+2q+1
       116: 2q^2+2q+1
       117: 2q^2+2q+1
       118: 2q^2+2q+1
       119: q+1
       120: q^2+2q+1
       121: 2q^2+2q+1
       122: 2q^2+2q+1
       123: 2q^2+2q+1
       124: q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: 2q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: 2q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: q+1
       163: q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q^2+2q+1
       167: q^2+2q+1
       168: 2q^2+2q+1
       169: 2q^2+2q+1
       170: q^2+2q+1
       171: 2q^2+2q+1
       172: q^2+2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+2q+1
       185: q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: q^2+2q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: 2q^2+2q+1
       205: q^2+2q+1
       206: q+1
       207: q+1
       208: q+1
       209: q^2+2q+1
       210: 2q^2+2q+1
       211: 2q^2+2q+1
       212: 2q^2+2q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: q+1
       221: q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q^2+2q+1
       263: q^2+2q+1
       264: 2q^2+2q+1
       265: q^2+2q+1
       266: q+1
       267: q+1
       268: q+1
       269: q^2+2q+1
       270: 2q^2+2q+1
       271: 2q^2+2q+1
       272: 2q^2+2q+1
       273: q+1
       274: q^2+2q+1
       275: 2q^2+2q+1
       276: 2q^2+2q+1
       277: 2q^2+2q+1
       278: q+1
       279: q^2+2q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: q^2+2q+1
       284: 2q^2+2q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q^2+2q+1
       326: q^2+2q+1
       327: q+1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q^2+2q+1
       333: q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q^2+2q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q^2+2q+1
       364: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q^2+2q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q^2+2q+1
       409: q^2+2q+1
       410: 2q^2+2q+1
       411: q^2+2q+1
       412: q+1
       413: q+1
       414: q+1
       415: q^2+2q+1
       416: 2q^2+2q+1
       417: 2q^2+2q+1
       418: 2q^2+2q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q^2+2q+1
       424: q^2+2q+1
       425: q^2+2q+1
       426: q+1
       427: q^2+2q+1
       428: q^2+2q+1
       429: q^2+2q+1
       430: q^2+2q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q^2+2q+1
       463: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q^2+2q+1
       490: q^2+2q+1
       491: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q^2+2q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: q^2+2q+1
       508: q^2+2q+1
       509: 1
       510: 1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q^2+2q+1
       580: q^2+2q+1
       581: q+1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q^2+2q+1
       587: q^2+2q+1
       588: 2q^2+2q+1
       589: q^2+2q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: q+1
       595: q+1
       596: q^2+2q+1
       597: q^2+2q+1
       598: q+1
       599: q+1
       600: q+1
       601: q+1
       602: q^2+2q+1
       603: q^2+2q+1
       604: q^2+2q+1
       605: 1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q^2+2q+1
       618: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: q+1
       654: 1
       655: 1
       656: 1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: q+1
       668: q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: q+1
       685: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q^2+2q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       723: 1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: 1
       763: q+1
       766: q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: q+1
       772: q+1
       773: q+1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q^2+2q+1
       781: q^2+2q+1
       782: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q^2+2q+1
       791: q+1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: q+1
       797: q+1
       798: q^2+2q+1
       799: q^2+2q+1
       800: 1
       801: 1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: q+1
       866: 1
       867: 1
       868: 1
       872: q+1
       873: q+1
       874: q+1
       875: q+1
       876: 1
       877: q+1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       932: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       942: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       964: q+1
       965: 1
       966: 1
       967: 1
       971: q+1
       972: q+1
       973: q+1
       974: q+1
       975: 1
       976: q+1
       979: q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: q+1
       985: q+1
       986: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: q+1
       996: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q^2+2q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1034: 1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1155: 1
      1157: 1
      1163: 1
      1164: 1
      1169: 1
      1170: 1
      1171: 1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1183: q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: q+1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: q+1
      1207: q+1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1243: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1253: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1290: 1
      1291: 1
      1292: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1314: 1
      1334: 1
      1356: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: q+1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1403: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1446: 1
      1448: 1
      1454: 1
      1455: 1
      1465: 1
      1470: 1
      1475: 1
      1476: 1
      1477: 1
      1482: 1
      1532: 1
      1537: 1
      1538: 1
      1539: 1
      1544: 1
      1545: 1
      1546: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1568: 1
      1588: 1
      1610: 1
      1624: 1
      1671: 1
      1676: 1
      1681: 1
      1682: 1
      1683: 1
      1688: 1
      1778: 1

1779:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q+1
         5: q^3+q^2+q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q^3+q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^3+q^2+q+1
        17: q^3+q^2+q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q^3+q^2+q+1
        21: q^3+q^2+q+1
        22: q^3+q^2+q+1
        23: q^2+1
        24: 1
        25: q^3+q^2+q+1
        26: q^3+q^2+q+1
        27: q^3+q^2+q+1
        28: q^3+q^2+q+1
        29: q^3+q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^3+q^2+q+1
        41: q^3+q^2+q+1
        42: q^3+q^2+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+1
        51: 1
        52: q^3+q^2+q+1
        53: q^3+q^2+q+1
        54: q^2+1
        55: 1
        56: 1
        57: q^3+q^2+q+1
        58: q^3+q^2+q+1
        59: q^3+q^2+q+1
        60: q^2+1
        61: 1
        62: q^3+q^2+q+1
        63: q^3+q^2+q+1
        64: q^3+q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^3+q^2+q+1
        85: q^3+q^2+q+1
        86: q^3+q^2+q+1
        87: q^2+1
        88: 1
        89: q^3+q^2+q+1
        90: q^3+q^2+q+1
        91: q^3+q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: q^2+1
       106: 1
       107: q^3+q^2+q+1
       108: q^2+1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       113: 1
       114: q^3+q^2+q+1
       115: q^3+q^2+q+1
       116: q^2+1
       117: 1
       118: 1
       119: q^3+q^2+q+1
       120: q^3+q^2+q+1
       121: q^3+q^2+q+1
       122: q^2+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+1
       156: 1
       157: q^3+q^2+q+1
       158: q^3+q^2+q+1
       159: q^2+1
       160: 1
       161: 1
       162: q^3+q^2+q+1
       163: q^3+q^2+q+1
       164: q^3+q^2+q+1
       165: q^2+1
       166: 1
       167: q^3+q^2+q+1
       168: q^3+q^2+q+1
       169: q^3+q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q^2+1
       192: 1
       193: q^2+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q^2+1
       200: 1
       201: q^3+q^2+q+1
       202: q^2+1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       207: 1
       208: q^3+q^2+q+1
       209: q^3+q^2+q+1
       210: q^2+1
       211: 1
       212: 1
       213: 1
       214: 1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: q^2+1
       260: 1
       261: q^3+q^2+q+1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       267: 1
       268: q^3+q^2+q+1
       269: q^3+q^2+q+1
       270: q^2+1
       271: 1
       272: 1
       273: q^3+q^2+q+1
       274: q^3+q^2+q+1
       275: q^3+q^2+q+1
       276: q^2+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: q^2+1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q^2+1
       322: 1
       323: q^2+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q^2+1
       330: 1
       331: q^3+q^2+q+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: q+1
       376: q+1
       377: 1
       380: 1
       381: 1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: q^2+1
       398: 1
       399: q^2+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q^2+1
       406: 1
       407: q^3+q^2+q+1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q^3+q^2+q+1
       415: q^3+q^2+q+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: q^2+1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q^2+1
       486: 1
       487: q^2+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: q+1
       539: 1
       543: 1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: q+1
       554: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q^2+1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q^2+1
       576: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q^2+1
       584: 1
       585: q^3+q^2+q+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: q+1
       601: q+1
       602: 1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: q+1
       630: q+1
       631: 1
       634: 1
       635: 1
       636: q+1
       637: q+1
       638: 1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: q^2+1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: 1
       750: q+1
       751: q+1
       752: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q^2+1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: q+1
       803: q+1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: q+1
       830: 1
       834: 1
       835: 1
       836: 1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: q+1
       845: q+1
       846: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       854: 1
       861: 1
       862: 1
       868: 1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       913: 1
       914: 1
       915: 1
       916: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: q+1
       956: 1
       960: 1
       961: 1
       967: 1
       968: 1
       969: 1
       970: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q^2+1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: q+1
      1055: 1
      1059: 1
      1061: q+1
      1062: q+1
      1063: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1086: 1
      1087: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1256: 1
      1258: 1
      1264: 1
      1266: q+1
      1267: 1
      1279: 1
      1286: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1315: 1
      1330: 1
      1331: 1
      1337: 1
      1350: 1
      1362: 1
      1369: 1
      1370: 1
      1376: 1
      1377: 1
      1378: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1411: 1
      1412: 1
      1418: 1
      1428: 1
      1429: 1
      1430: 1
      1435: 1
      1436: 1
      1440: 1
      1449: 1
      1451: 1
      1471: 1
      1478: 1
      1479: 1
      1485: 1
      1501: 1
      1533: 1
      1540: 1
      1547: 1
      1548: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1562: 1
      1563: 1
      1569: 1
      1584: 1
      1585: 1
      1591: 1
      1604: 1
      1625: 1
      1677: 1
      1684: 1
      1685: 1
      1691: 1
      1707: 1
      1779: 1

1780:    0: 2q^3+5q^2+3q+1
         1: 2q^3+5q^2+3q+1
         2: 2q^3+5q^2+3q+1
         3: 2q^3+5q^2+3q+1
         4: 2q^3+5q^2+3q+1
         5: 2q^3+5q^2+3q+1
         6: 2q^3+5q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^3+3q^2+3q+1
         9: 2q^3+5q^2+3q+1
        10: 2q^3+5q^2+3q+1
        11: 2q^3+5q^2+3q+1
        12: 2q^3+5q^2+3q+1
        13: 2q^3+5q^2+3q+1
        14: 2q^3+5q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 2q^3+5q^2+3q+1
        17: 2q^3+5q^2+3q+1
        18: 2q^3+5q^2+3q+1
        19: 2q^3+5q^2+3q+1
        20: q^3+3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: q^2+2q+1
        24: q^3+3q^2+3q+1
        25: 2q^3+5q^2+3q+1
        26: q^3+3q^2+3q+1
        27: q^3+3q^2+3q+1
        28: 2q^3+5q^2+3q+1
        29: 2q^3+5q^2+3q+1
        30: 2q^3+5q^2+3q+1
        31: 2q^3+5q^2+3q+1
        32: 2q^3+5q^2+3q+1
        33: 2q^3+5q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 2q^2+3q+1
        36: q^3+4q^2+3q+1
        37: q^3+4q^2+3q+1
        38: q^3+3q^2+3q+1
        39: q^3+4q^2+3q+1
        40: 2q^3+5q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q^3+3q^2+3q+1
        43: 2q^3+5q^2+3q+1
        44: 2q^3+5q^2+3q+1
        45: 2q^3+5q^2+3q+1
        46: 2q^3+5q^2+3q+1
        47: 2q^3+5q^2+3q+1
        48: 2q^3+5q^2+3q+1
        49: q^3+4q^2+3q+1
        50: q^2+2q+1
        51: q^3+3q^2+3q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: 2q+1
        55: q^2+3q+1
        56: q^2+2q+1
        57: q^3+3q^2+3q+1
        58: q^3+3q^2+3q+1
        59: q^2+3q+1
        60: q^2+2q+1
        61: q^3+3q^2+3q+1
        62: 2q^3+5q^2+3q+1
        63: q^3+3q^2+3q+1
        64: q^3+3q^2+3q+1
        65: 2q^3+5q^2+3q+1
        66: q^3+3q^2+3q+1
        67: 2q^2+3q+1
        68: 2q^3+5q^2+3q+1
        69: 2q^3+5q^2+3q+1
        70: q^3+4q^2+3q+1
        71: 2q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: 2q+1
        75: 2q^2+3q+1
        76: q^3+4q^2+3q+1
        77: q^2+2q+1
        78: 2q^2+3q+1
        79: q^3+3q^2+3q+1
        80: q^3+3q^2+3q+1
        81: q^3+4q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+3q^2+3q+1
        84: q^3+3q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: q^2+2q+1
        88: q^3+3q^2+3q+1
        89: 2q^3+5q^2+3q+1
        90: q^3+3q^2+3q+1
        91: q^3+3q^2+3q+1
        92: 2q^3+5q^2+3q+1
        93: 2q^3+5q^2+3q+1
        94: 2q^3+5q^2+3q+1
        95: 2q^3+5q^2+3q+1
        96: 2q^3+5q^2+3q+1
        97: 2q^3+5q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 2q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: q^3+3q^2+3q+1
       103: q^3+4q^2+3q+1
       104: q^2+2q+1
       105: 2q+1
       106: q^2+3q+1
       107: q^2+3q+1
       108: 2q+1
       109: q^2+3q+1
       110: 2q+1
       111: q+1
       112: q^2+2q+1
       113: q^3+3q^2+3q+1
       114: q^2+3q+1
       115: q^2+3q+1
       116: 2q+1
       117: q^2+3q+1
       118: q^2+2q+1
       119: q^3+3q^2+3q+1
       120: q^3+3q^2+3q+1
       121: q^2+3q+1
       122: q^2+2q+1
       123: q^3+3q^2+3q+1
       124: 2q^2+3q+1
       125: q^3+3q^2+3q+1
       126: q^2+3q+1
       127: 2q+1
       128: 2q^2+3q+1
       129: 2q^3+5q^2+3q+1
       130: q^3+3q^2+3q+1
       131: 2q^2+3q+1
       132: q^3+4q^2+3q+1
       133: q^3+4q^2+3q+1
       134: 2q+1
       135: 2q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: q^2+3q+1
       140: 2q+1
       141: 2q^2+3q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q+1
       145: 2q^2+3q+1
       146: q^3+3q^2+3q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: q^3+4q^2+3q+1
       150: q^2+2q+1
       151: 2q^2+3q+1
       152: q^3+3q^2+3q+1
       153: q^3+3q^2+3q+1
       154: q^3+3q^2+3q+1
       155: q^2+2q+1
       156: q^3+3q^2+3q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: 2q+1
       160: q^2+3q+1
       161: q^2+2q+1
       162: q^3+3q^2+3q+1
       163: q^3+3q^2+3q+1
       164: q^2+3q+1
       165: q^2+2q+1
       166: q^3+3q^2+3q+1
       167: 2q^3+5q^2+3q+1
       168: q^3+3q^2+3q+1
       169: q^3+3q^2+3q+1
       170: 2q^3+5q^2+3q+1
       171: q^3+3q^2+3q+1
       172: 2q^2+3q+1
       173: 2q^3+5q^2+3q+1
       174: 2q^3+5q^2+3q+1
       175: q^3+4q^2+3q+1
       176: 2q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: 2q+1
       180: 2q^2+3q+1
       181: q^3+4q^2+3q+1
       182: q^2+2q+1
       183: 2q^2+3q+1
       184: q^3+3q^2+3q+1
       185: q^3+3q^2+3q+1
       186: q^3+4q^2+3q+1
       187: q^3+4q^2+3q+1
       188: q^3+3q^2+3q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: q^2+3q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: 2q+1
       200: q^2+3q+1
       201: q^2+3q+1
       202: 2q+1
       203: q^2+3q+1
       204: 2q+1
       205: q+1
       206: q^2+2q+1
       207: q^3+3q^2+3q+1
       208: q^2+3q+1
       209: q^2+3q+1
       210: 2q+1
       211: q^2+3q+1
       212: q^2+2q+1
       213: 2q+1
       214: 2q^2+3q+1
       215: q^2+3q+1
       216: q^2+3q+1
       217: 2q+1
       218: q^2+3q+1
       219: 2q+1
       220: 2q^2+3q+1
       221: q^3+3q^2+3q+1
       222: q^2+3q+1
       223: 2q+1
       224: 2q^2+3q+1
       225: q^3+4q^2+3q+1
       226: q^2+2q+1
       227: 2q^2+3q+1
       228: 2q+1
       229: 2q+1
       230: q^2+3q+1
       231: q^2+3q+1
       232: 2q+1
       233: q^2+3q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q^2+3q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: 2q+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       247: q^2+2q+1
       248: 2q^2+3q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: 2q^2+3q+1
       253: q^3+3q^2+3q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^3+3q^2+3q+1
       257: q^3+3q^2+3q+1
       258: q^2+2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q^2+3q+1
       262: 2q+1
       263: q^2+3q+1
       264: 2q+1
       265: q+1
       266: q^2+2q+1
       267: q^3+3q^2+3q+1
       268: q^2+3q+1
       269: q^2+3q+1
       270: 2q+1
       271: q^2+3q+1
       272: q^2+2q+1
       273: q^3+3q^2+3q+1
       274: q^3+3q^2+3q+1
       275: q^2+3q+1
       276: q^2+2q+1
       277: q^3+3q^2+3q+1
       278: 2q^2+3q+1
       279: q^3+3q^2+3q+1
       280: q^2+3q+1
       281: 2q+1
       282: 2q^2+3q+1
       283: 2q^3+5q^2+3q+1
       284: q^3+3q^2+3q+1
       285: 2q^2+3q+1
       286: q^3+4q^2+3q+1
       287: q^3+4q^2+3q+1
       288: 2q+1
       289: 2q^2+3q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: 2q+1
       293: q^2+3q+1
       294: 2q+1
       295: 2q^2+3q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q+1
       299: 2q^2+3q+1
       300: q^3+3q^2+3q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: q^3+4q^2+3q+1
       304: q^2+2q+1
       305: 2q^2+3q+1
       306: q^3+3q^2+3q+1
       307: q^3+3q^2+3q+1
       308: q^3+3q^2+3q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       315: q+1
       316: 1
       317: q+1
       319: q+1
       320: 2q+1
       321: 2q+1
       322: q^2+3q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       328: q^2+2q+1
       329: 2q+1
       330: q^2+3q+1
       331: q^2+3q+1
       332: 2q+1
       333: q^2+3q+1
       334: 2q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: q^2+3q+1
       339: q^2+3q+1
       340: 2q+1
       341: q^2+3q+1
       342: 2q+1
       343: q+1
       344: 2q+1
       345: 2q^2+3q+1
       346: q^2+3q+1
       347: q^2+3q+1
       348: 2q+1
       349: q^2+3q+1
       350: 2q+1
       351: 2q^2+3q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: 2q^2+3q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: q^2+3q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: q+1
       374: q^2+2q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: q+1
       380: 2q+1
       381: 2q^2+3q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: 2q+1
       387: q^2+2q+1
       388: q^2+2q+1
       389: q+1
       390: q+1
       391: q^2+2q+1
       392: q^3+3q^2+3q+1
       393: q^2+2q+1
       394: q^2+2q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: q^2+3q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: q^2+2q+1
       405: 2q+1
       406: q^2+3q+1
       407: q^2+3q+1
       408: 2q+1
       409: q^2+3q+1
       410: 2q+1
       411: q+1
       412: q^2+2q+1
       413: q^3+3q^2+3q+1
       414: q^2+3q+1
       415: q^2+3q+1
       416: 2q+1
       417: q^2+3q+1
       418: q^2+2q+1
       419: 2q+1
       420: 2q^2+3q+1
       421: q^2+3q+1
       422: q^2+3q+1
       423: 2q+1
       424: q^2+3q+1
       425: 2q+1
       426: 2q^2+3q+1
       427: q^3+3q^2+3q+1
       428: q^2+3q+1
       429: 2q+1
       430: 2q^2+3q+1
       431: q^3+4q^2+3q+1
       432: q^2+2q+1
       433: 2q^2+3q+1
       434: 2q+1
       435: 2q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: 2q+1
       439: q^2+3q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q^2+3q+1
       444: 2q+1
       445: 2q+1
       446: q+1
       447: 2q+1
       448: 2q+1
       449: q^2+2q+1
       450: q^2+2q+1
       451: q+1
       452: q+1
       453: q^2+2q+1
       454: 2q^2+3q+1
       455: q^2+2q+1
       456: 2q+1
       457: 2q+1
       458: 2q^2+3q+1
       459: q^3+3q^2+3q+1
       460: q^2+2q+1
       461: q^2+2q+1
       462: q^3+3q^2+3q+1
       463: q^3+3q^2+3q+1
       465: q+1
       466: 1
       467: q+1
       470: 1
       471: 1
       473: q+1
       474: q+1
       475: 2q+1
       476: q+1
       477: q+1
       479: q+1
       480: 1
       481: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: q^2+3q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: q^2+3q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: q^2+3q+1
       504: q^2+3q+1
       505: 2q+1
       506: q^2+3q+1
       507: 2q+1
       508: q+1
       509: 2q+1
       510: 2q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: q+1
       514: 2q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: 2q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 1
       551: q+1
       552: q^2+2q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: q+1
       558: q^2+2q+1
       559: q^2+2q+1
       560: q+1
       561: q+1
       562: q^2+2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       569: q+1
       570: 1
       571: q+1
       573: q+1
       574: 2q+1
       575: 2q+1
       576: q^2+3q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: q+1
       581: q+1
       582: q^2+2q+1
       583: 2q+1
       584: q^2+3q+1
       585: q^2+3q+1
       586: 2q+1
       587: q^2+3q+1
       588: 2q+1
       589: q+1
       590: 2q+1
       591: 2q+1
       592: q^2+3q+1
       593: q^2+3q+1
       594: 2q+1
       595: q^2+3q+1
       596: 2q+1
       597: q+1
       598: 2q+1
       599: 2q^2+3q+1
       600: q^2+3q+1
       601: q^2+3q+1
       602: 2q+1
       603: q^2+3q+1
       604: 2q+1
       605: 2q^2+3q+1
       606: q^2+2q+1
       607: 2q+1
       608: 2q+1
       609: 2q^2+3q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: q^2+3q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: 2q+1
       622: 2q+1
       623: q+1
       624: 2q+1
       625: q+1
       626: 1
       627: q+1
       628: q^2+2q+1
       629: q+1
       630: q+1
       631: 1
       632: q+1
       633: q+1
       634: 2q+1
       635: 2q^2+3q+1
       636: 2q+1
       637: 2q+1
       638: q+1
       639: 2q+1
       640: 2q+1
       641: q^2+2q+1
       642: q^2+2q+1
       643: q+1
       644: q+1
       645: q^2+2q+1
       646: q^3+3q^2+3q+1
       647: q^2+2q+1
       648: q^2+2q+1
       650: 1
       651: 1
       655: 1
       658: q+1
       659: 1
       660: q+1
       663: 1
       664: 1
       666: q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       672: q+1
       673: 1
       674: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       682: q+1
       683: 1
       684: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: q^2+3q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       696: q+1
       697: 2q+1
       698: 2q+1
       699: q+1
       700: 2q+1
       701: q+1
       702: 1
       704: q+1
       705: 1
       706: q+1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: q+1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: q+1
       749: q^2+2q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: q+1
       756: q+1
       757: 1
       758: q+1
       761: 1
       762: 1
       764: q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       770: q+1
       771: 1
       772: q+1
       774: q+1
       775: 2q+1
       776: 2q+1
       777: q^2+3q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: q+1
       782: q+1
       783: q+1
       784: 2q+1
       785: 2q+1
       786: q^2+3q+1
       787: q+1
       788: q+1
       789: 2q+1
       790: q+1
       791: q+1
       792: 2q+1
       793: 2q+1
       794: q^2+3q+1
       795: q^2+3q+1
       796: 2q+1
       797: q^2+3q+1
       798: 2q+1
       799: q+1
       800: 2q+1
       801: 2q^2+3q+1
       802: 2q+1
       803: 2q+1
       804: q+1
       805: 2q+1
       806: 2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: 2q+1
       821: 1
       822: q+1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: q+1
       829: q+1
       830: 1
       831: q+1
       832: 1
       833: 1
       834: 2q+1
       835: q+1
       836: 2q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: q+1
       841: 1
       842: q+1
       843: q^2+2q+1
       844: q+1
       845: q+1
       846: 1
       847: q+1
       848: q+1
       849: q^2+2q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       853: q^2+2q+1
       855: 1
       862: 1
       863: 1
       867: 1
       870: q+1
       871: 1
       872: q+1
       875: 1
       876: 1
       879: q+1
       880: 1
       881: q+1
       884: 1
       885: 1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       893: q+1
       894: 1
       895: q+1
       897: 1
       898: q+1
       899: q+1
       900: 2q+1
       901: 1
       902: q+1
       903: q+1
       904: 1
       905: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       952: q+1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: 1
       961: 1
       962: 1
       966: 1
       969: q+1
       970: 1
       971: q+1
       974: 1
       975: 1
       977: q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       983: q+1
       984: 1
       985: q+1
       987: q+1
       988: q+1
       989: 2q+1
       990: q+1
       991: q+1
       993: q+1
       994: 1
       995: q+1
       997: q+1
       998: 2q+1
       999: 2q+1
      1000: q^2+3q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1006: 2q+1
      1007: q+1
      1008: 2q+1
      1009: 2q+1
      1010: q+1
      1011: 2q+1
      1012: q+1
      1013: 1
      1015: q+1
      1016: 1
      1017: q+1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: q+1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: 2q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: q+1
      1052: 1
      1053: q+1
      1054: q+1
      1055: 1
      1056: q+1
      1057: 1
      1058: 1
      1059: q+1
      1060: q^2+2q+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: q+1
      1065: q+1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1092: 1
      1095: q+1
      1096: 1
      1097: q+1
      1100: 1
      1101: 1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1111: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1131: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: q+1
      1182: 1
      1183: q+1
      1186: 1
      1187: 1
      1190: q+1
      1191: 1
      1192: q+1
      1195: 1
      1196: 1
      1198: q+1
      1199: q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1204: q+1
      1205: 1
      1206: q+1
      1208: 1
      1209: q+1
      1210: q+1
      1211: 2q+1
      1212: 1
      1213: q+1
      1214: q+1
      1215: 1
      1216: 1
      1218: 1
      1219: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1250: q+1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: q+1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: q+1
      1264: 1
      1265: q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1270: 1
      1280: 1
      1287: 1
      1294: 1
      1295: 1
      1299: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1316: 1
      1331: 1
      1332: 1
      1336: 1
      1339: 1
      1341: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1363: 1
      1370: 1
      1371: 1
      1375: 1
      1378: 1
      1379: 1
      1383: 1
      1386: q+1
      1387: 1
      1388: q+1
      1391: 1
      1392: 1
      1394: 1
      1395: 1
      1396: q+1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1402: 1
      1405: 1
      1412: 1
      1413: 1
      1417: 1
      1420: 1
      1422: 1
      1429: 1
      1430: 1
      1431: 1
      1434: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1447: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1453: 1
      1454: 1
      1455: 1
      1472: 1
      1479: 1
      1480: 1
      1484: 1
      1502: 1
      1517: 1
      1519: 1
      1534: 1
      1541: 1
      1548: 1
      1549: 1
      1553: 1
      1556: 1
      1557: 1
      1558: 1
      1561: 1
      1562: 1
      1570: 1
      1585: 1
      1586: 1
      1590: 1
      1593: 1
      1595: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1609: 1
      1626: 1
      1678: 1
      1685: 1
      1686: 1
      1690: 1
      1708: 1
      1723: 1
      1725: 1
      1780: 1

1781:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: 1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: 1
        62: q^2+q+1
        63: q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: 1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: 1
        89: q^2+q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q^2+q+1
       113: 1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q^2+q+1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: 1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: 1
       167: q^2+q+1
       168: q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q^2+q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       226: 1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: q+1
       249: 1
       250: 1
       251: q+1
       252: 1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q^2+q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q^2+q+1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: 1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: q+1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: 1
       389: 1
       390: q+1
       392: q+1
       393: 1
       394: q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q^2+q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: 1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: q+1
       455: 1
       456: 1
       457: q+1
       458: 1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q+1
       553: 1
       554: 1
       555: 1
       558: q+1
       559: 1
       560: 1
       561: q+1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: 1
       607: 1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: q+1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: q+1
       642: 1
       643: 1
       644: q+1
       646: q+1
       647: 1
       648: q+1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: q+1
       750: 1
       751: 1
       752: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       787: q+1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: 1
       845: 1
       846: 1
       849: q+1
       850: 1
       851: 1
       852: q+1
       856: 1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       907: 1
       909: 1
       911: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: q+1
       992: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: q+1
      1061: 1
      1062: 1
      1063: 1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1149: 1
      1158: 1
      1160: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1267: 1
      1281: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1317: 1
      1331: 1
      1333: 1
      1335: 1
      1350: 1
      1364: 1
      1370: 1
      1372: 1
      1374: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1406: 1
      1412: 1
      1414: 1
      1416: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1440: 1
      1449: 1
      1451: 1
      1473: 1
      1479: 1
      1481: 1
      1483: 1
      1503: 1
      1535: 1
      1542: 1
      1548: 1
      1550: 1
      1552: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1571: 1
      1585: 1
      1587: 1
      1589: 1
      1604: 1
      1627: 1
      1679: 1
      1685: 1
      1687: 1
      1689: 1
      1709: 1
      1781: 1

1782:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: 1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q+1
        49: q^2+q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+q+1
        69: q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q^2+q+1
        80: 1
        81: q^2+q+1
        82: 1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q^2+q+1
        95: q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: 1
       102: q^2+q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q^2+q+1
       153: 1
       154: q^2+q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+q+1
       174: q+1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q^2+q+1
       185: 1
       186: q^2+q+1
       187: 1
       188: q^2+q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+q+1
       307: 1
       308: q^2+q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+q+1
       463: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: q+1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: q+1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       943: 1
       944: 1
       950: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: q+1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       988: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1040: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1088: 1
      1089: 1
      1090: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: 1
      1156: 1
      1157: 1
      1163: 1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1219: 1
      1220: 1
      1221: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1261: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1282: 1
      1289: 1
      1295: 1
      1296: 1
      1297: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1348: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1379: 1
      1380: 1
      1381: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1407: 1
      1413: 1
      1414: 1
      1415: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1438: 1
      1447: 1
      1448: 1
      1454: 1
      1474: 1
      1480: 1
      1481: 1
      1482: 1
      1504: 1
      1536: 1
      1543: 1
      1549: 1
      1550: 1
      1551: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1572: 1
      1586: 1
      1587: 1
      1588: 1
      1602: 1
      1628: 1
      1680: 1
      1686: 1
      1687: 1
      1688: 1
      1710: 1
      1782: 1

1783:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^2+q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q+1
        78: 2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 2q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+q+1
       105: q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+q+1
       113: q^2+q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: q^2+q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q+1
       148: q+1
       149: q^2+2q+1
       150: q+1
       151: 2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q^2+q+1
       156: q^2+q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: q^2+2q+1
       162: q^2+q+1
       163: q^2+2q+1
       164: 2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: 2q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q^2+2q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       182: q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       198: q^2+q+1
       199: q+1
       200: q+1
       201: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: q^2+q+1
       207: q^2+q+1
       208: q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: q^2+2q+1
       213: q+1
       214: q+1
       215: q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: 2q+1
       253: q^2+2q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q^2+q+1
       267: q^2+q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: q^2+2q+1
       273: q^2+q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q^2+2q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q+1
       302: q+1
       303: q^2+2q+1
       304: q+1
       305: 2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: 1
       325: 2q+1
       326: q+1
       327: q+1
       328: q^2+q+1
       329: q+1
       330: q+1
       331: q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: q+1
       352: q+1
       353: q+1
       354: 2q+1
       355: 2q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: 2q+1
       387: q+1
       388: q+1
       389: 1
       390: q+1
       391: q+1
       392: q^2+2q+1
       393: q+1
       394: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       404: q^2+q+1
       405: q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q+1
       412: q^2+q+1
       413: q^2+q+1
       414: q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: q^2+2q+1
       419: q+1
       420: q+1
       421: q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: q+1
       427: q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q^2+2q+1
       432: q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       457: 2q+1
       458: 2q+1
       459: q^2+2q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: 1
       480: 1
       481: q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: 2q+1
       490: q+1
       491: q+1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: 1
       498: 2q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: q+1
       510: q+1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: 2q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: 1
       523: 1
       524: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: q+1
       552: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q+1
       558: q+1
       559: q+1
       560: 1
       561: q+1
       562: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: 2q+1
       580: q+1
       581: q+1
       582: q^2+q+1
       583: q+1
       584: q+1
       585: q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: q+1
       606: q+1
       607: q+1
       608: 2q+1
       609: 2q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: q+1
       635: q+1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: 2q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q+1
       653: 1
       654: 1
       655: 1
       660: q+1
       661: 1
       662: 1
       663: 1
       664: 1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: q+1
       678: q+1
       679: q+1
       680: q+1
       681: 1
       682: 1
       683: 1
       684: q+1
       687: q+1
       688: q+1
       689: q+1
       690: q+1
       691: 1
       692: 2q+1
       693: q+1
       694: q+1
       695: q+1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       706: q+1
       707: 1
       708: 1
       709: 1
       710: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: q+1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: 2q+1
       781: q+1
       782: q+1
       784: q+1
       785: q+1
       786: q+1
       787: q+1
       788: 1
       789: 2q+1
       790: q+1
       791: q+1
       792: q+1
       793: q+1
       794: q+1
       795: q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: q+1
       800: q+1
       801: q+1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: 2q+1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: 1
       814: 1
       815: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       858: 1
       865: 1
       866: 1
       867: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       881: q+1
       882: 1
       883: 1
       884: 1
       885: 1
       889: q+1
       890: q+1
       891: q+1
       892: 1
       893: 1
       894: 1
       895: q+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       910: 1
       911: 1
       912: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       931: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       964: 1
       965: 1
       966: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: q+1
       989: q+1
       990: q+1
       991: q+1
       992: 1
       993: 1
       994: 1
       995: q+1
       998: q+1
       999: q+1
      1000: q+1
      1001: q+1
      1002: 1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1017: q+1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1090: 1
      1091: 1
      1092: 1
      1097: q+1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1192: q+1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1200: q+1
      1201: q+1
      1202: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: q+1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1283: 1
      1290: 1
      1297: 1
      1298: 1
      1299: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1319: 1
      1334: 1
      1335: 1
      1336: 1
      1341: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1366: 1
      1373: 1
      1374: 1
      1375: 1
      1381: 1
      1382: 1
      1383: 1
      1388: q+1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1408: 1
      1415: 1
      1416: 1
      1417: 1
      1422: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1453: 1
      1454: 1
      1455: 1
      1475: 1
      1482: 1
      1483: 1
      1484: 1
      1505: 1
      1519: 1
      1537: 1
      1544: 1
      1551: 1
      1552: 1
      1553: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1573: 1
      1588: 1
      1589: 1
      1590: 1
      1595: 1
      1603: 1
      1604: 1
      1605: 1
      1609: 1
      1629: 1
      1681: 1
      1688: 1
      1689: 1
      1690: 1
      1711: 1
      1725: 1
      1783: 1

1784:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: 1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: q^2+1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: 1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       105: q^2+1
       107: q^2+1
       108: q^2+1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: 1
       118: 1
       119: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q^2+1
       157: q^2+1
       158: q^2+1
       159: q^2+1
       160: 1
       161: 1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       191: q^2+1
       193: q^2+1
       194: 1
       195: 1
       196: 1
       197: 1
       199: q^2+1
       201: q^2+1
       202: q^2+1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       259: q^2+1
       261: q^2+1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: 1
       273: q^2+1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: q^2+1
       314: 1
       316: 1
       317: 1
       318: 1
       321: q^2+1
       323: q^2+1
       324: 1
       325: 1
       326: 1
       327: 1
       329: q^2+1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       397: q^2+1
       399: q^2+1
       400: 1
       401: 1
       402: 1
       403: 1
       405: q^2+1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       469: 1
       471: 1
       472: 1
       476: q^2+1
       478: 1
       480: 1
       481: 1
       482: 1
       485: q^2+1
       487: q^2+1
       488: 1
       489: 1
       490: 1
       491: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       519: 1
       521: 1
       523: 1
       524: 1
       525: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       566: q^2+1
       568: 1
       570: 1
       571: 1
       572: 1
       575: q^2+1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: 1
       583: q^2+1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       634: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       654: 1
       656: 1
       662: 1
       664: 1
       665: 1
       669: q^2+1
       671: 1
       673: 1
       674: 1
       675: 1
       679: 1
       681: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 1
       710: 1
       711: 1
       715: 1
       717: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       760: 1
       762: 1
       763: 1
       767: q^2+1
       769: 1
       771: 1
       772: 1
       773: 1
       776: q^2+1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: 1
       816: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       859: 1
       866: 1
       868: 1
       874: 1
       876: 1
       877: 1
       883: 1
       885: 1
       886: 1
       890: 1
       892: 1
       894: 1
       895: 1
       896: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       911: 1
       913: 1
       919: 1
       921: 1
       922: 1
       926: 1
       936: 1
       938: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       965: 1
       967: 1
       973: 1
       975: 1
       976: 1
       980: q^2+1
       982: 1
       984: 1
       985: 1
       986: 1
       990: 1
       992: 1
       994: 1
       995: 1
       996: 1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1022: 1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1076: 1
      1083: 1
      1085: 1
      1091: 1
      1093: 1
      1099: 1
      1101: 1
      1102: 1
      1106: 1
      1108: 1
      1110: 1
      1111: 1
      1112: 1
      1118: 1
      1125: 1
      1127: 1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1170: 1
      1177: 1
      1179: 1
      1185: 1
      1187: 1
      1188: 1
      1194: 1
      1196: 1
      1197: 1
      1201: 1
      1203: 1
      1205: 1
      1206: 1
      1207: 1
      1210: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1222: 1
      1224: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1247: 1
      1249: 1
      1251: 1
      1252: 1
      1253: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1267: 1
      1284: 1
      1291: 1
      1298: 1
      1300: 1
      1306: 1
      1308: 1
      1309: 1
      1320: 1
      1335: 1
      1337: 1
      1350: 1
      1367: 1
      1374: 1
      1376: 1
      1382: 1
      1384: 1
      1390: 1
      1392: 1
      1393: 1
      1397: 1
      1399: 1
      1401: 1
      1402: 1
      1403: 1
      1409: 1
      1416: 1
      1418: 1
      1433: 1
      1435: 1
      1436: 1
      1440: 1
      1449: 1
      1451: 1
      1476: 1
      1483: 1
      1485: 1
      1506: 1
      1538: 1
      1545: 1
      1552: 1
      1554: 1
      1560: 1
      1562: 1
      1563: 1
      1574: 1
      1589: 1
      1591: 1
      1604: 1
      1630: 1
      1682: 1
      1689: 1
      1691: 1
      1712: 1
      1784: 1

1785:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        51: q^2+1
        52: q^2+1
        53: q^2+q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q+1
        71: 1
        72: q^2+q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       106: q^2+1
       107: q^2+1
       108: q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q+1
       113: q^2+1
       114: q^2+1
       115: q^2+q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q^2+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q^2+q+1
       124: 1
       125: q^2+q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q+1
       132: q+1
       133: q+1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       156: q^2+1
       157: q^2+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q^2+q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q^2+q+1
       171: q^2+q+1
       172: q+1
       173: q^2+q+1
       174: q^2+q+1
       175: q+1
       176: 1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       192: q^2+1
       193: q^2+1
       194: 1
       195: q^2+q+1
       196: q+1
       197: q+1
       200: q^2+1
       201: q^2+1
       202: q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q+1
       207: q^2+1
       208: q^2+1
       209: q^2+q+1
       210: q^2+q+1
       211: q^2+q+1
       212: q^2+q+1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       260: q^2+1
       261: q^2+1
       262: q^2+q+1
       263: q^2+q+1
       264: q^2+q+1
       265: q+1
       267: q^2+1
       268: q^2+1
       269: q^2+q+1
       270: q^2+q+1
       271: q^2+q+1
       272: q^2+q+1
       273: q^2+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q^2+q+1
       278: 1
       279: q^2+q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+q+1
       284: q^2+q+1
       285: q+1
       286: q+1
       287: q+1
       289: 1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       313: q^2+1
       315: 1
       316: 1
       317: q+1
       318: q+1
       322: q^2+1
       323: q^2+1
       324: 1
       325: q^2+q+1
       326: q+1
       327: q+1
       330: q^2+1
       331: q^2+1
       332: q^2+q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       345: 1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       398: q^2+1
       399: q^2+1
       400: 1
       401: q^2+q+1
       402: q+1
       403: q+1
       406: q^2+1
       407: q^2+1
       408: q^2+q+1
       409: q^2+q+1
       410: q^2+q+1
       411: q+1
       413: q^2+1
       414: q^2+1
       415: q^2+q+1
       416: q^2+q+1
       417: q^2+q+1
       418: q^2+q+1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q^2+q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       436: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       470: 1
       471: 1
       472: q+1
       477: q^2+1
       479: 1
       480: 1
       481: q+1
       482: q+1
       486: q^2+1
       487: q^2+1
       488: 1
       489: q^2+q+1
       490: q+1
       491: q+1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       510: 1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       520: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       567: q^2+1
       569: 1
       570: 1
       571: q+1
       572: q+1
       576: q^2+1
       577: q^2+1
       578: 1
       579: q^2+q+1
       580: q+1
       581: q+1
       584: q^2+1
       585: q^2+1
       586: q^2+q+1
       587: q^2+q+1
       588: q^2+q+1
       589: q+1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       599: 1
       600: 1
       601: q+1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       655: 1
       656: 1
       663: 1
       664: 1
       665: q+1
       670: q^2+1
       672: 1
       673: 1
       674: q+1
       675: q+1
       680: 1
       682: 1
       683: 1
       684: q+1
       685: q+1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       709: 1
       710: 1
       711: q+1
       716: 1
       718: 1
       719: 1
       720: 1
       721: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       761: 1
       762: 1
       763: q+1
       768: q^2+1
       770: 1
       771: 1
       772: q+1
       773: q+1
       777: q^2+1
       778: q^2+1
       779: 1
       780: q^2+q+1
       781: q+1
       782: q+1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       791: q+1
       794: 1
       795: 1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       801: 1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: q+1
       811: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       860: 1
       867: 1
       868: 1
       875: 1
       876: 1
       877: q+1
       884: 1
       885: 1
       886: q+1
       891: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       912: 1
       913: 1
       920: 1
       921: 1
       922: 1
       927: 1
       931: 1
       932: 1
       937: 1
       939: 1
       940: 1
       941: 1
       942: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: q+1
       981: q^2+1
       983: 1
       984: 1
       985: q+1
       986: q+1
       991: 1
       993: 1
       994: 1
       995: q+1
       996: q+1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1005: q+1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1020: 1
      1021: 1
      1022: q+1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1077: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1100: 1
      1101: 1
      1102: q+1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1119: 1
      1126: 1
      1127: 1
      1136: 1
      1143: 1
      1144: 1
      1145: 1
      1150: 1
      1154: 1
      1155: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1171: 1
      1178: 1
      1179: 1
      1186: 1
      1187: 1
      1188: q+1
      1195: 1
      1196: 1
      1197: q+1
      1202: 1
      1204: 1
      1205: 1
      1206: q+1
      1207: q+1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: 1
      1216: 1
      1223: 1
      1224: 1
      1231: 1
      1232: 1
      1233: 1
      1238: 1
      1242: 1
      1243: 1
      1248: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1285: 1
      1292: 1
      1299: 1
      1300: 1
      1307: 1
      1308: 1
      1309: 1
      1321: 1
      1336: 1
      1337: 1
      1346: 1
      1351: 1
      1355: 1
      1356: 1
      1368: 1
      1375: 1
      1376: 1
      1383: 1
      1384: 1
      1391: 1
      1392: 1
      1393: q+1
      1398: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1410: 1
      1417: 1
      1418: 1
      1427: 1
      1434: 1
      1435: 1
      1436: 1
      1441: 1
      1445: 1
      1446: 1
      1450: 1
      1451: 1
      1453: 1
      1454: 1
      1455: 1
      1477: 1
      1484: 1
      1485: 1
      1507: 1
      1524: 1
      1539: 1
      1546: 1
      1553: 1
      1554: 1
      1561: 1
      1562: 1
      1563: 1
      1575: 1
      1590: 1
      1591: 1
      1600: 1
      1605: 1
      1609: 1
      1610: 1
      1631: 1
      1683: 1
      1690: 1
      1691: 1
      1713: 1
      1730: 1
      1785: 1

1786:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: 1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: 1
        26: 1
        27: 1
        28: q+1
        29: 1
        30: q+1
        31: 1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: q+1
        69: 1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       482: 1
       483: 1
       484: 1
       490: 1
       491: 1
       492: 1
       493: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       666: 1
       667: 1
       675: 1
       676: 1
       677: 1
       685: 1
       686: 1
       687: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       869: 1
       878: 1
       887: 1
       888: 1
       896: 1
       897: 1
       898: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       977: 1
       978: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1074: 1
      1094: 1
      1103: 1
      1104: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1301: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1318: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1365: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1456: 1
      1486: 1
      1487: 1
      1488: 1
      1516: 1
      1525: 1
      1526: 1
      1527: 1
      1555: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1572: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1632: 1
      1662: 1
      1692: 1
      1693: 1
      1694: 1
      1722: 1
      1786: 1

1787:    0: q^3+3q^2+3q+1
         1: 2q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: 2q^2+3q+1
         7: 2q^2+3q+1
         8: 2q^2+3q+1
         9: q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: 2q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: 2q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: 2q+1
        21: 2q^2+3q+1
        22: q^2+3q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: q^2+3q+1
        26: 2q+1
        27: 2q^2+3q+1
        28: q^2+3q+1
        29: 2q^2+3q+1
        30: q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: 2q^2+3q+1
        34: 2q^2+3q+1
        35: 2q^2+3q+1
        36: q^2+3q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: 2q^2+3q+1
        41: 2q^2+3q+1
        42: 2q^2+3q+1
        43: q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: 2q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: 2q^2+3q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q^2+3q+1
        61: 2q^2+3q+1
        62: q^2+3q+1
        63: 2q+1
        64: q^2+2q+1
        65: q^2+3q+1
        66: 2q+1
        67: q^2+2q+1
        68: q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+3q+1
        71: 2q+1
        72: 2q^2+3q+1
        73: q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: q^2+3q+1
        77: 2q+1
        78: 2q^2+3q+1
        79: q^2+3q+1
        80: 2q^2+3q+1
        81: q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: 2q+1
        85: 2q^2+3q+1
        86: q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: q^2+3q+1
        90: 2q+1
        91: 2q^2+3q+1
        92: q^2+3q+1
        93: 2q^2+3q+1
        94: q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: 2q^2+3q+1
        98: 2q^2+3q+1
        99: 2q^2+3q+1
       100: q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: q^2+3q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q^2+3q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q+1
       125: 2q+1
       126: q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+3q+1
       130: 2q+1
       131: 2q+1
       132: q^2+3q+1
       133: q^2+3q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: q^2+3q+1
       140: 2q^2+3q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q^2+3q+1
       145: 2q^2+3q+1
       146: q^2+3q+1
       147: 2q+1
       148: q^2+2q+1
       149: q^2+3q+1
       150: 2q+1
       151: q^2+2q+1
       152: q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+3q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: 2q^2+3q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q^2+3q+1
       166: 2q^2+3q+1
       167: q^2+3q+1
       168: 2q+1
       169: q^2+2q+1
       170: q^2+3q+1
       171: 2q+1
       172: q^2+2q+1
       173: q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+3q+1
       176: 2q+1
       177: 2q^2+3q+1
       178: q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: q^2+3q+1
       182: 2q+1
       183: 2q^2+3q+1
       184: q^2+3q+1
       185: 2q^2+3q+1
       186: q^2+3q+1
       187: 2q^2+3q+1
       188: 2q^2+3q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: q^2+3q+1
       196: q^2+3q+1
       197: q^2+3q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: q+1
       207: q+1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q^2+2q+1
       213: q+1
       214: q+1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+2q+1
       220: q+1
       221: 2q+1
       222: q+1
       223: 2q+1
       224: 2q+1
       225: q^2+3q+1
       226: q+1
       227: 2q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: q^2+3q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q^2+3q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q+1
       249: 2q+1
       250: q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+3q+1
       254: 2q+1
       255: 2q+1
       256: q^2+3q+1
       257: q^2+3q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: q^2+3q+1
       263: q^2+3q+1
       264: q^2+3q+1
       265: q^2+3q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q^2+3q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: q^2+3q+1
       284: 2q+1
       285: 2q+1
       286: q^2+3q+1
       287: q^2+3q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: q^2+3q+1
       292: q^2+3q+1
       293: q^2+3q+1
       294: 2q^2+3q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q^2+3q+1
       299: 2q^2+3q+1
       300: q^2+3q+1
       301: 2q+1
       302: q^2+2q+1
       303: q^2+3q+1
       304: 2q+1
       305: q^2+2q+1
       306: q^2+3q+1
       307: 2q^2+3q+1
       308: q^2+3q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: q^2+3q+1
       318: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: 2q+1
       326: q+1
       327: 2q+1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 2q+1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 2q+1
       344: q+1
       345: q+1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: 2q+1
       351: q+1
       352: q+1
       353: 1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: q^2+3q+1
       363: q^2+3q+1
       364: q^2+3q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: q+1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q^2+2q+1
       380: q+1
       381: q+1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q^2+2q+1
       387: q+1
       388: 2q+1
       389: q+1
       390: 2q+1
       391: 2q+1
       392: q^2+3q+1
       393: q+1
       394: 2q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: q^2+3q+1
       402: q^2+3q+1
       403: q^2+3q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: q+1
       413: q+1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q^2+2q+1
       419: q+1
       420: q+1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q^2+2q+1
       426: q+1
       427: 2q+1
       428: q+1
       429: 2q+1
       430: 2q+1
       431: q^2+3q+1
       432: q+1
       433: 2q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: q^2+3q+1
       439: q^2+3q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q^2+3q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q^2+2q+1
       453: q^2+2q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q^2+2q+1
       458: q^2+2q+1
       459: q^2+3q+1
       460: 2q+1
       461: 2q+1
       462: q^2+3q+1
       463: q^2+3q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: q+1
       490: q+1
       491: 2q+1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       502: 1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       524: q^2+3q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: 2q+1
       533: q+1
       534: 2q+1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 2q+1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 2q+1
       551: q+1
       552: q+1
       553: 1
       554: q+1
       555: q+1
       556: q+1
       557: 2q+1
       558: q+1
       559: q+1
       560: 1
       561: 2q+1
       562: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: q^2+3q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: 2q+1
       580: q+1
       581: 2q+1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 2q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 2q+1
       598: q+1
       599: q+1
       600: 1
       601: q+1
       602: q+1
       603: q+1
       604: 2q+1
       605: q+1
       606: q+1
       607: 1
       608: 2q+1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: q^2+3q+1
       617: q^2+3q+1
       618: q^2+3q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: q+1
       628: q+1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q^2+2q+1
       634: q+1
       635: q+1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q^2+2q+1
       641: q+1
       642: 2q+1
       643: q+1
       644: 2q+1
       645: 2q+1
       646: q^2+3q+1
       647: q+1
       648: 2q+1
       650: 1
       651: 1
       652: 1
       653: q+1
       654: q+1
       655: q+1
       656: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: q+1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: q+1
       693: q+1
       694: 2q+1
       695: q+1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: q+1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: q+1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: q+1
       729: q+1
       730: 2q+1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: q+1
       738: q+1
       739: 2q+1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: q+1
       745: q+1
       746: q+1
       747: 2q+1
       748: q+1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 2q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: q+1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: q+1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: q+1
       781: q+1
       782: 2q+1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: q+1
       790: q+1
       791: 2q+1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: q+1
       797: q+1
       798: q+1
       799: 2q+1
       800: q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: q+1
       815: q^2+3q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: 2q+1
       824: q+1
       825: 2q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 2q+1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 2q+1
       842: q+1
       843: q+1
       844: 1
       845: q+1
       846: q+1
       847: q+1
       848: 2q+1
       849: q+1
       850: q+1
       851: 1
       852: 2q+1
       853: 2q+1
       855: 1
       856: 1
       857: 1
       858: q+1
       859: 1
       860: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       870: 1
       872: 1
       877: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: q+1
       907: 1
       908: 1
       909: 1
       910: q+1
       911: q+1
       912: q+1
       913: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: q+1
       932: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: q+1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: q+1
       950: q+1
       951: 2q+1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q+1
       961: 1
       962: 1
       963: 1
       964: q+1
       965: q+1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: q+1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: q+1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: q+1
      1004: q+1
      1005: 2q+1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: q+1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: q+1
      1040: q+1
      1041: 2q+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: q+1
      1049: q+1
      1050: 2q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: q+1
      1056: q+1
      1057: q+1
      1058: 2q+1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 2q+1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: q+1
      1118: 1
      1119: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1129: 1
      1131: 1
      1136: 1
      1138: 1
      1141: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: q+1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 1
      1167: 1
      1168: 1
      1169: q+1
      1170: 1
      1171: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1181: 1
      1183: 1
      1188: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: q+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: q+1
      1222: q+1
      1223: q+1
      1224: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: q+1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: q+1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: q+1
      1261: q+1
      1262: 2q+1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q+1
      1272: 1
      1273: 1
      1276: 1
      1278: 1
      1302: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1339: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1386: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1402: 1
      1403: 1
      1405: 1
      1406: 1
      1407: 1
      1408: q+1
      1409: 1
      1410: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1420: 1
      1422: 1
      1427: 1
      1429: 1
      1432: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1445: q+1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1454: 1
      1455: q+1
      1457: 1
      1487: 1
      1488: 1
      1491: 1
      1493: 1
      1517: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1532: 1
      1556: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1593: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1609: 1
      1610: 1
      1633: 1
      1663: 1
      1693: 1
      1694: 1
      1697: 1
      1699: 1
      1723: 1
      1730: 1
      1787: 1

1788:    0: 2q^3+3q^2+3q+1
         1: 2q^3+3q^2+3q+1
         2: 2q^3+3q^2+3q+1
         3: q^2+3q+1
         4: 2q^3+3q^2+3q+1
         5: 2q^3+3q^2+3q+1
         6: 2q^3+3q^2+3q+1
         7: 2q^3+3q^2+3q+1
         8: q^2+3q+1
         9: q^2+3q+1
        10: q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 2q^3+3q^2+3q+1
        14: 2q^3+3q^2+3q+1
        15: q^2+3q+1
        16: 2q^3+3q^2+3q+1
        17: 2q^3+3q^2+3q+1
        18: q^2+3q+1
        19: 2q^3+3q^2+3q+1
        20: q^2+3q+1
        21: 2q^3+3q^2+3q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: q^2+3q+1
        26: q^2+3q+1
        27: q^2+3q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: q^2+3q+1
        33: 2q^3+3q^2+3q+1
        34: 2q^3+3q^2+3q+1
        35: q^2+3q+1
        36: q^2+3q+1
        37: q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: 2q^3+3q^2+3q+1
        41: 2q^3+3q^2+3q+1
        42: q^2+3q+1
        43: q^2+3q+1
        44: q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 2q^3+3q^2+3q+1
        48: 2q^3+3q^2+3q+1
        49: q^2+3q+1
        50: q^2+3q+1
        51: q^2+3q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: q^2+3q+1
        57: q^2+3q+1
        58: q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q^2+3q+1
        64: q+1
        65: q^2+3q+1
        66: q^2+3q+1
        67: q+1
        68: q^2+3q+1
        69: q^2+3q+1
        70: 2q+1
        71: q^2+3q+1
        72: 2q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: q^2+3q+1
        77: q^2+3q+1
        78: q^2+3q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: q^2+3q+1
        84: q^2+3q+1
        85: 2q^3+3q^2+3q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: q^2+3q+1
        90: q^2+3q+1
        91: q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: q^2+3q+1
        97: 2q^3+3q^2+3q+1
        98: 2q^3+3q^2+3q+1
        99: q^2+3q+1
       100: q^2+3q+1
       101: q^2+3q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: q^2+3q+1
       105: q^2+3q+1
       106: q^2+3q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: q^2+3q+1
       111: 2q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: q^2+3q+1
       118: q^2+3q+1
       119: q+1
       120: q^2+3q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q^2+3q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+3q+1
       130: q^2+3q+1
       131: 1
       132: 2q+1
       133: 2q+1
       134: q^2+3q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: q^2+3q+1
       140: q^2+3q+1
       141: q^2+3q+1
       142: q^2+3q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: q^2+3q+1
       147: q^2+3q+1
       148: q+1
       149: q^2+3q+1
       150: q^2+3q+1
       151: q+1
       152: q^2+3q+1
       153: q^2+3q+1
       154: 2q+1
       155: q^2+3q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: q^2+3q+1
       162: q^2+3q+1
       163: q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q^2+3q+1
       169: q+1
       170: q^2+3q+1
       171: q^2+3q+1
       172: q+1
       173: q^2+3q+1
       174: q^2+3q+1
       175: 2q+1
       176: q^2+3q+1
       177: 2q^3+3q^2+3q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: q^2+3q+1
       181: q^2+3q+1
       182: q^2+3q+1
       183: q^2+3q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: q^2+3q+1
       189: 2q+1
       190: q^2+3q+1
       191: q^2+3q+1
       192: q^2+3q+1
       193: q+1
       194: q+1
       195: q^2+3q+1
       196: 2q+1
       197: 2q+1
       198: q^2+3q+1
       199: q^2+3q+1
       200: q^2+3q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: q^2+3q+1
       204: q^2+3q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q^2+3q+1
       222: 1
       223: 1
       224: 1
       225: 2q+1
       226: 2q+1
       227: 1
       228: q^2+3q+1
       229: q^2+3q+1
       230: q^2+3q+1
       231: q^2+3q+1
       232: q^2+3q+1
       233: q^2+3q+1
       234: q^2+3q+1
       235: 2q+1
       236: q^2+3q+1
       237: q^2+3q+1
       238: q^2+3q+1
       239: q^2+3q+1
       240: q^2+3q+1
       241: q^2+3q+1
       242: q^2+3q+1
       243: q+1
       244: q^2+3q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q^2+3q+1
       250: q+1
       251: q+1
       252: q+1
       253: q^2+3q+1
       254: q^2+3q+1
       255: 1
       256: 2q+1
       257: 2q+1
       258: q^2+3q+1
       259: q^2+3q+1
       260: q^2+3q+1
       261: q^2+3q+1
       262: q^2+3q+1
       263: q^2+3q+1
       264: q^2+3q+1
       265: 2q+1
       266: q^2+3q+1
       267: q^2+3q+1
       268: q^2+3q+1
       269: q^2+3q+1
       270: q^2+3q+1
       271: q^2+3q+1
       272: q^2+3q+1
       273: q+1
       274: q^2+3q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q^2+3q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+3q+1
       284: q^2+3q+1
       285: 1
       286: 2q+1
       287: 2q+1
       288: q^2+3q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: q^2+3q+1
       293: q^2+3q+1
       294: q^2+3q+1
       295: q^2+3q+1
       296: q^2+3q+1
       297: q^2+3q+1
       298: q^2+3q+1
       299: q^2+3q+1
       300: q^2+3q+1
       301: q^2+3q+1
       302: q+1
       303: q^2+3q+1
       304: q^2+3q+1
       305: q+1
       306: q^2+3q+1
       307: q^2+3q+1
       308: 2q+1
       309: 2q+1
       310: 2q+1
       311: q^2+3q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: 2q+1
       318: 2q+1
       319: 1
       320: q^2+3q+1
       321: q^2+3q+1
       322: q^2+3q+1
       323: q+1
       324: q+1
       325: q^2+3q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 2q+1
       353: 1
       354: 1
       355: 1
       356: 2q+1
       357: q^2+3q+1
       358: q^2+3q+1
       359: q^2+3q+1
       360: q+1
       361: q+1
       362: q^2+3q+1
       363: 2q+1
       364: 2q+1
       365: q^2+3q+1
       366: q^2+3q+1
       367: q^2+3q+1
       368: q^2+3q+1
       369: q^2+3q+1
       370: q^2+3q+1
       371: q^2+3q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q^2+3q+1
       389: 1
       390: 1
       391: 1
       392: 2q+1
       393: 2q+1
       394: 1
       395: 2q+1
       396: q^2+3q+1
       397: q^2+3q+1
       398: q^2+3q+1
       399: q+1
       400: q+1
       401: q^2+3q+1
       402: 2q+1
       403: 2q+1
       404: q^2+3q+1
       405: q^2+3q+1
       406: q^2+3q+1
       407: q^2+3q+1
       408: q^2+3q+1
       409: q^2+3q+1
       410: q^2+3q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q^2+3q+1
       428: 1
       429: 1
       430: 1
       431: 2q+1
       432: 2q+1
       433: 1
       434: q^2+3q+1
       435: q^2+3q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: q^2+3q+1
       439: q^2+3q+1
       440: q^2+3q+1
       441: 2q+1
       442: q^2+3q+1
       443: q^2+3q+1
       444: q^2+3q+1
       445: q^2+3q+1
       446: q^2+3q+1
       447: q^2+3q+1
       448: q^2+3q+1
       449: q+1
       450: q^2+3q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: q^2+3q+1
       456: q+1
       457: q+1
       458: q+1
       459: q^2+3q+1
       460: q^2+3q+1
       461: 1
       462: 2q+1
       463: 2q+1
       464: 2q+1
       465: 2q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: 2q+1
       473: 1
       474: 1
       475: q^2+3q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 2q+1
       517: 2q+1
       518: q^2+3q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: 2q+1
       525: 2q+1
       526: 1
       527: q^2+3q+1
       528: q^2+3q+1
       529: q^2+3q+1
       530: q+1
       531: q+1
       532: q^2+3q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 2q+1
       560: 1
       561: 1
       562: 1
       563: 2q+1
       564: 2q+1
       565: q^2+3q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: 2q+1
       572: 2q+1
       573: 1
       574: q^2+3q+1
       575: q^2+3q+1
       576: q^2+3q+1
       577: q+1
       578: q+1
       579: q^2+3q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 2q+1
       607: 1
       608: 1
       609: 1
       610: 2q+1
       611: q^2+3q+1
       612: q^2+3q+1
       613: q^2+3q+1
       614: q+1
       615: q+1
       616: q^2+3q+1
       617: 2q+1
       618: 2q+1
       619: q^2+3q+1
       620: q^2+3q+1
       621: q^2+3q+1
       622: q^2+3q+1
       623: q^2+3q+1
       624: q^2+3q+1
       625: q^2+3q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q^2+3q+1
       643: 1
       644: 1
       645: 1
       646: 2q+1
       647: 2q+1
       648: 1
       649: 2q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       674: 1
       675: 1
       676: 1
       677: 1
       678: q+1
       681: q+1
       682: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: 2q+1
       704: 2q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: 2q+1
       712: 1
       713: 1
       714: q^2+3q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: 2q+1
       756: 2q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: 2q+1
       764: 1
       765: 1
       766: q^2+3q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       785: q+1
       786: q+1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 2q+1
       808: 2q+1
       809: q^2+3q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: 2q+1
       816: 2q+1
       817: 1
       818: q^2+3q+1
       819: q^2+3q+1
       820: q^2+3q+1
       821: q+1
       822: q+1
       823: q^2+3q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 2q+1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: q+1
       877: 1
       878: 1
       879: 1
       882: q+1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       903: 1
       906: 2q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       927: q+1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       938: q+1
       939: q+1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       960: 2q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       985: 1
       986: 1
       987: 1
       988: 1
       989: q+1
       992: q+1
       993: q+1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1014: 2q+1
      1015: 2q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: 2q+1
      1023: 1
      1024: 1
      1025: q^2+3q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1105: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: q+1
      1136: 1
      1137: 1
      1138: 1
      1141: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: q+1
      1188: 1
      1189: 1
      1190: 1
      1193: q+1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1217: 2q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1249: q+1
      1250: q+1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1293: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1338: 1
      1339: 1
      1346: 1
      1349: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1377: 1
      1385: 1
      1386: 1
      1393: 1
      1396: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: q+1
      1427: 1
      1428: 1
      1429: 1
      1432: q+1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1458: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1508: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1547: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1584: 1
      1592: 1
      1593: 1
      1600: 1
      1603: 1
      1634: 1
      1664: 1
      1692: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1714: 1
      1788: 1

1789:    0: 3q^2+3q+1
         1: 3q^2+3q+1
         2: 3q^2+3q+1
         3: 3q^2+3q+1
         4: 3q^2+3q+1
         5: 3q^2+3q+1
         6: 3q^2+3q+1
         7: 3q^2+3q+1
         8: 3q^2+3q+1
         9: 3q^2+3q+1
        10: 3q^2+3q+1
        11: q^2+3q+1
        12: q^2+3q+1
        13: 3q^2+3q+1
        14: 3q^2+3q+1
        15: 3q^2+3q+1
        16: 3q^2+3q+1
        17: 3q^2+3q+1
        18: 3q^2+3q+1
        19: 3q^2+3q+1
        20: 3q^2+3q+1
        21: 3q^2+3q+1
        22: 3q^2+3q+1
        23: q^2+3q+1
        24: q^2+3q+1
        25: 3q^2+3q+1
        26: q^2+q+1
        27: 3q^2+3q+1
        28: q^2+3q+1
        29: q^2+3q+1
        30: q^2+3q+1
        31: q^2+3q+1
        32: 3q+1
        33: 3q^2+3q+1
        34: 3q^2+3q+1
        35: 3q^2+3q+1
        36: 3q^2+3q+1
        37: 3q^2+3q+1
        38: q^2+3q+1
        39: q^2+3q+1
        40: 3q^2+3q+1
        41: 3q^2+3q+1
        42: 3q^2+3q+1
        43: 3q^2+3q+1
        44: 3q^2+3q+1
        45: q^2+3q+1
        46: q^2+3q+1
        47: 3q^2+3q+1
        48: 3q^2+3q+1
        49: 3q^2+3q+1
        50: q^2+3q+1
        51: q^2+3q+1
        52: 3q^2+3q+1
        53: 3q^2+3q+1
        54: q^2+3q+1
        55: q^2+3q+1
        56: 3q+1
        57: 3q^2+3q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: q^2+3q+1
        63: q+1
        64: q^2+3q+1
        65: q^2+3q+1
        66: q+1
        67: q^2+3q+1
        68: 3q+1
        69: 3q+1
        70: 3q+1
        71: 3q^2+3q+1
        72: 3q^2+3q+1
        73: 3q^2+3q+1
        74: q^2+3q+1
        75: q^2+3q+1
        76: 3q^2+3q+1
        77: q^2+q+1
        78: 3q^2+3q+1
        79: q^2+3q+1
        80: q^2+3q+1
        81: q^2+3q+1
        82: q^2+3q+1
        83: 3q+1
        84: 3q^2+3q+1
        85: 3q^2+3q+1
        86: 3q^2+3q+1
        87: q^2+3q+1
        88: q^2+3q+1
        89: 3q^2+3q+1
        90: q^2+q+1
        91: 3q^2+3q+1
        92: q^2+3q+1
        93: q^2+3q+1
        94: q^2+3q+1
        95: q^2+3q+1
        96: 3q+1
        97: 3q^2+3q+1
        98: 3q^2+3q+1
        99: 3q^2+3q+1
       100: 3q^2+3q+1
       101: 3q^2+3q+1
       102: q^2+3q+1
       103: q^2+3q+1
       104: 3q+1
       105: q^2+3q+1
       106: q^2+3q+1
       107: 3q^2+3q+1
       108: q^2+3q+1
       109: q^2+3q+1
       110: 3q+1
       111: 3q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q+1
       118: 3q+1
       119: q^2+3q+1
       120: q+1
       121: q+1
       122: q^2+3q+1
       123: q+1
       124: q^2+3q+1
       125: q+1
       126: q+1
       127: q+1
       128: q^2+3q+1
       129: 3q+1
       130: q+1
       131: 3q+1
       132: 3q+1
       133: 3q+1
       134: q^2+3q+1
       135: q^2+3q+1
       136: 3q^2+3q+1
       137: 3q^2+3q+1
       138: q^2+3q+1
       139: q^2+3q+1
       140: 3q+1
       141: 3q^2+3q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: q^2+3q+1
       147: q+1
       148: q^2+3q+1
       149: q^2+3q+1
       150: q+1
       151: q^2+3q+1
       152: 3q+1
       153: 3q+1
       154: 3q+1
       155: q^2+3q+1
       156: q^2+3q+1
       157: 3q^2+3q+1
       158: 3q^2+3q+1
       159: q^2+3q+1
       160: q^2+3q+1
       161: 3q+1
       162: 3q^2+3q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: q^2+3q+1
       168: q+1
       169: q^2+3q+1
       170: q^2+3q+1
       171: q+1
       172: q^2+3q+1
       173: 3q+1
       174: 3q+1
       175: 3q+1
       176: 3q^2+3q+1
       177: 3q^2+3q+1
       178: 3q^2+3q+1
       179: q^2+3q+1
       180: q^2+3q+1
       181: 3q^2+3q+1
       182: q^2+q+1
       183: 3q^2+3q+1
       184: q^2+3q+1
       185: q^2+3q+1
       186: q^2+3q+1
       187: q^2+3q+1
       188: 3q+1
       189: 3q+1
       190: 3q+1
       191: q^2+3q+1
       192: q^2+3q+1
       193: q^2+3q+1
       194: q^2+3q+1
       195: 3q+1
       196: 3q+1
       197: 3q+1
       198: 3q+1
       199: q+1
       200: q+1
       201: q^2+q+1
       202: q+1
       203: q+1
       204: q+1
       205: 3q+1
       206: q^2+3q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: q+1
       213: q+1
       214: q^2+3q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: q+1
       220: 3q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 3q+1
       227: 3q+1
       228: 3q+1
       229: q^2+3q+1
       230: q^2+3q+1
       231: 3q^2+3q+1
       232: q^2+3q+1
       233: q^2+3q+1
       234: 3q+1
       235: 3q+1
       236: q^2+3q+1
       237: q^2+3q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q+1
       242: 3q+1
       243: q^2+3q+1
       244: q+1
       245: q+1
       246: q^2+3q+1
       247: q+1
       248: q^2+3q+1
       249: q+1
       250: q+1
       251: q+1
       252: q^2+3q+1
       253: 3q+1
       254: q+1
       255: 3q+1
       256: 3q+1
       257: 3q+1
       258: 3q+1
       259: q^2+3q+1
       260: q^2+3q+1
       261: 3q^2+3q+1
       262: q^2+3q+1
       263: q^2+3q+1
       264: 3q+1
       265: 3q+1
       266: q^2+3q+1
       267: q^2+3q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q+1
       271: q+1
       272: 3q+1
       273: q^2+3q+1
       274: q+1
       275: q+1
       276: q^2+3q+1
       277: q+1
       278: q^2+3q+1
       279: q+1
       280: q+1
       281: q+1
       282: q^2+3q+1
       283: 3q+1
       284: q+1
       285: 3q+1
       286: 3q+1
       287: 3q+1
       288: q^2+3q+1
       289: q^2+3q+1
       290: 3q^2+3q+1
       291: 3q^2+3q+1
       292: q^2+3q+1
       293: q^2+3q+1
       294: 3q+1
       295: 3q^2+3q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q^2+3q+1
       299: q^2+3q+1
       300: q^2+3q+1
       301: q+1
       302: q^2+3q+1
       303: q^2+3q+1
       304: q+1
       305: q^2+3q+1
       306: 3q+1
       307: 3q+1
       308: 3q+1
       309: 3q+1
       310: 3q+1
       311: 3q+1
       312: q^2+3q+1
       313: q+1
       314: q+1
       315: q^2+3q+1
       316: 3q+1
       317: 3q+1
       319: 3q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 3q+1
       328: q+1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: q+1
       336: q+1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: 3q+1
       354: q+1
       355: q+1
       356: 3q+1
       357: 3q+1
       358: q^2+3q+1
       359: q^2+3q+1
       360: q^2+3q+1
       361: q^2+3q+1
       362: 3q+1
       363: 3q+1
       364: 3q+1
       365: 3q+1
       366: q+1
       367: q+1
       368: q^2+q+1
       369: q+1
       370: q+1
       371: q+1
       372: 3q+1
       373: q^2+3q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: 1
       379: q+1
       380: q+1
       381: q^2+3q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: q+1
       387: 3q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 3q+1
       394: 3q+1
       395: 3q+1
       396: 3q+1
       397: q^2+3q+1
       398: q^2+3q+1
       399: q^2+3q+1
       400: q^2+3q+1
       401: 3q+1
       402: 3q+1
       403: 3q+1
       404: 3q+1
       405: q+1
       406: q+1
       407: q^2+q+1
       408: q+1
       409: q+1
       410: q+1
       411: 3q+1
       412: q^2+3q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: q+1
       419: q+1
       420: q^2+3q+1
       421: q+1
       422: q+1
       423: 1
       424: q+1
       425: q+1
       426: 3q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 3q+1
       433: 3q+1
       434: 3q+1
       435: q^2+3q+1
       436: q^2+3q+1
       437: 3q^2+3q+1
       438: q^2+3q+1
       439: q^2+3q+1
       440: 3q+1
       441: 3q+1
       442: q^2+3q+1
       443: q^2+3q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q+1
       447: q+1
       448: 3q+1
       449: q^2+3q+1
       450: q+1
       451: q+1
       452: q^2+3q+1
       453: q+1
       454: q^2+3q+1
       455: q+1
       456: q+1
       457: q+1
       458: q^2+3q+1
       459: 3q+1
       460: q+1
       461: 3q+1
       462: 3q+1
       463: 3q+1
       465: 3q+1
       466: 3q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 3q+1
       473: 3q+1
       474: q+1
       475: q+1
       476: q+1
       477: 1
       478: 1
       479: q+1
       480: q+1
       481: q+1
       483: q+1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: q+1
       492: q+1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: q+1
       515: 1
       516: 3q+1
       517: 3q+1
       518: 3q+1
       519: q^2+3q+1
       520: q+1
       521: q+1
       522: q^2+3q+1
       523: 3q+1
       524: 3q+1
       526: 3q+1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: 3q+1
       535: q+1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: 1
       541: 1
       542: q+1
       543: q+1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: 1
       557: 1
       558: 3q+1
       561: q+1
       562: q+1
       563: 3q+1
       564: 3q+1
       565: 3q+1
       566: q^2+3q+1
       567: q+1
       568: q+1
       569: q^2+3q+1
       570: 3q+1
       571: 3q+1
       573: 3q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: 3q+1
       582: q+1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: q+1
       590: q+1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: q+1
       596: 1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: q+1
       602: 1
       603: 1
       604: 1
       605: 3q+1
       608: q+1
       609: q+1
       610: 3q+1
       611: 3q+1
       612: q^2+3q+1
       613: q^2+3q+1
       614: q^2+3q+1
       615: q^2+3q+1
       616: 3q+1
       617: 3q+1
       618: 3q+1
       619: 3q+1
       620: q+1
       621: q+1
       622: q^2+q+1
       623: q+1
       624: q+1
       625: q+1
       626: 3q+1
       627: q^2+3q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: 1
       633: q+1
       634: q+1
       635: q^2+3q+1
       636: q+1
       637: q+1
       638: 1
       639: q+1
       640: q+1
       641: 3q+1
       642: q+1
       643: q+1
       644: q+1
       645: q+1
       646: 3q+1
       648: 3q+1
       650: 3q+1
       651: q+1
       652: q+1
       653: 1
       654: q+1
       655: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: q+1
       666: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 3q+1
       705: 3q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: 3q+1
       712: 3q+1
       713: q+1
       714: q+1
       715: q+1
       716: 1
       717: 1
       718: q+1
       719: q+1
       720: q+1
       722: q+1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: 1
       730: q+1
       731: q+1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: q+1
       754: 1
       756: 3q+1
       757: 3q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: 3q+1
       764: 3q+1
       765: q+1
       766: q+1
       767: q+1
       768: 1
       769: 1
       770: q+1
       771: q+1
       772: q+1
       774: q+1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: q+1
       783: q+1
       784: 1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: 1
       791: q+1
       792: 1
       793: 1
       794: 1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: q+1
       806: 1
       807: 3q+1
       808: 3q+1
       809: 3q+1
       810: q^2+3q+1
       811: q+1
       812: q+1
       813: q^2+3q+1
       814: 3q+1
       815: 3q+1
       817: 3q+1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: 3q+1
       826: q+1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: q+1
       834: q+1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: q+1
       842: q+1
       843: q+1
       844: q+1
       845: q+1
       846: 1
       847: 1
       848: 1
       849: 3q+1
       852: q+1
       853: q+1
       855: q+1
       856: q+1
       857: 1
       858: 1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 3q+1
       908: q+1
       909: q+1
       910: 1
       911: q+1
       912: q+1
       915: q+1
       916: q+1
       917: 1
       918: 1
       919: 1
       920: 1
       921: q+1
       923: q+1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: 3q+1
       962: q+1
       963: q+1
       964: 1
       965: q+1
       966: q+1
       969: q+1
       970: q+1
       971: 1
       972: 1
       973: 1
       974: 1
       975: q+1
       977: q+1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: 1
       985: 1
       987: q+1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 3q+1
      1016: 3q+1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1021: 3q+1
      1023: 3q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 1
      1028: 1
      1029: q+1
      1030: q+1
      1031: q+1
      1033: q+1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: q+1
      1042: q+1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: q+1
      1051: 1
      1052: 1
      1053: 1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1065: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1114: q+1
      1115: q+1
      1116: 1
      1117: 1
      1121: q+1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1166: q+1
      1167: q+1
      1168: 1
      1169: 1
      1173: q+1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: 3q+1
      1219: q+1
      1220: q+1
      1221: 1
      1222: q+1
      1223: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: q+1
      1234: q+1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1244: q+1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1270: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1288: 1
      1294: 1
      1312: 1
      1313: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1328: 1
      1331: 1
      1333: 1
      1335: 1
      1339: 1
      1340: 1
      1345: 1
      1347: 1
      1359: 1
      1360: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1375: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1387: 1
      1392: 1
      1394: 1
      1405: q+1
      1406: q+1
      1407: 1
      1408: 1
      1412: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1455: 1
      1459: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1503: 1
      1509: 1
      1526: 1
      1530: 1
      1531: 1
      1534: 1
      1542: 1
      1548: 1
      1566: 1
      1567: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1582: 1
      1585: 1
      1587: 1
      1589: 1
      1593: 1
      1594: 1
      1599: 1
      1601: 1
      1635: 1
      1665: 1
      1693: 1
      1697: 1
      1698: 1
      1701: 1
      1709: 1
      1715: 1
      1789: 1

1790:    0: 5q^2+4q+1
         1: 5q^2+4q+1
         2: 5q^2+4q+1
         3: 5q^2+4q+1
         4: 5q^2+4q+1
         5: 5q^2+4q+1
         6: 3q^2+4q+1
         7: 5q^2+4q+1
         8: 5q^2+4q+1
         9: 5q^2+4q+1
        10: 3q^2+4q+1
        11: 3q^2+4q+1
        12: 3q^2+4q+1
        13: 5q^2+4q+1
        14: 5q^2+4q+1
        15: 5q^2+4q+1
        16: 5q^2+4q+1
        17: 5q^2+4q+1
        18: 5q^2+4q+1
        19: 5q^2+4q+1
        20: 3q^2+4q+1
        21: 3q^2+4q+1
        22: 5q^2+4q+1
        23: 3q^2+4q+1
        24: 3q^2+4q+1
        25: q^2+4q+1
        26: 3q^2+4q+1
        27: 3q^2+4q+1
        28: 3q^2+4q+1
        29: q^2+4q+1
        30: 3q^2+4q+1
        31: q^2+4q+1
        32: 2q^2+4q+1
        33: 3q^2+4q+1
        34: 5q^2+4q+1
        35: 5q^2+4q+1
        36: 5q^2+4q+1
        37: 3q^2+4q+1
        38: 3q^2+4q+1
        39: 3q^2+4q+1
        40: 3q^2+4q+1
        41: 5q^2+4q+1
        42: 5q^2+4q+1
        43: 5q^2+4q+1
        44: 3q^2+4q+1
        45: 3q^2+4q+1
        46: 3q^2+4q+1
        47: 5q^2+4q+1
        48: 5q^2+4q+1
        49: 5q^2+4q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: 3q^2+4q+1
        53: q^2+4q+1
        54: 3q^2+4q+1
        55: 3q^2+4q+1
        56: 2q^2+4q+1
        57: q^2+4q+1
        58: q^2+4q+1
        59: 3q^2+4q+1
        60: q^2+4q+1
        61: q^2+4q+1
        62: 4q+1
        63: q^2+4q+1
        64: q^2+4q+1
        65: 4q+1
        66: q^2+4q+1
        67: q^2+4q+1
        68: 2q^2+4q+1
        69: 4q+1
        70: 2q^2+4q+1
        71: 3q^2+4q+1
        72: 3q^2+4q+1
        73: 5q^2+4q+1
        74: 3q^2+4q+1
        75: 3q^2+4q+1
        76: q^2+4q+1
        77: 3q^2+4q+1
        78: 3q^2+4q+1
        79: 3q^2+4q+1
        80: q^2+4q+1
        81: 3q^2+4q+1
        82: q^2+4q+1
        83: 2q^2+4q+1
        84: 3q^2+4q+1
        85: 3q^2+4q+1
        86: 5q^2+4q+1
        87: 3q^2+4q+1
        88: 3q^2+4q+1
        89: q^2+4q+1
        90: 3q^2+4q+1
        91: 3q^2+4q+1
        92: 3q^2+4q+1
        93: q^2+4q+1
        94: 3q^2+4q+1
        95: q^2+4q+1
        96: 2q^2+4q+1
        97: 3q^2+4q+1
        98: 5q^2+4q+1
        99: 5q^2+4q+1
       100: 5q^2+4q+1
       101: 3q^2+4q+1
       102: 3q^2+4q+1
       103: 3q^2+4q+1
       104: q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+4q+1
       108: 4q+1
       109: 4q+1
       110: 2q^2+4q+1
       111: 2q^2+4q+1
       112: 2q+1
       113: 2q+1
       114: q^2+4q+1
       115: q^2+4q+1
       116: q^2+4q+1
       117: q^2+4q+1
       118: 4q+1
       119: 4q+1
       120: 4q+1
       121: q^2+4q+1
       122: q^2+4q+1
       123: 2q+1
       124: 4q+1
       125: 4q+1
       126: q^2+4q+1
       127: 2q+1
       128: q^2+4q+1
       129: 4q+1
       130: 4q+1
       131: 4q+1
       132: 2q^2+4q+1
       133: 3q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 3q^2+4q+1
       137: q^2+4q+1
       138: 3q^2+4q+1
       139: 3q^2+4q+1
       140: 2q^2+4q+1
       141: q^2+4q+1
       142: q^2+4q+1
       143: 3q^2+4q+1
       144: q^2+4q+1
       145: q^2+4q+1
       146: 4q+1
       147: q^2+4q+1
       148: q^2+4q+1
       149: 4q+1
       150: q^2+4q+1
       151: q^2+4q+1
       152: 2q^2+4q+1
       153: 4q+1
       154: 2q^2+4q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: 3q^2+4q+1
       158: q^2+4q+1
       159: 3q^2+4q+1
       160: 3q^2+4q+1
       161: 2q^2+4q+1
       162: q^2+4q+1
       163: q^2+4q+1
       164: 3q^2+4q+1
       165: q^2+4q+1
       166: q^2+4q+1
       167: 4q+1
       168: q^2+4q+1
       169: q^2+4q+1
       170: 4q+1
       171: q^2+4q+1
       172: q^2+4q+1
       173: 2q^2+4q+1
       174: 4q+1
       175: 2q^2+4q+1
       176: 3q^2+4q+1
       177: 3q^2+4q+1
       178: 5q^2+4q+1
       179: 3q^2+4q+1
       180: 3q^2+4q+1
       181: q^2+4q+1
       182: 3q^2+4q+1
       183: 3q^2+4q+1
       184: 3q^2+4q+1
       185: q^2+4q+1
       186: 3q^2+4q+1
       187: q^2+4q+1
       188: 2q^2+4q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: 2q+1
       193: 4q+1
       194: 4q+1
       195: 4q+1
       196: 2q^2+4q+1
       197: 3q+1
       198: q+1
       199: 2q+1
       200: 2q+1
       201: q^2+4q+1
       202: 4q+1
       203: 4q+1
       204: 4q+1
       205: 4q+1
       206: 2q+1
       207: q+1
       208: 4q+1
       209: 2q+1
       210: q^2+4q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: 2q+1
       215: 4q+1
       216: 2q+1
       217: 2q+1
       218: q^2+4q+1
       219: 2q+1
       220: 4q+1
       221: 4q+1
       222: 4q+1
       223: 2q+1
       224: 2q+1
       225: 3q+1
       226: 3q+1
       227: 3q+1
       228: q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+4q+1
       232: 4q+1
       233: 4q+1
       234: 2q^2+4q+1
       235: 2q^2+4q+1
       236: 2q+1
       237: 2q+1
       238: q^2+4q+1
       239: q^2+4q+1
       240: q^2+4q+1
       241: q^2+4q+1
       242: 4q+1
       243: 4q+1
       244: 4q+1
       245: q^2+4q+1
       246: q^2+4q+1
       247: 2q+1
       248: 4q+1
       249: 4q+1
       250: q^2+4q+1
       251: 2q+1
       252: q^2+4q+1
       253: 4q+1
       254: 4q+1
       255: 4q+1
       256: 2q^2+4q+1
       257: 3q+1
       258: q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q^2+4q+1
       262: 4q+1
       263: 4q+1
       264: 2q^2+4q+1
       265: 2q^2+4q+1
       266: 2q+1
       267: 2q+1
       268: q^2+4q+1
       269: q^2+4q+1
       270: q^2+4q+1
       271: q^2+4q+1
       272: 4q+1
       273: 4q+1
       274: 4q+1
       275: q^2+4q+1
       276: q^2+4q+1
       277: 2q+1
       278: 4q+1
       279: 4q+1
       280: q^2+4q+1
       281: 2q+1
       282: q^2+4q+1
       283: 4q+1
       284: 4q+1
       285: 4q+1
       286: 2q^2+4q+1
       287: 3q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: 3q^2+4q+1
       291: q^2+4q+1
       292: 3q^2+4q+1
       293: 3q^2+4q+1
       294: 2q^2+4q+1
       295: q^2+4q+1
       296: q^2+4q+1
       297: 3q^2+4q+1
       298: q^2+4q+1
       299: q^2+4q+1
       300: 4q+1
       301: q^2+4q+1
       302: q^2+4q+1
       303: 4q+1
       304: q^2+4q+1
       305: q^2+4q+1
       306: 2q^2+4q+1
       307: 4q+1
       308: 2q^2+4q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: q+1
       314: q+1
       315: 2q+1
       316: 4q+1
       317: 3q+1
       318: 3q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: 2q+1
       323: 4q+1
       324: 4q+1
       325: 4q+1
       326: 4q+1
       327: 3q+1
       328: 1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: q+1
       345: q+1
       346: 4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: 3q+1
       352: 3q+1
       353: 3q+1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: 2q+1
       359: 2q+1
       360: 4q+1
       361: 4q+1
       362: 4q+1
       363: 2q^2+4q+1
       364: 3q+1
       365: q+1
       366: 2q+1
       367: 2q+1
       368: q^2+4q+1
       369: 4q+1
       370: 4q+1
       371: 4q+1
       372: 4q+1
       373: 2q+1
       374: q+1
       375: 4q+1
       376: 2q+1
       377: q^2+4q+1
       378: 2q+1
       379: 2q+1
       380: q+1
       381: 2q+1
       382: 4q+1
       383: 2q+1
       384: 2q+1
       385: q^2+4q+1
       386: 2q+1
       387: 4q+1
       388: 4q+1
       389: 4q+1
       390: 2q+1
       391: 2q+1
       392: 3q+1
       393: 3q+1
       394: 3q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: 2q+1
       399: 4q+1
       400: 4q+1
       401: 4q+1
       402: 2q^2+4q+1
       403: 3q+1
       404: q+1
       405: 2q+1
       406: 2q+1
       407: q^2+4q+1
       408: 4q+1
       409: 4q+1
       410: 4q+1
       411: 4q+1
       412: 2q+1
       413: q+1
       414: 4q+1
       415: 2q+1
       416: q^2+4q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: 2q+1
       421: 4q+1
       422: 2q+1
       423: 2q+1
       424: q^2+4q+1
       425: 2q+1
       426: 4q+1
       427: 4q+1
       428: 4q+1
       429: 2q+1
       430: 2q+1
       431: 3q+1
       432: 3q+1
       433: 3q+1
       434: q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q^2+4q+1
       438: 4q+1
       439: 4q+1
       440: 2q^2+4q+1
       441: 2q^2+4q+1
       442: 2q+1
       443: 2q+1
       444: q^2+4q+1
       445: q^2+4q+1
       446: q^2+4q+1
       447: q^2+4q+1
       448: 4q+1
       449: 4q+1
       450: 4q+1
       451: q^2+4q+1
       452: q^2+4q+1
       453: 2q+1
       454: 4q+1
       455: 4q+1
       456: q^2+4q+1
       457: 2q+1
       458: q^2+4q+1
       459: 4q+1
       460: 4q+1
       461: 4q+1
       462: 2q^2+4q+1
       463: 3q+1
       466: q+1
       467: 1
       468: 1
       469: q+1
       470: q+1
       471: 3q+1
       472: 3q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: q+1
       478: q+1
       479: 2q+1
       480: 4q+1
       481: q+1
       482: 3q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: 2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: 2q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: 1
       502: q+1
       503: q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 3q+1
       512: q+1
       513: q+1
       514: q+1
       515: 1
       517: q+1
       518: q+1
       519: 2q+1
       520: q+1
       521: q+1
       522: 2q+1
       523: 4q+1
       524: 3q+1
       525: 3q+1
       526: q+1
       527: q+1
       528: 2q+1
       529: 2q+1
       530: 4q+1
       531: 4q+1
       532: 4q+1
       533: 4q+1
       534: 3q+1
       535: 1
       536: 2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: 1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: 2q+1
       550: 2q+1
       551: q+1
       552: q+1
       553: 4q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: q+1
       558: 3q+1
       559: 3q+1
       560: 3q+1
       561: q+1
       562: q+1
       564: q+1
       565: q+1
       566: 2q+1
       567: q+1
       568: q+1
       569: 2q+1
       570: 4q+1
       571: 3q+1
       572: 3q+1
       573: q+1
       574: q+1
       575: 2q+1
       576: 2q+1
       577: 4q+1
       578: 4q+1
       579: 4q+1
       580: 4q+1
       581: 3q+1
       582: 1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: 1
       591: q+1
       592: 2q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: 2q+1
       597: 2q+1
       598: q+1
       599: q+1
       600: 4q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: q+1
       605: 3q+1
       606: 3q+1
       607: 3q+1
       608: q+1
       609: q+1
       610: q+1
       611: q+1
       612: 2q+1
       613: 2q+1
       614: 4q+1
       615: 4q+1
       616: 4q+1
       617: 2q^2+4q+1
       618: 3q+1
       619: q+1
       620: 2q+1
       621: 2q+1
       622: q^2+4q+1
       623: 4q+1
       624: 4q+1
       625: 4q+1
       626: 4q+1
       627: 2q+1
       628: q+1
       629: 4q+1
       630: 2q+1
       631: q^2+4q+1
       632: 2q+1
       633: 2q+1
       634: q+1
       635: 2q+1
       636: 4q+1
       637: 2q+1
       638: 2q+1
       639: q^2+4q+1
       640: 2q+1
       641: 4q+1
       642: 4q+1
       643: 4q+1
       644: 2q+1
       645: 2q+1
       646: 3q+1
       647: 3q+1
       648: 3q+1
       651: 1
       652: 1
       653: 1
       654: q+1
       655: q+1
       656: 3q+1
       659: q+1
       660: 1
       661: 1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: q+1
       674: 1
       675: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: q+1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       705: q+1
       706: 1
       707: 1
       708: q+1
       709: q+1
       710: 3q+1
       711: 3q+1
       713: q+1
       714: q+1
       715: 2q+1
       716: q+1
       717: q+1
       718: 2q+1
       719: 4q+1
       720: q+1
       721: 3q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: 2q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: 2q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: 1
       741: q+1
       742: q+1
       743: q+1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: q+1
       750: 3q+1
       751: q+1
       752: q+1
       753: q+1
       754: 1
       757: q+1
       758: 1
       759: 1
       760: q+1
       761: q+1
       762: 3q+1
       763: 3q+1
       765: q+1
       766: q+1
       767: 2q+1
       768: q+1
       769: q+1
       770: 2q+1
       771: 4q+1
       772: q+1
       773: 3q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: 2q+1
       789: q+1
       790: 2q+1
       791: q+1
       792: 1
       793: q+1
       794: q+1
       795: q+1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: q+1
       802: 3q+1
       803: q+1
       804: q+1
       805: q+1
       806: 1
       808: q+1
       809: q+1
       810: 2q+1
       811: q+1
       812: q+1
       813: 2q+1
       814: 4q+1
       815: 3q+1
       816: 3q+1
       817: q+1
       818: q+1
       819: 2q+1
       820: 2q+1
       821: 4q+1
       822: 4q+1
       823: 4q+1
       824: 4q+1
       825: 3q+1
       826: 1
       827: 2q+1
       828: q+1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       834: 1
       835: q+1
       836: 2q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: 2q+1
       841: 2q+1
       842: q+1
       843: q+1
       844: 4q+1
       845: q+1
       846: 2q+1
       847: 2q+1
       848: q+1
       849: 3q+1
       850: 3q+1
       851: 3q+1
       852: q+1
       853: q+1
       857: 1
       858: 1
       859: q+1
       860: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: q+1
       912: q+1
       913: 3q+1
       916: q+1
       917: 1
       918: 1
       919: q+1
       920: q+1
       921: q+1
       922: q+1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: q+1
       931: 1
       932: q+1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q+1
       954: q+1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       962: 1
       963: 1
       964: 1
       965: q+1
       966: q+1
       967: 3q+1
       970: q+1
       971: 1
       972: 1
       973: q+1
       974: q+1
       975: q+1
       976: q+1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: q+1
       985: 1
       986: q+1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: q+1
       995: 1
       996: q+1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: q+1
      1008: q+1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: q+1
      1017: 1
      1018: 1
      1019: q+1
      1020: q+1
      1021: 3q+1
      1022: 3q+1
      1024: q+1
      1025: q+1
      1026: 2q+1
      1027: q+1
      1028: q+1
      1029: 2q+1
      1030: 4q+1
      1031: q+1
      1032: 3q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: 2q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: 2q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1051: 1
      1052: q+1
      1053: q+1
      1054: q+1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: q+1
      1061: 3q+1
      1062: q+1
      1063: q+1
      1064: q+1
      1065: 1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1084: 1
      1085: 1
      1089: 1
      1091: 1
      1093: 1
      1096: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1116: 1
      1117: 1
      1118: q+1
      1119: q+1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: q+1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1168: 1
      1169: 1
      1170: q+1
      1171: q+1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: q+1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1219: 1
      1220: 1
      1221: 1
      1222: q+1
      1223: q+1
      1224: 3q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: q+1
      1231: q+1
      1232: q+1
      1233: q+1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: q+1
      1242: 1
      1243: q+1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: q+1
      1265: q+1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1273: 1
      1277: 1
      1278: 1
      1285: 1
      1291: 1
      1300: 1
      1303: 1
      1313: 1
      1314: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1324: 1
      1328: 1
      1329: 1
      1333: 1
      1335: 1
      1337: 1
      1340: 1
      1345: 1
      1346: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1356: 1
      1360: 1
      1361: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1371: 1
      1375: 1
      1376: 1
      1380: 1
      1382: 1
      1384: 1
      1387: 1
      1392: 1
      1393: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1403: 1
      1407: 1
      1408: 1
      1409: q+1
      1410: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: q+1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1460: 1
      1488: 1
      1492: 1
      1493: 1
      1500: 1
      1506: 1
      1515: 1
      1518: 1
      1527: 1
      1531: 1
      1532: 1
      1539: 1
      1545: 1
      1554: 1
      1557: 1
      1567: 1
      1568: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1578: 1
      1582: 1
      1583: 1
      1587: 1
      1589: 1
      1591: 1
      1594: 1
      1599: 1
      1600: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1610: 1
      1636: 1
      1666: 1
      1694: 1
      1698: 1
      1699: 1
      1706: 1
      1712: 1
      1721: 1
      1724: 1
      1790: 1

1791:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: 1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: 1
        29: 1
        30: q+1
        31: q+1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: 1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: 1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: 1
        63: 1
        64: 1
        65: q+1
        66: q+1
        67: q+1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: 1
        80: 1
        81: q+1
        82: q+1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: 1
        93: 1
        94: q+1
        95: q+1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: 1
       103: q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       128: q+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: 1
       147: 1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: 1
       168: 1
       169: 1
       170: q+1
       171: q+1
       172: q+1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: 1
       185: 1
       186: q+1
       187: q+1
       188: 1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q+1
       215: q+1
       216: q+1
       218: q+1
       220: 1
       221: 1
       222: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       252: q+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: 1
       301: 1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: q+1
       339: q+1
       341: q+1
       345: 1
       346: 1
       347: 1
       349: 1
       351: 1
       352: 1
       353: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q+1
       382: q+1
       383: q+1
       385: q+1
       387: 1
       388: 1
       389: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q+1
       421: q+1
       422: q+1
       424: q+1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: q+1
       497: q+1
       503: 1
       504: 1
       506: 1
       510: 1
       511: 1
       512: 1
       514: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: q+1
       546: q+1
       548: q+1
       552: 1
       553: 1
       554: 1
       556: 1
       558: 1
       559: 1
       560: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: q+1
       593: q+1
       595: q+1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q+1
       636: q+1
       637: q+1
       639: q+1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       682: q+1
       689: 1
       691: 1
       697: 1
       698: 1
       700: 1
       703: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: q+1
       736: q+1
       742: 1
       743: 1
       745: 1
       749: 1
       750: 1
       751: 1
       753: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: q+1
       788: q+1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: q+1
       837: q+1
       839: q+1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       893: 1
       900: 1
       902: 1
       906: 1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       939: q+1
       946: 1
       948: 1
       954: 1
       955: 1
       957: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: q+1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: q+1
      1047: q+1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1109: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1152: 1
      1159: 1
      1161: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1250: q+1
      1257: 1
      1259: 1
      1265: 1
      1266: 1
      1268: 1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1353: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1443: 1
      1450: 1
      1452: 1
      1461: 1
      1489: 1
      1494: 1
      1495: 1
      1500: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1607: 1
      1637: 1
      1667: 1
      1695: 1
      1700: 1
      1701: 1
      1706: 1
      1791: 1

1792:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: q^2+3q+1
        24: 2q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: q^2+3q+1
        51: 2q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: q^2+3q+1
        55: 2q+1
        56: 2q+1
        57: q^2+3q+1
        58: 2q^2+3q+1
        59: q^2+3q+1
        60: q^2+3q+1
        61: 2q+1
        62: 2q^2+3q+1
        63: 2q^2+3q+1
        64: 2q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: q^2+2q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+2q+1
        71: q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: q^2+3q+1
        75: 2q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: q^2+3q+1
        88: 2q+1
        89: 2q^2+3q+1
        90: 2q^2+3q+1
        91: q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: q^2+3q+1
       106: 2q+1
       107: q^2+3q+1
       108: q^2+3q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+3q+1
       113: 2q+1
       114: q^2+3q+1
       115: q^2+3q+1
       116: q^2+3q+1
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q^2+3q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q^2+2q+1
       125: 2q^2+3q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q+1
       129: 2q^2+3q+1
       130: 2q^2+3q+1
       131: q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q^2+3q+1
       135: 2q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: q^2+3q+1
       139: 2q+1
       140: 2q+1
       141: q^2+3q+1
       142: 2q^2+3q+1
       143: q^2+3q+1
       144: q^2+3q+1
       145: 2q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: 2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: q^2+2q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+2q+1
       155: q^2+3q+1
       156: 2q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: q^2+3q+1
       160: 2q+1
       161: 2q+1
       162: q^2+3q+1
       163: 2q^2+3q+1
       164: q^2+3q+1
       165: q^2+3q+1
       166: 2q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: 2q+1
       170: 2q^2+3q+1
       171: 2q^2+3q+1
       172: q^2+2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: q^2+3q+1
       180: 2q+1
       181: 2q^2+3q+1
       182: 2q^2+3q+1
       183: q^2+3q+1
       184: 2q^2+3q+1
       185: 2q^2+3q+1
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: 2q^2+3q+1
       189: q+1
       190: 2q+1
       191: q^2+3q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q^2+3q+1
       200: 2q+1
       201: q^2+3q+1
       202: q^2+3q+1
       203: 2q+1
       204: 2q+1
       205: 1
       206: 2q+1
       207: q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: q^2+2q+1
       214: q+1
       215: q^2+2q+1
       216: q^2+2q+1
       217: q^2+2q+1
       218: q+1
       219: q+1
       220: q+1
       221: 2q^2+3q+1
       222: q+1
       223: q+1
       224: 1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: 2q+1
       229: q^2+3q+1
       230: 2q+1
       231: q^2+3q+1
       232: q^2+3q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q^2+3q+1
       237: 2q+1
       238: q^2+3q+1
       239: q^2+3q+1
       240: q^2+3q+1
       241: 2q+1
       242: 2q+1
       243: 2q+1
       244: 2q^2+3q+1
       245: 2q+1
       246: 2q+1
       247: q+1
       248: q^2+2q+1
       249: 2q^2+3q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: q^2+3q+1
       260: 2q+1
       261: q^2+3q+1
       262: q^2+3q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q^2+3q+1
       267: 2q+1
       268: q^2+3q+1
       269: q^2+3q+1
       270: q^2+3q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: 2q^2+3q+1
       275: 2q+1
       276: 2q+1
       277: q+1
       278: q^2+2q+1
       279: 2q^2+3q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: q+1
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q^2+3q+1
       289: 2q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: q^2+3q+1
       293: 2q+1
       294: 2q+1
       295: q^2+3q+1
       296: 2q^2+3q+1
       297: q^2+3q+1
       298: q^2+3q+1
       299: 2q+1
       300: 2q^2+3q+1
       301: 2q^2+3q+1
       302: 2q+1
       303: 2q^2+3q+1
       304: 2q^2+3q+1
       305: q^2+2q+1
       306: 2q^2+3q+1
       307: 2q^2+3q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: 2q+1
       321: q^2+3q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: 1
       327: 1
       328: q+1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: q^2+2q+1
       338: q+1
       339: q^2+2q+1
       340: q^2+2q+1
       341: q+1
       342: q+1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: q^2+2q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: 2q+1
       358: q^2+3q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q^2+3q+1
       367: 2q+1
       368: q^2+3q+1
       369: q^2+3q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: 2q+1
       374: q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: q+1
       379: q+1
       380: q^2+2q+1
       381: q+1
       382: q^2+2q+1
       383: q^2+2q+1
       384: q^2+2q+1
       385: q+1
       386: q+1
       387: q+1
       388: 2q^2+3q+1
       389: q+1
       390: q+1
       391: 1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q+1
       395: q+1
       396: 2q+1
       397: q^2+3q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q^2+3q+1
       406: 2q+1
       407: q^2+3q+1
       408: q^2+3q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: 2q+1
       413: q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: q+1
       419: q^2+2q+1
       420: q+1
       421: q^2+2q+1
       422: q^2+2q+1
       423: q^2+2q+1
       424: q+1
       425: q+1
       426: q+1
       427: 2q^2+3q+1
       428: q+1
       429: q+1
       430: 1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q+1
       434: 2q+1
       435: q^2+3q+1
       436: 2q+1
       437: q^2+3q+1
       438: q^2+3q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q^2+3q+1
       443: 2q+1
       444: q^2+3q+1
       445: q^2+3q+1
       446: q^2+3q+1
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: 2q^2+3q+1
       451: 2q+1
       452: 2q+1
       453: q+1
       454: q^2+2q+1
       455: 2q^2+3q+1
       456: q^2+2q+1
       457: q^2+2q+1
       458: q+1
       459: 2q^2+3q+1
       460: 2q^2+3q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: 1
       468: q+1
       469: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: 2q+1
       476: q+1
       478: q+1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q^2+2q+1
       495: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       511: q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: q^2+3q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: 2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: q^2+2q+1
       545: q+1
       546: q^2+2q+1
       547: q^2+2q+1
       548: q+1
       549: q+1
       550: 1
       551: q+1
       552: 1
       553: q+1
       554: q+1
       555: q+1
       556: 1
       557: 1
       558: q+1
       559: q^2+2q+1
       560: q+1
       561: q+1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: q^2+3q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: q+1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q^2+2q+1
       592: q+1
       593: q^2+2q+1
       594: q^2+2q+1
       595: q+1
       596: q+1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q^2+2q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: 2q+1
       612: q^2+3q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q^2+3q+1
       621: 2q+1
       622: q^2+3q+1
       623: q^2+3q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: 2q+1
       628: q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: q+1
       633: q+1
       634: q^2+2q+1
       635: q+1
       636: q^2+2q+1
       637: q^2+2q+1
       638: q^2+2q+1
       639: q+1
       640: q+1
       641: q+1
       642: 2q^2+3q+1
       643: q+1
       644: q+1
       645: 1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: q+1
       662: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: q+1
       681: q+1
       682: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       703: q+1
       704: q+1
       705: 1
       707: q+1
       708: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       715: q+1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: q+1
       724: 2q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q^2+2q+1
       734: q+1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: q+1
       742: 1
       743: q+1
       744: q+1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       750: q+1
       751: q+1
       752: q+1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 1
       759: q+1
       760: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       767: q+1
       769: q+1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: 2q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       785: q^2+2q+1
       786: q+1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: q^2+3q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: 2q+1
       828: q+1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q^2+2q+1
       836: q+1
       837: q^2+2q+1
       838: q^2+2q+1
       839: q+1
       840: q+1
       841: 1
       842: q+1
       843: 1
       844: q+1
       845: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       853: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       869: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       877: 1
       878: 1
       879: 1
       882: q+1
       886: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: q+1
       900: 1
       902: 1
       903: 1
       906: q+1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: q+1
       919: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       938: q+1
       939: q+1
       941: 1
       942: 1
       943: 1
       944: 1
       945: q+1
       946: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       960: q+1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       969: 1
       970: 1
       972: q+1
       973: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: q+1
       992: q+1
       993: q+1
       995: 1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1014: q+1
      1015: q+1
      1016: 1
      1018: q+1
      1019: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: 2q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q^2+2q+1
      1045: q+1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: q+1
      1053: 1
      1054: q+1
      1055: q+1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: 1
      1065: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: 1
      1094: 1
      1095: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1141: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1155: 1
      1157: 1
      1158: q+1
      1159: 1
      1161: 1
      1162: 1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: 1
      1177: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: q+1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1209: 1
      1210: q+1
      1211: 1
      1213: 1
      1214: 1
      1217: q+1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: q+1
      1230: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1249: q+1
      1250: q+1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: q+1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1293: 1
      1305: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1322: 1
      1323: 1
      1325: 1
      1327: 1
      1329: 1
      1330: 1
      1338: 1
      1339: 1
      1342: 1
      1346: 1
      1349: 1
      1352: 1
      1353: 1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1369: 1
      1370: 1
      1372: 1
      1374: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1396: 1
      1399: 1
      1400: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1423: 1
      1424: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1432: q+1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1446: 1
      1448: 1
      1449: q+1
      1450: 1
      1452: 1
      1453: 1
      1462: 1
      1490: 1
      1494: 1
      1496: 1
      1499: 1
      1508: 1
      1520: 1
      1529: 1
      1533: 1
      1535: 1
      1538: 1
      1547: 1
      1559: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1576: 1
      1577: 1
      1579: 1
      1581: 1
      1583: 1
      1584: 1
      1592: 1
      1593: 1
      1596: 1
      1600: 1
      1603: 1
      1606: 1
      1607: 1
      1638: 1
      1668: 1
      1696: 1
      1700: 1
      1702: 1
      1705: 1
      1714: 1
      1726: 1
      1792: 1

1793:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: 1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: 1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: q+1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: q+1
       716: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       882: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: q+1
       918: 1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       927: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: q+1
      1027: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1095: 1
      1098: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: q+1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 1
      1141: 1
      1146: 1
      1147: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1190: 1
      1193: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1339: 1
      1342: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1386: 1
      1389: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: q+1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1429: 1
      1432: 1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1463: 1
      1491: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1530: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1566: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1593: 1
      1596: 1
      1639: 1
      1669: 1
      1697: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1793: 1

1794:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q^2+2q+1
        25: 2q+1
        26: q^2+q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: 2q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: 2q+1
        54: 2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: q+1
        59: q^2+q+1
        60: q^2+2q+1
        61: 2q+1
        62: 2q+1
        63: q^2+q+1
        64: q^2+2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: 2q^2+2q+1
        75: q^2+2q+1
        76: 2q+1
        77: q^2+q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: q^2+2q+1
        89: 2q+1
        90: q^2+q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q^2+q+1
       117: q+1
       118: 2q+1
       119: 2q+1
       120: q+1
       121: q^2+q+1
       122: q^2+2q+1
       123: q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: 2q+1
       138: 2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       142: q+1
       143: q^2+q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+q+1
       148: q^2+2q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: 2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: q+1
       164: q^2+q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q^2+q+1
       169: q^2+2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: 2q^2+2q+1
       180: q^2+2q+1
       181: 2q+1
       182: q^2+q+1
       183: q^2+2q+1
       184: 2q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: q+1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q+1
       206: 2q+1
       207: 1
       208: q+1
       209: q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: q+1
       225: q+1
       227: q+1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: q+1
       238: q+1
       239: q+1
       240: q^2+q+1
       241: q+1
       242: 2q+1
       243: 2q+1
       244: q+1
       245: q^2+q+1
       246: q^2+2q+1
       247: q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: q+1
       268: q+1
       269: q+1
       270: q^2+q+1
       271: q+1
       272: 2q+1
       273: 2q+1
       274: q+1
       275: q^2+q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: 2q+1
       292: 2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: q+1
       297: q^2+q+1
       298: q^2+2q+1
       299: 2q+1
       300: 2q+1
       301: q^2+q+1
       302: q^2+2q+1
       303: 2q+1
       304: q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: 1
       314: 2q+1
       315: q+1
       316: 2q+1
       317: q+1
       319: q+1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: 2q+1
       344: 2q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: 2q+1
       359: q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 2q+1
       373: 2q+1
       374: 1
       375: q+1
       376: q+1
       377: q^2+q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: 2q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: q+1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 2q+1
       412: 2q+1
       413: 1
       414: q+1
       415: q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: 2q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: 2q+1
       426: 2q+1
       427: q+1
       428: q+1
       429: 2q+1
       430: q+1
       431: q+1
       433: q+1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: q+1
       444: q+1
       445: q+1
       446: q^2+q+1
       447: q+1
       448: 2q+1
       449: 2q+1
       450: q+1
       451: q^2+q+1
       452: q^2+2q+1
       453: q+1
       454: 2q+1
       455: q+1
       456: q+1
       457: 2q+1
       458: 2q+1
       459: 2q+1
       460: q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       466: q+1
       467: 1
       468: q+1
       469: 2q+1
       470: 1
       471: q+1
       474: 1
       475: 1
       476: q+1
       477: 1
       478: q+1
       479: 1
       480: q+1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: q+1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       515: 1
       517: q+1
       518: q+1
       519: 2q+1
       520: 1
       521: 2q+1
       522: q+1
       523: 2q+1
       524: q+1
       526: q+1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: 1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: 2q+1
       551: 2q+1
       552: 1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: q+1
       561: q+1
       562: 1
       564: q+1
       565: q+1
       566: 2q+1
       567: 1
       568: 2q+1
       569: q+1
       570: 2q+1
       571: q+1
       573: q+1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: q+1
       591: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: 2q+1
       598: 2q+1
       599: 1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: 2q+1
       613: q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 2q+1
       627: 2q+1
       628: 1
       629: q+1
       630: q+1
       631: q^2+q+1
       632: q+1
       633: q+1
       634: 2q+1
       635: q+1
       636: q+1
       637: 1
       638: q+1
       639: q+1
       640: 2q+1
       641: 2q+1
       642: q+1
       643: q+1
       644: 2q+1
       645: q+1
       646: q+1
       648: q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       659: 1
       660: 1
       661: 1
       662: q+1
       663: 1
       664: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: q+1
       706: 1
       707: q+1
       708: 2q+1
       709: 1
       710: q+1
       713: 1
       714: 1
       715: q+1
       716: 1
       717: q+1
       718: 1
       719: q+1
       720: 1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: q+1
       728: q+1
       729: q+1
       730: 1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       739: q+1
       740: 1
       741: q+1
       742: 1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       754: 1
       757: q+1
       758: 1
       759: q+1
       760: 2q+1
       761: 1
       762: q+1
       765: 1
       766: 1
       767: q+1
       768: 1
       769: q+1
       770: 1
       771: q+1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: q+1
       792: 1
       793: q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: 1
       806: 1
       808: q+1
       809: q+1
       810: 2q+1
       811: 1
       812: 2q+1
       813: q+1
       814: 2q+1
       815: q+1
       817: q+1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       834: q+1
       835: q+1
       836: 1
       837: 1
       838: 1
       839: 1
       840: q+1
       841: 2q+1
       842: 2q+1
       843: 1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       852: q+1
       853: 1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       880: 1
       882: 1
       883: 1
       885: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       916: 1
       917: 1
       918: 1
       919: q+1
       920: 1
       921: 1
       924: 1
       925: 1
       926: q+1
       927: 1
       928: q+1
       929: 1
       930: q+1
       931: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       959: 1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       970: 1
       971: 1
       972: 1
       973: q+1
       974: 1
       975: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       985: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1013: 1
      1016: q+1
      1017: 1
      1018: q+1
      1019: 2q+1
      1020: 1
      1021: q+1
      1024: 1
      1025: 1
      1026: q+1
      1027: 1
      1028: q+1
      1029: 1
      1030: q+1
      1031: 1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: 1
      1042: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: q+1
      1050: q+1
      1051: 1
      1052: q+1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: 1
      1065: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1089: 1
      1091: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1132: 1
      1133: q+1
      1134: 1
      1135: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1168: 1
      1169: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1187: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1227: 1
      1228: 1
      1229: 1
      1230: q+1
      1231: 1
      1232: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1239: q+1
      1240: 1
      1241: q+1
      1242: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1270: 1
      1277: 1
      1282: 1
      1283: 1
      1296: 1
      1298: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1333: 1
      1335: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1360: 1
      1365: 1
      1366: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1380: 1
      1382: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1407: 1
      1408: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1421: 1
      1422: 1
      1423: 1
      1424: q+1
      1425: 1
      1426: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1455: 1
      1464: 1
      1492: 1
      1497: 1
      1498: 1
      1511: 1
      1513: 1
      1531: 1
      1536: 1
      1537: 1
      1550: 1
      1552: 1
      1567: 1
      1572: 1
      1573: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1587: 1
      1589: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1640: 1
      1670: 1
      1698: 1
      1703: 1
      1704: 1
      1717: 1
      1719: 1
      1794: 1

1795:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 1
       120: 2q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: 1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       312: 1
       313: 1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: q+1
       325: 2q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q+1
       463: q+1
       467: 1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: q+1
       475: q+1
       476: 1
       477: 1
       478: q+1
       479: q+1
       480: 1
       481: 1
       482: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: 1
       491: 1
       493: q+1
       494: q+1
       495: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: q+1
       566: 1
       567: 1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: q+1
       662: 1
       663: 1
       664: 1
       665: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       678: q+1
       681: q+1
       682: q+1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: 1
       730: 1
       732: q+1
       733: q+1
       734: q+1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       758: 1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: q+1
       767: 1
       768: 1
       769: q+1
       770: q+1
       771: 1
       772: 1
       773: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       784: q+1
       785: q+1
       786: q+1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: q+1
       810: 1
       811: 1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       882: q+1
       886: 1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       935: q+1
       938: q+1
       939: q+1
       941: 1
       942: 1
       944: 1
       945: 1
       946: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: q+1
       973: 1
       974: 1
       975: 1
       976: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       989: q+1
       992: q+1
       993: q+1
       995: 1
       996: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1017: 1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: q+1
      1026: 1
      1027: 1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1141: q+1
      1145: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1161: 1
      1162: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1193: q+1
      1197: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1246: q+1
      1249: q+1
      1250: q+1
      1252: 1
      1253: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1305: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1342: 1
      1346: 1
      1349: 1
      1352: 1
      1353: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1389: 1
      1393: 1
      1396: 1
      1399: 1
      1400: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1432: q+1
      1436: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1452: 1
      1453: 1
      1465: 1
      1493: 1
      1498: 1
      1499: 1
      1500: 1
      1520: 1
      1532: 1
      1537: 1
      1538: 1
      1539: 1
      1559: 1
      1568: 1
      1573: 1
      1574: 1
      1575: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1596: 1
      1600: 1
      1603: 1
      1606: 1
      1607: 1
      1641: 1
      1671: 1
      1699: 1
      1704: 1
      1705: 1
      1706: 1
      1726: 1
      1795: 1

1796:    0: q^3+3q^2+3q+1
         1: q^3+3q^2+3q+1
         2: q^3+3q^2+3q+1
         3: 2q^2+3q+1
         4: q^3+3q^2+3q+1
         5: q^3+3q^2+3q+1
         6: q^3+3q^2+3q+1
         7: q^3+3q^2+3q+1
         8: q^2+3q+1
         9: 2q^2+3q+1
        10: 2q^2+3q+1
        11: 2q^2+3q+1
        12: 2q^2+3q+1
        13: q^3+3q^2+3q+1
        14: q^3+3q^2+3q+1
        15: 2q^2+3q+1
        16: q^3+3q^2+3q+1
        17: q^3+3q^2+3q+1
        18: 2q^2+3q+1
        19: q^3+3q^2+3q+1
        20: q^2+3q+1
        21: q^3+3q^2+3q+1
        22: q^2+3q+1
        23: 2q+1
        24: q^2+3q+1
        25: 2q^2+3q+1
        26: 2q^2+3q+1
        27: q^2+3q+1
        28: 2q^2+3q+1
        29: 2q^2+3q+1
        30: 2q^2+3q+1
        31: 2q^2+3q+1
        32: 2q^2+3q+1
        33: q^3+3q^2+3q+1
        34: q^3+3q^2+3q+1
        35: q^2+3q+1
        36: 2q^2+3q+1
        37: 2q^2+3q+1
        38: 2q^2+3q+1
        39: 2q^2+3q+1
        40: q^3+3q^2+3q+1
        41: q^3+3q^2+3q+1
        42: q^2+3q+1
        43: 2q^2+3q+1
        44: 2q^2+3q+1
        45: 2q^2+3q+1
        46: 2q^2+3q+1
        47: q^3+3q^2+3q+1
        48: q^3+3q^2+3q+1
        49: 2q^2+3q+1
        50: 2q+1
        51: q^2+3q+1
        52: q^2+3q+1
        53: q^2+3q+1
        54: 2q+1
        55: q^2+3q+1
        56: 2q+1
        57: q^2+3q+1
        58: 2q^2+3q+1
        59: q^2+3q+1
        60: 2q+1
        61: q^2+3q+1
        62: 2q^2+3q+1
        63: 2q^2+3q+1
        64: q^2+2q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: 2q+1
        68: 2q^2+3q+1
        69: 2q^2+3q+1
        70: q^2+2q+1
        71: q^2+3q+1
        72: q^3+3q^2+3q+1
        73: q^2+3q+1
        74: 2q+1
        75: q^2+3q+1
        76: 2q^2+3q+1
        77: 2q^2+3q+1
        78: q^2+3q+1
        79: 2q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^2+3q+1
        82: 2q^2+3q+1
        83: 2q^2+3q+1
        84: q^2+3q+1
        85: q^3+3q^2+3q+1
        86: q^2+3q+1
        87: 2q+1
        88: q^2+3q+1
        89: 2q^2+3q+1
        90: 2q^2+3q+1
        91: q^2+3q+1
        92: 2q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^2+3q+1
        95: 2q^2+3q+1
        96: 2q^2+3q+1
        97: q^3+3q^2+3q+1
        98: q^3+3q^2+3q+1
        99: q^2+3q+1
       100: 2q^2+3q+1
       101: 2q^2+3q+1
       102: 2q^2+3q+1
       103: 2q^2+3q+1
       104: 2q+1
       105: 2q+1
       106: q^2+3q+1
       107: q^2+3q+1
       108: 2q+1
       109: q^2+3q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: q^2+3q+1
       114: q^2+3q+1
       115: q^2+3q+1
       116: 2q+1
       117: q^2+3q+1
       118: 2q+1
       119: q^2+2q+1
       120: 2q^2+3q+1
       121: q^2+2q+1
       122: q+1
       123: q^2+2q+1
       124: 2q+1
       125: 2q^2+3q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: 2q^2+3q+1
       130: 2q^2+3q+1
       131: q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q+1
       135: q^2+3q+1
       136: q^2+3q+1
       137: q^2+3q+1
       138: 2q+1
       139: q^2+3q+1
       140: 2q+1
       141: q^2+3q+1
       142: 2q^2+3q+1
       143: q^2+3q+1
       144: 2q+1
       145: q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: q^2+2q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 2q+1
       152: 2q^2+3q+1
       153: 2q^2+3q+1
       154: q^2+2q+1
       155: 2q+1
       156: q^2+3q+1
       157: q^2+3q+1
       158: q^2+3q+1
       159: 2q+1
       160: q^2+3q+1
       161: 2q+1
       162: q^2+3q+1
       163: 2q^2+3q+1
       164: q^2+3q+1
       165: 2q+1
       166: q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: q^2+2q+1
       170: 2q^2+3q+1
       171: 2q^2+3q+1
       172: 2q+1
       173: 2q^2+3q+1
       174: 2q^2+3q+1
       175: q^2+2q+1
       176: q^2+3q+1
       177: q^3+3q^2+3q+1
       178: q^2+3q+1
       179: 2q+1
       180: q^2+3q+1
       181: 2q^2+3q+1
       182: 2q^2+3q+1
       183: q^2+3q+1
       184: 2q^2+3q+1
       185: 2q^2+3q+1
       186: 2q^2+3q+1
       187: 2q^2+3q+1
       188: 2q^2+3q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: q^2+3q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: q^2+3q+1
       201: q^2+3q+1
       202: 2q+1
       203: q^2+3q+1
       204: 2q+1
       205: 1
       206: q+1
       207: q^2+2q+1
       208: q^2+2q+1
       209: q^2+2q+1
       210: q+1
       211: q^2+2q+1
       212: q+1
       213: q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: q+1
       221: 2q^2+3q+1
       222: q+1
       223: 1
       224: q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q+1
       228: 2q+1
       229: 2q+1
       230: q^2+3q+1
       231: q^2+3q+1
       232: 2q+1
       233: q^2+3q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: q^2+3q+1
       238: q^2+3q+1
       239: q^2+3q+1
       240: 2q+1
       241: q^2+3q+1
       242: 2q+1
       243: q^2+2q+1
       244: 2q^2+3q+1
       245: q^2+2q+1
       246: q+1
       247: q^2+2q+1
       248: 2q+1
       249: 2q^2+3q+1
       250: 2q+1
       251: q+1
       252: 2q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: q^2+3q+1
       261: q^2+3q+1
       262: 2q+1
       263: q^2+3q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: q^2+3q+1
       268: q^2+3q+1
       269: q^2+3q+1
       270: 2q+1
       271: q^2+3q+1
       272: 2q+1
       273: q^2+2q+1
       274: 2q^2+3q+1
       275: q^2+2q+1
       276: q+1
       277: q^2+2q+1
       278: 2q+1
       279: 2q^2+3q+1
       280: 2q+1
       281: q+1
       282: 2q+1
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: q^2+3q+1
       290: q^2+3q+1
       291: q^2+3q+1
       292: 2q+1
       293: q^2+3q+1
       294: 2q+1
       295: q^2+3q+1
       296: 2q^2+3q+1
       297: q^2+3q+1
       298: 2q+1
       299: q^2+3q+1
       300: 2q^2+3q+1
       301: 2q^2+3q+1
       302: q^2+2q+1
       303: 2q^2+3q+1
       304: 2q^2+3q+1
       305: 2q+1
       306: 2q^2+3q+1
       307: 2q^2+3q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: 2q+1
       321: 2q+1
       322: q^2+3q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q^2+2q+1
       331: q^2+2q+1
       332: q+1
       333: q^2+2q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q+1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       352: q^2+2q+1
       353: q+1
       354: 1
       355: q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: q^2+3q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: q^2+3q+1
       368: q^2+3q+1
       369: 2q+1
       370: q^2+3q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       377: q+1
       378: q^2+2q+1
       379: q+1
       380: q+1
       381: 2q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: q+1
       387: q+1
       388: 2q^2+3q+1
       389: q+1
       390: 1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: q^2+3q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: q^2+3q+1
       407: q^2+3q+1
       408: 2q+1
       409: q^2+3q+1
       410: 2q+1
       411: 1
       412: q+1
       413: q^2+2q+1
       414: q^2+2q+1
       415: q^2+2q+1
       416: q+1
       417: q^2+2q+1
       418: q+1
       419: q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: q+1
       424: 2q+1
       425: q+1
       426: q+1
       427: 2q^2+3q+1
       428: q+1
       429: 1
       430: q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q+1
       434: 2q+1
       435: 2q+1
       436: q^2+3q+1
       437: q^2+3q+1
       438: 2q+1
       439: q^2+3q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: q^2+3q+1
       444: q^2+3q+1
       445: q^2+3q+1
       446: 2q+1
       447: q^2+3q+1
       448: 2q+1
       449: q^2+2q+1
       450: 2q^2+3q+1
       451: q^2+2q+1
       452: q+1
       453: q^2+2q+1
       454: 2q+1
       455: 2q^2+3q+1
       456: 2q+1
       457: q+1
       458: 2q+1
       459: 2q^2+3q+1
       460: 2q^2+3q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: 1
       467: q+1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: 2q+1
       476: q+1
       477: q+1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: q+1
       486: q^2+2q+1
       487: q+1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: 2q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: 2q+1
       529: q^2+3q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q^2+2q+1
       538: q^2+2q+1
       539: q+1
       540: q^2+2q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q^2+2q+1
       560: q+1
       561: 1
       562: q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: 2q+1
       576: q^2+3q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q^2+2q+1
       585: q^2+2q+1
       586: q+1
       587: q^2+2q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: 2q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: q+1
       597: 1
       598: 1
       599: q+1
       600: q+1
       601: q+1
       602: 1
       603: q+1
       604: 1
       605: q+1
       606: q^2+2q+1
       607: q+1
       608: 1
       609: q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: q^2+3q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: q^2+3q+1
       622: q^2+3q+1
       623: 2q+1
       624: q^2+3q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q^2+2q+1
       629: q^2+2q+1
       630: q^2+2q+1
       631: q+1
       632: q^2+2q+1
       633: q+1
       634: q+1
       635: 2q+1
       636: 2q+1
       637: 2q+1
       638: q+1
       639: 2q+1
       640: q+1
       641: q+1
       642: 2q^2+3q+1
       643: q+1
       644: 1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: q+1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       674: 1
       675: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       715: q+1
       716: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: q+1
       724: q+1
       725: q^2+2q+1
       726: q+1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       767: q+1
       768: q+1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q^2+2q+1
       778: q+1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       785: q+1
       786: 2q+1
       787: 1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: q+1
       796: 1
       797: q+1
       798: 1
       799: 1
       800: 1
       801: q+1
       802: q+1
       803: q+1
       804: 1
       805: q+1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: q^2+3q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q^2+2q+1
       829: q^2+2q+1
       830: q+1
       831: q^2+2q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: 2q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: q+1
       841: 1
       842: 1
       843: q+1
       844: q+1
       845: q+1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: 1
       853: q+1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: q+1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       903: 1
       906: q+1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: q+1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       927: q+1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       960: q+1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       985: 1
       986: 1
       987: 1
       988: 1
       989: q+1
       990: 1
       991: 1
       993: q+1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q^2+2q+1
      1037: q+1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: 2q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: q+1
      1055: 1
      1056: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: q+1
      1065: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1086: 1
      1087: 1
      1088: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: q+1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1162: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: q+1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1214: 1
      1217: q+1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: q+1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: q+1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1274: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1304: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1349: 1
      1350: 1
      1351: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1377: 1
      1378: 1
      1379: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1388: 1
      1393: 1
      1396: 1
      1397: 1
      1398: 1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: q+1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1431: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1453: 1
      1466: 1
      1489: 1
      1501: 1
      1502: 1
      1507: 1
      1508: 1
      1519: 1
      1528: 1
      1540: 1
      1541: 1
      1546: 1
      1547: 1
      1558: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1584: 1
      1585: 1
      1586: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1595: 1
      1600: 1
      1603: 1
      1604: 1
      1605: 1
      1642: 1
      1672: 1
      1695: 1
      1707: 1
      1708: 1
      1713: 1
      1714: 1
      1725: 1
      1796: 1

1797:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: 1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: 1
        31: 1
        32: 1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: 1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: 1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: 1
        82: 1
        83: 1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: 1
        95: 1
        96: 1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: 1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q+1
       208: q+1
       209: q+1
       210: q+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       329: q+1
       331: q+1
       332: q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       346: 1
       347: 1
       348: 1
       351: 1
       352: 1
       353: 1
       354: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       376: q+1
       377: q+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       414: q+1
       415: q+1
       416: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       485: q+1
       487: q+1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       509: 1
       511: 1
       512: 1
       513: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       538: q+1
       539: q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       583: q+1
       585: q+1
       586: q+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       600: 1
       601: 1
       602: 1
       605: 1
       606: 1
       607: 1
       608: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       630: q+1
       631: q+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       665: 1
       669: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       688: 1
       690: 1
       696: 1
       698: 1
       699: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: q+1
       726: q+1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       776: q+1
       778: q+1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       800: 1
       802: 1
       803: 1
       804: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       829: q+1
       830: q+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       890: 1
       899: 1
       901: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: q+1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       976: 1
       980: q+1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       999: 1
      1001: 1
      1007: 1
      1009: 1
      1010: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: q+1
      1037: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1106: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: 1
      1177: 1
      1179: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1201: 1
      1210: 1
      1212: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: q+1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1267: 1
      1275: 1
      1286: 1
      1288: 1
      1291: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1397: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1428: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1440: 1
      1449: 1
      1451: 1
      1467: 1
      1490: 1
      1501: 1
      1503: 1
      1506: 1
      1529: 1
      1540: 1
      1542: 1
      1545: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1584: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1604: 1
      1643: 1
      1673: 1
      1696: 1
      1707: 1
      1709: 1
      1712: 1
      1797: 1

1798:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: q+1
        65: 2q+1
        66: q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: 2q+1
       119: q+1
       120: q+1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: q+1
       149: 2q+1
       150: q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: q+1
       170: 2q+1
       171: q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: q+1
       274: q+1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: q+1
       303: 2q+1
       304: q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: q+1
       325: q+1
       326: 1
       327: 1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       394: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: q+1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: q+1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       769: q+1
       770: q+1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: q+1
       785: q+1
       786: q+1
       787: 1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: q+1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       852: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       872: 1
       879: 1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: 1
       970: 1
       971: 1
       972: q+1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       987: 1
       988: 1
       989: q+1
       990: 1
       991: 1
       992: q+1
       993: q+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1097: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1131: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1183: 1
      1190: 1
      1191: 1
      1192: 1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1249: q+1
      1250: q+1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1276: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: 1
      1341: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: 1
      1388: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1422: 1
      1429: 1
      1430: 1
      1431: 1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1468: 1
      1491: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1530: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1566: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1593: 1
      1595: 1
      1644: 1
      1674: 1
      1697: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1798: 1

1799:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: q^2+2q+1
        24: 2q^2+2q+1
        25: 2q+1
        26: q^2+q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q^2+2q+1
        55: 2q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: q+1
        59: q^2+q+1
        60: 2q+1
        61: q^2+2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q^2+q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        75: 2q^2+2q+1
        76: 2q+1
        77: q^2+q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+2q+1
        89: 2q+1
        90: q^2+q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: q+1
       113: 2q+1
       114: q+1
       115: q+1
       116: q+1
       117: q^2+q+1
       118: 2q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q^2+q+1
       127: q+1
       128: q^2+2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       142: q+1
       143: q^2+q+1
       144: 2q+1
       145: q^2+2q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q+1
       150: q^2+q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: q^2+2q+1
       160: 2q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: q+1
       164: q^2+q+1
       165: 2q+1
       166: q^2+2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q^2+q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: q^2+2q+1
       180: 2q^2+2q+1
       181: 2q+1
       182: q^2+q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: 2q+1
       186: 2q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: q+1
       199: 1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 2q+1
       206: q+1
       207: 2q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: 2q+1
       213: 1
       214: 2q+1
       215: q+1
       216: q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: q+1
       224: 2q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q^2+q+1
       242: 2q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q^2+q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q^2+q+1
       272: 2q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: 2q+1
       277: 2q+1
       278: 2q+1
       279: q+1
       280: q^2+q+1
       281: q+1
       282: q^2+2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: q+1
       297: q^2+q+1
       298: 2q+1
       299: q^2+2q+1
       300: 2q+1
       301: q+1
       302: 2q+1
       303: 2q+1
       304: q^2+q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: q+1
       313: 2q+1
       314: 1
       315: 2q+1
       316: 2q+1
       317: q+1
       319: q+1
       320: 1
       321: 1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: q+1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: 2q+1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: 2q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: 1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: 2q+1
       380: 1
       381: 2q+1
       382: q+1
       383: q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: q+1
       391: 2q+1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: 1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 2q+1
       412: q+1
       413: 2q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: 2q+1
       419: 1
       420: 2q+1
       421: q+1
       422: q+1
       423: q+1
       424: q^2+q+1
       425: q+1
       426: 2q+1
       427: q+1
       428: q+1
       429: q+1
       430: 2q+1
       431: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q^2+q+1
       448: 2q+1
       449: 2q+1
       450: q+1
       451: q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: q+1
       456: q^2+q+1
       457: q+1
       458: q^2+2q+1
       459: 2q+1
       460: q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       466: q+1
       467: q+1
       468: 1
       469: 1
       470: 2q+1
       471: q+1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: 1
       479: q+1
       480: q+1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       515: 1
       517: q+1
       518: q+1
       519: q+1
       520: 2q+1
       521: 1
       522: 2q+1
       523: 2q+1
       524: q+1
       526: q+1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: q+1
       535: q+1
       536: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: 2q+1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: 1
       552: 2q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: q+1
       561: 1
       562: q+1
       564: q+1
       565: q+1
       566: q+1
       567: 2q+1
       568: 1
       569: 2q+1
       570: 2q+1
       571: q+1
       573: q+1
       574: 1
       575: 1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: q+1
       583: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: 2q+1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: 1
       599: 2q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: 1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 2q+1
       627: q+1
       628: 2q+1
       629: q+1
       630: 1
       631: q+1
       632: q+1
       633: 2q+1
       634: 1
       635: 2q+1
       636: q+1
       637: q+1
       638: q+1
       639: q^2+q+1
       640: q+1
       641: 2q+1
       642: q+1
       643: q+1
       644: q+1
       645: 2q+1
       646: q+1
       648: q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       659: 1
       660: 1
       661: 1
       662: 1
       663: q+1
       664: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q+1
       683: q+1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       702: 1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: 2q+1
       710: q+1
       713: 1
       714: 1
       715: 1
       716: q+1
       717: 1
       718: q+1
       719: q+1
       720: 1
       722: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: q+1
       754: 1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: 2q+1
       762: q+1
       765: 1
       766: 1
       767: 1
       768: q+1
       769: 1
       770: q+1
       771: q+1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: q+1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       806: 1
       808: q+1
       809: q+1
       810: q+1
       811: 2q+1
       812: 1
       813: 2q+1
       814: 2q+1
       815: q+1
       817: q+1
       818: 1
       819: 1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: q+1
       827: 1
       828: q+1
       829: 1
       830: 1
       831: 1
       832: q+1
       833: 2q+1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       842: 1
       843: 2q+1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       852: 1
       853: q+1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       875: 1
       876: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       921: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q+1
       940: q+1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       959: 1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       970: 1
       971: 1
       972: 1
       973: 1
       974: q+1
       975: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       988: 1
       989: 1
       990: 1
       991: q+1
       992: 1
       993: q+1
       994: q+1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1013: 1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: 2q+1
      1021: q+1
      1024: 1
      1025: 1
      1026: 1
      1027: q+1
      1028: 1
      1029: q+1
      1030: q+1
      1031: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: q+1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: q+1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: 1
      1060: q+1
      1065: 1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1084: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1168: 1
      1169: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: q+1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: q+1
      1232: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1245: 1
      1246: 1
      1247: 1
      1248: q+1
      1249: 1
      1250: q+1
      1251: q+1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1270: 1
      1277: 1
      1289: 1
      1290: 1
      1295: 1
      1299: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1328: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1360: 1
      1365: 1
      1366: 1
      1371: 1
      1375: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1407: 1
      1408: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: q+1
      1435: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1455: 1
      1469: 1
      1492: 1
      1504: 1
      1505: 1
      1510: 1
      1514: 1
      1531: 1
      1543: 1
      1544: 1
      1549: 1
      1553: 1
      1567: 1
      1572: 1
      1573: 1
      1578: 1
      1582: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1645: 1
      1675: 1
      1698: 1
      1710: 1
      1711: 1
      1716: 1
      1720: 1
      1799: 1

1800:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: q+1
        51: q+1
        52: q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: 2q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: 1
       195: 2q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: 1
       325: 2q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: 1
       362: 2q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: 2q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q+1
       463: q+1
       467: q+1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       489: q+1
       490: 1
       491: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: 1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: 2q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: 1
       616: 2q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: q+1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       668: q+1
       669: q+1
       670: q+1
       674: 1
       675: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       706: q+1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: q+1
       715: q+1
       716: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       728: q+1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: 1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: q+1
       877: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: q+1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       925: q+1
       926: q+1
       927: q+1
       931: 1
       932: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       979: q+1
       980: q+1
       981: q+1
       985: 1
       986: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1017: q+1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: q+1
      1026: q+1
      1027: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1039: q+1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1131: q+1
      1136: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1183: q+1
      1188: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1214: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: q+1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1242: 1
      1243: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1278: 1
      1290: 1
      1291: 1
      1292: 1
      1304: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1341: 1
      1346: 1
      1349: 1
      1350: 1
      1351: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1388: 1
      1393: 1
      1396: 1
      1397: 1
      1398: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1422: q+1
      1427: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1453: 1
      1470: 1
      1493: 1
      1505: 1
      1506: 1
      1507: 1
      1519: 1
      1532: 1
      1544: 1
      1545: 1
      1546: 1
      1558: 1
      1568: 1
      1573: 1
      1574: 1
      1575: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1595: 1
      1600: 1
      1603: 1
      1604: 1
      1605: 1
      1646: 1
      1676: 1
      1699: 1
      1711: 1
      1712: 1
      1713: 1
      1725: 1
      1800: 1

1801:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: q^3+5q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: 3q^3+6q^2+4q+1
         5: 3q^3+6q^2+4q+1
         6: q^3+5q^2+4q+1
         7: q^3+5q^2+4q+1
         8: q^3+5q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: 4q^2+4q+1
        11: 2q^3+5q^2+4q+1
        12: 2q^3+5q^2+4q+1
        13: 3q^3+6q^2+4q+1
        14: q^3+5q^2+4q+1
        15: 3q^3+6q^2+4q+1
        16: 3q^3+6q^2+4q+1
        17: q^3+5q^2+4q+1
        18: 3q^3+6q^2+4q+1
        19: 3q^3+6q^2+4q+1
        20: q^3+5q^2+4q+1
        21: q^3+5q^2+4q+1
        22: q^3+5q^2+4q+1
        23: 2q^2+3q+1
        24: 2q^2+3q+1
        25: 4q^2+4q+1
        26: 4q^2+4q+1
        27: 4q^2+4q+1
        28: 2q^3+5q^2+4q+1
        29: 3q^2+4q+1
        30: 2q^3+5q^2+4q+1
        31: 3q^2+4q+1
        32: q^3+4q^2+4q+1
        33: q^3+5q^2+4q+1
        34: q^3+5q^2+4q+1
        35: q^3+5q^2+4q+1
        36: 3q^3+6q^2+4q+1
        37: 4q^2+4q+1
        38: 2q^3+5q^2+4q+1
        39: 2q^3+5q^2+4q+1
        40: q^3+5q^2+4q+1
        41: q^3+5q^2+4q+1
        42: q^3+5q^2+4q+1
        43: 3q^3+6q^2+4q+1
        44: 4q^2+4q+1
        45: 2q^3+5q^2+4q+1
        46: 2q^3+5q^2+4q+1
        47: 3q^3+6q^2+4q+1
        48: q^3+5q^2+4q+1
        49: 3q^3+6q^2+4q+1
        50: 2q^2+3q+1
        51: 2q^2+3q+1
        52: q^3+5q^2+4q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: q^2+3q+1
        57: 4q^2+4q+1
        58: 4q^2+4q+1
        59: 4q^2+4q+1
        60: q^2+3q+1
        61: q^2+3q+1
        62: 3q^2+4q+1
        63: 3q^2+4q+1
        64: 3q^2+4q+1
        65: 3q^2+4q+1
        66: 3q^2+4q+1
        67: 3q^2+4q+1
        68: q^3+4q^2+4q+1
        69: 2q^2+4q+1
        70: q^3+4q^2+4q+1
        71: q^3+5q^2+4q+1
        72: q^3+5q^2+4q+1
        73: q^3+5q^2+4q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: 4q^2+4q+1
        77: 4q^2+4q+1
        78: 4q^2+4q+1
        79: 2q^3+5q^2+4q+1
        80: 3q^2+4q+1
        81: 2q^3+5q^2+4q+1
        82: 3q^2+4q+1
        83: q^3+4q^2+4q+1
        84: q^3+5q^2+4q+1
        85: q^3+5q^2+4q+1
        86: q^3+5q^2+4q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: 4q^2+4q+1
        90: 4q^2+4q+1
        91: 4q^2+4q+1
        92: 2q^3+5q^2+4q+1
        93: 3q^2+4q+1
        94: 2q^3+5q^2+4q+1
        95: 3q^2+4q+1
        96: q^3+4q^2+4q+1
        97: q^3+5q^2+4q+1
        98: q^3+5q^2+4q+1
        99: q^3+5q^2+4q+1
       100: 3q^3+6q^2+4q+1
       101: 4q^2+4q+1
       102: 2q^3+5q^2+4q+1
       103: 2q^3+5q^2+4q+1
       104: q^2+3q+1
       105: 2q^2+3q+1
       106: 2q^2+3q+1
       107: 2q^2+3q+1
       108: 2q+1
       109: 2q+1
       110: q^2+3q+1
       111: q^2+3q+1
       112: q^2+3q+1
       113: q^2+3q+1
       114: 4q^2+4q+1
       115: 2q^2+3q+1
       116: q^2+3q+1
       117: q^2+3q+1
       118: 3q+1
       119: 3q^2+4q+1
       120: 3q^2+4q+1
       121: 3q^2+4q+1
       122: q^2+3q+1
       123: 2q+1
       124: 3q^2+4q+1
       125: 3q^2+4q+1
       126: 3q^2+4q+1
       127: 2q+1
       128: q^2+3q+1
       129: 2q^2+4q+1
       130: 2q^2+4q+1
       131: 2q^2+4q+1
       132: q^3+4q^2+4q+1
       133: q^2+3q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: q^3+5q^2+4q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: q^2+3q+1
       141: 4q^2+4q+1
       142: 4q^2+4q+1
       143: 4q^2+4q+1
       144: q^2+3q+1
       145: q^2+3q+1
       146: 3q^2+4q+1
       147: 3q^2+4q+1
       148: 3q^2+4q+1
       149: 3q^2+4q+1
       150: 3q^2+4q+1
       151: 3q^2+4q+1
       152: q^3+4q^2+4q+1
       153: 2q^2+4q+1
       154: q^3+4q^2+4q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: q^3+5q^2+4q+1
       158: 2q^2+3q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: q^2+3q+1
       162: 4q^2+4q+1
       163: 4q^2+4q+1
       164: 4q^2+4q+1
       165: q^2+3q+1
       166: q^2+3q+1
       167: 3q^2+4q+1
       168: 3q^2+4q+1
       169: 3q^2+4q+1
       170: 3q^2+4q+1
       171: 3q^2+4q+1
       172: 3q^2+4q+1
       173: q^3+4q^2+4q+1
       174: 2q^2+4q+1
       175: q^3+4q^2+4q+1
       176: q^3+5q^2+4q+1
       177: q^3+5q^2+4q+1
       178: q^3+5q^2+4q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: 4q^2+4q+1
       182: 4q^2+4q+1
       183: 4q^2+4q+1
       184: 2q^3+5q^2+4q+1
       185: 3q^2+4q+1
       186: 2q^3+5q^2+4q+1
       187: 3q^2+4q+1
       188: q^3+4q^2+4q+1
       189: q^2+3q+1
       190: q^2+3q+1
       191: 2q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+3q+1
       197: 2q+1
       198: 3q+1
       199: q^2+3q+1
       200: q^2+3q+1
       201: 2q^2+3q+1
       202: 2q+1
       203: 2q+1
       204: 3q+1
       205: 3q+1
       206: q^2+3q+1
       207: 2q+1
       208: 3q^2+4q+1
       209: q^2+2q+1
       210: q^2+3q+1
       211: 2q+1
       212: 2q+1
       213: 2q+1
       214: q^2+3q+1
       215: 3q^2+4q+1
       216: q^2+2q+1
       217: 2q+1
       218: q^2+3q+1
       219: 2q+1
       220: 2q^2+4q+1
       221: 2q^2+4q+1
       222: 2q^2+4q+1
       223: 2q+1
       224: 2q+1
       225: q^2+3q+1
       226: q^2+3q+1
       227: q^2+3q+1
       228: q^2+3q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: 2q^2+3q+1
       232: 2q+1
       233: 2q+1
       234: q^2+3q+1
       235: q^2+3q+1
       236: q^2+3q+1
       237: q^2+3q+1
       238: 4q^2+4q+1
       239: 2q^2+3q+1
       240: q^2+3q+1
       241: q^2+3q+1
       242: 3q+1
       243: 3q^2+4q+1
       244: 3q^2+4q+1
       245: 3q^2+4q+1
       246: q^2+3q+1
       247: 2q+1
       248: 3q^2+4q+1
       249: 3q^2+4q+1
       250: 3q^2+4q+1
       251: 2q+1
       252: q^2+3q+1
       253: 2q^2+4q+1
       254: 2q^2+4q+1
       255: 2q^2+4q+1
       256: q^3+4q^2+4q+1
       257: q^2+3q+1
       258: q^2+3q+1
       259: 2q^2+3q+1
       260: 2q^2+3q+1
       261: 2q^2+3q+1
       262: 2q+1
       263: 2q+1
       264: q^2+3q+1
       265: q^2+3q+1
       266: q^2+3q+1
       267: q^2+3q+1
       268: 4q^2+4q+1
       269: 2q^2+3q+1
       270: q^2+3q+1
       271: q^2+3q+1
       272: 3q+1
       273: 3q^2+4q+1
       274: 3q^2+4q+1
       275: 3q^2+4q+1
       276: q^2+3q+1
       277: 2q+1
       278: 3q^2+4q+1
       279: 3q^2+4q+1
       280: 3q^2+4q+1
       281: 2q+1
       282: q^2+3q+1
       283: 2q^2+4q+1
       284: 2q^2+4q+1
       285: 2q^2+4q+1
       286: q^3+4q^2+4q+1
       287: q^2+3q+1
       288: 2q^2+3q+1
       289: 2q^2+3q+1
       290: q^3+5q^2+4q+1
       291: 2q^2+3q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: q^2+3q+1
       295: 4q^2+4q+1
       296: 4q^2+4q+1
       297: 4q^2+4q+1
       298: q^2+3q+1
       299: q^2+3q+1
       300: 3q^2+4q+1
       301: 3q^2+4q+1
       302: 3q^2+4q+1
       303: 3q^2+4q+1
       304: 3q^2+4q+1
       305: 3q^2+4q+1
       306: q^3+4q^2+4q+1
       307: 2q^2+4q+1
       308: q^3+4q^2+4q+1
       309: 2q+1
       310: q^2+3q+1
       311: 2q+1
       312: 2q+1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: 2q+1
       319: 3q+1
       320: 3q+1
       321: 2q+1
       322: 2q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: 3q+1
       327: 2q+1
       328: 2q+1
       329: q^2+3q+1
       330: 2q+1
       331: q^2+2q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: 2q+1
       338: q^2+3q+1
       339: q^2+2q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: 2q+1
       346: 2q^2+4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: q^2+3q+1
       352: q^2+3q+1
       353: q^2+3q+1
       354: q+1
       355: q+1
       356: q^2+3q+1
       357: q^2+3q+1
       358: 2q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+3q+1
       364: 2q+1
       365: 3q+1
       366: q^2+3q+1
       367: q^2+3q+1
       368: 2q^2+3q+1
       369: 2q+1
       370: 2q+1
       371: 3q+1
       372: 3q+1
       373: q^2+3q+1
       374: 2q+1
       375: 3q^2+4q+1
       376: q^2+2q+1
       377: q^2+3q+1
       378: 2q+1
       379: 2q+1
       380: 2q+1
       381: q^2+3q+1
       382: 3q^2+4q+1
       383: q^2+2q+1
       384: 2q+1
       385: q^2+3q+1
       386: 2q+1
       387: 2q^2+4q+1
       388: 2q^2+4q+1
       389: 2q^2+4q+1
       390: 2q+1
       391: 2q+1
       392: q^2+3q+1
       393: q^2+3q+1
       394: q^2+3q+1
       395: q^2+3q+1
       396: q^2+3q+1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+3q+1
       403: 2q+1
       404: 3q+1
       405: q^2+3q+1
       406: q^2+3q+1
       407: 2q^2+3q+1
       408: 2q+1
       409: 2q+1
       410: 3q+1
       411: 3q+1
       412: q^2+3q+1
       413: 2q+1
       414: 3q^2+4q+1
       415: q^2+2q+1
       416: q^2+3q+1
       417: 2q+1
       418: 2q+1
       419: 2q+1
       420: q^2+3q+1
       421: 3q^2+4q+1
       422: q^2+2q+1
       423: 2q+1
       424: q^2+3q+1
       425: 2q+1
       426: 2q^2+4q+1
       427: 2q^2+4q+1
       428: 2q^2+4q+1
       429: 2q+1
       430: 2q+1
       431: q^2+3q+1
       432: q^2+3q+1
       433: q^2+3q+1
       434: q^2+3q+1
       435: 2q^2+3q+1
       436: 2q^2+3q+1
       437: 2q^2+3q+1
       438: 2q+1
       439: 2q+1
       440: q^2+3q+1
       441: q^2+3q+1
       442: q^2+3q+1
       443: q^2+3q+1
       444: 4q^2+4q+1
       445: 2q^2+3q+1
       446: q^2+3q+1
       447: q^2+3q+1
       448: 3q+1
       449: 3q^2+4q+1
       450: 3q^2+4q+1
       451: 3q^2+4q+1
       452: q^2+3q+1
       453: 2q+1
       454: 3q^2+4q+1
       455: 3q^2+4q+1
       456: 3q^2+4q+1
       457: 2q+1
       458: q^2+3q+1
       459: 2q^2+4q+1
       460: 2q^2+4q+1
       461: 2q^2+4q+1
       462: q^3+4q^2+4q+1
       463: q^2+3q+1
       464: 2q+1
       465: q+1
       466: 2q+1
       471: q+1
       472: q+1
       473: 2q+1
       474: 3q+1
       475: 2q+1
       476: 2q+1
       479: 2q+1
       480: 2q+1
       481: 1
       482: 2q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: 2q+1
       503: 2q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q^2+3q+1
       512: q+1
       513: q+1
       514: q+1
       515: 1
       516: 2q+1
       517: q^2+3q+1
       518: 2q+1
       519: 2q+1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: 2q+1
       526: 3q+1
       527: 3q+1
       528: 2q+1
       529: 2q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 3q+1
       534: 2q+1
       535: 2q+1
       536: q^2+3q+1
       537: 2q+1
       538: q^2+2q+1
       539: q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: 2q+1
       544: 2q+1
       545: q^2+3q+1
       546: q^2+2q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: 2q+1
       553: 2q^2+4q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: q+1
       558: q^2+3q+1
       559: q^2+3q+1
       560: q^2+3q+1
       561: q+1
       562: q+1
       563: 2q+1
       564: q^2+3q+1
       565: 2q+1
       566: 2q+1
       569: 2q+1
       570: 2q+1
       571: q+1
       572: 2q+1
       573: 3q+1
       574: 3q+1
       575: 2q+1
       576: 2q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 3q+1
       581: 2q+1
       582: 2q+1
       583: q^2+3q+1
       584: 2q+1
       585: q^2+2q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: 2q+1
       591: 2q+1
       592: q^2+3q+1
       593: q^2+2q+1
       594: q+1
       595: q+1
       596: 2q+1
       597: 2q+1
       598: 2q+1
       599: 2q+1
       600: 2q^2+4q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: q+1
       605: q^2+3q+1
       606: q^2+3q+1
       607: q^2+3q+1
       608: q+1
       609: q+1
       610: q^2+3q+1
       611: q^2+3q+1
       612: 2q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+3q+1
       618: 2q+1
       619: 3q+1
       620: q^2+3q+1
       621: q^2+3q+1
       622: 2q^2+3q+1
       623: 2q+1
       624: 2q+1
       625: 3q+1
       626: 3q+1
       627: q^2+3q+1
       628: 2q+1
       629: 3q^2+4q+1
       630: q^2+2q+1
       631: q^2+3q+1
       632: 2q+1
       633: 2q+1
       634: 2q+1
       635: q^2+3q+1
       636: 3q^2+4q+1
       637: q^2+2q+1
       638: 2q+1
       639: q^2+3q+1
       640: 2q+1
       641: 2q^2+4q+1
       642: 2q^2+4q+1
       643: 2q^2+4q+1
       644: 2q+1
       645: 2q+1
       646: q^2+3q+1
       647: q^2+3q+1
       648: q^2+3q+1
       649: q+1
       650: q+1
       656: q+1
       657: 2q+1
       658: 1
       659: 2q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: q+1
       669: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: q+1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 2q+1
       704: q+1
       705: 2q+1
       710: q+1
       711: q+1
       712: 2q+1
       713: 3q+1
       714: 2q+1
       715: 2q+1
       718: 2q+1
       719: 2q+1
       720: 1
       721: 2q+1
       722: 2q+1
       723: 2q+1
       724: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       731: 2q+1
       732: 2q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: q+1
       741: 2q+1
       742: 2q+1
       743: q+1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: q+1
       750: q^2+3q+1
       751: q+1
       752: q+1
       753: q+1
       754: 1
       755: 2q+1
       756: q+1
       757: 2q+1
       762: q+1
       763: q+1
       764: 2q+1
       765: 3q+1
       766: 2q+1
       767: 2q+1
       770: 2q+1
       771: 2q+1
       772: 1
       773: 2q+1
       774: 2q+1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: 2q+1
       784: 2q+1
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: 2q+1
       791: q+1
       792: q+1
       793: 2q+1
       794: 2q+1
       795: q+1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: q+1
       802: q^2+3q+1
       803: q+1
       804: q+1
       805: q+1
       806: 1
       807: 2q+1
       808: q^2+3q+1
       809: 2q+1
       810: 2q+1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: 2q+1
       817: 3q+1
       818: 3q+1
       819: 2q+1
       820: 2q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 3q+1
       825: 2q+1
       826: 2q+1
       827: q^2+3q+1
       828: 2q+1
       829: q^2+2q+1
       830: q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       834: 2q+1
       835: 2q+1
       836: q^2+3q+1
       837: q^2+2q+1
       838: q+1
       839: q+1
       840: 2q+1
       841: 2q+1
       842: 2q+1
       843: 2q+1
       844: 2q^2+4q+1
       845: q+1
       846: 2q+1
       847: 2q+1
       848: q+1
       849: q^2+3q+1
       850: q^2+3q+1
       851: q^2+3q+1
       852: q+1
       853: q+1
       854: q+1
       861: 1
       862: 1
       868: 1
       869: q+1
       870: 1
       871: q+1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       913: q+1
       914: 2q+1
       915: 1
       916: 2q+1
       921: 1
       922: 1
       923: q+1
       924: 2q+1
       925: q+1
       926: q+1
       929: q+1
       930: q+1
       931: 1
       932: q+1
       933: q+1
       934: 2q+1
       935: q+1
       936: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q+1
       954: q+1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       967: q+1
       968: 2q+1
       969: 1
       970: 2q+1
       975: 1
       976: 1
       977: q+1
       978: 2q+1
       979: q+1
       980: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       987: q+1
       988: 2q+1
       989: q+1
       990: q+1
       993: q+1
       994: q+1
       995: 1
       996: q+1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: q+1
      1008: q+1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 2q+1
      1015: q+1
      1016: 2q+1
      1021: q+1
      1022: q+1
      1023: 2q+1
      1024: 3q+1
      1025: 2q+1
      1026: 2q+1
      1029: 2q+1
      1030: 2q+1
      1031: 1
      1032: 2q+1
      1033: 2q+1
      1034: 2q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1042: 2q+1
      1043: 2q+1
      1044: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1051: q+1
      1052: 2q+1
      1053: 2q+1
      1054: q+1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: q+1
      1061: q^2+3q+1
      1062: q+1
      1063: q+1
      1064: q+1
      1065: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1086: 1
      1087: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1113: q+1
      1120: 1
      1121: 1
      1127: 1
      1128: q+1
      1129: 1
      1130: q+1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1172: 1
      1173: 1
      1179: 1
      1180: q+1
      1181: 1
      1182: q+1
      1187: 1
      1188: 1
      1189: q+1
      1190: 1
      1191: q+1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1224: q+1
      1225: 2q+1
      1226: 1
      1227: 2q+1
      1232: 1
      1233: 1
      1234: q+1
      1235: 2q+1
      1236: q+1
      1237: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: q+1
      1244: q+1
      1245: 2q+1
      1246: q+1
      1247: q+1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: q+1
      1255: q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: q+1
      1265: q+1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1279: 1
      1286: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1303: 1
      1315: 1
      1322: 1
      1323: 1
      1329: 1
      1330: 1
      1331: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1356: 1
      1362: 1
      1369: 1
      1370: 1
      1376: 1
      1377: 1
      1378: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1403: 1
      1404: q+1
      1411: 1
      1412: 1
      1418: 1
      1419: q+1
      1420: 1
      1421: q+1
      1426: 1
      1427: 1
      1428: q+1
      1429: 1
      1430: q+1
      1435: 1
      1436: 1
      1437: 1
      1438: q+1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1471: 1
      1494: 1
      1501: 1
      1508: 1
      1509: 1
      1515: 1
      1516: 1
      1518: 1
      1533: 1
      1540: 1
      1547: 1
      1548: 1
      1554: 1
      1555: 1
      1557: 1
      1569: 1
      1576: 1
      1577: 1
      1583: 1
      1584: 1
      1585: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1610: 1
      1647: 1
      1677: 1
      1700: 1
      1707: 1
      1714: 1
      1715: 1
      1721: 1
      1722: 1
      1724: 1
      1801: 1

1802:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q+1
        24: 2q^2+2q+1
        25: 2q^2+2q+1
        26: q+1
        27: 2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q+1
        51: 2q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q+1
        55: q^2+2q+1
        56: q+1
        57: 2q^2+2q+1
        58: q+1
        59: q+1
        60: q+1
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: q+1
        67: 2q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q+1
        75: 2q^2+2q+1
        76: 2q^2+2q+1
        77: q+1
        78: 2q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: q+1
        91: 2q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q+1
       109: q^2+2q+1
       110: q+1
       111: q+1
       112: q+1
       113: 2q^2+2q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: q+1
       119: q^2+2q+1
       120: q+1
       121: q+1
       122: q+1
       123: q^2+2q+1
       124: 2q^2+2q+1
       125: q+1
       126: q+1
       127: 1
       128: 2q^2+2q+1
       129: q^2+2q+1
       130: q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q+1
       139: q^2+2q+1
       140: q+1
       141: 2q^2+2q+1
       142: q+1
       143: q+1
       144: q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: q+1
       151: 2q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: 2q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q+1
       160: q^2+2q+1
       161: q+1
       162: 2q^2+2q+1
       163: q+1
       164: q+1
       165: q+1
       166: 2q^2+2q+1
       167: q^2+2q+1
       168: q+1
       169: q^2+2q+1
       170: 2q^2+2q+1
       171: q+1
       172: 2q^2+2q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q+1
       180: 2q^2+2q+1
       181: 2q^2+2q+1
       182: q+1
       183: 2q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: 2q^2+2q+1
       187: 2q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^2+2q+1
       193: q+1
       194: q^2+2q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: q+1
       206: q+1
       207: q^2+2q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: q+1
       213: 1
       214: 2q^2+2q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q^2+2q+1
       221: q+1
       222: q+1
       223: 1
       224: q^2+2q+1
       225: q^2+2q+1
       227: q^2+2q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q+1
       233: q^2+2q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q^2+2q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: q+1
       243: q^2+2q+1
       244: q+1
       245: q+1
       246: q+1
       247: q^2+2q+1
       248: 2q^2+2q+1
       249: q+1
       250: q+1
       251: 1
       252: 2q^2+2q+1
       253: q^2+2q+1
       254: q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: q+1
       263: q^2+2q+1
       264: q+1
       265: q+1
       266: q+1
       267: 2q^2+2q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: q+1
       273: q^2+2q+1
       274: q+1
       275: q+1
       276: q+1
       277: q^2+2q+1
       278: 2q^2+2q+1
       279: q+1
       280: q+1
       281: 1
       282: 2q^2+2q+1
       283: q^2+2q+1
       284: q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q+1
       289: 2q^2+2q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q+1
       293: q^2+2q+1
       294: q+1
       295: 2q^2+2q+1
       296: q+1
       297: q+1
       298: q+1
       299: 2q^2+2q+1
       300: q^2+2q+1
       301: q+1
       302: q^2+2q+1
       303: 2q^2+2q+1
       304: q+1
       305: 2q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       315: q^2+2q+1
       316: q+1
       317: q+1
       319: q+1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: q+1
       328: q+1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: q^2+2q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q^2+2q+1
       354: 1
       355: q^2+2q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+2q+1
       360: q+1
       361: q^2+2q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: q+1
       373: q+1
       374: q^2+2q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: q+1
       380: 1
       381: 2q^2+2q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q^2+2q+1
       388: q+1
       389: q+1
       390: 1
       391: q^2+2q+1
       392: q^2+2q+1
       394: q^2+2q+1
       395: q+1
       396: q+1
       397: q+1
       398: q^2+2q+1
       399: q+1
       400: q^2+2q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: q+1
       412: q+1
       413: q^2+2q+1
       414: q+1
       415: q+1
       416: 1
       417: q+1
       418: q+1
       419: 1
       420: 2q^2+2q+1
       421: q+1
       422: q+1
       423: 1
       424: q+1
       425: 1
       426: q^2+2q+1
       427: q+1
       428: q+1
       429: 1
       430: q^2+2q+1
       431: q^2+2q+1
       433: q^2+2q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: q^2+2q+1
       438: q+1
       439: q^2+2q+1
       440: q+1
       441: q+1
       442: q+1
       443: 2q^2+2q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: q+1
       449: q^2+2q+1
       450: q+1
       451: q+1
       452: q+1
       453: q^2+2q+1
       454: 2q^2+2q+1
       455: q+1
       456: q+1
       457: 1
       458: 2q^2+2q+1
       459: q^2+2q+1
       460: q+1
       461: q^2+2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: q+1
       467: q+1
       470: q+1
       471: q+1
       473: q+1
       474: 1
       475: 1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q^2+2q+1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       522: q^2+2q+1
       523: q+1
       524: q+1
       526: q+1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: q+1
       535: q+1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: q+1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       552: q^2+2q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q^2+2q+1
       561: 1
       562: q^2+2q+1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       569: q^2+2q+1
       570: q+1
       571: q+1
       573: q+1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: q+1
       582: q+1
       583: 1
       584: q+1
       585: q+1
       586: 1
       587: q+1
       588: 1
       589: q+1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: q+1
       596: 1
       597: 1
       598: 1
       599: q^2+2q+1
       600: q+1
       601: q+1
       602: 1
       603: q+1
       604: 1
       605: q^2+2q+1
       608: 1
       609: q^2+2q+1
       610: q+1
       611: q+1
       612: q+1
       613: q^2+2q+1
       614: q+1
       615: q^2+2q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: q+1
       627: q+1
       628: q^2+2q+1
       629: q+1
       630: q+1
       631: 1
       632: q+1
       633: q+1
       634: 1
       635: 2q^2+2q+1
       636: q+1
       637: q+1
       638: 1
       639: q+1
       640: 1
       641: q^2+2q+1
       642: q+1
       643: q+1
       644: 1
       645: q^2+2q+1
       646: q^2+2q+1
       648: q^2+2q+1
       650: q+1
       651: q+1
       655: q+1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: q+1
       705: q+1
       706: q+1
       709: q+1
       710: q+1
       712: q+1
       713: 1
       714: 1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       722: q+1
       723: 1
       724: 1
       725: q+1
       726: 1
       727: q+1
       728: 1
       729: 1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q^2+2q+1
       754: 1
       756: q+1
       757: q+1
       758: q+1
       761: q+1
       762: q+1
       764: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       770: q+1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: q+1
       778: 1
       779: q+1
       780: 1
       781: 1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: q+1
       796: 1
       797: q+1
       798: 1
       799: 1
       800: 1
       801: q^2+2q+1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: q+1
       813: q^2+2q+1
       814: q+1
       815: q+1
       817: q+1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: q+1
       826: q+1
       827: 1
       828: q+1
       829: q+1
       830: 1
       831: q+1
       832: 1
       833: q+1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: 1
       842: 1
       843: q^2+2q+1
       844: q+1
       845: q+1
       846: 1
       847: q+1
       848: 1
       849: q^2+2q+1
       852: 1
       853: q^2+2q+1
       855: q+1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       897: 1
       905: 1
       907: q+1
       908: q+1
       912: q+1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: q+1
       924: 1
       925: 1
       926: 1
       927: 1
       929: q+1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: q+1
       962: q+1
       966: q+1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: q+1
       978: 1
       979: 1
       980: 1
       981: 1
       983: q+1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       991: 1
       993: q+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: 1
      1002: q+1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: q+1
      1016: q+1
      1017: q+1
      1020: q+1
      1021: q+1
      1023: q+1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: q+1
      1037: 1
      1038: q+1
      1039: 1
      1040: 1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: q+1
      1055: 1
      1056: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q^2+2q+1
      1065: 1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1114: q+1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: q+1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1166: q+1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: q+1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: q+1
      1219: q+1
      1223: q+1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1234: q+1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: q+1
      1241: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1250: q+1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: q+1
      1258: 1
      1259: q+1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1270: 1
      1280: 1
      1287: 1
      1294: 1
      1295: 1
      1299: 1
      1316: 1
      1323: 1
      1324: 1
      1328: 1
      1331: 1
      1332: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1347: 1
      1363: 1
      1370: 1
      1371: 1
      1375: 1
      1378: 1
      1379: 1
      1383: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1394: 1
      1405: q+1
      1412: 1
      1413: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1431: 1
      1434: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: q+1
      1444: 1
      1445: 1
      1447: 1
      1455: 1
      1472: 1
      1495: 1
      1502: 1
      1509: 1
      1510: 1
      1514: 1
      1534: 1
      1541: 1
      1548: 1
      1549: 1
      1553: 1
      1570: 1
      1577: 1
      1578: 1
      1582: 1
      1585: 1
      1586: 1
      1590: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1601: 1
      1648: 1
      1678: 1
      1701: 1
      1708: 1
      1715: 1
      1716: 1
      1720: 1
      1802: 1

1803:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: 2q^2+2q+1
        24: q+1
        25: 2q^2+2q+1
        26: q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: 2q^2+2q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q+1
        56: q+1
        57: 2q^2+2q+1
        58: q+1
        59: q+1
        60: 2q^2+2q+1
        61: q+1
        62: 2q^2+2q+1
        63: q+1
        64: 2q^2+2q+1
        65: q^2+2q+1
        66: q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q^2+2q+1
        75: q+1
        76: 2q^2+2q+1
        77: q+1
        78: 2q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: 2q^2+2q+1
        88: q+1
        89: 2q^2+2q+1
        90: q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q+1
       110: q+1
       111: q+1
       112: 2q^2+2q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: q+1
       119: 2q^2+2q+1
       120: q+1
       121: q+1
       122: 2q^2+2q+1
       123: 1
       124: q^2+2q+1
       125: q+1
       126: q+1
       127: q^2+2q+1
       128: q+1
       129: q^2+2q+1
       130: q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q+1
       140: q+1
       141: 2q^2+2q+1
       142: q+1
       143: q+1
       144: 2q^2+2q+1
       145: q+1
       146: 2q^2+2q+1
       147: q+1
       148: 2q^2+2q+1
       149: q^2+2q+1
       150: q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q+1
       161: q+1
       162: 2q^2+2q+1
       163: q+1
       164: q+1
       165: 2q^2+2q+1
       166: q+1
       167: 2q^2+2q+1
       168: q+1
       169: 2q^2+2q+1
       170: q^2+2q+1
       171: q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: 2q^2+2q+1
       180: q+1
       181: 2q^2+2q+1
       182: q+1
       183: 2q^2+2q+1
       184: 2q^2+2q+1
       185: 2q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q^2+2q+1
       192: q+1
       193: q^2+2q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: q+1
       206: 2q^2+2q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: q^2+2q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: q+1
       220: q^2+2q+1
       221: q+1
       222: q+1
       223: q^2+2q+1
       224: 1
       225: q^2+2q+1
       227: q^2+2q+1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q+1
       234: q+1
       235: q+1
       236: 2q^2+2q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: q+1
       243: 2q^2+2q+1
       244: q+1
       245: q+1
       246: 2q^2+2q+1
       247: 1
       248: q^2+2q+1
       249: q+1
       250: q+1
       251: q^2+2q+1
       252: q+1
       253: q^2+2q+1
       254: q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: q^2+2q+1
       262: q^2+2q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q^2+2q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: q+1
       273: 2q^2+2q+1
       274: q+1
       275: q+1
       276: 2q^2+2q+1
       277: 1
       278: q^2+2q+1
       279: q+1
       280: q+1
       281: q^2+2q+1
       282: q+1
       283: q^2+2q+1
       284: q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: q+1
       294: q+1
       295: 2q^2+2q+1
       296: q+1
       297: q+1
       298: 2q^2+2q+1
       299: q+1
       300: 2q^2+2q+1
       301: q+1
       302: 2q^2+2q+1
       303: q^2+2q+1
       304: q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q+1
       312: q^2+2q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       319: q+1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: q+1
       344: q^2+2q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q^2+2q+1
       354: q^2+2q+1
       355: 1
       356: q+1
       357: q+1
       358: q^2+2q+1
       359: q+1
       360: q^2+2q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: q+1
       373: 2q^2+2q+1
       374: 1
       375: q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       380: q^2+2q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: 1
       386: q+1
       387: q^2+2q+1
       388: q+1
       389: q+1
       390: q^2+2q+1
       391: 1
       392: q^2+2q+1
       394: q^2+2q+1
       395: q+1
       396: q+1
       397: q^2+2q+1
       398: q+1
       399: q^2+2q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: q+1
       412: 2q^2+2q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       419: q^2+2q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: q+1
       426: q^2+2q+1
       427: q+1
       428: q+1
       429: q^2+2q+1
       430: 1
       431: q^2+2q+1
       433: q^2+2q+1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: q^2+2q+1
       438: q^2+2q+1
       439: q+1
       440: q+1
       441: q+1
       442: 2q^2+2q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: q+1
       449: 2q^2+2q+1
       450: q+1
       451: q+1
       452: 2q^2+2q+1
       453: 1
       454: q^2+2q+1
       455: q+1
       456: q+1
       457: q^2+2q+1
       458: q+1
       459: q^2+2q+1
       460: q+1
       461: q^2+2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: q+1
       468: q+1
       469: q+1
       471: q+1
       473: q+1
       474: 1
       475: 1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q^2+2q+1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q^2+2q+1
       521: q+1
       522: q+1
       523: q+1
       524: q+1
       526: q+1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: q+1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 1
       546: q+1
       547: q+1
       548: 1
       549: 1
       550: q+1
       551: q^2+2q+1
       552: 1
       553: q+1
       554: q+1
       555: q+1
       556: 1
       557: 1
       558: q^2+2q+1
       561: q^2+2q+1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+2q+1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       573: q+1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: q+1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: q+1
       598: q^2+2q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q^2+2q+1
       608: q^2+2q+1
       609: 1
       610: q+1
       611: q+1
       612: q^2+2q+1
       613: q+1
       614: q^2+2q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: q+1
       627: 2q^2+2q+1
       628: 1
       629: q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       634: q^2+2q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: q+1
       641: q^2+2q+1
       642: q+1
       643: q+1
       644: q^2+2q+1
       645: 1
       646: q^2+2q+1
       648: q^2+2q+1
       650: q+1
       652: q+1
       654: q+1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: q+1
       705: q+1
       707: q+1
       708: q+1
       710: q+1
       712: q+1
       713: 1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: q+1
       732: 1
       733: q+1
       734: 1
       735: q+1
       736: 1
       737: 1
       738: 1
       739: q+1
       740: 1
       741: q+1
       742: 1
       743: q+1
       744: q+1
       745: 1
       746: 1
       747: 1
       748: q^2+2q+1
       749: 1
       754: 1
       756: q+1
       757: q+1
       759: q+1
       760: q+1
       762: q+1
       764: q+1
       765: 1
       766: 1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: q+1
       784: 1
       785: q+1
       786: 1
       787: q+1
       788: 1
       789: 1
       790: 1
       791: q+1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q^2+2q+1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q^2+2q+1
       812: q+1
       813: q+1
       814: q+1
       815: q+1
       817: q+1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: q+1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       841: q+1
       842: q^2+2q+1
       843: 1
       844: q+1
       845: q+1
       846: q+1
       847: 1
       848: 1
       849: q^2+2q+1
       852: q^2+2q+1
       853: 1
       856: q+1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: q+1
       909: q+1
       911: q+1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: q+1
       938: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: q+1
       946: 1
       947: q+1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: q+1
       963: q+1
       965: q+1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: q+1
       988: 1
       989: 1
       990: q+1
       992: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: q+1
      1016: q+1
      1018: q+1
      1019: q+1
      1021: q+1
      1023: q+1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: q+1
      1043: 1
      1044: q+1
      1045: 1
      1046: q+1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1051: 1
      1052: q+1
      1053: 1
      1054: q+1
      1055: q+1
      1056: 1
      1057: 1
      1058: 1
      1059: q^2+2q+1
      1060: 1
      1065: 1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1115: q+1
      1121: 1
      1123: 1
      1125: 1
      1129: 1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1167: q+1
      1173: 1
      1175: 1
      1177: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: q+1
      1220: q+1
      1222: q+1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: q+1
      1245: 1
      1246: 1
      1247: q+1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: q+1
      1257: 1
      1258: q+1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1270: 1
      1281: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1317: 1
      1323: 1
      1325: 1
      1327: 1
      1331: 1
      1333: 1
      1335: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1347: 1
      1364: 1
      1370: 1
      1372: 1
      1374: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1394: 1
      1406: q+1
      1412: 1
      1414: 1
      1416: 1
      1420: 1
      1421: 1
      1423: 1
      1424: 1
      1426: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: q+1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1455: 1
      1473: 1
      1496: 1
      1503: 1
      1509: 1
      1511: 1
      1513: 1
      1535: 1
      1542: 1
      1548: 1
      1550: 1
      1552: 1
      1571: 1
      1577: 1
      1579: 1
      1581: 1
      1585: 1
      1587: 1
      1589: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1601: 1
      1649: 1
      1679: 1
      1702: 1
      1709: 1
      1715: 1
      1717: 1
      1719: 1
      1803: 1

1804:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+2q^2+2q+1
        10: 2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q+1
        26: q+1
        27: 2q+1
        28: q^3+2q^2+2q+1
        29: 2q+1
        30: q^3+2q^2+2q+1
        31: 2q+1
        32: q^3+2q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^3+2q^2+2q+1
        37: 2q+1
        38: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^3+2q^2+2q+1
        44: 2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: q+1
        59: q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: q+1
        64: 2q+1
        65: 2q+1
        66: q+1
        67: 2q+1
        68: q^3+2q^2+2q+1
        69: 2q+1
        70: q^3+2q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 2q+1
        77: q+1
        78: 2q+1
        79: q^3+2q^2+2q+1
        80: 2q+1
        81: q^3+2q^2+2q+1
        82: 2q+1
        83: q^3+2q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 2q+1
        90: q+1
        91: 2q+1
        92: q^3+2q^2+2q+1
        93: 2q+1
        94: q^3+2q^2+2q+1
        95: 2q+1
        96: q^3+2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^3+2q^2+2q+1
       101: 2q+1
       102: q^3+2q^2+2q+1
       103: q^3+2q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 2q+1
       113: 2q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: 2q+1
       119: 2q+1
       120: q+1
       121: q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: q+1
       126: q+1
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: q+1
       131: 2q+1
       132: q^3+2q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: q+1
       148: 2q+1
       149: 2q+1
       150: q+1
       151: 2q+1
       152: q^3+2q^2+2q+1
       153: 2q+1
       154: q^3+2q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: q+1
       169: 2q+1
       170: 2q+1
       171: q+1
       172: 2q+1
       173: q^3+2q^2+2q+1
       174: 2q+1
       175: q^3+2q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: 2q+1
       182: q+1
       183: 2q+1
       184: q^3+2q^2+2q+1
       185: 2q+1
       186: q^3+2q^2+2q+1
       187: 2q+1
       188: q^3+2q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q^2+2q+1
       198: 2q+1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: 2q+1
       213: 2q+1
       214: 2q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: 2q+1
       220: 2q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q+1
       232: q+1
       233: q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: 2q+1
       243: 2q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: 2q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: q+1
       255: 2q+1
       256: q^3+2q^2+2q+1
       257: q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q+1
       262: q+1
       263: q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: 2q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: 2q+1
       277: 2q+1
       278: 2q+1
       279: q+1
       280: q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       284: q+1
       285: 2q+1
       286: q^3+2q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: q+1
       302: 2q+1
       303: 2q+1
       304: q+1
       305: 2q+1
       306: q^3+2q^2+2q+1
       307: 2q+1
       308: q^3+2q^2+2q+1
       310: q^2+2q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       319: 2q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       328: 2q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: 2q+1
       336: 2q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: 2q+1
       344: 2q+1
       345: 2q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: 2q+1
       351: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q^2+2q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: 2q+1
       373: 2q+1
       374: 2q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: 2q+1
       380: 2q+1
       381: 2q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: 2q+1
       387: 2q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: 2q+1
       392: q+1
       394: q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q^2+2q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: 2q+1
       412: 2q+1
       413: 2q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: 2q+1
       419: 2q+1
       420: 2q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: 2q+1
       426: 2q+1
       427: q+1
       428: q+1
       429: 2q+1
       430: 2q+1
       431: q+1
       433: q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q+1
       438: q+1
       439: q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: 1
       446: q+1
       447: q+1
       448: 2q+1
       449: 2q+1
       450: q+1
       451: q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: q+1
       456: q+1
       457: 2q+1
       458: 2q+1
       459: 2q+1
       460: q+1
       461: 2q+1
       462: q^3+2q^2+2q+1
       463: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       474: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: 2q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: 2q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: 2q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: 2q+1
       509: q+1
       510: q+1
       515: q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       526: 2q+1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       535: 2q+1
       536: q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: 2q+1
       543: 2q+1
       544: q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: 2q+1
       551: 2q+1
       552: 2q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: 2q+1
       558: q+1
       561: q+1
       562: q+1
       564: q^2+2q+1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       573: 2q+1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       582: 2q+1
       583: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: 2q+1
       590: 2q+1
       591: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: 2q+1
       598: 2q+1
       599: 2q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: 2q+1
       605: q+1
       608: q+1
       609: q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q^2+2q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: 1
       623: 1
       624: 1
       625: q+1
       626: 2q+1
       627: 2q+1
       628: 2q+1
       629: q+1
       630: 1
       631: q+1
       632: q+1
       633: 2q+1
       634: 2q+1
       635: 2q+1
       636: q+1
       637: 1
       638: q+1
       639: q+1
       640: 2q+1
       641: 2q+1
       642: q+1
       643: q+1
       644: 2q+1
       645: 2q+1
       646: q+1
       648: q+1
       651: q+1
       652: q+1
       653: q+1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: 2q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: q+1
       702: q+1
       705: q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       713: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: 2q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       731: 2q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       740: 2q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: 2q+1
       748: q+1
       749: q+1
       754: q+1
       757: q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       765: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: 2q+1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       783: 2q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       792: 2q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: 2q+1
       800: q+1
       801: q+1
       806: q+1
       808: q^2+2q+1
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: q+1
       817: 2q+1
       818: q+1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: q+1
       826: 2q+1
       827: q+1
       828: q+1
       829: 1
       830: 1
       831: 1
       832: q+1
       833: 2q+1
       834: 2q+1
       835: q+1
       836: q+1
       837: 1
       838: 1
       839: 1
       840: q+1
       841: 2q+1
       842: 2q+1
       843: 2q+1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: 2q+1
       849: q+1
       852: q+1
       853: q+1
       857: q+1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       897: q+1
       908: q+1
       909: q+1
       910: q+1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: q+1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       934: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       943: 2q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       952: q+1
       959: q+1
       962: q+1
       963: q+1
       964: q+1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: q+1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       988: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       997: 2q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1006: q+1
      1013: q+1
      1016: q+1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1024: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 2q+1
      1034: q+1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: q+1
      1042: 2q+1
      1043: q+1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: q+1
      1051: 2q+1
      1052: q+1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: 2q+1
      1059: q+1
      1060: q+1
      1065: q+1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1088: 1
      1089: 1
      1090: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1116: q+1
      1122: 1
      1123: 1
      1124: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1156: q+1
      1168: q+1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1208: q+1
      1219: q+1
      1220: q+1
      1221: q+1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: q+1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1245: q+1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1254: 2q+1
      1255: q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1263: q+1
      1270: q+1
      1282: 1
      1289: 1
      1295: 1
      1296: 1
      1297: 1
      1318: 1
      1324: 1
      1325: 1
      1326: 1
      1332: 1
      1333: 1
      1334: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1379: 1
      1380: 1
      1381: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1407: q+1
      1413: 1
      1414: 1
      1415: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1438: q+1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1447: q+1
      1474: 1
      1497: 1
      1504: 1
      1510: 1
      1511: 1
      1512: 1
      1536: 1
      1543: 1
      1549: 1
      1550: 1
      1551: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1586: 1
      1587: 1
      1588: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1650: 1
      1680: 1
      1703: 1
      1710: 1
      1716: 1
      1717: 1
      1718: 1
      1804: 1

1805:    0: q^3+2q^2+2q+1
         1: q^2+2q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q^2+2q+1
         9: q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^2+2q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+2q+1
        16: q^2+2q+1
        17: q^3+2q^2+2q+1
        18: 2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: 2q^2+2q+1
        24: 2q^2+2q+1
        25: q^2+2q+1
        26: q+1
        27: 2q^2+2q+1
        28: q^2+2q+1
        29: 2q^2+2q+1
        30: q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q^2+2q+1
        36: q^2+2q+1
        37: 2q^2+2q+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q^2+2q+1
        43: q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: q^2+2q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: 2q^2+2q+1
        57: q+1
        58: q+1
        59: q+1
        60: 2q^2+2q+1
        61: 2q^2+2q+1
        62: q^2+2q+1
        63: q+1
        64: q^2+2q+1
        65: q^2+2q+1
        66: q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: 2q^2+2q+1
        75: 2q^2+2q+1
        76: q^2+2q+1
        77: q+1
        78: 2q^2+2q+1
        79: q^2+2q+1
        80: 2q^2+2q+1
        81: q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^2+2q+1
        89: q^2+2q+1
        90: q+1
        91: 2q^2+2q+1
        92: q^2+2q+1
        93: 2q^2+2q+1
        94: q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q^2+2q+1
       100: q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: 2q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: q+1
       113: q+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: 2q^2+2q+1
       119: q+1
       120: q+1
       121: q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q+1
       125: q+1
       126: q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q+1
       135: q+1
       136: q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: 2q^2+2q+1
       141: q+1
       142: q+1
       143: q+1
       144: 2q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: q^2+2q+1
       149: q^2+2q+1
       150: q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: 2q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: 2q^2+2q+1
       162: q+1
       163: q+1
       164: q+1
       165: 2q^2+2q+1
       166: 2q^2+2q+1
       167: q^2+2q+1
       168: q+1
       169: q^2+2q+1
       170: q^2+2q+1
       171: q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: 2q^2+2q+1
       175: q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: 2q^2+2q+1
       180: 2q^2+2q+1
       181: q^2+2q+1
       182: q+1
       183: 2q^2+2q+1
       184: q^2+2q+1
       185: 2q^2+2q+1
       186: q^2+2q+1
       187: 2q^2+2q+1
       188: 2q^2+2q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q^2+2q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: 2q+1
       206: q+1
       207: q+1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q^2+2q+1
       213: q+1
       214: q+1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+2q+1
       220: q+1
       221: q+1
       222: q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: q+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: 2q^2+2q+1
       243: q+1
       244: q+1
       245: q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q+1
       249: q+1
       250: q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q+1
       255: 2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q^2+2q+1
       263: q^2+2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: q+1
       267: q+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: 2q^2+2q+1
       273: q+1
       274: q+1
       275: q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q+1
       279: q+1
       280: q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: q^2+2q+1
       284: q+1
       285: 2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q+1
       289: q+1
       290: q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: 2q^2+2q+1
       295: q+1
       296: q+1
       297: q+1
       298: 2q^2+2q+1
       299: 2q^2+2q+1
       300: q^2+2q+1
       301: q+1
       302: q^2+2q+1
       303: q^2+2q+1
       304: q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: 2q^2+2q+1
       308: q^2+2q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: q^2+2q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       327: 2q+1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: 2q+1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: 2q+1
       344: q+1
       345: q+1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: 2q+1
       351: q+1
       354: 2q+1
       355: 2q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q^2+2q+1
       363: q^2+2q+1
       364: q^2+2q+1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 2q+1
       373: q+1
       374: q+1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q^2+2q+1
       380: q+1
       381: q+1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q^2+2q+1
       387: q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: 2q+1
       392: q^2+2q+1
       394: 2q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q^2+2q+1
       402: q^2+2q+1
       403: q^2+2q+1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 2q+1
       412: q+1
       413: q+1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q^2+2q+1
       419: q+1
       420: q+1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q^2+2q+1
       426: q+1
       427: q+1
       428: q+1
       429: 2q+1
       430: 2q+1
       431: q^2+2q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q^2+2q+1
       439: q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q+1
       443: q+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: 2q^2+2q+1
       449: q+1
       450: q+1
       451: q+1
       452: q^2+2q+1
       453: q^2+2q+1
       454: q+1
       455: q+1
       456: q+1
       457: q^2+2q+1
       458: q^2+2q+1
       459: q^2+2q+1
       460: q+1
       461: 2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: 2q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: 2q+1
       501: q+1
       502: 1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: 2q+1
       509: q+1
       510: q+1
       515: 2q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       524: q^2+2q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       534: 2q+1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: 2q+1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 2q+1
       551: q+1
       552: q+1
       553: 1
       554: q+1
       555: q+1
       556: q+1
       557: 2q+1
       558: q+1
       561: 2q+1
       562: 2q+1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: q^2+2q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       581: 2q+1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 2q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: 2q+1
       598: q+1
       599: q+1
       600: 1
       601: q+1
       602: q+1
       603: q+1
       604: 2q+1
       605: q+1
       608: 2q+1
       609: 2q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q^2+2q+1
       617: q^2+2q+1
       618: q^2+2q+1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 2q+1
       627: q+1
       628: q+1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q^2+2q+1
       634: q+1
       635: q+1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q^2+2q+1
       641: q+1
       642: q+1
       643: q+1
       644: 2q+1
       645: 2q+1
       646: q^2+2q+1
       648: 2q+1
       653: q+1
       654: q+1
       655: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: 2q+1
       695: q+1
       702: q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       730: 2q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       739: 2q+1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: q+1
       745: q+1
       746: q+1
       747: 2q+1
       748: q+1
       749: q+1
       754: 2q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       782: 2q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       791: 2q+1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: q+1
       797: q+1
       798: q+1
       799: 2q+1
       800: q+1
       801: q+1
       806: 2q+1
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: q+1
       815: q^2+2q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: q+1
       825: 2q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 2q+1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 2q+1
       842: q+1
       843: q+1
       844: 1
       845: q+1
       846: q+1
       847: q+1
       848: 2q+1
       849: q+1
       852: 2q+1
       853: 2q+1
       858: q+1
       865: 1
       866: 1
       867: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       905: q+1
       910: q+1
       911: q+1
       912: q+1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       951: 2q+1
       952: q+1
       959: q+1
       964: q+1
       965: q+1
       966: q+1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: q+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1005: 2q+1
      1006: q+1
      1013: q+1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1021: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: q+1
      1041: 2q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: q+1
      1050: 2q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: q+1
      1056: q+1
      1057: q+1
      1058: 2q+1
      1059: q+1
      1060: q+1
      1065: 2q+1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1117: q+1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1164: q+1
      1169: q+1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: q+1
      1216: q+1
      1221: q+1
      1222: q+1
      1223: q+1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: q+1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: q+1
      1261: q+1
      1262: 2q+1
      1263: q+1
      1270: q+1
      1283: 1
      1290: 1
      1297: 1
      1298: 1
      1299: 1
      1319: 1
      1326: 1
      1327: 1
      1328: 1
      1334: 1
      1335: 1
      1336: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1366: 1
      1373: 1
      1374: 1
      1375: 1
      1381: 1
      1382: 1
      1383: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1408: q+1
      1415: 1
      1416: 1
      1417: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: q+1
      1455: q+1
      1475: 1
      1498: 1
      1505: 1
      1512: 1
      1513: 1
      1514: 1
      1537: 1
      1544: 1
      1551: 1
      1552: 1
      1553: 1
      1573: 1
      1580: 1
      1581: 1
      1582: 1
      1588: 1
      1589: 1
      1590: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1651: 1
      1681: 1
      1704: 1
      1711: 1
      1718: 1
      1719: 1
      1720: 1
      1805: 1

1806:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q^2+2q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: 2q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: 2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: 2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: 2q+1
        62: 2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: 2q^2+2q+1
        75: q^2+2q+1
        76: 2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: q^2+2q+1
        89: 2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       105: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 2q+1
       114: 2q+1
       115: 2q+1
       116: q^2+2q+1
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q+1
       124: 2q+1
       125: 2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: 2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       142: 2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q+1
       171: 2q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: 2q^2+2q+1
       180: q^2+2q+1
       181: 2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: 2q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       191: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       199: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       208: 2q+1
       209: q+1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: 2q+1
       215: 2q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       229: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       238: 2q+1
       239: 2q+1
       240: q^2+2q+1
       241: 2q+1
       242: 2q+1
       243: 2q+1
       244: 2q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       259: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       268: 2q+1
       269: 2q+1
       270: q^2+2q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       279: 2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: 2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: 2q+1
       297: q^2+2q+1
       298: q^2+2q+1
       299: 2q+1
       300: 2q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       312: 2q+1
       314: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       321: 2q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       329: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       337: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       346: 2q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       358: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       366: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: 2q+1
       375: 2q+1
       376: q+1
       377: q^2+2q+1
       378: q+1
       379: q+1
       380: 2q+1
       382: 2q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       397: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       405: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       414: 2q+1
       415: q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: 2q+1
       421: 2q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       429: 2q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       435: q^2+2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       444: 2q+1
       445: 2q+1
       446: q^2+2q+1
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: q^2+2q+1
       452: q^2+2q+1
       453: q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       469: 2q+1
       471: q+1
       472: q+1
       476: 2q+1
       478: 2q+1
       480: 2q+1
       481: 1
       482: q+1
       485: q+1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       494: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       502: 2q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       519: 2q+1
       521: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       528: 2q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       536: 2q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       544: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       553: 2q+1
       554: 1
       555: 2q+1
       556: q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       566: 2q+1
       568: 2q+1
       570: 2q+1
       571: q+1
       572: q+1
       575: 2q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       583: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       591: 2q+1
       593: q+1
       594: q+1
       595: q+1
       596: 2q+1
       597: 2q+1
       598: 2q+1
       600: 2q+1
       601: 1
       602: 2q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       612: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       620: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: 2q+1
       629: 2q+1
       630: q+1
       631: q^2+2q+1
       632: q+1
       633: q+1
       634: 2q+1
       636: 2q+1
       637: q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       654: q+1
       656: q+1
       662: 2q+1
       664: 1
       665: 1
       669: q+1
       671: q+1
       673: q+1
       674: 1
       675: 1
       679: q+1
       681: q+1
       683: q+1
       684: 1
       685: q+1
       688: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       696: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 2q+1
       710: q+1
       711: q+1
       715: 2q+1
       717: 2q+1
       719: 2q+1
       720: 1
       721: q+1
       724: q+1
       726: q+1
       727: q+1
       728: q+1
       729: q+1
       730: 1
       733: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       741: 2q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       750: q+1
       751: 1
       752: q+1
       753: 1
       754: 1
       760: 2q+1
       762: q+1
       763: q+1
       767: 2q+1
       769: 2q+1
       771: 2q+1
       772: 1
       773: q+1
       776: q+1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       785: q+1
       787: q+1
       788: q+1
       789: q+1
       790: 2q+1
       791: q+1
       793: 2q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       802: q+1
       803: 1
       804: q+1
       805: 1
       806: 1
       810: 2q+1
       812: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       819: 2q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       827: 2q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       835: 2q+1
       837: q+1
       838: q+1
       839: q+1
       840: 2q+1
       841: 2q+1
       842: 2q+1
       844: 2q+1
       845: 1
       846: 2q+1
       847: q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       859: q+1
       866: 1
       868: 1
       874: q+1
       876: 1
       877: 1
       883: q+1
       885: 1
       886: 1
       890: 1
       892: 1
       894: 1
       895: 1
       896: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       911: q+1
       913: q+1
       919: 2q+1
       921: 1
       922: 1
       926: q+1
       928: q+1
       930: q+1
       931: 1
       932: 1
       936: q+1
       938: q+1
       940: q+1
       941: 1
       942: q+1
       945: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       953: q+1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       965: q+1
       967: q+1
       973: 2q+1
       975: 1
       976: 1
       980: q+1
       982: q+1
       984: q+1
       985: 1
       986: 1
       990: q+1
       992: q+1
       994: q+1
       995: 1
       996: q+1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1007: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 2q+1
      1021: q+1
      1022: q+1
      1026: 2q+1
      1028: 2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1035: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: 1
      1044: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1052: 2q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1061: q+1
      1062: 1
      1063: q+1
      1064: 1
      1065: 1
      1076: 1
      1083: 1
      1085: 1
      1091: 1
      1093: 1
      1099: 1
      1101: 1
      1102: 1
      1106: 1
      1108: 1
      1110: 1
      1112: 1
      1118: q+1
      1125: 1
      1127: 1
      1133: q+1
      1135: 1
      1136: 1
      1142: q+1
      1144: 1
      1145: 1
      1149: 1
      1151: 1
      1153: 1
      1154: 1
      1155: 1
      1158: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1170: q+1
      1177: 1
      1179: 1
      1185: q+1
      1187: 1
      1188: 1
      1194: q+1
      1196: 1
      1197: 1
      1201: 1
      1203: 1
      1205: 1
      1206: 1
      1207: 1
      1210: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1222: q+1
      1224: q+1
      1230: 2q+1
      1232: 1
      1233: 1
      1237: q+1
      1239: q+1
      1241: q+1
      1242: 1
      1243: 1
      1247: q+1
      1249: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1256: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1264: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1284: 1
      1291: 1
      1298: 1
      1300: 1
      1306: 1
      1320: 1
      1327: 1
      1329: 1
      1335: 1
      1337: 1
      1343: 1
      1345: 1
      1346: 1
      1350: 1
      1352: 1
      1354: 1
      1356: 1
      1367: 1
      1374: 1
      1376: 1
      1382: 1
      1384: 1
      1390: 1
      1392: 1
      1393: 1
      1397: 1
      1399: 1
      1401: 1
      1403: 1
      1409: q+1
      1416: 1
      1418: 1
      1424: q+1
      1426: 1
      1427: 1
      1433: q+1
      1435: 1
      1436: 1
      1440: 1
      1442: 1
      1444: 1
      1445: 1
      1446: 1
      1449: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1476: 1
      1499: 1
      1506: 1
      1513: 1
      1515: 1
      1521: 1
      1538: 1
      1545: 1
      1552: 1
      1554: 1
      1560: 1
      1574: 1
      1581: 1
      1583: 1
      1589: 1
      1591: 1
      1597: 1
      1599: 1
      1600: 1
      1604: 1
      1606: 1
      1608: 1
      1610: 1
      1652: 1
      1682: 1
      1705: 1
      1712: 1
      1719: 1
      1721: 1
      1727: 1
      1806: 1

1807:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: q^2+2q+1
        24: 2q^2+2q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q^2+2q+1
        55: 2q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: 2q+1
        59: q^2+2q+1
        60: 2q+1
        61: q^2+2q+1
        62: 2q+1
        63: 2q+1
        64: 2q+1
        65: 2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        75: 2q^2+2q+1
        76: 2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+2q+1
        89: 2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       106: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q^2+2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+2q+1
       129: 2q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       142: 2q+1
       143: q^2+2q+1
       144: 2q+1
       145: q^2+2q+1
       146: 2q+1
       147: 2q+1
       148: 2q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: q^2+2q+1
       160: 2q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: q^2+2q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: 2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: q^2+2q+1
       180: 2q^2+2q+1
       181: 2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: 2q+1
       186: 2q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: 2q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+2q+1
       242: 2q+1
       243: 2q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: 2q+1
       249: 2q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q^2+2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: 2q+1
       279: 2q+1
       280: q^2+2q+1
       281: q+1
       282: q^2+2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: 2q+1
       297: q^2+2q+1
       298: 2q+1
       299: q^2+2q+1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: 2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       313: 2q+1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       322: 2q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       330: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       345: 2q+1
       346: 2q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: q+1
       391: 2q+1
       392: q+1
       393: q+1
       394: q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       420: 2q+1
       421: 2q+1
       422: q+1
       423: q+1
       424: q^2+2q+1
       425: q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: q+1
       432: q+1
       433: q+1
       436: q^2+2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: q^2+2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: 2q+1
       456: q^2+2q+1
       457: q+1
       458: q^2+2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       470: 2q+1
       471: q+1
       472: q+1
       477: 2q+1
       479: 2q+1
       480: 2q+1
       481: 1
       482: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       503: 2q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       510: q+1
       511: q+1
       512: 1
       513: 1
       514: q+1
       515: 1
       520: 2q+1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       529: 2q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       537: 2q+1
       538: q+1
       539: q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       552: 2q+1
       553: 2q+1
       554: 1
       555: q+1
       556: 2q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       567: 2q+1
       569: 2q+1
       570: 2q+1
       571: q+1
       572: q+1
       576: 2q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       584: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       592: 2q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       599: 2q+1
       600: 2q+1
       601: 1
       602: q+1
       603: 2q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       628: 2q+1
       629: 2q+1
       630: q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       635: 2q+1
       636: 2q+1
       637: q+1
       638: q+1
       639: q^2+2q+1
       640: q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: q+1
       645: 2q+1
       646: q+1
       647: q+1
       648: q+1
       655: q+1
       656: q+1
       663: 2q+1
       664: 1
       665: 1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       680: q+1
       682: q+1
       683: q+1
       684: 1
       685: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 2q+1
       710: q+1
       711: q+1
       716: 2q+1
       718: 2q+1
       719: 2q+1
       720: 1
       721: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       742: 2q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       749: q+1
       750: q+1
       751: 1
       752: 1
       753: q+1
       754: 1
       761: 2q+1
       762: q+1
       763: q+1
       768: 2q+1
       770: 2q+1
       771: 2q+1
       772: 1
       773: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: q+1
       791: 1
       794: 2q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       801: q+1
       802: q+1
       803: 1
       804: 1
       805: q+1
       806: 1
       811: 2q+1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       820: 2q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       828: 2q+1
       829: q+1
       830: q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       836: 2q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       843: 2q+1
       844: 2q+1
       845: 1
       846: q+1
       847: 2q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       860: q+1
       867: 1
       868: 1
       875: q+1
       876: 1
       877: 1
       884: q+1
       885: 1
       886: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       912: q+1
       913: q+1
       920: 2q+1
       921: 1
       922: 1
       927: q+1
       929: q+1
       930: q+1
       931: 1
       932: q+1
       937: q+1
       939: q+1
       940: q+1
       941: 1
       942: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: q+1
       967: q+1
       974: 2q+1
       975: 1
       976: 1
       981: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       991: q+1
       993: q+1
       994: q+1
       995: 1
       996: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1020: 2q+1
      1021: q+1
      1022: q+1
      1027: 2q+1
      1029: 2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: q+1
      1050: 1
      1053: 2q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1060: q+1
      1061: q+1
      1062: 1
      1063: 1
      1064: q+1
      1065: 1
      1077: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1100: 1
      1101: 1
      1102: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1119: q+1
      1126: 1
      1127: 1
      1134: q+1
      1135: 1
      1136: 1
      1143: q+1
      1144: 1
      1145: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1171: q+1
      1178: 1
      1179: 1
      1186: q+1
      1187: 1
      1188: 1
      1195: q+1
      1196: 1
      1197: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1223: q+1
      1224: q+1
      1231: 2q+1
      1232: 1
      1233: 1
      1238: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: q+1
      1248: q+1
      1250: q+1
      1251: q+1
      1252: 1
      1253: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1285: 1
      1292: 1
      1299: 1
      1300: 1
      1307: 1
      1321: 1
      1328: 1
      1329: 1
      1336: 1
      1337: 1
      1344: 1
      1345: 1
      1346: 1
      1351: 1
      1353: 1
      1354: 1
      1356: 1
      1368: 1
      1375: 1
      1376: 1
      1383: 1
      1384: 1
      1391: 1
      1392: 1
      1393: 1
      1398: 1
      1400: 1
      1401: 1
      1403: 1
      1410: q+1
      1417: 1
      1418: 1
      1425: q+1
      1426: 1
      1427: 1
      1434: q+1
      1435: 1
      1436: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1477: 1
      1500: 1
      1507: 1
      1514: 1
      1515: 1
      1522: 1
      1539: 1
      1546: 1
      1553: 1
      1554: 1
      1561: 1
      1575: 1
      1582: 1
      1583: 1
      1590: 1
      1591: 1
      1598: 1
      1599: 1
      1600: 1
      1605: 1
      1607: 1
      1608: 1
      1610: 1
      1653: 1
      1683: 1
      1706: 1
      1713: 1
      1720: 1
      1721: 1
      1728: 1
      1807: 1

1808:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: 1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: 1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: 1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: 1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: 1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: q+1
        59: 1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: 1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: 1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: 1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: 1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: 1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: q+1
       143: 1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: q+1
       164: 1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: 1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: 1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: q+1
       297: 1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: 1
       465: 1
       472: 1
       473: 1
       474: 1
       475: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: 1
       657: 1
       658: 1
       665: 1
       666: 1
       667: 1
       668: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       711: 1
       712: 1
       713: 1
       714: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       763: 1
       764: 1
       765: 1
       766: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       861: 1
       869: 1
       870: 1
       877: 1
       878: 1
       879: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       906: 1
       914: 1
       915: 1
       922: 1
       923: 1
       924: 1
       925: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: 1
       968: 1
       969: 1
       976: 1
       977: 1
       978: 1
       979: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1120: 1
      1128: 1
      1129: 1
      1136: 1
      1137: 1
      1138: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1163: 1
      1164: 1
      1172: 1
      1180: 1
      1181: 1
      1188: 1
      1189: 1
      1190: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1225: 1
      1226: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1293: 1
      1301: 1
      1302: 1
      1309: 1
      1322: 1
      1330: 1
      1338: 1
      1339: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1355: 1
      1356: 1
      1369: 1
      1377: 1
      1385: 1
      1386: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1402: 1
      1403: 1
      1411: 1
      1419: 1
      1420: 1
      1427: 1
      1428: 1
      1429: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1454: 1
      1455: 1
      1478: 1
      1508: 1
      1516: 1
      1517: 1
      1524: 1
      1547: 1
      1555: 1
      1556: 1
      1563: 1
      1576: 1
      1584: 1
      1592: 1
      1593: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1609: 1
      1610: 1
      1654: 1
      1684: 1
      1714: 1
      1722: 1
      1723: 1
      1730: 1
      1808: 1

1809:    0: 2q^2+q+1
         1: 2q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: 2q^2+q+1
         5: 2q^2+q+1
         6: 2q^2+q+1
         7: q+1
         8: 2q^2+q+1
         9: 2q^2+q+1
        10: 2q^2+q+1
        11: 2q^2+q+1
        12: 2q^2+q+1
        13: 2q^2+q+1
        14: 2q^2+q+1
        15: 2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: 2q^2+q+1
        19: 2q^2+q+1
        20: 2q^2+q+1
        21: q+1
        22: q+1
        23: q^2+1
        24: q^2+1
        25: 2q^2+q+1
        26: q+1
        27: 2q^2+q+1
        28: 2q^2+q+1
        29: 2q^2+q+1
        30: 2q^2+q+1
        31: 2q^2+q+1
        32: 2q^2+q+1
        33: 2q^2+q+1
        34: q+1
        35: 2q^2+q+1
        36: 2q^2+q+1
        37: 2q^2+q+1
        38: 2q^2+q+1
        39: 2q^2+q+1
        40: 2q^2+q+1
        41: q+1
        42: 2q^2+q+1
        43: 2q^2+q+1
        44: 2q^2+q+1
        45: 2q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: 2q^2+q+1
        49: 2q^2+q+1
        50: q^2+1
        51: q^2+1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: 2q^2+q+1
        58: q+1
        59: q+1
        60: q^2+1
        61: q^2+1
        62: 2q^2+q+1
        63: q+1
        64: 2q^2+q+1
        65: 2q^2+q+1
        66: q+1
        67: 2q^2+q+1
        68: 2q^2+q+1
        69: 2q^2+q+1
        70: 2q^2+q+1
        71: 2q^2+q+1
        72: q+1
        73: q+1
        74: q^2+1
        75: q^2+1
        76: 2q^2+q+1
        77: q+1
        78: 2q^2+q+1
        79: 2q^2+q+1
        80: 2q^2+q+1
        81: 2q^2+q+1
        82: 2q^2+q+1
        83: 2q^2+q+1
        84: 2q^2+q+1
        85: q+1
        86: q+1
        87: q^2+1
        88: q^2+1
        89: 2q^2+q+1
        90: q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: 2q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: 2q^2+q+1
        97: 2q^2+q+1
        98: q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: 2q^2+q+1
       102: 2q^2+q+1
       103: 2q^2+q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       113: q^2+1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: 2q^2+q+1
       120: q+1
       121: q+1
       122: q^2+1
       123: q^2+1
       124: 2q^2+q+1
       125: q+1
       126: q+1
       127: q^2+1
       128: q^2+1
       129: 2q^2+q+1
       130: q+1
       131: 2q^2+q+1
       132: 2q^2+q+1
       133: 2q^2+q+1
       134: q^2+1
       135: q^2+1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: 2q^2+q+1
       142: q+1
       143: q+1
       144: q^2+1
       145: q^2+1
       146: 2q^2+q+1
       147: q+1
       148: 2q^2+q+1
       149: 2q^2+q+1
       150: q+1
       151: 2q^2+q+1
       152: 2q^2+q+1
       153: 2q^2+q+1
       154: 2q^2+q+1
       155: q^2+1
       156: q^2+1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: 2q^2+q+1
       163: q+1
       164: q+1
       165: q^2+1
       166: q^2+1
       167: 2q^2+q+1
       168: q+1
       169: 2q^2+q+1
       170: 2q^2+q+1
       171: q+1
       172: 2q^2+q+1
       173: 2q^2+q+1
       174: 2q^2+q+1
       175: 2q^2+q+1
       176: 2q^2+q+1
       177: q+1
       178: q+1
       179: q^2+1
       180: q^2+1
       181: 2q^2+q+1
       182: q+1
       183: 2q^2+q+1
       184: 2q^2+q+1
       185: 2q^2+q+1
       186: 2q^2+q+1
       187: 2q^2+q+1
       188: 2q^2+q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       207: q^2+1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       213: q^2+1
       214: q^2+1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: 2q^2+q+1
       221: q+1
       222: q+1
       223: q^2+1
       224: q^2+1
       225: 2q^2+q+1
       226: q+1
       227: 2q^2+q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q^2+1
       237: q^2+1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: 2q^2+q+1
       244: q+1
       245: q+1
       246: q^2+1
       247: q^2+1
       248: 2q^2+q+1
       249: q+1
       250: q+1
       251: q^2+1
       252: q^2+1
       253: 2q^2+q+1
       254: q+1
       255: 2q^2+q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       267: q^2+1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: 2q^2+q+1
       274: q+1
       275: q+1
       276: q^2+1
       277: q^2+1
       278: 2q^2+q+1
       279: q+1
       280: q+1
       281: q^2+1
       282: q^2+1
       283: 2q^2+q+1
       284: q+1
       285: 2q^2+q+1
       286: 2q^2+q+1
       287: 2q^2+q+1
       288: q^2+1
       289: q^2+1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: 2q^2+q+1
       296: q+1
       297: q+1
       298: q^2+1
       299: q^2+1
       300: 2q^2+q+1
       301: q+1
       302: 2q^2+q+1
       303: 2q^2+q+1
       304: q+1
       305: 2q^2+q+1
       306: 2q^2+q+1
       307: 2q^2+q+1
       308: 2q^2+q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q^2+1
       345: q^2+1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: 2q^2+q+1
       352: q+1
       353: q+1
       354: q^2+1
       355: q^2+1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q^2+1
       374: q^2+1
       375: q+1
       376: q+1
       377: 1
       378: 1
       379: 1
       380: q^2+1
       381: q^2+1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: 1
       387: 2q^2+q+1
       388: q+1
       389: q+1
       390: q^2+1
       391: q^2+1
       392: 2q^2+q+1
       393: q+1
       394: 2q^2+q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: q^2+1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: 1
       419: q^2+1
       420: q^2+1
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: 2q^2+q+1
       427: q+1
       428: q+1
       429: q^2+1
       430: q^2+1
       431: 2q^2+q+1
       432: q+1
       433: 2q^2+q+1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q^2+1
       443: q^2+1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: 2q^2+q+1
       450: q+1
       451: q+1
       452: q^2+1
       453: q^2+1
       454: 2q^2+q+1
       455: q+1
       456: q+1
       457: q^2+1
       458: q^2+1
       459: 2q^2+q+1
       460: q+1
       461: 2q^2+q+1
       462: 2q^2+q+1
       463: 2q^2+q+1
       465: 1
       466: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q^2+1
       510: q^2+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q^2+1
       552: q^2+1
       553: q+1
       554: q+1
       555: 1
       556: 1
       557: 1
       558: 2q^2+q+1
       559: q+1
       560: q+1
       561: q^2+1
       562: q^2+1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q^2+1
       599: q^2+1
       600: q+1
       601: q+1
       602: 1
       603: 1
       604: 1
       605: 2q^2+q+1
       606: q+1
       607: q+1
       608: q^2+1
       609: q^2+1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q^2+1
       628: q^2+1
       629: q+1
       630: q+1
       631: 1
       632: 1
       633: 1
       634: q^2+1
       635: q^2+1
       636: q+1
       637: q+1
       638: 1
       639: 1
       640: 1
       641: 2q^2+q+1
       642: q+1
       643: q+1
       644: q^2+1
       645: q^2+1
       646: 2q^2+q+1
       647: q+1
       648: 2q^2+q+1
       650: 1
       658: 1
       659: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       704: 1
       705: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q^2+1
       749: q^2+1
       750: q+1
       751: q+1
       752: 1
       753: 1
       754: 1
       756: 1
       757: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q^2+1
       801: q^2+1
       802: q+1
       803: q+1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q^2+1
       843: q^2+1
       844: q+1
       845: q+1
       846: 1
       847: 1
       848: 1
       849: 2q^2+q+1
       850: q+1
       851: q+1
       852: q^2+1
       853: q^2+1
       862: 1
       870: 1
       871: 1
       876: 1
       879: 1
       880: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       907: 1
       915: 1
       916: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       961: 1
       969: 1
       970: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1015: 1
      1016: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q^2+1
      1060: q^2+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: 1
      1065: 1
      1079: 1
      1087: 1
      1095: 1
      1096: 1
      1101: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1121: 1
      1129: 1
      1130: 1
      1135: 1
      1138: 1
      1139: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1173: 1
      1181: 1
      1182: 1
      1187: 1
      1190: 1
      1191: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1218: 1
      1226: 1
      1227: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1294: 1
      1302: 1
      1303: 1
      1308: 1
      1323: 1
      1331: 1
      1339: 1
      1340: 1
      1345: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1355: 1
      1370: 1
      1378: 1
      1386: 1
      1387: 1
      1392: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1402: 1
      1412: 1
      1420: 1
      1421: 1
      1426: 1
      1429: 1
      1430: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1479: 1
      1509: 1
      1517: 1
      1518: 1
      1523: 1
      1548: 1
      1556: 1
      1557: 1
      1562: 1
      1577: 1
      1585: 1
      1593: 1
      1594: 1
      1599: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1609: 1
      1655: 1
      1685: 1
      1715: 1
      1723: 1
      1724: 1
      1729: 1
      1809: 1

1810:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q+1
        49: q^2+q+1
        50: 1
        51: q+1
        52: q+1
        53: 1
        54: 1
        55: q+1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+q+1
        69: q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q^2+q+1
        95: q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: q+1
       102: q^2+q+1
       103: q^2+q+1
       104: 1
       105: 1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: q+1
       114: q+1
       115: 1
       116: 1
       117: q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+q+1
       133: q+1
       134: 1
       135: q+1
       136: q+1
       137: 1
       138: 1
       139: q+1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+q+1
       153: q+1
       154: q^2+q+1
       155: 1
       156: q+1
       157: q+1
       158: 1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+q+1
       174: q+1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+q+1
       185: q+1
       186: q^2+q+1
       187: q+1
       188: q^2+q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: 1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: 1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: 1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: q+1
       238: q+1
       239: 1
       240: 1
       241: q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q+1
       269: 1
       270: 1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: 1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+q+1
       307: q+1
       308: q^2+q+1
       310: 1
       311: 1
       312: 1
       313: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: 1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: 1
       348: 1
       349: q+1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: 1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: 1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q+1
       382: q+1
       383: 1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: 1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: q+1
       414: q+1
       415: 1
       416: 1
       417: q+1
       418: 1
       419: 1
       420: q+1
       421: q+1
       422: 1
       423: 1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: 1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q+1
       445: 1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+q+1
       463: q+1
       466: 1
       467: 1
       470: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: 1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: 1
       513: 1
       514: q+1
       515: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: 1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: 1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: q+1
       600: q+1
       601: 1
       602: 1
       603: q+1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: 1
       621: q+1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: q+1
       629: q+1
       630: 1
       631: 1
       632: q+1
       633: 1
       634: 1
       635: q+1
       636: q+1
       637: 1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       651: 1
       659: 1
       660: 1
       663: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       696: 1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       709: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       751: 1
       752: 1
       753: q+1
       754: 1
       757: 1
       758: 1
       761: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: 1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: q+1
       802: q+1
       803: 1
       804: 1
       805: q+1
       806: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: 1
       828: q+1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: q+1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: q+1
       844: q+1
       845: 1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       863: 1
       871: 1
       872: 1
       875: 1
       880: 1
       881: 1
       884: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       908: 1
       916: 1
       917: 1
       920: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       953: 1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       962: 1
       970: 1
       971: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       991: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1020: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1061: q+1
      1062: 1
      1063: 1
      1064: q+1
      1065: 1
      1080: 1
      1088: 1
      1096: 1
      1097: 1
      1100: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1122: 1
      1130: 1
      1131: 1
      1134: 1
      1139: 1
      1140: 1
      1143: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1174: 1
      1182: 1
      1183: 1
      1186: 1
      1191: 1
      1192: 1
      1195: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1219: 1
      1227: 1
      1228: 1
      1231: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1263: 1
      1264: 1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1295: 1
      1303: 1
      1304: 1
      1307: 1
      1324: 1
      1332: 1
      1340: 1
      1341: 1
      1344: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1371: 1
      1379: 1
      1387: 1
      1388: 1
      1391: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: 1
      1401: 1
      1413: 1
      1421: 1
      1422: 1
      1425: 1
      1430: 1
      1431: 1
      1434: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1480: 1
      1510: 1
      1518: 1
      1519: 1
      1522: 1
      1549: 1
      1557: 1
      1558: 1
      1561: 1
      1578: 1
      1586: 1
      1594: 1
      1595: 1
      1598: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: 1
      1608: 1
      1656: 1
      1686: 1
      1716: 1
      1724: 1
      1725: 1
      1728: 1
      1810: 1

1811:    0: q^2+q+1
         1: q^2+q+1
         2: q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^2+q+1
        10: q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q^2+q+1
        29: q+1
        30: q^2+q+1
        31: q+1
        32: q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^2+q+1
        37: q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^2+q+1
        44: q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q+1
        49: q^2+q+1
        50: q+1
        51: 1
        52: q+1
        53: 1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^2+q+1
        69: q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q^2+q+1
        80: q+1
        81: q^2+q+1
        82: q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q^2+q+1
        93: q+1
        94: q^2+q+1
        95: q+1
        96: q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^2+q+1
       101: q+1
       102: q^2+q+1
       103: q^2+q+1
       104: 1
       105: q+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       115: 1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q^2+q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: 1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^2+q+1
       153: q+1
       154: q^2+q+1
       155: q+1
       156: 1
       157: q+1
       158: 1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+q+1
       174: q+1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q^2+q+1
       185: q+1
       186: q^2+q+1
       187: q+1
       188: q^2+q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       198: 1
       199: q+1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: 1
       208: q+1
       209: 1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       216: 1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       239: 1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: 1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: 1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+q+1
       307: q+1
       308: q^2+q+1
       310: 1
       311: 1
       312: 1
       314: 1
       315: 1
       316: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       328: 1
       329: q+1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: 1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       365: 1
       366: q+1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q+1
       374: 1
       375: q+1
       376: 1
       377: q+1
       378: 1
       379: 1
       380: q+1
       381: 1
       382: q+1
       383: 1
       384: q+1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       404: 1
       405: q+1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: 1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       422: 1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       445: 1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+q+1
       463: q+1
       466: 1
       468: 1
       469: 1
       474: 1
       475: 1
       476: 1
       478: 1
       479: 1
       480: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       501: 1
       502: q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       535: 1
       536: q+1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: q+1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q+1
       552: 1
       553: q+1
       554: 1
       555: q+1
       556: 1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       564: 1
       565: 1
       566: 1
       568: 1
       569: 1
       570: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       582: 1
       583: q+1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: 1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       619: 1
       620: q+1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: 1
       629: q+1
       630: 1
       631: q+1
       632: 1
       633: 1
       634: q+1
       635: 1
       636: q+1
       637: 1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       652: 1
       659: 1
       661: 1
       662: 1
       667: 1
       668: 1
       669: 1
       671: 1
       672: 1
       673: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       695: 1
       696: q+1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       707: 1
       708: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       740: 1
       741: q+1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       750: q+1
       751: 1
       752: q+1
       753: 1
       754: 1
       757: 1
       759: 1
       760: 1
       765: 1
       766: 1
       767: 1
       769: 1
       770: 1
       771: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       792: 1
       793: q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       803: 1
       804: q+1
       805: 1
       806: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       826: 1
       827: q+1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: q+1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       843: 1
       844: q+1
       845: 1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       864: 1
       871: 1
       873: 1
       874: 1
       880: 1
       882: 1
       883: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       909: 1
       916: 1
       918: 1
       919: 1
       924: 1
       925: 1
       926: 1
       928: 1
       929: 1
       930: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       952: 1
       953: q+1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       963: 1
       970: 1
       972: 1
       973: 1
       978: 1
       979: 1
       980: 1
       982: 1
       983: 1
       984: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: 1
      1018: 1
      1019: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1051: 1
      1052: q+1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1062: 1
      1063: q+1
      1064: 1
      1065: 1
      1081: 1
      1089: 1
      1096: 1
      1098: 1
      1099: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1123: 1
      1130: 1
      1132: 1
      1133: 1
      1139: 1
      1141: 1
      1142: 1
      1147: 1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1175: 1
      1182: 1
      1184: 1
      1185: 1
      1191: 1
      1193: 1
      1194: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1220: 1
      1227: 1
      1229: 1
      1230: 1
      1235: 1
      1236: 1
      1237: 1
      1239: 1
      1240: 1
      1241: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1263: 1
      1264: q+1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1296: 1
      1303: 1
      1305: 1
      1306: 1
      1325: 1
      1333: 1
      1340: 1
      1342: 1
      1343: 1
      1348: 1
      1349: 1
      1350: 1
      1352: 1
      1353: 1
      1354: 1
      1372: 1
      1380: 1
      1387: 1
      1389: 1
      1390: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1414: 1
      1421: 1
      1423: 1
      1424: 1
      1430: 1
      1432: 1
      1433: 1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1481: 1
      1511: 1
      1518: 1
      1520: 1
      1521: 1
      1550: 1
      1557: 1
      1559: 1
      1560: 1
      1579: 1
      1587: 1
      1594: 1
      1596: 1
      1597: 1
      1602: 1
      1603: 1
      1604: 1
      1606: 1
      1607: 1
      1608: 1
      1657: 1
      1687: 1
      1717: 1
      1724: 1
      1726: 1
      1727: 1
      1811: 1

1812:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: 2q+1
        28: q^3+2q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^3+2q^2+2q+1
        37: q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^3+2q^2+2q+1
        44: q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: q^3+2q^2+2q+1
        69: q^2+2q+1
        70: q^3+2q^2+2q+1
        71: q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: q^3+2q^2+2q+1
        80: q^2+2q+1
        81: q^3+2q^2+2q+1
        82: q^2+2q+1
        83: q^3+2q^2+2q+1
        84: q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^2+2q+1
        96: q^3+2q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^3+2q^2+2q+1
       101: q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^3+2q^2+2q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: q+1
       109: q+1
       110: 2q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^3+2q^2+2q+1
       133: q^2+2q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 2q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: 2q+1
       152: q^3+2q^2+2q+1
       153: q^2+2q+1
       154: q^3+2q^2+2q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: 2q+1
       173: q^3+2q^2+2q+1
       174: q^2+2q+1
       175: q^3+2q^2+2q+1
       176: q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: 2q+1
       184: q^3+2q^2+2q+1
       185: q^2+2q+1
       186: q^3+2q^2+2q+1
       187: q^2+2q+1
       188: q^3+2q^2+2q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: q+1
       203: q+1
       204: 2q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: q+1
       233: q+1
       234: 2q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^3+2q^2+2q+1
       257: q^2+2q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: q+1
       263: q+1
       264: 2q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^3+2q^2+2q+1
       287: q^2+2q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: 2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: 2q+1
       306: q^3+2q^2+2q+1
       307: q^2+2q+1
       308: q^3+2q^2+2q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: q+1
       333: q+1
       334: 2q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: q+1
       341: q+1
       342: 2q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: q+1
       370: q+1
       371: 2q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: q+1
       388: q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: 2q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: q+1
       409: q+1
       410: 2q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: q+1
       427: q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: q+1
       439: q+1
       440: 2q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q^2+2q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: q+1
       455: q^2+2q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: 2q+1
       462: q^3+2q^2+2q+1
       463: q^2+2q+1
       467: 1
       468: 1
       469: 1
       470: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: q+1
       506: q+1
       507: 2q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: q+1
       540: q+1
       541: 2q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: q+1
       548: q+1
       549: 2q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q+1
       562: 2q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: q+1
       587: q+1
       588: 2q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: q+1
       595: q+1
       596: 2q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: q+1
       606: q^2+2q+1
       607: 2q+1
       608: 2q+1
       609: 2q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       619: q+1
       620: q+1
       621: q+1
       622: 1
       623: q+1
       624: q+1
       625: 2q+1
       626: q+1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: q+1
       642: q^2+2q+1
       643: 2q+1
       644: 2q+1
       645: 2q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: 2q+1
       653: 1
       660: 1
       661: 1
       662: 1
       663: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       695: q+1
       696: q+1
       697: q+1
       698: 1
       699: q+1
       700: q+1
       701: 2q+1
       702: q+1
       706: 1
       707: 1
       708: 1
       709: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: q+1
       745: q+1
       746: 2q+1
       747: q+1
       748: q+1
       749: q+1
       750: q+1
       751: q+1
       752: 2q+1
       753: 2q+1
       754: 2q+1
       758: 1
       759: 1
       760: 1
       761: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: q+1
       797: q+1
       798: 2q+1
       799: q+1
       800: q+1
       801: q+1
       802: q+1
       803: q+1
       804: 2q+1
       805: 2q+1
       806: 2q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       818: q+1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: q+1
       826: q+1
       827: q+1
       828: q+1
       829: 1
       830: q+1
       831: q+1
       832: 2q+1
       833: q+1
       834: q+1
       835: q+1
       836: q+1
       837: 1
       838: q+1
       839: q+1
       840: 2q+1
       841: q+1
       842: q+1
       843: q+1
       844: q+1
       845: q+1
       846: 2q+1
       847: 2q+1
       848: 2q+1
       849: q+1
       850: q^2+2q+1
       851: 2q+1
       852: 2q+1
       853: 2q+1
       865: 1
       872: 1
       873: 1
       874: 1
       875: 1
       881: 1
       882: 1
       883: 1
       884: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       898: q+1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: q+1
       910: 1
       917: 1
       918: 1
       919: 1
       920: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       952: q+1
       953: q+1
       954: q+1
       955: 1
       956: q+1
       957: q+1
       958: 2q+1
       959: q+1
       964: 1
       971: 1
       972: 1
       973: 1
       974: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1006: q+1
      1007: q+1
      1008: q+1
      1009: 1
      1010: q+1
      1011: q+1
      1012: 2q+1
      1013: q+1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1034: q+1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: q+1
      1043: q+1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: q+1
      1051: q+1
      1052: q+1
      1053: q+1
      1054: 1
      1055: q+1
      1056: q+1
      1057: 2q+1
      1058: q+1
      1059: q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: 2q+1
      1064: 2q+1
      1065: 2q+1
      1082: 1
      1090: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1124: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1157: q+1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: q+1
      1176: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1209: q+1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: q+1
      1221: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1255: q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: q+1
      1261: q+1
      1263: q+1
      1264: q+1
      1265: q+1
      1266: 1
      1267: q+1
      1268: q+1
      1269: 2q+1
      1270: q+1
      1297: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1326: 1
      1334: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1373: 1
      1381: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1415: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1448: q+1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: q+1
      1454: q+1
      1482: 1
      1512: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1551: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1580: 1
      1588: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1658: 1
      1688: 1
      1718: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1812: 1

1813:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: q^2+1
         7: 1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: q^2+1
        21: 1
        22: 1
        23: q^2+1
        24: 1
        25: q^2+1
        26: 1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: q^2+1
        31: q^2+1
        32: q^2+1
        33: q^2+1
        34: 1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: q^2+1
        39: q^2+1
        40: q^2+1
        41: 1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: q^2+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: q^2+1
        58: 1
        59: 1
        60: q^2+1
        61: 1
        62: q^2+1
        63: 1
        64: q^2+1
        65: q^2+1
        66: 1
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: q^2+1
        72: 1
        73: 1
        74: q^2+1
        75: 1
        76: q^2+1
        77: 1
        78: q^2+1
        79: q^2+1
        80: q^2+1
        81: q^2+1
        82: q^2+1
        83: q^2+1
        84: q^2+1
        85: 1
        86: 1
        87: q^2+1
        88: 1
        89: q^2+1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: q^2+1
        98: 1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: q^2+1
       103: q^2+1
       105: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: q^2+1
       120: 1
       121: 1
       122: q^2+1
       123: 1
       124: q^2+1
       125: 1
       126: 1
       127: q^2+1
       128: 1
       129: q^2+1
       130: 1
       131: q^2+1
       132: q^2+1
       133: q^2+1
       134: q^2+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: q^2+1
       142: 1
       143: 1
       144: q^2+1
       145: 1
       146: q^2+1
       147: 1
       148: q^2+1
       149: q^2+1
       150: 1
       151: q^2+1
       152: q^2+1
       153: q^2+1
       154: q^2+1
       155: q^2+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: q^2+1
       163: 1
       164: 1
       165: q^2+1
       166: 1
       167: q^2+1
       168: 1
       169: q^2+1
       170: q^2+1
       171: 1
       172: q^2+1
       173: q^2+1
       174: q^2+1
       175: q^2+1
       176: q^2+1
       177: 1
       178: 1
       179: q^2+1
       180: 1
       181: q^2+1
       182: 1
       183: q^2+1
       184: q^2+1
       185: q^2+1
       186: q^2+1
       187: q^2+1
       188: q^2+1
       191: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       199: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: q^2+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: q^2+1
       221: 1
       222: 1
       223: q^2+1
       224: 1
       225: q^2+1
       226: 1
       227: q^2+1
       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: q^2+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q^2+1
       244: 1
       245: 1
       246: q^2+1
       247: 1
       248: q^2+1
       249: 1
       250: 1
       251: q^2+1
       252: 1
       253: q^2+1
       254: 1
       255: q^2+1
       256: q^2+1
       257: q^2+1
       259: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q^2+1
       274: 1
       275: 1
       276: q^2+1
       277: 1
       278: q^2+1
       279: 1
       280: 1
       281: q^2+1
       282: 1
       283: q^2+1
       284: 1
       285: q^2+1
       286: q^2+1
       287: q^2+1
       288: q^2+1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: q^2+1
       296: 1
       297: 1
       298: q^2+1
       299: 1
       300: q^2+1
       301: 1
       302: q^2+1
       303: q^2+1
       304: 1
       305: q^2+1
       306: q^2+1
       307: q^2+1
       308: q^2+1
       312: 1
       314: 1
       316: 1
       317: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: q^2+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q^2+1
       352: 1
       353: 1
       354: q^2+1
       355: 1
       358: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       366: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: q^2+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q^2+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: q^2+1
       388: 1
       389: 1
       390: q^2+1
       391: 1
       392: q^2+1
       393: 1
       394: q^2+1
       397: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       405: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: q^2+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: q^2+1
       427: 1
       428: 1
       429: q^2+1
       430: 1
       431: q^2+1
       432: 1
       433: q^2+1
       435: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: q^2+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q^2+1
       450: 1
       451: 1
       452: q^2+1
       453: 1
       454: q^2+1
       455: 1
       456: 1
       457: q^2+1
       458: 1
       459: q^2+1
       460: 1
       461: q^2+1
       462: q^2+1
       463: q^2+1
       469: 1
       471: 1
       476: 1
       478: 1
       480: 1
       481: 1
       485: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       494: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       502: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q^2+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       519: 1
       521: 1
       523: 1
       524: 1
       528: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       544: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: q^2+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: q^2+1
       559: 1
       560: 1
       561: q^2+1
       562: 1
       566: 1
       568: 1
       570: 1
       571: 1
       575: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       591: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q^2+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: q^2+1
       606: 1
       607: 1
       608: q^2+1
       609: 1
       612: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       620: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: q^2+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: q^2+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: q^2+1
       642: 1
       643: 1
       644: q^2+1
       645: 1
       646: q^2+1
       647: 1
       648: q^2+1
       654: 1
       662: 1
       664: 1
       669: 1
       671: 1
       673: 1
       674: 1
       679: 1
       681: 1
       683: 1
       684: 1
       688: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       696: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       708: 1
       710: 1
       715: 1
       717: 1
       719: 1
       720: 1
       724: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q^2+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       760: 1
       762: 1
       767: 1
       769: 1
       771: 1
       772: 1
       776: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q^2+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       810: 1
       812: 1
       814: 1
       815: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q^2+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: q^2+1
       850: 1
       851: 1
       852: q^2+1
       853: 1
       866: 1
       874: 1
       876: 1
       883: 1
       885: 1
       890: 1
       892: 1
       894: 1
       895: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       911: 1
       919: 1
       921: 1
       926: 1
       928: 1
       930: 1
       931: 1
       936: 1
       938: 1
       940: 1
       941: 1
       945: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       953: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       965: 1
       973: 1
       975: 1
       980: 1
       982: 1
       984: 1
       985: 1
       990: 1
       992: 1
       994: 1
       995: 1
       999: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1007: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1019: 1
      1021: 1
      1026: 1
      1028: 1
      1030: 1
      1031: 1
      1035: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1044: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q^2+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1083: 1
      1091: 1
      1099: 1
      1101: 1
      1106: 1
      1108: 1
      1110: 1
      1111: 1
      1125: 1
      1133: 1
      1135: 1
      1142: 1
      1144: 1
      1149: 1
      1151: 1
      1153: 1
      1154: 1
      1158: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1177: 1
      1185: 1
      1187: 1
      1194: 1
      1196: 1
      1201: 1
      1203: 1
      1205: 1
      1206: 1
      1210: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1222: 1
      1230: 1
      1232: 1
      1237: 1
      1239: 1
      1241: 1
      1242: 1
      1247: 1
      1249: 1
      1251: 1
      1252: 1
      1256: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1264: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1298: 1
      1306: 1
      1308: 1
      1327: 1
      1335: 1
      1343: 1
      1345: 1
      1350: 1
      1352: 1
      1354: 1
      1355: 1
      1374: 1
      1382: 1
      1390: 1
      1392: 1
      1397: 1
      1399: 1
      1401: 1
      1402: 1
      1416: 1
      1424: 1
      1426: 1
      1433: 1
      1435: 1
      1440: 1
      1442: 1
      1444: 1
      1445: 1
      1449: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1483: 1
      1513: 1
      1521: 1
      1523: 1
      1552: 1
      1560: 1
      1562: 1
      1581: 1
      1589: 1
      1597: 1
      1599: 1
      1604: 1
      1606: 1
      1608: 1
      1609: 1
      1659: 1
      1689: 1
      1719: 1
      1727: 1
      1729: 1
      1813: 1

1814:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: q^2+1
         7: 1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: q^2+1
        21: 1
        22: 1
        23: 1
        24: q^2+1
        25: q^2+1
        26: 1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: q^2+1
        31: q^2+1
        32: q^2+1
        33: q^2+1
        34: 1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: q^2+1
        39: q^2+1
        40: q^2+1
        41: 1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        51: q^2+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: q^2+1
        58: 1
        59: 1
        60: 1
        61: q^2+1
        62: q^2+1
        63: 1
        64: q^2+1
        65: q^2+1
        66: 1
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: q^2+1
        72: 1
        73: 1
        74: 1
        75: q^2+1
        76: q^2+1
        77: 1
        78: q^2+1
        79: q^2+1
        80: q^2+1
        81: q^2+1
        82: q^2+1
        83: q^2+1
        84: q^2+1
        85: 1
        86: 1
        87: 1
        88: q^2+1
        89: q^2+1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: q^2+1
        98: 1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: q^2+1
       103: q^2+1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       113: q^2+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: q^2+1
       120: 1
       121: 1
       122: 1
       123: q^2+1
       124: q^2+1
       125: 1
       126: 1
       127: 1
       128: q^2+1
       129: q^2+1
       130: 1
       131: q^2+1
       132: q^2+1
       133: q^2+1
       135: q^2+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: q^2+1
       142: 1
       143: 1
       144: 1
       145: q^2+1
       146: q^2+1
       147: 1
       148: q^2+1
       149: q^2+1
       150: 1
       151: q^2+1
       152: q^2+1
       153: q^2+1
       154: q^2+1
       156: q^2+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: q^2+1
       163: 1
       164: 1
       165: 1
       166: q^2+1
       167: q^2+1
       168: 1
       169: q^2+1
       170: q^2+1
       171: 1
       172: q^2+1
       173: q^2+1
       174: q^2+1
       175: q^2+1
       176: q^2+1
       177: 1
       178: 1
       179: 1
       180: q^2+1
       181: q^2+1
       182: 1
       183: q^2+1
       184: q^2+1
       185: q^2+1
       186: q^2+1
       187: q^2+1
       188: q^2+1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       207: q^2+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       214: q^2+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: q^2+1
       221: 1
       222: 1
       223: 1
       224: q^2+1
       225: q^2+1
       226: 1
       227: q^2+1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       237: q^2+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: q^2+1
       244: 1
       245: 1
       246: 1
       247: q^2+1
       248: q^2+1
       249: 1
       250: 1
       251: 1
       252: q^2+1
       253: q^2+1
       254: 1
       255: q^2+1
       256: q^2+1
       257: q^2+1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       267: q^2+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: q^2+1
       274: 1
       275: 1
       276: 1
       277: q^2+1
       278: q^2+1
       279: 1
       280: 1
       281: 1
       282: q^2+1
       283: q^2+1
       284: 1
       285: q^2+1
       286: q^2+1
       287: q^2+1
       289: q^2+1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: q^2+1
       296: 1
       297: 1
       298: 1
       299: q^2+1
       300: q^2+1
       301: 1
       302: q^2+1
       303: q^2+1
       304: 1
       305: q^2+1
       306: q^2+1
       307: q^2+1
       308: q^2+1
       313: 1
       315: 1
       316: 1
       317: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       345: q^2+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q^2+1
       352: 1
       353: 1
       354: 1
       355: q^2+1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       374: q^2+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       381: q^2+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: q^2+1
       388: 1
       389: 1
       390: 1
       391: q^2+1
       392: q^2+1
       393: 1
       394: q^2+1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       413: q^2+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: q^2+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: q^2+1
       427: 1
       428: 1
       429: 1
       430: q^2+1
       431: q^2+1
       432: 1
       433: q^2+1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       443: q^2+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: q^2+1
       450: 1
       451: 1
       452: 1
       453: q^2+1
       454: q^2+1
       455: 1
       456: 1
       457: 1
       458: q^2+1
       459: q^2+1
       460: 1
       461: q^2+1
       462: q^2+1
       463: q^2+1
       470: 1
       471: 1
       477: 1
       479: 1
       480: 1
       481: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       510: q^2+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       520: 1
       522: 1
       523: 1
       524: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       552: q^2+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: q^2+1
       559: 1
       560: 1
       561: 1
       562: q^2+1
       567: 1
       569: 1
       570: 1
       571: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       599: q^2+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: q^2+1
       606: 1
       607: 1
       608: 1
       609: q^2+1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       628: q^2+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: q^2+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: q^2+1
       642: 1
       643: 1
       644: 1
       645: q^2+1
       646: q^2+1
       647: 1
       648: q^2+1
       655: 1
       663: 1
       664: 1
       670: 1
       672: 1
       673: 1
       674: 1
       680: 1
       682: 1
       683: 1
       684: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       709: 1
       710: 1
       716: 1
       718: 1
       719: 1
       720: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       749: q^2+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       761: 1
       762: 1
       768: 1
       770: 1
       771: 1
       772: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       801: q^2+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       811: 1
       813: 1
       814: 1
       815: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       843: q^2+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: q^2+1
       850: 1
       851: 1
       852: 1
       853: q^2+1
       867: 1
       875: 1
       876: 1
       884: 1
       885: 1
       891: 1
       893: 1
       894: 1
       895: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       912: 1
       920: 1
       921: 1
       927: 1
       929: 1
       930: 1
       931: 1
       937: 1
       939: 1
       940: 1
       941: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: 1
       974: 1
       975: 1
       981: 1
       983: 1
       984: 1
       985: 1
       991: 1
       993: 1
       994: 1
       995: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1020: 1
      1021: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1060: q^2+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1084: 1
      1092: 1
      1100: 1
      1101: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1126: 1
      1134: 1
      1135: 1
      1143: 1
      1144: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1178: 1
      1186: 1
      1187: 1
      1195: 1
      1196: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1223: 1
      1231: 1
      1232: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1248: 1
      1250: 1
      1251: 1
      1252: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1299: 1
      1307: 1
      1308: 1
      1328: 1
      1336: 1
      1344: 1
      1345: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1375: 1
      1383: 1
      1391: 1
      1392: 1
      1398: 1
      1400: 1
      1401: 1
      1402: 1
      1417: 1
      1425: 1
      1426: 1
      1434: 1
      1435: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1484: 1
      1514: 1
      1522: 1
      1523: 1
      1553: 1
      1561: 1
      1562: 1
      1582: 1
      1590: 1
      1598: 1
      1599: 1
      1605: 1
      1607: 1
      1608: 1
      1609: 1
      1660: 1
      1690: 1
      1720: 1
      1728: 1
      1729: 1
      1814: 1

1815:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       316: 1
       317: 1
       318: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       471: 1
       472: 1
       480: 1
       481: 1
       482: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       523: 1
       524: 1
       525: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       570: 1
       571: 1
       572: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       656: 1
       664: 1
       665: 1
       673: 1
       674: 1
       675: 1
       683: 1
       684: 1
       685: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       710: 1
       711: 1
       719: 1
       720: 1
       721: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       762: 1
       763: 1
       771: 1
       772: 1
       773: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       814: 1
       815: 1
       816: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       868: 1
       876: 1
       877: 1
       885: 1
       886: 1
       894: 1
       895: 1
       896: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       913: 1
       921: 1
       922: 1
       930: 1
       931: 1
       932: 1
       940: 1
       941: 1
       942: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       967: 1
       975: 1
       976: 1
       984: 1
       985: 1
       986: 1
       994: 1
       995: 1
       996: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1021: 1
      1022: 1
      1030: 1
      1031: 1
      1032: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1085: 1
      1093: 1
      1101: 1
      1102: 1
      1110: 1
      1111: 1
      1112: 1
      1127: 1
      1135: 1
      1136: 1
      1144: 1
      1145: 1
      1153: 1
      1154: 1
      1155: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1179: 1
      1187: 1
      1188: 1
      1196: 1
      1197: 1
      1205: 1
      1206: 1
      1207: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1224: 1
      1232: 1
      1233: 1
      1241: 1
      1242: 1
      1243: 1
      1251: 1
      1252: 1
      1253: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1300: 1
      1308: 1
      1309: 1
      1329: 1
      1337: 1
      1345: 1
      1346: 1
      1354: 1
      1355: 1
      1356: 1
      1376: 1
      1384: 1
      1392: 1
      1393: 1
      1401: 1
      1402: 1
      1403: 1
      1418: 1
      1426: 1
      1427: 1
      1435: 1
      1436: 1
      1444: 1
      1445: 1
      1446: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1485: 1
      1515: 1
      1523: 1
      1524: 1
      1554: 1
      1562: 1
      1563: 1
      1583: 1
      1591: 1
      1599: 1
      1600: 1
      1608: 1
      1609: 1
      1610: 1
      1661: 1
      1691: 1
      1721: 1
      1729: 1
      1730: 1
      1815: 1

1816:    0: q^4+2q^2+q+1
         1: q^4+2q^2+q+1
         2: q^4+2q^2+q+1
         3: q^4+2q^2+q+1
         4: q^2+q+1
         5: q^4+2q^2+q+1
         6: q^4+2q^2+q+1
         7: q^4+2q^2+q+1
         8: q^4+2q^2+q+1
         9: q^4+2q^2+q+1
        10: q^4+2q^2+q+1
        11: q^4+2q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q+1
        16: q^4+2q^2+q+1
        17: q^4+2q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^4+2q^2+q+1
        21: q^4+2q^2+q+1
        22: q^4+2q^2+q+1
        23: q^4+2q^2+q+1
        24: q^2+q+1
        25: q^4+2q^2+q+1
        26: q^4+2q^2+q+1
        27: q^4+2q^2+q+1
        28: q^4+2q^2+q+1
        29: q^4+2q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^4+2q^2+q+1
        41: q^4+2q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q^4+2q^2+q+1
        51: q^2+q+1
        52: q^4+2q^2+q+1
        53: q^4+2q^2+q+1
        54: q^4+2q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^4+2q^2+q+1
        58: q^4+2q^2+q+1
        59: q^4+2q^2+q+1
        60: q^4+2q^2+q+1
        61: q^2+q+1
        62: q^4+2q^2+q+1
        63: q^4+2q^2+q+1
        64: q^2+q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^4+2q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+q+1
       105: q^4+2q^2+q+1
       106: q^2+q+1
       107: q^4+2q^2+q+1
       108: q^4+2q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q+1
       112: q^4+2q^2+q+1
       113: q^2+q+1
       114: q^4+2q^2+q+1
       115: q^4+2q^2+q+1
       116: q^4+2q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q^2+q+1
       120: q^4+2q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q+1
       124: q+1
       125: q^2+q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q^2+q+1
       191: q^4+2q^2+q+1
       192: q^2+q+1
       193: q^2+q+1
       194: q+1
       195: q^2+q+1
       196: q+1
       197: q+1
       198: q^2+q+1
       199: q^4+2q^2+q+1
       200: q^2+q+1
       201: q^4+2q^2+q+1
       202: q^4+2q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q+1
       206: q^2+q+1
       207: q+1
       208: q^2+q+1
       209: q^2+q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q+1
       260: q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+q+1
       267: q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q^2+q+1
       312: q^2+q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+q+1
       321: q^4+2q^2+q+1
       322: q^2+q+1
       323: q^2+q+1
       324: q+1
       325: q^2+q+1
       326: q+1
       327: q+1
       328: q+1
       329: q^2+q+1
       330: q+1
       331: q^2+q+1
       332: q^2+q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q+1
       399: q^2+q+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q^2+q+1
       406: q+1
       407: q^2+q+1
       408: q^2+q+1
       409: q+1
       410: q+1
       411: 1
       412: q^2+q+1
       413: q+1
       414: q^2+q+1
       415: q^2+q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+q+1
       476: q^2+q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: q+1
       485: q^2+q+1
       486: q+1
       487: q^2+q+1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q^2+q+1
       576: q+1
       577: q^2+q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q^2+q+1
       584: q+1
       585: q^2+q+1
       586: q^2+q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       666: q+1
       667: q+1
       668: q+1
       669: q^2+q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: q+1
       679: 1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       707: q+1
       708: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q^2+q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q^2+q+1
       777: q+1
       778: q^2+q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       854: q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       859: q+1
       860: q+1
       861: q+1
       862: q+1
       863: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       882: q+1
       883: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: q+1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       938: q+1
       939: q+1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q^2+q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1066: q+1
      1067: q+1
      1068: q+1
      1069: 1
      1070: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1141: q+1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1256: 1
      1264: 1
      1266: 1
      1267: 1
      1271: q+1
      1272: 1
      1273: 1
      1274: q+1
      1275: q+1
      1276: q+1
      1277: 1
      1278: q+1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: q+1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1428: 1
      1429: 1
      1432: 1
      1436: 1
      1449: 1
      1456: 1
      1457: 1
      1458: q+1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1478: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1490: 1
      1501: 1
      1503: 1
      1506: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1547: 1
      1555: 1
      1556: 1
      1559: 1
      1563: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1584: 1
      1611: 1
      1612: 1
      1613: 1
      1614: 1
      1615: 1
      1616: 1
      1621: 1
      1625: 1
      1627: 1
      1630: 1
      1643: 1
      1662: 1
      1663: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1684: 1
      1696: 1
      1731: 1
      1732: 1
      1733: 1
      1740: 1
      1765: 1
      1768: 1
      1816: 1

1817:    0: q^4+2q^2+q+1
         1: q^4+2q^2+q+1
         2: q^4+2q^2+q+1
         3: q^4+2q^2+q+1
         4: q^4+2q^2+q+1
         5: q^2+q+1
         6: q^4+2q^2+q+1
         7: q^4+2q^2+q+1
         8: q^4+2q^2+q+1
         9: q^4+2q^2+q+1
        10: q^4+2q^2+q+1
        11: q^2+q+1
        12: q^4+2q^2+q+1
        13: q^4+2q^2+q+1
        14: q^4+2q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: q^4+2q^2+q+1
        21: q^4+2q^2+q+1
        22: q^4+2q^2+q+1
        23: q^2+q+1
        24: q^4+2q^2+q+1
        25: q^4+2q^2+q+1
        26: q^4+2q^2+q+1
        27: q^4+2q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^4+2q^2+q+1
        31: q^4+2q^2+q+1
        32: q^2+q+1
        33: q^4+2q^2+q+1
        34: q^4+2q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q^2+q+1
        51: q^4+2q^2+q+1
        52: q^4+2q^2+q+1
        53: q^4+2q^2+q+1
        54: q^2+q+1
        55: q^4+2q^2+q+1
        56: q^2+q+1
        57: q^4+2q^2+q+1
        58: q^4+2q^2+q+1
        59: q^4+2q^2+q+1
        60: q^2+q+1
        61: q^4+2q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q+1
        65: q^4+2q^2+q+1
        66: q^4+2q^2+q+1
        67: q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q+1
        71: q^2+q+1
        72: q^4+2q^2+q+1
        73: q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+q+1
       105: q^2+q+1
       106: q^4+2q^2+q+1
       107: q^4+2q^2+q+1
       108: q^2+q+1
       109: q^4+2q^2+q+1
       110: q^2+q+1
       111: q+1
       112: q^2+q+1
       113: q^4+2q^2+q+1
       114: q^4+2q^2+q+1
       115: q^4+2q^2+q+1
       116: q^2+q+1
       117: q^4+2q^2+q+1
       118: q^2+q+1
       119: q+1
       120: q^2+q+1
       121: q+1
       122: q+1
       123: q+1
       124: q^2+q+1
       125: q^4+2q^2+q+1
       126: q^2+q+1
       127: q+1
       128: q^2+q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: 1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q^2+q+1
       191: q^2+q+1
       192: q^4+2q^2+q+1
       193: q+1
       194: q^2+q+1
       195: q^2+q+1
       196: q+1
       197: q+1
       198: q^2+q+1
       199: q^2+q+1
       200: q^4+2q^2+q+1
       201: q^4+2q^2+q+1
       202: q^2+q+1
       203: q^4+2q^2+q+1
       204: q^2+q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: q+1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+q+1
       231: q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q^2+q+1
       312: q+1
       313: q+1
       314: q+1
       315: q^2+q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+q+1
       321: q^2+q+1
       322: q^4+2q^2+q+1
       323: q+1
       324: q^2+q+1
       325: q^2+q+1
       326: q+1
       327: q+1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q^2+q+1
       339: q^2+q+1
       340: q+1
       341: q^2+q+1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+q+1
       360: 1
       361: q^2+q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q^2+q+1
       368: q^2+q+1
       369: q+1
       370: q^2+q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: q+1
       428: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+q+1
       476: q+1
       477: q+1
       478: q+1
       479: q^2+q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       492: q+1
       493: q+1
       494: q+1
       495: q^2+q+1
       496: 1
       497: q^2+q+1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q^2+q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q^2+q+1
       530: 1
       531: q^2+q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q^2+q+1
       546: q^2+q+1
       547: q+1
       548: q^2+q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: q+1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: q+1
       643: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       666: q+1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       672: 1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q^2+q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q^2+q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q^2+q+1
       735: 1
       736: q^2+q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: q+1
       851: 1
       853: 1
       854: q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       859: q+1
       860: q+1
       861: q+1
       862: q+1
       863: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: 1
       891: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q^2+q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1066: q+1
      1067: q+1
      1068: q+1
      1069: 1
      1070: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: q+1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1217: q+1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1250: 1
      1257: 1
      1265: 1
      1266: 1
      1268: 1
      1271: q+1
      1272: 1
      1273: 1
      1274: q+1
      1275: q+1
      1276: q+1
      1277: 1
      1278: q+1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: 1
      1427: 1
      1450: 1
      1456: 1
      1457: 1
      1458: q+1
      1459: 1
      1460: 1
      1461: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1516: 1
      1517: 1
      1519: 1
      1524: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1611: 1
      1612: 1
      1613: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1625: 1
      1626: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1654: 1
      1667: 1
      1695: 1
      1731: 1
      1734: 1
      1735: 1
      1739: 1
      1744: 1
      1750: 1
      1817: 1

1818:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1486: 1
      1487: 1
      1488: 1
      1504: 1
      1516: 1
      1525: 1
      1526: 1
      1527: 1
      1536: 1
      1555: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1572: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1628: 1
      1632: 1
      1662: 1
      1692: 1
      1693: 1
      1694: 1
      1722: 1
      1732: 1
      1734: 1
      1736: 1
      1737: 1
      1738: 1
      1786: 1
      1818: 1

1819:    0: 2q^3+3q^2+2q+1
         1: 3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 3q^2+2q+1
         7: 3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: 3q^2+2q+1
        10: 2q^3+3q^2+2q+1
        11: 2q^3+3q^2+2q+1
        12: 2q^3+3q^2+2q+1
        13: 3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: q^3+2q^2+2q+1
        16: 3q^2+2q+1
        17: 2q^3+3q^2+2q+1
        18: q^3+2q^2+2q+1
        19: 2q^3+3q^2+2q+1
        20: q^2+2q+1
        21: 3q^2+2q+1
        22: 3q^2+2q+1
        23: 2q^3+3q^2+2q+1
        24: 2q^3+3q^2+2q+1
        25: 3q^2+2q+1
        26: 3q^2+2q+1
        27: 2q^3+3q^2+2q+1
        28: 3q^2+2q+1
        29: 2q^3+3q^2+2q+1
        30: 3q^2+2q+1
        31: 2q^3+3q^2+2q+1
        32: 2q^3+3q^2+2q+1
        33: 3q^2+2q+1
        34: 3q^2+2q+1
        35: q^3+2q^2+2q+1
        36: 2q^2+2q+1
        37: q^3+2q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        40: 3q^2+2q+1
        41: 3q^2+2q+1
        42: q^3+2q^2+2q+1
        43: 2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: 3q^2+2q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 3q^2+2q+1
        54: 3q^2+2q+1
        55: 3q^2+2q+1
        56: 2q^3+3q^2+2q+1
        57: q^2+2q+1
        58: 3q^2+2q+1
        59: 3q^2+2q+1
        60: 2q^3+3q^2+2q+1
        61: 2q^3+3q^2+2q+1
        62: 3q^2+2q+1
        63: 3q^2+2q+1
        64: q^3+2q^2+2q+1
        65: 3q^2+2q+1
        66: 3q^2+2q+1
        67: q^3+2q^2+2q+1
        68: 3q^2+2q+1
        69: 2q^3+3q^2+2q+1
        70: 2q^2+2q+1
        71: 2q+1
        72: 3q^2+2q+1
        73: 2q^2+2q+1
        74: q^3+2q^2+2q+1
        75: q^3+2q^2+2q+1
        76: 2q^2+2q+1
        77: q^2+q+1
        78: q^3+2q^2+2q+1
        79: 2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: 2q^2+2q+1
        82: q^3+2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q+1
        85: 3q^2+2q+1
        86: 2q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^3+2q^2+2q+1
        89: 2q^2+2q+1
        90: q^2+q+1
        91: q^3+2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: 2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: q^3+2q^2+2q+1
        97: 3q^2+2q+1
        98: 3q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: 2q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: 3q^2+2q+1
       109: 3q^2+2q+1
       110: 3q^2+2q+1
       111: 2q^2+2q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: 3q^2+2q+1
       116: 3q^2+2q+1
       117: 3q^2+2q+1
       118: 2q^3+3q^2+2q+1
       119: 2q+1
       120: 3q^2+2q+1
       121: 2q^2+2q+1
       122: q^3+2q^2+2q+1
       123: q^3+2q^2+2q+1
       124: 2q+1
       125: 3q^2+2q+1
       126: 2q^2+2q+1
       127: q^3+2q^2+2q+1
       128: q^3+2q^2+2q+1
       129: 3q^2+2q+1
       130: 3q^2+2q+1
       131: 2q^2+2q+1
       132: 2q^2+2q+1
       133: 2q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q^3+2q^2+2q+1
       141: 2q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q^3+2q^2+2q+1
       145: q^3+2q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+q+1
       148: q^2+q+1
       149: 2q^2+2q+1
       150: q^2+q+1
       151: q^3+2q^2+2q+1
       152: 2q^2+2q+1
       153: q^3+2q^2+2q+1
       154: 2q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: 2q^2+2q+1
       161: q^3+2q^2+2q+1
       162: 2q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^3+2q^2+2q+1
       166: q^3+2q^2+2q+1
       167: 2q^2+2q+1
       168: q^2+q+1
       169: q^3+2q^2+2q+1
       170: 2q^2+2q+1
       171: q^2+q+1
       172: q^2+q+1
       173: 2q^2+2q+1
       174: q^3+2q^2+2q+1
       175: 2q^2+2q+1
       176: 2q+1
       177: 3q^2+2q+1
       178: 2q^2+2q+1
       179: 2q^2+2q+1
       180: 2q^2+2q+1
       181: 2q^2+2q+1
       182: q+1
       183: 2q^2+2q+1
       184: 2q^2+2q+1
       185: 2q^2+2q+1
       186: 2q^2+2q+1
       187: 2q^2+2q+1
       188: 2q^2+2q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: 2q+1
       194: 2q+1
       195: 3q^2+2q+1
       196: 2q^2+2q+1
       197: 2q^2+2q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: 3q^2+2q+1
       203: 3q^2+2q+1
       204: 3q^2+2q+1
       205: 2q^2+2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: 2q^2+2q+1
       210: 2q^2+2q+1
       211: 2q^2+2q+1
       212: q^3+2q^2+2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 2q^2+2q+1
       217: 2q^2+2q+1
       218: 2q^2+2q+1
       219: q^3+2q^2+2q+1
       220: 2q+1
       221: 3q^2+2q+1
       222: 2q^2+2q+1
       223: 2q^2+2q+1
       224: 2q^2+2q+1
       225: 2q^2+2q+1
       226: q+1
       227: 2q^2+2q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q^2+2q+1
       233: 2q^2+2q+1
       234: 2q^2+2q+1
       235: 2q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q^2+q+1
       240: q^2+q+1
       241: q^2+q+1
       242: q^3+2q^2+2q+1
       243: q+1
       244: q^2+q+1
       245: q^2+1
       246: q^2+q+1
       247: q^2+q+1
       248: 2q+1
       249: q^2+q+1
       250: q^2+q+1
       251: q^3+2q^2+2q+1
       252: q^3+2q^2+2q+1
       253: 2q^2+2q+1
       254: q^2+q+1
       255: q^2+q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q^2+2q+1
       263: 2q^2+2q+1
       264: 2q^2+2q+1
       265: 2q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q^2+q+1
       270: q^2+q+1
       271: q^2+q+1
       272: q^3+2q^2+2q+1
       273: 2q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^3+2q^2+2q+1
       277: q^3+2q^2+2q+1
       278: q+1
       279: q^2+q+1
       280: q^2+1
       281: q^2+q+1
       282: q^2+q+1
       283: 2q^2+2q+1
       284: q^2+q+1
       285: q^2+q+1
       286: 2q^2+2q+1
       287: 2q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q^2+2q+1
       292: 2q^2+2q+1
       293: 2q^2+2q+1
       294: 2q^2+2q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: 2q^2+2q+1
       299: 2q^2+2q+1
       300: 2q^2+2q+1
       301: q+1
       302: q^2+q+1
       303: 2q^2+2q+1
       304: q+1
       305: q^2+q+1
       306: 2q^2+2q+1
       307: 2q^2+2q+1
       308: 2q^2+2q+1
       309: q+1
       310: q+1
       311: q^2+2q+1
       312: 2q+1
       313: 2q+1
       314: 2q+1
       315: 2q+1
       316: 2q+1
       317: 2q^2+2q+1
       318: q+1
       319: q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: 2q+1
       324: 2q+1
       325: 3q^2+2q+1
       326: 2q^2+2q+1
       327: 2q^2+2q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q^2+2q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: 2q^2+2q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q^2+2q+1
       341: 2q^2+2q+1
       342: 2q^2+2q+1
       343: 2q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 2q^2+2q+1
       348: 2q^2+2q+1
       349: 2q^2+2q+1
       350: 2q^2+2q+1
       351: 2q+1
       352: q+1
       353: q+1
       354: 2q^2+2q+1
       355: 2q^2+2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: 2q^2+2q+1
       363: 2q^2+2q+1
       364: 2q^2+2q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q^2+q+1
       370: q^2+q+1
       371: q^2+q+1
       372: q^2+q+1
       373: q+1
       374: q+1
       375: 1
       376: q^2+1
       377: q^2+1
       378: q^2+1
       379: q^2+q+1
       380: 2q+1
       381: 2q+1
       382: q+1
       383: q^2+q+1
       384: q^2+q+1
       385: q^2+q+1
       386: q^3+2q^2+2q+1
       387: q+1
       388: q^2+q+1
       389: q^2+1
       390: q^2+q+1
       391: q^2+q+1
       392: 2q^2+2q+1
       393: q+1
       394: q^2+q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: q+1
       401: 2q^2+2q+1
       402: 2q^2+2q+1
       403: 2q^2+2q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q^2+q+1
       409: q^2+q+1
       410: q^2+q+1
       411: q^2+q+1
       412: 2q+1
       413: 2q+1
       414: q+1
       415: q^2+q+1
       416: q^2+q+1
       417: q^2+q+1
       418: q^3+2q^2+2q+1
       419: q+1
       420: q+1
       421: 1
       422: q^2+1
       423: q^2+1
       424: q^2+1
       425: q^2+q+1
       426: q+1
       427: q^2+q+1
       428: q^2+1
       429: q^2+q+1
       430: q^2+q+1
       431: 2q^2+2q+1
       432: q+1
       433: q^2+q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q^2+2q+1
       439: 2q^2+2q+1
       440: 2q^2+2q+1
       441: 2q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q^2+2q+1
       449: q+1
       450: q+1
       451: 1
       452: q^2+q+1
       453: q^2+q+1
       454: q+1
       455: q+1
       456: 1
       457: q^2+q+1
       458: q^2+q+1
       459: 2q^2+2q+1
       460: q+1
       461: q+1
       462: 2q^2+2q+1
       463: 2q^2+2q+1
       465: q+1
       466: q+1
       467: 2q+1
       468: 2q+1
       469: 2q+1
       470: 2q+1
       471: 2q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+2q+1
       476: 2q+1
       477: 2q+1
       478: 2q+1
       479: 2q+1
       480: 2q+1
       481: 2q^2+2q+1
       482: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: q+1
       489: 2q^2+2q+1
       490: 2q^2+2q+1
       491: 2q^2+2q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: 2q+1
       498: 2q^2+2q+1
       499: 2q^2+2q+1
       500: 2q^2+2q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q^2+2q+1
       506: 2q^2+2q+1
       507: 2q^2+2q+1
       508: 2q^2+2q+1
       509: 2q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2q^2+2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: 2q+1
       522: 2q+1
       523: q+1
       524: 2q^2+2q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q^2+q+1
       533: q^2+1
       534: q^2+q+1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: q^2+1
       540: q^2+1
       541: q^2+1
       542: q^2+q+1
       543: 2q+1
       544: q+1
       545: q+1
       546: q+1
       547: q^2+q+1
       548: q^2+q+1
       549: q^2+q+1
       550: q^2+q+1
       551: q+1
       552: q+1
       553: 1
       554: q^2+1
       555: q^2+1
       556: q^2+1
       557: q^2+q+1
       558: q+1
       559: q+1
       560: 1
       561: q^2+q+1
       562: q^2+q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       568: q+1
       569: q+1
       570: q+1
       571: 2q^2+2q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q^2+q+1
       580: q^2+1
       581: q^2+q+1
       582: 2q+1
       583: q+1
       584: q+1
       585: q+1
       586: q^2+q+1
       587: q^2+q+1
       588: q^2+q+1
       589: q^2+q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: q^2+1
       595: q^2+1
       596: q^2+1
       597: q^2+q+1
       598: q+1
       599: q+1
       600: 1
       601: q^2+1
       602: q^2+1
       603: q^2+1
       604: q^2+q+1
       605: q+1
       606: q+1
       607: 1
       608: q^2+q+1
       609: q^2+q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q^2+2q+1
       617: 2q^2+2q+1
       618: 2q^2+2q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q^2+q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q^2+q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: 2q^2+2q+1
       647: q+1
       648: q+1
       650: q+1
       651: q+1
       652: q+1
       653: 2q+1
       654: 2q+1
       655: 2q+1
       656: q+1
       658: q+1
       659: q+1
       660: 2q+1
       661: 2q+1
       662: 2q+1
       663: 2q+1
       664: 2q+1
       665: q+1
       666: q+1
       667: q+1
       668: 2q+1
       669: 2q+1
       670: 2q+1
       671: q+1
       672: q+1
       673: q+1
       674: 2q^2+2q+1
       675: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: 2q+1
       682: 2q+1
       683: q+1
       684: 2q^2+2q+1
       685: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q^2+2q+1
       693: 2q^2+2q+1
       694: 2q^2+2q+1
       695: 2q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       704: q+1
       705: 1
       706: q+1
       707: 2q+1
       708: q+1
       709: q+1
       710: q+1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: q^2+1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: q^2+1
       729: q^2+1
       730: q^2+q+1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q^2+q+1
       738: q^2+1
       739: q^2+q+1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: q^2+1
       745: q^2+1
       746: q^2+1
       747: q^2+q+1
       748: q+1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q^2+q+1
       756: q+1
       757: 1
       758: 2q+1
       759: q+1
       760: q+1
       761: q+1
       762: q+1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: q^2+1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q^2+q+1
       781: q^2+1
       782: q^2+q+1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: q^2+1
       790: q^2+1
       791: q^2+q+1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: q^2+1
       797: q^2+1
       798: q^2+1
       799: q^2+q+1
       800: q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q^2+q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: q+1
       815: 2q^2+2q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       855: q+1
       856: q+1
       857: q+1
       858: 2q+1
       859: q+1
       860: q+1
       862: q+1
       863: q+1
       864: q+1
       865: 2q+1
       866: 2q+1
       867: 2q+1
       868: q+1
       870: q+1
       871: 1
       872: 2q+1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       879: q+1
       880: 1
       881: q+1
       882: 2q+1
       883: q+1
       884: q+1
       885: q+1
       886: q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: q+1
       895: 2q^2+2q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: q+1
       907: 1
       908: 1
       909: 1
       910: q+1
       911: q+1
       912: q+1
       913: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: q^2+1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: q^2+1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: q^2+1
       950: q^2+1
       951: q^2+q+1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q+1
       961: 1
       962: 1
       963: 1
       964: q+1
       965: q+1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: q^2+1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: q^2+1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: q^2+1
      1004: q^2+1
      1005: q^2+q+1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q+1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1068: q+1
      1069: 1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: q+1
      1083: q+1
      1084: q+1
      1085: 1
      1087: 1
      1088: 1
      1089: 1
      1090: q+1
      1091: q+1
      1092: q+1
      1093: 1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: q+1
      1100: q+1
      1101: q+1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: q+1
      1118: 1
      1119: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1129: 1
      1131: 1
      1136: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: q^2+1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 1
      1167: 1
      1168: 1
      1169: q+1
      1170: 1
      1171: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: q^2+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: q+1
      1222: q+1
      1223: q+1
      1224: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: q+1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q+1
      1272: 1
      1273: 1
      1276: q+1
      1277: 1
      1278: q+1
      1280: 1
      1281: 1
      1282: 1
      1283: q+1
      1284: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: q+1
      1291: 1
      1292: 1
      1294: 1
      1295: 1
      1296: 1
      1297: q+1
      1298: q+1
      1299: q+1
      1300: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1405: 1
      1406: 1
      1407: 1
      1408: q+1
      1409: 1
      1410: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1420: 1
      1422: 1
      1427: 1
      1429: 1
      1432: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1454: 1
      1455: q+1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1473: 1
      1474: 1
      1475: q+1
      1476: 1
      1477: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1493: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1517: 1
      1519: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1532: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1556: 1
      1559: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1593: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1609: 1
      1610: 1
      1613: 1
      1615: 1
      1616: 1
      1618: 1
      1619: 1
      1622: 1
      1623: 1
      1624: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1633: 1
      1644: 1
      1646: 1
      1663: 1
      1669: 1
      1671: 1
      1693: 1
      1694: 1
      1697: 1
      1699: 1
      1723: 1
      1730: 1
      1733: 1
      1735: 1
      1737: 1
      1738: 1
      1741: 1
      1743: 1
      1787: 1
      1819: 1

1820:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: 3q^3+6q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: 3q^3+6q^2+4q+1
         5: 3q^3+6q^2+4q+1
         6: 3q^3+6q^2+4q+1
         7: 3q^3+6q^2+4q+1
         8: q^3+4q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: 3q^3+6q^2+4q+1
        11: 3q^3+6q^2+4q+1
        12: 3q^3+6q^2+4q+1
        13: 3q^3+6q^2+4q+1
        14: 3q^3+6q^2+4q+1
        15: q^3+4q^2+4q+1
        16: 3q^3+6q^2+4q+1
        17: 3q^3+6q^2+4q+1
        18: q^3+4q^2+4q+1
        19: 3q^3+6q^2+4q+1
        20: q^3+4q^2+4q+1
        21: 3q^3+6q^2+4q+1
        22: q^3+4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: q^3+4q^2+4q+1
        25: 3q^3+6q^2+4q+1
        26: 3q^3+6q^2+4q+1
        27: q^3+4q^2+4q+1
        28: 3q^3+6q^2+4q+1
        29: 3q^3+6q^2+4q+1
        30: 3q^3+6q^2+4q+1
        31: 3q^3+6q^2+4q+1
        32: 3q^3+6q^2+4q+1
        33: 3q^3+6q^2+4q+1
        34: 3q^3+6q^2+4q+1
        35: 2q^2+4q+1
        36: q^3+4q^2+4q+1
        37: q^3+4q^2+4q+1
        38: q^3+4q^2+4q+1
        39: q^3+4q^2+4q+1
        40: 3q^3+6q^2+4q+1
        41: 3q^3+6q^2+4q+1
        42: 2q^2+4q+1
        43: q^3+4q^2+4q+1
        44: q^3+4q^2+4q+1
        45: q^3+4q^2+4q+1
        46: q^3+4q^2+4q+1
        47: 3q^3+6q^2+4q+1
        48: 3q^3+6q^2+4q+1
        49: 3q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+4q^2+4q+1
        52: q^3+4q^2+4q+1
        53: q^3+4q^2+4q+1
        54: q^3+4q^2+4q+1
        55: q^3+4q^2+4q+1
        56: q^3+4q^2+4q+1
        57: q^3+4q^2+4q+1
        58: 3q^3+6q^2+4q+1
        59: q^3+4q^2+4q+1
        60: q^3+4q^2+4q+1
        61: q^3+4q^2+4q+1
        62: 3q^3+6q^2+4q+1
        63: 3q^3+6q^2+4q+1
        64: 2q^2+4q+1
        65: 3q^3+6q^2+4q+1
        66: 3q^3+6q^2+4q+1
        67: 2q^2+4q+1
        68: 3q^3+6q^2+4q+1
        69: 3q^3+6q^2+4q+1
        70: 3q^2+4q+1
        71: 2q^2+4q+1
        72: 3q^3+6q^2+4q+1
        73: 2q^2+4q+1
        74: 2q^2+4q+1
        75: 2q^2+4q+1
        76: q^3+4q^2+4q+1
        77: q^3+4q^2+4q+1
        78: 2q^2+4q+1
        79: q^3+4q^2+4q+1
        80: q^3+4q^2+4q+1
        81: q^3+4q^2+4q+1
        82: q^3+4q^2+4q+1
        83: q^3+4q^2+4q+1
        84: 2q^2+4q+1
        85: 3q^3+6q^2+4q+1
        86: 2q^2+4q+1
        87: 2q^2+4q+1
        88: 2q^2+4q+1
        89: q^3+4q^2+4q+1
        90: q^3+4q^2+4q+1
        91: 2q^2+4q+1
        92: q^3+4q^2+4q+1
        93: q^3+4q^2+4q+1
        94: q^3+4q^2+4q+1
        95: q^3+4q^2+4q+1
        96: q^3+4q^2+4q+1
        97: 3q^3+6q^2+4q+1
        98: 3q^3+6q^2+4q+1
        99: q^2+4q+1
       100: 3q^2+4q+1
       101: 3q^2+4q+1
       102: 3q^2+4q+1
       103: 3q^2+4q+1
       104: q^3+4q^2+4q+1
       105: q^3+4q^2+4q+1
       106: q^3+4q^2+4q+1
       107: q^3+4q^2+4q+1
       108: q^3+4q^2+4q+1
       109: q^3+4q^2+4q+1
       110: q^3+4q^2+4q+1
       111: 3q+1
       112: q^3+4q^2+4q+1
       113: q^3+4q^2+4q+1
       114: q^3+4q^2+4q+1
       115: q^3+4q^2+4q+1
       116: q^3+4q^2+4q+1
       117: q^3+4q^2+4q+1
       118: q^3+4q^2+4q+1
       119: 2q^2+4q+1
       120: 3q^3+6q^2+4q+1
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: 2q^2+4q+1
       124: 2q^2+4q+1
       125: 3q^3+6q^2+4q+1
       126: 2q^2+4q+1
       127: 2q^2+4q+1
       128: 2q^2+4q+1
       129: 3q^3+6q^2+4q+1
       130: 3q^3+6q^2+4q+1
       131: q^2+4q+1
       132: 3q^2+4q+1
       133: 3q^2+4q+1
       134: 2q^2+4q+1
       135: 2q^2+4q+1
       136: 2q^2+4q+1
       137: 2q^2+4q+1
       138: 2q^2+4q+1
       139: 2q^2+4q+1
       140: 2q^2+4q+1
       141: 2q^2+4q+1
       142: q^3+4q^2+4q+1
       143: 2q^2+4q+1
       144: 2q^2+4q+1
       145: 2q^2+4q+1
       146: q^3+4q^2+4q+1
       147: q^3+4q^2+4q+1
       148: 2q+1
       149: q^3+4q^2+4q+1
       150: q^3+4q^2+4q+1
       151: 2q^2+4q+1
       152: q^3+4q^2+4q+1
       153: q^3+4q^2+4q+1
       154: 3q^2+4q+1
       155: 2q^2+4q+1
       156: 2q^2+4q+1
       157: 2q^2+4q+1
       158: 2q^2+4q+1
       159: 2q^2+4q+1
       160: 2q^2+4q+1
       161: 2q^2+4q+1
       162: 2q^2+4q+1
       163: q^3+4q^2+4q+1
       164: 2q^2+4q+1
       165: 2q^2+4q+1
       166: 2q^2+4q+1
       167: q^3+4q^2+4q+1
       168: q^3+4q^2+4q+1
       169: 2q^2+4q+1
       170: q^3+4q^2+4q+1
       171: q^3+4q^2+4q+1
       172: 2q+1
       173: q^3+4q^2+4q+1
       174: q^3+4q^2+4q+1
       175: 3q^2+4q+1
       176: q^2+4q+1
       177: 3q^3+6q^2+4q+1
       178: q^2+4q+1
       179: q^2+4q+1
       180: q^2+4q+1
       181: 3q^2+4q+1
       182: 3q^2+4q+1
       183: q^2+4q+1
       184: 3q^2+4q+1
       185: 3q^2+4q+1
       186: 3q^2+4q+1
       187: 3q^2+4q+1
       188: 3q^2+4q+1
       189: 3q+1
       190: q^3+4q^2+4q+1
       191: q^3+4q^2+4q+1
       192: q^3+4q^2+4q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: q^3+4q^2+4q+1
       196: 3q+1
       197: 3q+1
       198: q^3+4q^2+4q+1
       199: q^3+4q^2+4q+1
       200: q^3+4q^2+4q+1
       201: q^3+4q^2+4q+1
       202: q^3+4q^2+4q+1
       203: q^3+4q^2+4q+1
       204: q^3+4q^2+4q+1
       205: 3q+1
       206: 2q^2+4q+1
       207: 2q^2+4q+1
       208: 2q^2+4q+1
       209: 2q^2+4q+1
       210: 2q^2+4q+1
       211: 2q^2+4q+1
       212: 2q^2+4q+1
       213: 2q^2+4q+1
       214: 2q^2+4q+1
       215: 2q^2+4q+1
       216: 2q^2+4q+1
       217: 2q^2+4q+1
       218: 2q^2+4q+1
       219: 2q^2+4q+1
       220: q^2+4q+1
       221: 3q^3+6q^2+4q+1
       222: q^2+4q+1
       223: q^2+4q+1
       224: q^2+4q+1
       225: 3q^2+4q+1
       226: 3q^2+4q+1
       227: q^2+4q+1
       228: 2q^2+4q+1
       229: 2q^2+4q+1
       230: 2q^2+4q+1
       231: 2q^2+4q+1
       232: 2q^2+4q+1
       233: 2q^2+4q+1
       234: 2q^2+4q+1
       235: 3q+1
       236: 2q^2+4q+1
       237: 2q^2+4q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+4q+1
       242: 2q^2+4q+1
       243: 2q+1
       244: q^3+4q^2+4q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: 2q^2+4q+1
       249: q^3+4q^2+4q+1
       250: 2q^2+4q+1
       251: 2q^2+4q+1
       252: 2q^2+4q+1
       253: q^3+4q^2+4q+1
       254: q^3+4q^2+4q+1
       255: 2q+1
       256: 3q^2+4q+1
       257: 3q^2+4q+1
       258: 2q^2+4q+1
       259: 2q^2+4q+1
       260: 2q^2+4q+1
       261: 2q^2+4q+1
       262: 2q^2+4q+1
       263: 2q^2+4q+1
       264: 2q^2+4q+1
       265: 3q+1
       266: 2q^2+4q+1
       267: 2q^2+4q+1
       268: 2q^2+4q+1
       269: 2q^2+4q+1
       270: 2q^2+4q+1
       271: 2q^2+4q+1
       272: 2q^2+4q+1
       273: 2q^2+4q+1
       274: q^3+4q^2+4q+1
       275: 2q^2+4q+1
       276: 2q^2+4q+1
       277: 2q^2+4q+1
       278: 2q+1
       279: q^3+4q^2+4q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: q^3+4q^2+4q+1
       284: q^3+4q^2+4q+1
       285: 2q+1
       286: 3q^2+4q+1
       287: 3q^2+4q+1
       288: q^2+4q+1
       289: q^2+4q+1
       290: q^2+4q+1
       291: q^2+4q+1
       292: q^2+4q+1
       293: q^2+4q+1
       294: q^2+4q+1
       295: q^2+4q+1
       296: 3q^2+4q+1
       297: q^2+4q+1
       298: q^2+4q+1
       299: q^2+4q+1
       300: 3q^2+4q+1
       301: 3q^2+4q+1
       302: 2q+1
       303: 3q^2+4q+1
       304: 3q^2+4q+1
       305: 2q+1
       306: 3q^2+4q+1
       307: 3q^2+4q+1
       308: 3q^2+4q+1
       309: 3q+1
       310: 3q+1
       311: q^3+4q^2+4q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: q+1
       317: 3q+1
       318: 3q+1
       319: 3q+1
       320: q^3+4q^2+4q+1
       321: q^3+4q^2+4q+1
       322: q^3+4q^2+4q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: q^3+4q^2+4q+1
       326: 3q+1
       327: 3q+1
       328: 2q^2+4q+1
       329: 2q^2+4q+1
       330: 2q^2+4q+1
       331: 2q^2+4q+1
       332: 2q^2+4q+1
       333: 2q^2+4q+1
       334: 2q^2+4q+1
       335: 3q+1
       336: 2q^2+4q+1
       337: 2q^2+4q+1
       338: 2q^2+4q+1
       339: 2q^2+4q+1
       340: 2q^2+4q+1
       341: 2q^2+4q+1
       342: 2q^2+4q+1
       343: 3q+1
       344: q^2+4q+1
       345: q^2+4q+1
       346: q^2+4q+1
       347: q^2+4q+1
       348: q^2+4q+1
       349: q^2+4q+1
       350: q^2+4q+1
       351: q^2+4q+1
       352: 3q^2+4q+1
       353: q^2+4q+1
       354: q^2+4q+1
       355: q^2+4q+1
       356: 3q+1
       357: 2q^2+4q+1
       358: 2q^2+4q+1
       359: 2q^2+4q+1
       360: q+1
       361: q^2+2q+1
       362: 2q^2+4q+1
       363: 3q+1
       364: 3q+1
       365: 2q^2+4q+1
       366: 2q^2+4q+1
       367: 2q^2+4q+1
       368: 2q^2+4q+1
       369: 2q^2+4q+1
       370: 2q^2+4q+1
       371: 2q^2+4q+1
       372: q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: 2q^2+4q+1
       381: 2q^2+4q+1
       382: 2q^2+4q+1
       383: 2q^2+4q+1
       384: 2q^2+4q+1
       385: 2q^2+4q+1
       386: 2q^2+4q+1
       387: 2q+1
       388: q^3+4q^2+4q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: 3q^2+4q+1
       393: 3q^2+4q+1
       394: 2q+1
       395: 3q+1
       396: 2q^2+4q+1
       397: 2q^2+4q+1
       398: 2q^2+4q+1
       399: q^2+2q+1
       400: q+1
       401: 2q^2+4q+1
       402: 3q+1
       403: 3q+1
       404: 2q^2+4q+1
       405: 2q^2+4q+1
       406: 2q^2+4q+1
       407: 2q^2+4q+1
       408: 2q^2+4q+1
       409: 2q^2+4q+1
       410: 2q^2+4q+1
       411: q+1
       412: 2q^2+4q+1
       413: 2q^2+4q+1
       414: 2q^2+4q+1
       415: 2q^2+4q+1
       416: 2q^2+4q+1
       417: 2q^2+4q+1
       418: 2q^2+4q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: q^3+4q^2+4q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: 3q^2+4q+1
       432: 3q^2+4q+1
       433: 2q+1
       434: q^2+4q+1
       435: q^2+4q+1
       436: q^2+4q+1
       437: q^2+4q+1
       438: q^2+4q+1
       439: q^2+4q+1
       440: q^2+4q+1
       441: 3q+1
       442: q^2+4q+1
       443: q^2+4q+1
       444: q^2+4q+1
       445: q^2+4q+1
       446: q^2+4q+1
       447: q^2+4q+1
       448: q^2+4q+1
       449: 2q+1
       450: 3q^2+4q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: 3q^2+4q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: 3q^2+4q+1
       460: 3q^2+4q+1
       461: q+1
       462: 3q^2+4q+1
       463: 3q^2+4q+1
       464: 3q+1
       465: 3q+1
       466: q+1
       467: q^2+2q+1
       468: q^2+2q+1
       469: q+1
       470: q+1
       471: q+1
       472: 3q+1
       473: 3q+1
       474: 3q+1
       475: q^3+4q^2+4q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: q+1
       481: 3q+1
       482: 3q+1
       483: 3q+1
       484: 2q^2+4q+1
       485: 2q^2+4q+1
       486: 2q^2+4q+1
       487: q^2+2q+1
       488: q+1
       489: 2q^2+4q+1
       490: 3q+1
       491: 3q+1
       492: 3q+1
       493: 2q^2+4q+1
       494: 2q^2+4q+1
       495: 2q^2+4q+1
       496: q+1
       497: q^2+2q+1
       498: 2q^2+4q+1
       499: 3q+1
       500: 3q+1
       501: q^2+4q+1
       502: q^2+4q+1
       503: q^2+4q+1
       504: q^2+4q+1
       505: q^2+4q+1
       506: q^2+4q+1
       507: q^2+4q+1
       508: 3q+1
       509: q^2+4q+1
       510: q^2+4q+1
       511: q^2+4q+1
       512: q^2+4q+1
       513: q^2+4q+1
       514: q^2+4q+1
       515: q^2+4q+1
       516: 3q+1
       517: 3q+1
       518: 2q^2+4q+1
       519: q+1
       520: q+1
       521: q^2+2q+1
       522: q^2+2q+1
       523: 1
       524: 3q+1
       525: 3q+1
       526: q+1
       527: 2q^2+4q+1
       528: 2q^2+4q+1
       529: 2q^2+4q+1
       530: q+1
       531: q^2+2q+1
       532: 2q^2+4q+1
       533: q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       543: 2q^2+4q+1
       544: 2q^2+4q+1
       545: 2q^2+4q+1
       546: 2q^2+4q+1
       547: 2q^2+4q+1
       548: 2q^2+4q+1
       549: 2q^2+4q+1
       550: q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 2q+1
       559: 3q^2+4q+1
       560: 2q+1
       561: 2q+1
       562: 2q+1
       563: 3q+1
       564: 3q+1
       565: 2q^2+4q+1
       566: q^2+2q+1
       567: q^2+2q+1
       568: q+1
       569: q+1
       570: 1
       571: 3q+1
       572: 3q+1
       573: q+1
       574: 2q^2+4q+1
       575: 2q^2+4q+1
       576: 2q^2+4q+1
       577: q^2+2q+1
       578: q+1
       579: 2q^2+4q+1
       580: q+1
       581: q+1
       582: 2q^2+4q+1
       583: 2q^2+4q+1
       584: 2q^2+4q+1
       585: 2q^2+4q+1
       586: 2q^2+4q+1
       587: 2q^2+4q+1
       588: 2q^2+4q+1
       589: q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 2q+1
       606: 3q^2+4q+1
       607: 2q+1
       608: 2q+1
       609: 2q+1
       610: 3q+1
       611: q^2+4q+1
       612: q^2+4q+1
       613: q^2+4q+1
       614: q+1
       615: q+1
       616: q^2+4q+1
       617: 3q+1
       618: 3q+1
       619: q^2+4q+1
       620: q^2+4q+1
       621: q^2+4q+1
       622: q^2+4q+1
       623: q^2+4q+1
       624: q^2+4q+1
       625: q^2+4q+1
       626: 1
       627: 2q+1
       628: 2q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: 2q+1
       635: 2q+1
       636: 2q+1
       637: 2q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: q+1
       642: 3q^2+4q+1
       643: q+1
       644: q+1
       645: q+1
       646: 3q^2+4q+1
       647: 3q^2+4q+1
       648: q+1
       649: 3q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       656: q+1
       657: 3q+1
       658: 3q+1
       659: q+1
       660: q^2+2q+1
       661: q^2+2q+1
       662: q+1
       663: q+1
       664: q+1
       665: 3q+1
       666: 3q+1
       667: 3q+1
       668: 2q^2+4q+1
       669: q^2+2q+1
       670: q^2+2q+1
       671: q+1
       672: q+1
       673: 1
       674: 3q+1
       675: 3q+1
       676: 3q+1
       677: 3q+1
       678: 2q^2+4q+1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: q^2+2q+1
       683: 1
       684: 3q+1
       685: 3q+1
       686: 3q+1
       687: q^2+4q+1
       688: q^2+4q+1
       689: q^2+4q+1
       690: q+1
       691: q+1
       692: q^2+4q+1
       693: 3q+1
       694: 3q+1
       695: q^2+4q+1
       696: q^2+4q+1
       697: q^2+4q+1
       698: q^2+4q+1
       699: q^2+4q+1
       700: q^2+4q+1
       701: q^2+4q+1
       702: 1
       703: 3q+1
       704: 3q+1
       705: 1
       706: q+1
       707: q^2+2q+1
       708: 1
       709: 1
       710: 1
       711: 3q+1
       712: q+1
       713: q+1
       714: 2q^2+4q+1
       715: q+1
       716: q+1
       717: q^2+2q+1
       718: q^2+2q+1
       719: 1
       720: q+1
       721: q+1
       722: q+1
       723: 2q+1
       724: 2q+1
       725: 2q+1
       726: q+1
       728: 2q+1
       729: q+1
       730: q+1
       731: q+1
       732: 2q^2+4q+1
       733: 2q^2+4q+1
       734: 2q^2+4q+1
       735: q+1
       736: q^2+2q+1
       737: 2q^2+4q+1
       738: q+1
       739: q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: 2q+1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: 2q+1
       754: 2q+1
       755: 3q+1
       756: 3q+1
       757: 1
       758: q^2+2q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: 3q+1
       764: q+1
       765: q+1
       766: 2q^2+4q+1
       767: q^2+2q+1
       768: q^2+2q+1
       769: q+1
       770: q+1
       771: 1
       772: q+1
       773: q+1
       774: q+1
       775: 2q^2+4q+1
       776: 2q^2+4q+1
       777: 2q^2+4q+1
       778: q^2+2q+1
       779: q+1
       780: 2q^2+4q+1
       781: q+1
       782: q+1
       783: q+1
       784: 2q+1
       785: 2q+1
       786: 2q+1
       788: q+1
       789: 2q+1
       790: q+1
       791: q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: q+1
       800: 2q+1
       801: 2q+1
       802: 2q+1
       803: 2q+1
       804: 2q+1
       805: 2q+1
       806: 2q+1
       807: 3q+1
       808: 3q+1
       809: q^2+4q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: 3q+1
       816: 3q+1
       817: 1
       818: q^2+4q+1
       819: q^2+4q+1
       820: q^2+4q+1
       821: q+1
       822: q+1
       823: q^2+4q+1
       824: 1
       825: 1
       826: 2q+1
       827: 2q+1
       828: 2q+1
       829: 2q+1
       830: 2q+1
       831: 2q+1
       832: 2q+1
       833: 1
       834: 2q+1
       835: 2q+1
       836: 2q+1
       837: 2q+1
       838: 2q+1
       839: 2q+1
       840: 2q+1
       841: 1
       842: q+1
       843: q+1
       844: q+1
       845: q+1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       850: 3q^2+4q+1
       851: q+1
       852: q+1
       853: q+1
       854: q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       859: q+1
       860: q+1
       861: 3q+1
       862: q+1
       863: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: 3q+1
       870: 3q+1
       871: 1
       872: q^2+2q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: 3q+1
       878: 3q+1
       879: 3q+1
       880: 1
       881: q+1
       882: q^2+2q+1
       883: 1
       884: 1
       885: 1
       886: 3q+1
       887: 3q+1
       888: 3q+1
       889: q^2+4q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: 3q+1
       896: 3q+1
       897: 1
       898: q^2+4q+1
       899: q^2+4q+1
       900: q^2+4q+1
       901: q+1
       902: q+1
       903: q^2+4q+1
       904: 1
       905: 1
       906: 3q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: q+1
       915: q+1
       916: 1
       917: q+1
       918: q^2+2q+1
       919: 1
       920: 1
       921: 1
       922: q+1
       923: q+1
       924: q+1
       925: 2q+1
       926: q+1
       927: q+1
       931: q+1
       932: q+1
       933: q+1
       934: q+1
       935: 2q^2+4q+1
       936: q+1
       937: q+1
       938: q^2+2q+1
       939: q^2+2q+1
       940: 1
       941: q+1
       942: q+1
       943: q+1
       944: 2q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       949: 2q+1
       950: q+1
       951: q+1
       952: 2q+1
       953: 2q+1
       954: 2q+1
       955: 2q+1
       956: 2q+1
       957: 2q+1
       958: 2q+1
       959: 1
       960: 3q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: q+1
       969: q+1
       970: 1
       971: q^2+2q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       976: q+1
       977: q+1
       978: q+1
       979: 2q^2+4q+1
       980: q^2+2q+1
       981: q^2+2q+1
       982: q+1
       983: q+1
       984: 1
       985: q+1
       986: q+1
       987: q+1
       988: q+1
       989: 2q+1
       992: q+1
       993: q+1
       995: q+1
       996: q+1
       997: q+1
       998: 2q+1
       999: 2q+1
      1000: 2q+1
      1002: q+1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1006: 2q+1
      1007: 2q+1
      1008: 2q+1
      1009: 2q+1
      1010: 2q+1
      1011: 2q+1
      1012: 2q+1
      1013: 1
      1014: 3q+1
      1015: 3q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: 3q+1
      1023: 1
      1024: 1
      1025: q^2+4q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 2q+1
      1035: 2q+1
      1036: 2q+1
      1037: q+1
      1039: 2q+1
      1040: 1
      1041: 1
      1042: 1
      1043: 2q+1
      1044: 2q+1
      1045: 2q+1
      1047: q+1
      1048: 2q+1
      1049: 1
      1050: 1
      1051: q+1
      1052: q+1
      1053: q+1
      1054: q+1
      1055: q+1
      1056: q+1
      1057: q+1
      1058: 1
      1059: q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: q+1
      1065: q+1
      1066: q+1
      1067: q+1
      1068: q+1
      1070: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: 3q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 3q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 3q+1
      1095: 3q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1102: 3q+1
      1103: 1
      1104: 1
      1105: q^2+4q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: q+1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: q+1
      1129: q+1
      1131: q+1
      1136: q+1
      1137: q+1
      1138: q+1
      1139: 1
      1140: q+1
      1141: q^2+2q+1
      1142: 1
      1143: 1
      1144: 1
      1145: q+1
      1146: q+1
      1147: q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1154: q+1
      1155: q+1
      1156: 1
      1157: 2q+1
      1158: 2q+1
      1159: 2q+1
      1160: q+1
      1162: 2q+1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: q+1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: q+1
      1181: q+1
      1182: 1
      1183: q^2+2q+1
      1184: q+1
      1185: 1
      1186: 1
      1187: 1
      1188: q+1
      1189: q+1
      1190: q+1
      1193: q+1
      1197: q+1
      1198: q+1
      1199: q+1
      1200: 2q+1
      1203: q+1
      1204: q+1
      1206: q+1
      1207: q+1
      1208: 1
      1209: 2q+1
      1210: 2q+1
      1211: 2q+1
      1213: q+1
      1214: 2q+1
      1215: 1
      1216: 1
      1217: 3q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 2q+1
      1237: q+1
      1238: q+1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 2q+1
      1249: q+1
      1250: q+1
      1252: 1
      1253: 1
      1254: 1
      1255: q+1
      1256: q+1
      1257: q+1
      1260: q+1
      1261: 1
      1262: 1
      1263: q+1
      1264: q+1
      1265: q+1
      1266: q+1
      1267: q+1
      1268: q+1
      1269: q+1
      1270: 1
      1271: q+1
      1274: q+1
      1275: q+1
      1276: q+1
      1278: q+1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 3q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: q+1
      1330: q+1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: q+1
      1339: q+1
      1341: q+1
      1346: q+1
      1347: 1
      1348: 1
      1349: 2q+1
      1350: q+1
      1351: q+1
      1355: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: q+1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: q+1
      1385: q+1
      1386: q+1
      1389: q+1
      1393: q+1
      1394: 1
      1395: 1
      1396: 2q+1
      1399: q+1
      1400: q+1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: q+1
      1427: 1
      1428: 1
      1429: 1
      1432: q+1
      1436: 1
      1437: 1
      1438: 1
      1439: q+1
      1445: 1
      1446: 1
      1447: 1
      1448: q+1
      1449: q+1
      1450: q+1
      1453: q+1
      1454: 1
      1455: 1
      1458: q+1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: q+1
      1516: 1
      1517: 1
      1519: q+1
      1524: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1547: q+1
      1555: 1
      1556: 1
      1559: q+1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1584: 1
      1592: 1
      1593: 1
      1600: 1
      1601: 1
      1602: 1
      1603: q+1
      1609: 1
      1610: 1
      1614: 1
      1617: 1
      1620: 1
      1621: 1
      1622: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1634: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1654: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1684: 1
      1692: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1714: 1
      1722: 1
      1723: 1
      1730: 1
      1736: 1
      1739: 1
      1740: 1
      1741: 1
      1743: 1
      1750: 1
      1768: 1
      1788: 1
      1808: 1
      1820: 1

1821:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: 3q^3+6q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: q^3+6q^2+4q+1
         5: q^3+6q^2+4q+1
         6: 3q^3+6q^2+4q+1
         7: q^3+4q^2+4q+1
         8: 3q^3+6q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: 3q^3+6q^2+4q+1
        11: q^3+6q^2+4q+1
        12: q^3+6q^2+4q+1
        13: q^3+6q^2+4q+1
        14: q^3+6q^2+4q+1
        15: q^3+6q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^3+6q^2+4q+1
        19: 6q^2+4q+1
        20: 3q^3+6q^2+4q+1
        21: q^3+4q^2+4q+1
        22: q^3+4q^2+4q+1
        23: q^3+4q^2+4q+1
        24: q^3+4q^2+4q+1
        25: 3q^3+6q^2+4q+1
        26: q^3+4q^2+4q+1
        27: 3q^3+6q^2+4q+1
        28: q^3+6q^2+4q+1
        29: q^3+6q^2+4q+1
        30: q^3+6q^2+4q+1
        31: q^3+6q^2+4q+1
        32: 6q^2+4q+1
        33: q^3+6q^2+4q+1
        34: 4q^2+4q+1
        35: q^3+6q^2+4q+1
        36: q^3+6q^2+4q+1
        37: q^3+6q^2+4q+1
        38: 4q^2+4q+1
        39: q^3+6q^2+4q+1
        40: q^3+6q^2+4q+1
        41: 4q^2+4q+1
        42: q^3+6q^2+4q+1
        43: q^3+6q^2+4q+1
        44: q^3+6q^2+4q+1
        45: q^3+6q^2+4q+1
        46: 4q^2+4q+1
        47: 6q^2+4q+1
        48: 6q^2+4q+1
        49: 6q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+4q^2+4q+1
        52: q^3+4q^2+4q+1
        53: q^3+4q^2+4q+1
        54: 2q^2+4q+1
        55: 2q^2+4q+1
        56: 3q^2+4q+1
        57: 3q^3+6q^2+4q+1
        58: q^3+4q^2+4q+1
        59: q^3+4q^2+4q+1
        60: q^3+4q^2+4q+1
        61: q^3+4q^2+4q+1
        62: q^3+6q^2+4q+1
        63: 4q^2+4q+1
        64: q^3+6q^2+4q+1
        65: q^3+6q^2+4q+1
        66: 4q^2+4q+1
        67: q^3+6q^2+4q+1
        68: 6q^2+4q+1
        69: 6q^2+4q+1
        70: 6q^2+4q+1
        71: q^3+6q^2+4q+1
        72: 4q^2+4q+1
        73: 4q^2+4q+1
        74: 2q^2+4q+1
        75: q^3+4q^2+4q+1
        76: q^3+6q^2+4q+1
        77: 2q^2+2q+1
        78: q^3+6q^2+4q+1
        79: 4q^2+4q+1
        80: 4q^2+4q+1
        81: q^3+6q^2+4q+1
        82: q^3+6q^2+4q+1
        83: 4q^2+4q+1
        84: q^3+6q^2+4q+1
        85: 4q^2+4q+1
        86: 4q^2+4q+1
        87: q^3+4q^2+4q+1
        88: 2q^2+4q+1
        89: q^3+6q^2+4q+1
        90: 2q^2+2q+1
        91: q^3+6q^2+4q+1
        92: q^3+6q^2+4q+1
        93: q^3+6q^2+4q+1
        94: 4q^2+4q+1
        95: 4q^2+4q+1
        96: 4q^2+4q+1
        97: 6q^2+4q+1
        98: 4q^2+4q+1
        99: 6q^2+4q+1
       100: 6q^2+4q+1
       101: 6q^2+4q+1
       102: 4q^2+4q+1
       103: 4q^2+4q+1
       104: 3q^2+4q+1
       105: 2q^2+4q+1
       106: 2q^2+4q+1
       107: q^3+4q^2+4q+1
       108: 2q^2+4q+1
       109: 2q^2+4q+1
       110: q^2+4q+1
       111: 3q^2+4q+1
       112: q^3+4q^2+4q+1
       113: q^3+4q^2+4q+1
       114: q^3+4q^2+4q+1
       115: q^3+4q^2+4q+1
       116: 2q^2+4q+1
       117: 2q^2+4q+1
       118: 3q^2+4q+1
       119: q^3+6q^2+4q+1
       120: 4q^2+4q+1
       121: 4q^2+4q+1
       122: q^3+4q^2+4q+1
       123: 2q^2+4q+1
       124: q^3+6q^2+4q+1
       125: 4q^2+4q+1
       126: 4q^2+4q+1
       127: 2q^2+4q+1
       128: q^3+4q^2+4q+1
       129: 6q^2+4q+1
       130: 4q^2+4q+1
       131: 6q^2+4q+1
       132: 6q^2+4q+1
       133: 6q^2+4q+1
       134: 2q^2+4q+1
       135: q^3+4q^2+4q+1
       136: 4q^2+4q+1
       137: 4q^2+4q+1
       138: q^2+4q+1
       139: 2q^2+4q+1
       140: q^2+4q+1
       141: q^3+6q^2+4q+1
       142: 2q^2+2q+1
       143: 2q^2+2q+1
       144: 2q^2+4q+1
       145: q^3+4q^2+4q+1
       146: 4q^2+4q+1
       147: q^2+2q+1
       148: 4q^2+4q+1
       149: q^3+6q^2+4q+1
       150: 2q^2+2q+1
       151: q^3+6q^2+4q+1
       152: 4q^2+4q+1
       153: 4q^2+4q+1
       154: 4q^2+4q+1
       155: q^3+4q^2+4q+1
       156: 2q^2+4q+1
       157: 4q^2+4q+1
       158: 4q^2+4q+1
       159: 2q^2+4q+1
       160: q^2+4q+1
       161: q^2+4q+1
       162: q^3+6q^2+4q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+4q^2+4q+1
       166: 2q^2+4q+1
       167: q^3+6q^2+4q+1
       168: 2q^2+2q+1
       169: q^3+6q^2+4q+1
       170: 4q^2+4q+1
       171: q^2+2q+1
       172: 4q^2+4q+1
       173: 4q^2+4q+1
       174: 4q^2+4q+1
       175: 4q^2+4q+1
       176: 6q^2+4q+1
       177: 4q^2+4q+1
       178: 4q^2+4q+1
       179: 2q^2+4q+1
       180: 2q^2+4q+1
       181: 6q^2+4q+1
       182: q^2+q+1
       183: 6q^2+4q+1
       184: 4q^2+4q+1
       185: 4q^2+4q+1
       186: 4q^2+4q+1
       187: 4q^2+4q+1
       188: 3q^2+4q+1
       189: 3q^2+4q+1
       190: q^2+4q+1
       191: 2q^2+4q+1
       192: 2q^2+4q+1
       193: 2q^2+4q+1
       194: 2q^2+4q+1
       195: q^2+4q+1
       196: q^2+4q+1
       197: 3q^2+4q+1
       198: 3q^2+4q+1
       199: 2q^2+4q+1
       200: 2q^2+4q+1
       201: q^3+4q^2+4q+1
       202: 2q^2+4q+1
       203: 2q^2+4q+1
       204: q^2+4q+1
       205: 3q^2+4q+1
       206: q^3+4q^2+4q+1
       207: 2q^2+4q+1
       208: 4q^2+4q+1
       209: 4q^2+4q+1
       210: 2q^2+4q+1
       211: q^2+4q+1
       212: q^2+4q+1
       213: 2q^2+4q+1
       214: q^3+4q^2+4q+1
       215: 4q^2+4q+1
       216: 4q^2+4q+1
       217: q^2+4q+1
       218: 2q^2+4q+1
       219: q^2+4q+1
       220: 6q^2+4q+1
       221: 4q^2+4q+1
       222: 4q^2+4q+1
       223: 2q^2+4q+1
       224: 2q^2+4q+1
       225: 6q^2+4q+1
       226: q^2+q+1
       227: 6q^2+4q+1
       228: q^2+4q+1
       229: q^2+4q+1
       230: 2q^2+4q+1
       231: 4q^2+4q+1
       232: q^2+4q+1
       233: 2q^2+4q+1
       234: 4q+1
       235: q^2+4q+1
       236: 2q^2+4q+1
       237: q^3+4q^2+4q+1
       238: 2q^2+2q+1
       239: 2q^2+2q+1
       240: 2q+1
       241: q^2+2q+1
       242: q^2+4q+1
       243: 4q^2+4q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: 2q^2+4q+1
       247: q^2+2q+1
       248: q^3+6q^2+4q+1
       249: 2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q^2+4q+1
       252: q^3+4q^2+4q+1
       253: 4q^2+4q+1
       254: q^2+2q+1
       255: 4q^2+4q+1
       256: 4q^2+4q+1
       257: 4q^2+4q+1
       258: q^2+4q+1
       259: 2q^2+4q+1
       260: q^2+4q+1
       261: 4q^2+4q+1
       262: 2q^2+4q+1
       263: q^2+4q+1
       264: 4q+1
       265: q^2+4q+1
       266: q^3+4q^2+4q+1
       267: 2q^2+4q+1
       268: 2q^2+2q+1
       269: 2q^2+2q+1
       270: q^2+2q+1
       271: 2q+1
       272: q^2+4q+1
       273: q^3+6q^2+4q+1
       274: 2q^2+2q+1
       275: 2q^2+2q+1
       276: q^3+4q^2+4q+1
       277: 2q^2+4q+1
       278: 4q^2+4q+1
       279: q^2+2q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: 2q^2+4q+1
       283: 4q^2+4q+1
       284: q^2+2q+1
       285: 4q^2+4q+1
       286: 4q^2+4q+1
       287: 4q^2+4q+1
       288: 2q^2+4q+1
       289: 2q^2+4q+1
       290: 4q^2+4q+1
       291: 4q^2+4q+1
       292: q^2+4q+1
       293: q^2+4q+1
       294: 4q+1
       295: 6q^2+4q+1
       296: q^2+q+1
       297: q^2+q+1
       298: 2q^2+4q+1
       299: 2q^2+4q+1
       300: 4q^2+4q+1
       301: q+1
       302: 4q^2+4q+1
       303: 4q^2+4q+1
       304: q+1
       305: 4q^2+4q+1
       306: 3q^2+4q+1
       307: 3q^2+4q+1
       308: 3q^2+4q+1
       309: 3q^2+4q+1
       310: q^2+4q+1
       311: q^2+4q+1
       312: 2q^2+4q+1
       313: 2q+1
       314: 2q+1
       315: 2q^2+4q+1
       316: q^2+4q+1
       317: q^2+4q+1
       319: 3q^2+4q+1
       320: q^2+4q+1
       321: 2q^2+4q+1
       322: 2q^2+4q+1
       323: 2q^2+4q+1
       324: 2q^2+4q+1
       325: q^2+4q+1
       326: q^2+4q+1
       327: 3q^2+4q+1
       328: q^2+4q+1
       329: 2q^2+4q+1
       330: q^2+4q+1
       331: 4q^2+4q+1
       332: 2q^2+4q+1
       333: q^2+4q+1
       334: 4q+1
       335: q^2+4q+1
       336: q^2+4q+1
       337: q^2+4q+1
       338: 2q^2+4q+1
       339: 4q^2+4q+1
       340: q^2+4q+1
       341: 2q^2+4q+1
       342: 4q+1
       343: q^2+4q+1
       344: 2q^2+4q+1
       345: 2q^2+4q+1
       346: 4q^2+4q+1
       347: 4q^2+4q+1
       348: q^2+4q+1
       349: q^2+4q+1
       350: 4q+1
       351: 6q^2+4q+1
       352: q^2+q+1
       353: q^2+q+1
       354: 2q^2+4q+1
       355: 2q^2+4q+1
       356: q^2+4q+1
       357: 4q+1
       358: q^2+4q+1
       359: 2q^2+4q+1
       360: q^2+4q+1
       361: 2q^2+4q+1
       362: 4q+1
       363: 4q+1
       364: q^2+4q+1
       365: q^2+4q+1
       366: 2q+1
       367: q^2+2q+1
       368: 2q^2+2q+1
       369: 2q+1
       370: q^2+2q+1
       371: 2q+1
       372: q^2+4q+1
       373: 2q^2+4q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       377: 2q+1
       378: q+1
       379: 2q+1
       380: 2q^2+4q+1
       381: q^3+4q^2+4q+1
       382: 2q^2+2q+1
       383: 2q^2+2q+1
       384: 2q+1
       385: q^2+2q+1
       386: q^2+4q+1
       387: 4q^2+4q+1
       388: q^2+2q+1
       389: q^2+2q+1
       390: 2q^2+4q+1
       391: q^2+2q+1
       392: 4q^2+4q+1
       393: q+1
       394: 4q^2+4q+1
       395: q^2+4q+1
       396: 4q+1
       397: 2q^2+4q+1
       398: q^2+4q+1
       399: 2q^2+4q+1
       400: q^2+4q+1
       401: 4q+1
       402: 4q+1
       403: q^2+4q+1
       404: q^2+4q+1
       405: q^2+2q+1
       406: 2q+1
       407: 2q^2+2q+1
       408: q^2+2q+1
       409: 2q+1
       410: 2q+1
       411: q^2+4q+1
       412: q^3+4q^2+4q+1
       413: 2q^2+4q+1
       414: 2q^2+2q+1
       415: 2q^2+2q+1
       416: q^2+2q+1
       417: 2q+1
       418: q^2+4q+1
       419: q^2+2q+1
       420: 2q^2+4q+1
       421: q^2+2q+1
       422: q^2+2q+1
       423: q+1
       424: 2q+1
       425: 2q+1
       426: 4q^2+4q+1
       427: q^2+2q+1
       428: q^2+2q+1
       429: q^2+2q+1
       430: 2q^2+4q+1
       431: 4q^2+4q+1
       432: q+1
       433: 4q^2+4q+1
       434: 4q+1
       435: q^2+4q+1
       436: q^2+4q+1
       437: 4q^2+4q+1
       438: q^2+4q+1
       439: q^2+4q+1
       440: 4q+1
       441: 4q+1
       442: 2q^2+4q+1
       443: 2q^2+4q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q+1
       447: q+1
       448: 4q+1
       449: 4q^2+4q+1
       450: q+1
       451: q+1
       452: 2q^2+4q+1
       453: q^2+2q+1
       454: 4q^2+4q+1
       455: q+1
       456: q+1
       457: q^2+2q+1
       458: 2q^2+4q+1
       459: 3q^2+4q+1
       460: q+1
       461: 3q^2+4q+1
       462: 3q^2+4q+1
       463: 3q^2+4q+1
       465: q^2+4q+1
       466: q^2+4q+1
       467: 2q+1
       468: 2q+1
       469: 2q+1
       470: 2q+1
       471: q^2+4q+1
       473: 3q^2+4q+1
       474: q^2+4q+1
       475: q^2+4q+1
       476: 2q^2+4q+1
       477: 2q+1
       478: 2q+1
       479: 2q^2+4q+1
       480: q^2+4q+1
       481: q^2+4q+1
       483: q^2+4q+1
       484: 4q+1
       485: 2q^2+4q+1
       486: q^2+4q+1
       487: 2q^2+4q+1
       488: q^2+4q+1
       489: 4q+1
       490: 4q+1
       491: q^2+4q+1
       492: q^2+4q+1
       493: 4q+1
       494: q^2+4q+1
       495: 2q^2+4q+1
       496: q^2+4q+1
       497: 2q^2+4q+1
       498: 4q+1
       499: 4q+1
       500: q^2+4q+1
       501: 4q+1
       502: q^2+4q+1
       503: q^2+4q+1
       504: 4q^2+4q+1
       505: q^2+4q+1
       506: q^2+4q+1
       507: 4q+1
       508: 4q+1
       509: 2q^2+4q+1
       510: 2q^2+4q+1
       511: q^2+q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       515: 4q+1
       516: q^2+4q+1
       517: 4q+1
       518: 4q+1
       519: q^2+4q+1
       520: q+1
       521: 2q+1
       522: 2q^2+4q+1
       523: 4q+1
       524: 4q+1
       526: q^2+4q+1
       527: 2q+1
       528: 2q+1
       529: q^2+2q+1
       530: 2q+1
       531: q^2+2q+1
       532: 2q+1
       533: 2q+1
       534: q^2+4q+1
       535: 2q+1
       536: 2q+1
       537: q+1
       538: q^2+2q+1
       539: 2q+1
       540: q+1
       541: q+1
       542: 2q+1
       543: q^2+4q+1
       544: 2q+1
       545: q^2+2q+1
       546: 2q^2+2q+1
       547: 2q+1
       548: q^2+2q+1
       549: 2q+1
       550: q^2+4q+1
       551: 2q^2+4q+1
       552: q^2+2q+1
       553: q^2+2q+1
       554: q^2+2q+1
       555: 2q+1
       556: q+1
       557: 2q+1
       558: 4q^2+4q+1
       559: q+1
       560: q+1
       561: 2q^2+4q+1
       562: q^2+2q+1
       563: q^2+4q+1
       564: 4q+1
       565: 4q+1
       566: 2q^2+4q+1
       567: 2q+1
       568: q+1
       569: q^2+4q+1
       570: 4q+1
       571: 4q+1
       573: q^2+4q+1
       574: 2q+1
       575: q^2+2q+1
       576: 2q+1
       577: q^2+2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q^2+4q+1
       582: q^2+4q+1
       583: q^2+2q+1
       584: 2q+1
       585: 2q^2+2q+1
       586: q^2+2q+1
       587: 2q+1
       588: 2q+1
       589: q^2+4q+1
       590: 2q+1
       591: q+1
       592: 2q+1
       593: q^2+2q+1
       594: q+1
       595: 2q+1
       596: q+1
       597: 2q+1
       598: q^2+2q+1
       599: 2q^2+4q+1
       600: q^2+2q+1
       601: q^2+2q+1
       602: q+1
       603: 2q+1
       604: 2q+1
       605: 4q^2+4q+1
       606: q+1
       607: q+1
       608: q^2+2q+1
       609: 2q^2+4q+1
       610: 4q+1
       611: 4q+1
       612: q^2+4q+1
       613: q^2+4q+1
       614: q^2+4q+1
       615: q^2+4q+1
       616: 4q+1
       617: 4q+1
       618: 4q+1
       619: 4q+1
       620: q+1
       621: q+1
       622: q^2+q+1
       623: q+1
       624: q+1
       625: q+1
       626: 4q+1
       627: 2q^2+4q+1
       628: q^2+2q+1
       629: q+1
       630: q+1
       631: q+1
       632: 1
       633: 2q+1
       634: q^2+2q+1
       635: 2q^2+4q+1
       636: q+1
       637: q+1
       638: 1
       639: q+1
       640: 2q+1
       641: 3q^2+4q+1
       642: q+1
       643: q+1
       644: q^2+2q+1
       645: q^2+2q+1
       646: 3q^2+4q+1
       647: q+1
       648: 3q^2+4q+1
       650: q^2+4q+1
       651: 2q+1
       652: 2q+1
       653: q+1
       654: 2q+1
       655: 2q+1
       658: q^2+4q+1
       659: q^2+4q+1
       660: 2q+1
       661: 2q+1
       662: 2q+1
       663: 2q+1
       664: q^2+4q+1
       666: q^2+4q+1
       667: 4q+1
       668: 4q+1
       669: 2q^2+4q+1
       670: 2q+1
       671: q+1
       672: q^2+4q+1
       673: 4q+1
       674: 4q+1
       676: q^2+4q+1
       677: 4q+1
       678: 4q+1
       679: q^2+4q+1
       680: q+1
       681: 2q+1
       682: 2q^2+4q+1
       683: 4q+1
       684: 4q+1
       686: 4q+1
       687: 4q+1
       688: q^2+4q+1
       689: q^2+4q+1
       690: q^2+4q+1
       691: q^2+4q+1
       692: 4q+1
       693: 4q+1
       694: 4q+1
       695: 4q+1
       696: q+1
       697: q+1
       698: q^2+q+1
       699: q+1
       700: q+1
       701: q+1
       702: 4q+1
       704: 4q+1
       705: 4q+1
       706: q+1
       707: 2q+1
       708: 2q+1
       709: q+1
       710: 4q+1
       712: q^2+4q+1
       713: 2q+1
       714: 2q+1
       715: 2q+1
       716: 1
       717: q+1
       718: q^2+2q+1
       719: 2q+1
       720: 2q+1
       722: 2q+1
       723: q+1
       724: 2q+1
       725: q+1
       726: 2q+1
       727: q+1
       728: q+1
       729: q+1
       730: 2q+1
       731: q^2+4q+1
       732: 2q+1
       733: 2q+1
       734: q^2+2q+1
       735: 2q+1
       736: q^2+2q+1
       737: 2q+1
       738: 2q+1
       739: q^2+4q+1
       740: 2q+1
       741: 2q+1
       742: q+1
       743: q^2+2q+1
       744: 2q+1
       745: q+1
       746: q+1
       747: 2q+1
       748: 2q^2+4q+1
       749: q^2+2q+1
       750: q+1
       751: q+1
       752: q+1
       753: 1
       754: 2q+1
       756: 4q+1
       757: 4q+1
       758: 2q+1
       759: q+1
       760: q+1
       761: 2q+1
       762: 4q+1
       764: q^2+4q+1
       765: 2q+1
       766: 2q+1
       767: q^2+2q+1
       768: q+1
       769: 1
       770: 2q+1
       771: 2q+1
       772: 2q+1
       774: q^2+4q+1
       775: 2q+1
       776: q^2+2q+1
       777: 2q+1
       778: q^2+2q+1
       779: 2q+1
       780: 2q+1
       781: 2q+1
       782: q^2+4q+1
       783: 2q+1
       784: q+1
       785: q+1
       786: 2q+1
       787: q+1
       788: 2q+1
       789: q+1
       790: q+1
       791: 2q+1
       792: 2q+1
       793: q+1
       794: 2q+1
       795: q^2+2q+1
       796: q+1
       797: 2q+1
       798: q+1
       799: 2q+1
       800: q^2+2q+1
       801: 2q^2+4q+1
       802: q+1
       803: q+1
       804: 1
       805: q+1
       806: 2q+1
       807: 4q+1
       808: 4q+1
       809: 4q+1
       810: q^2+4q+1
       811: q+1
       812: q+1
       813: q^2+4q+1
       814: 4q+1
       815: 4q+1
       817: 4q+1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: 4q+1
       826: 2q+1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 2q+1
       834: 2q+1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: 2q+1
       842: q^2+2q+1
       843: q^2+2q+1
       844: q+1
       845: q+1
       846: 1
       847: 1
       848: q+1
       849: 3q^2+4q+1
       850: q+1
       851: q+1
       852: q^2+2q+1
       853: q^2+2q+1
       855: 2q+1
       856: 2q+1
       857: q+1
       858: q+1
       862: q^2+4q+1
       863: 2q+1
       864: 2q+1
       865: q+1
       866: 2q+1
       867: 2q+1
       870: 4q+1
       871: 4q+1
       872: 2q+1
       873: q+1
       874: q+1
       875: 2q+1
       876: 4q+1
       879: 4q+1
       880: 4q+1
       881: q+1
       882: 2q+1
       883: 2q+1
       884: q+1
       885: 4q+1
       887: 4q+1
       888: 4q+1
       889: 4q+1
       890: q^2+4q+1
       891: q+1
       892: q+1
       893: q^2+4q+1
       894: 4q+1
       895: 4q+1
       897: 4q+1
       898: q+1
       899: q+1
       900: q+1
       901: q+1
       902: q+1
       903: q+1
       904: q+1
       905: 4q+1
       907: 4q+1
       908: q+1
       909: 2q+1
       910: 1
       911: 2q+1
       912: q+1
       915: 2q+1
       916: 2q+1
       917: 1
       918: q+1
       919: q+1
       920: 1
       921: 2q+1
       923: 2q+1
       924: q+1
       925: q+1
       926: 2q+1
       927: 1
       929: q+1
       930: q+1
       931: q+1
       933: q^2+4q+1
       934: 2q+1
       935: 2q+1
       936: 2q+1
       937: 1
       938: q+1
       939: q^2+2q+1
       940: 2q+1
       941: 2q+1
       943: 2q+1
       944: q+1
       945: 2q+1
       946: q+1
       947: 2q+1
       948: q+1
       949: q+1
       950: q+1
       951: 2q+1
       952: 2q+1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       959: 2q+1
       961: 4q+1
       962: 2q+1
       963: q+1
       964: 1
       965: q+1
       966: 2q+1
       969: 2q+1
       970: 2q+1
       971: q+1
       972: 1
       973: 1
       974: q+1
       975: 2q+1
       977: q^2+4q+1
       978: 2q+1
       979: 2q+1
       980: q^2+2q+1
       981: q+1
       982: 1
       983: 2q+1
       984: 2q+1
       985: 2q+1
       987: 2q+1
       988: q+1
       989: q+1
       990: q+1
       992: 1
       993: 2q+1
       994: q+1
       995: q+1
       997: 2q+1
       998: q+1
       999: q+1
      1000: 2q+1
      1001: q+1
      1002: 2q+1
      1003: q+1
      1004: q+1
      1005: 2q+1
      1006: 2q+1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1013: 2q+1
      1015: 4q+1
      1016: 4q+1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1021: 4q+1
      1023: 4q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 1
      1028: 1
      1029: q+1
      1030: q+1
      1031: q+1
      1033: 2q+1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 2q+1
      1042: 2q+1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: 2q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: q+1
      1059: q^2+2q+1
      1060: q^2+2q+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: 1
      1065: q+1
      1068: q+1
      1069: q+1
      1072: 2q+1
      1073: 2q+1
      1074: q+1
      1075: q+1
      1079: 4q+1
      1080: 2q+1
      1081: q+1
      1082: 1
      1083: q+1
      1084: 2q+1
      1087: 4q+1
      1088: q+1
      1089: 2q+1
      1090: 1
      1091: 2q+1
      1092: q+1
      1095: 4q+1
      1096: 4q+1
      1097: q+1
      1098: q+1
      1099: q+1
      1100: q+1
      1101: 4q+1
      1103: 4q+1
      1104: q+1
      1105: q+1
      1106: q+1
      1107: 1
      1108: 1
      1109: q+1
      1110: q+1
      1111: q+1
      1114: q+1
      1115: 2q+1
      1116: 1
      1117: 1
      1121: 2q+1
      1122: 1
      1123: q+1
      1124: 1
      1125: q+1
      1126: 1
      1129: q+1
      1130: q+1
      1131: 1
      1134: 1
      1135: q+1
      1138: 2q+1
      1139: 2q+1
      1140: 1
      1141: q+1
      1142: q+1
      1143: 1
      1144: 2q+1
      1146: 2q+1
      1147: q+1
      1148: q+1
      1149: 2q+1
      1150: 1
      1152: q+1
      1153: q+1
      1154: q+1
      1156: 2q+1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: 1
      1162: 1
      1163: 1
      1164: 2q+1
      1166: 2q+1
      1167: q+1
      1168: 1
      1169: 1
      1173: 2q+1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: q+1
      1181: 2q+1
      1182: 2q+1
      1183: q+1
      1184: 1
      1185: 1
      1186: q+1
      1187: 2q+1
      1190: q+1
      1191: q+1
      1193: 1
      1194: 1
      1196: q+1
      1198: 2q+1
      1199: q+1
      1200: q+1
      1201: q+1
      1203: 1
      1204: 2q+1
      1205: q+1
      1206: q+1
      1208: 2q+1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1213: q+1
      1214: 1
      1215: 1
      1216: 2q+1
      1218: 4q+1
      1219: q+1
      1220: q+1
      1221: 1
      1222: q+1
      1223: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: q+1
      1234: 2q+1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1244: 2q+1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: 1
      1252: 1
      1254: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q+1
      1263: q+1
      1264: 1
      1265: 1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: q+1
      1272: q+1
      1276: q+1
      1277: q+1
      1280: 2q+1
      1281: q+1
      1282: 1
      1283: 1
      1287: q+1
      1288: 2q+1
      1289: 1
      1290: 1
      1294: 4q+1
      1295: q+1
      1296: q+1
      1297: 1
      1298: q+1
      1299: q+1
      1302: q+1
      1303: q+1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: q+1
      1312: 1
      1313: 1
      1316: 1
      1317: q+1
      1318: 1
      1319: 1
      1323: q+1
      1324: 1
      1328: 1
      1331: 2q+1
      1332: 1
      1333: q+1
      1334: 1
      1335: q+1
      1336: 1
      1339: q+1
      1340: q+1
      1341: 1
      1344: 1
      1345: q+1
      1347: 2q+1
      1348: 1
      1349: 1
      1350: q+1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1359: 1
      1360: 1
      1363: q+1
      1364: 1
      1365: 1
      1366: 1
      1370: 2q+1
      1371: q+1
      1372: 1
      1373: 1
      1374: 1
      1375: q+1
      1378: q+1
      1380: 1
      1382: 1
      1386: q+1
      1387: q+1
      1389: 1
      1390: 1
      1392: q+1
      1394: 2q+1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: q+1
      1401: 1
      1402: 1
      1405: q+1
      1406: q+1
      1407: 1
      1408: 1
      1412: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1437: q+1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q+1
      1459: q+1
      1463: 1
      1464: 1
      1468: 1
      1469: 1
      1472: q+1
      1473: q+1
      1474: 1
      1475: 1
      1479: q+1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1502: 1
      1503: q+1
      1504: 1
      1505: 1
      1509: q+1
      1510: 1
      1514: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1526: 1
      1530: 1
      1531: 1
      1534: q+1
      1535: 1
      1536: 1
      1537: 1
      1542: 1
      1548: q+1
      1550: 1
      1552: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1566: 1
      1567: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1582: 1
      1585: 1
      1587: 1
      1589: 1
      1593: 1
      1594: 1
      1599: 1
      1601: q+1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1609: 1
      1615: 1
      1618: 1
      1622: 1
      1623: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1635: 1
      1644: 1
      1645: 1
      1648: 1
      1655: 1
      1656: 1
      1660: 1
      1665: 1
      1669: 1
      1670: 1
      1679: 1
      1685: 1
      1687: 1
      1689: 1
      1693: 1
      1697: 1
      1698: 1
      1701: 1
      1709: 1
      1715: 1
      1723: 1
      1724: 1
      1729: 1
      1737: 1
      1741: 1
      1742: 1
      1751: 1
      1759: 1
      1769: 1
      1781: 1
      1789: 1
      1809: 1
      1821: 1

1822:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: 3q^3+6q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: q^3+6q^2+4q+1
         5: q^3+6q^2+4q+1
         6: q^3+4q^2+4q+1
         7: 3q^3+6q^2+4q+1
         8: 3q^3+6q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: 3q^3+6q^2+4q+1
        11: q^3+6q^2+4q+1
        12: q^3+6q^2+4q+1
        13: q^3+6q^2+4q+1
        14: q^3+6q^2+4q+1
        15: q^3+6q^2+4q+1
        16: q^3+6q^2+4q+1
        17: q^3+6q^2+4q+1
        18: q^3+6q^2+4q+1
        19: 6q^2+4q+1
        20: q^3+4q^2+4q+1
        21: q^3+4q^2+4q+1
        22: 3q^3+6q^2+4q+1
        23: q^3+6q^2+4q+1
        24: q^3+6q^2+4q+1
        25: q^3+4q^2+4q+1
        26: 3q^3+6q^2+4q+1
        27: 3q^3+6q^2+4q+1
        28: q^3+6q^2+4q+1
        29: q^3+6q^2+4q+1
        30: q^3+6q^2+4q+1
        31: q^3+6q^2+4q+1
        32: 6q^2+4q+1
        33: 4q^2+4q+1
        34: q^3+6q^2+4q+1
        35: q^3+6q^2+4q+1
        36: q^3+6q^2+4q+1
        37: q^3+4q^2+4q+1
        38: 4q^2+4q+1
        39: q^3+6q^2+4q+1
        40: 4q^2+4q+1
        41: q^3+6q^2+4q+1
        42: q^3+6q^2+4q+1
        43: q^3+6q^2+4q+1
        44: q^3+4q^2+4q+1
        45: q^3+6q^2+4q+1
        46: 4q^2+4q+1
        47: 6q^2+4q+1
        48: 6q^2+4q+1
        49: 6q^2+4q+1
        50: 2q^2+2q+1
        51: 2q^2+2q+1
        52: q^3+4q^2+4q+1
        53: q^3+4q^2+4q+1
        54: q^3+6q^2+4q+1
        55: q^3+6q^2+4q+1
        56: 6q^2+4q+1
        57: q^3+4q^2+4q+1
        58: q^3+4q^2+4q+1
        59: 3q^3+6q^2+4q+1
        60: q^3+6q^2+4q+1
        61: q^3+6q^2+4q+1
        62: 4q^2+4q+1
        63: q^3+6q^2+4q+1
        64: q^3+6q^2+4q+1
        65: 4q^2+4q+1
        66: q^3+6q^2+4q+1
        67: q^3+6q^2+4q+1
        68: 6q^2+4q+1
        69: 6q^2+4q+1
        70: 6q^2+4q+1
        71: 4q^2+4q+1
        72: 4q^2+4q+1
        73: q^3+6q^2+4q+1
        74: 4q^2+4q+1
        75: q^3+6q^2+4q+1
        76: 2q^2+4q+1
        77: q^3+4q^2+4q+1
        78: q^3+4q^2+4q+1
        79: 4q^2+4q+1
        80: 2q^2+4q+1
        81: q^3+6q^2+4q+1
        82: q^3+4q^2+4q+1
        83: 4q^2+4q+1
        84: 4q^2+4q+1
        85: 4q^2+4q+1
        86: q^3+6q^2+4q+1
        87: q^3+6q^2+4q+1
        88: 4q^2+4q+1
        89: 2q^2+4q+1
        90: q^3+4q^2+4q+1
        91: q^3+4q^2+4q+1
        92: q^3+6q^2+4q+1
        93: q^3+4q^2+4q+1
        94: 4q^2+4q+1
        95: 2q^2+4q+1
        96: 4q^2+4q+1
        97: 4q^2+4q+1
        98: 6q^2+4q+1
        99: 6q^2+4q+1
       100: 6q^2+4q+1
       101: 3q^2+4q+1
       102: 4q^2+4q+1
       103: 4q^2+4q+1
       104: q^2+q+1
       105: 2q^2+2q+1
       106: 2q^2+2q+1
       107: q^3+4q^2+4q+1
       108: 4q^2+4q+1
       109: 4q^2+4q+1
       110: 6q^2+4q+1
       111: 6q^2+4q+1
       112: 2q^2+2q+1
       113: 2q^2+2q+1
       114: q^3+4q^2+4q+1
       115: q^3+4q^2+4q+1
       116: q^3+6q^2+4q+1
       117: q^3+6q^2+4q+1
       118: 6q^2+4q+1
       119: 4q^2+4q+1
       120: 4q^2+4q+1
       121: q^3+6q^2+4q+1
       122: q^3+6q^2+4q+1
       123: 4q^2+4q+1
       124: 4q^2+4q+1
       125: 4q^2+4q+1
       126: q^3+6q^2+4q+1
       127: 4q^2+4q+1
       128: q^3+6q^2+4q+1
       129: 4q^2+4q+1
       130: 6q^2+4q+1
       131: 6q^2+4q+1
       132: 6q^2+4q+1
       133: 3q^2+4q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: 4q^2+4q+1
       137: 2q^2+4q+1
       138: 4q^2+4q+1
       139: q^3+6q^2+4q+1
       140: 4q^2+4q+1
       141: 2q^2+4q+1
       142: 2q^2+4q+1
       143: q^3+4q^2+4q+1
       144: 2q^2+4q+1
       145: q^3+4q^2+4q+1
       146: q^2+4q+1
       147: 2q^2+4q+1
       148: 2q^2+4q+1
       149: 2q^2+4q+1
       150: q^3+4q^2+4q+1
       151: q^3+4q^2+4q+1
       152: 4q^2+4q+1
       153: 2q^2+4q+1
       154: 4q^2+4q+1
       155: 2q^2+2q+1
       156: q^2+2q+1
       157: 4q^2+4q+1
       158: 2q^2+4q+1
       159: q^3+6q^2+4q+1
       160: 4q^2+4q+1
       161: 4q^2+4q+1
       162: 2q^2+4q+1
       163: 2q^2+4q+1
       164: q^3+4q^2+4q+1
       165: q^3+4q^2+4q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: q^3+4q^2+4q+1
       169: q^3+4q^2+4q+1
       170: q^2+4q+1
       171: 2q^2+4q+1
       172: 2q^2+4q+1
       173: 4q^2+4q+1
       174: 2q^2+4q+1
       175: 4q^2+4q+1
       176: 4q^2+4q+1
       177: 4q^2+4q+1
       178: 6q^2+4q+1
       179: 4q^2+4q+1
       180: 4q^2+4q+1
       181: q^2+4q+1
       182: 3q^2+4q+1
       183: 3q^2+4q+1
       184: 4q^2+4q+1
       185: q^2+4q+1
       186: 4q^2+4q+1
       187: q^2+4q+1
       188: 3q^2+4q+1
       189: q^2+q+1
       190: q^2+q+1
       191: 2q^2+2q+1
       192: 2q^2+2q+1
       193: 4q^2+4q+1
       194: 4q^2+4q+1
       195: 4q^2+4q+1
       196: 6q^2+4q+1
       197: 3q^2+4q+1
       198: q^2+q+1
       199: 2q^2+2q+1
       200: 2q^2+2q+1
       201: q^3+4q^2+4q+1
       202: 4q^2+4q+1
       203: 4q^2+4q+1
       204: 6q^2+4q+1
       205: 6q^2+4q+1
       206: 2q^2+2q+1
       207: q^2+2q+1
       208: 4q^2+4q+1
       209: 2q^2+4q+1
       210: q^3+6q^2+4q+1
       211: 4q^2+4q+1
       212: 4q^2+4q+1
       213: q^2+2q+1
       214: 2q^2+2q+1
       215: 4q^2+4q+1
       216: 2q^2+4q+1
       217: 4q^2+4q+1
       218: q^3+6q^2+4q+1
       219: 4q^2+4q+1
       220: 4q^2+4q+1
       221: 4q^2+4q+1
       222: 6q^2+4q+1
       223: 4q^2+4q+1
       224: 4q^2+4q+1
       225: q^2+4q+1
       226: 3q^2+4q+1
       227: 3q^2+4q+1
       228: q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q^2+4q+1
       232: q^2+4q+1
       233: 2q^2+4q+1
       234: 4q^2+4q+1
       235: 4q^2+4q+1
       236: 2q+1
       237: q^2+2q+1
       238: 2q^2+4q+1
       239: 2q^2+4q+1
       240: 2q^2+4q+1
       241: q^3+4q^2+4q+1
       242: 2q^2+4q+1
       243: q^2+4q+1
       244: q^2+4q+1
       245: 2q^2+4q+1
       246: 2q^2+4q+1
       247: q^2+2q+1
       248: 2q^2+4q+1
       249: 2q^2+4q+1
       250: q^3+4q^2+4q+1
       251: 2q^2+4q+1
       252: q^3+4q^2+4q+1
       253: q^2+4q+1
       254: 2q^2+4q+1
       255: 2q^2+4q+1
       256: 4q^2+4q+1
       257: q^2+4q+1
       258: q+1
       259: 2q^2+2q+1
       260: q^2+2q+1
       261: 2q^2+4q+1
       262: 2q^2+4q+1
       263: q^2+4q+1
       264: 4q^2+4q+1
       265: 4q^2+4q+1
       266: q^2+2q+1
       267: 2q+1
       268: 2q^2+4q+1
       269: 2q^2+4q+1
       270: q^3+4q^2+4q+1
       271: 2q^2+4q+1
       272: 2q^2+4q+1
       273: 2q^2+4q+1
       274: 2q^2+4q+1
       275: q^3+4q^2+4q+1
       276: q^3+4q^2+4q+1
       277: 2q^2+4q+1
       278: q^2+4q+1
       279: q^2+4q+1
       280: 2q^2+4q+1
       281: q^2+2q+1
       282: 2q^2+4q+1
       283: q^2+4q+1
       284: 2q^2+4q+1
       285: 2q^2+4q+1
       286: 4q^2+4q+1
       287: q^2+4q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: 4q^2+4q+1
       291: q^2+4q+1
       292: 4q^2+4q+1
       293: 4q^2+4q+1
       294: 3q^2+4q+1
       295: q^2+4q+1
       296: q^2+4q+1
       297: 3q^2+4q+1
       298: q^2+4q+1
       299: q^2+4q+1
       300: 4q+1
       301: q^2+4q+1
       302: q^2+4q+1
       303: 4q+1
       304: q^2+4q+1
       305: q^2+4q+1
       306: 3q^2+4q+1
       307: 4q+1
       308: 3q^2+4q+1
       310: q^2+q+1
       311: q^2+q+1
       312: 2q^2+2q+1
       313: q^2+2q+1
       314: q^2+2q+1
       315: 2q^2+2q+1
       316: 4q^2+4q+1
       317: q^2+4q+1
       318: 3q^2+4q+1
       319: q^2+q+1
       320: q^2+q+1
       321: 2q^2+2q+1
       322: 2q^2+2q+1
       323: 4q^2+4q+1
       324: 4q^2+4q+1
       325: 4q^2+4q+1
       326: 6q^2+4q+1
       327: 3q^2+4q+1
       328: q+1
       329: 2q^2+2q+1
       330: q^2+2q+1
       331: 2q^2+4q+1
       332: 2q^2+4q+1
       333: q^2+4q+1
       334: 4q^2+4q+1
       335: 4q^2+4q+1
       336: q+1
       337: q^2+2q+1
       338: 2q^2+2q+1
       339: 2q^2+4q+1
       340: q^2+4q+1
       341: 2q^2+4q+1
       342: 4q^2+4q+1
       343: 4q^2+4q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: 4q^2+4q+1
       347: q^2+4q+1
       348: 4q^2+4q+1
       349: 4q^2+4q+1
       350: 3q^2+4q+1
       351: q^2+4q+1
       352: q^2+4q+1
       353: 3q^2+4q+1
       354: q^2+4q+1
       355: q^2+4q+1
       356: q+1
       357: q+1
       358: 2q+1
       359: q^2+2q+1
       360: q^2+4q+1
       361: 2q^2+4q+1
       362: q^2+4q+1
       363: 4q^2+4q+1
       364: q^2+4q+1
       365: q+1
       366: 2q+1
       367: q^2+2q+1
       368: 2q^2+4q+1
       369: q^2+4q+1
       370: 2q^2+4q+1
       371: 2q^2+4q+1
       372: 2q^2+4q+1
       373: 2q+1
       374: q+1
       375: q^2+4q+1
       376: 2q+1
       377: 2q^2+4q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: 2q+1
       381: q^2+2q+1
       382: 2q^2+4q+1
       383: 2q^2+4q+1
       384: 2q^2+4q+1
       385: q^3+4q^2+4q+1
       386: 2q^2+4q+1
       387: q^2+4q+1
       388: q^2+4q+1
       389: 2q^2+4q+1
       390: 2q^2+4q+1
       391: q^2+2q+1
       392: 4q+1
       393: q^2+4q+1
       394: q^2+4q+1
       395: q+1
       396: q+1
       397: q^2+2q+1
       398: 2q+1
       399: 2q^2+4q+1
       400: q^2+4q+1
       401: q^2+4q+1
       402: 4q^2+4q+1
       403: q^2+4q+1
       404: q+1
       405: q^2+2q+1
       406: 2q+1
       407: 2q^2+4q+1
       408: 2q^2+4q+1
       409: q^2+4q+1
       410: 2q^2+4q+1
       411: 2q^2+4q+1
       412: q^2+2q+1
       413: 2q+1
       414: 2q^2+4q+1
       415: 2q^2+4q+1
       416: q^3+4q^2+4q+1
       417: 2q^2+4q+1
       418: 2q^2+4q+1
       419: q+1
       420: 2q+1
       421: q^2+4q+1
       422: 2q+1
       423: q^2+2q+1
       424: 2q^2+4q+1
       425: q^2+2q+1
       426: q^2+4q+1
       427: q^2+4q+1
       428: 2q^2+4q+1
       429: q^2+2q+1
       430: 2q^2+4q+1
       431: 4q+1
       432: q^2+4q+1
       433: q^2+4q+1
       434: q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: q^2+4q+1
       438: 4q+1
       439: 4q+1
       440: 3q^2+4q+1
       441: 3q^2+4q+1
       442: 2q+1
       443: 2q+1
       444: q^2+4q+1
       445: q^2+4q+1
       446: q^2+4q+1
       447: q^2+4q+1
       448: 4q+1
       449: 4q+1
       450: 4q+1
       451: q^2+4q+1
       452: q^2+4q+1
       453: 2q+1
       454: 4q+1
       455: 4q+1
       456: q^2+4q+1
       457: 2q+1
       458: q^2+4q+1
       459: 4q+1
       460: 4q+1
       461: 4q+1
       462: 3q^2+4q+1
       463: 4q+1
       466: q^2+q+1
       467: q+1
       468: q+1
       469: q^2+2q+1
       470: q^2+2q+1
       471: q^2+4q+1
       472: q^2+4q+1
       474: q^2+q+1
       475: q^2+q+1
       476: 2q^2+2q+1
       477: q^2+2q+1
       478: q^2+2q+1
       479: 2q^2+2q+1
       480: 4q^2+4q+1
       481: q^2+4q+1
       482: 3q^2+4q+1
       483: q+1
       484: q+1
       485: q^2+2q+1
       486: 2q+1
       487: 2q^2+4q+1
       488: q^2+4q+1
       489: q^2+4q+1
       490: 4q^2+4q+1
       491: q^2+4q+1
       492: q+1
       493: q+1
       494: 2q+1
       495: q^2+2q+1
       496: q^2+4q+1
       497: 2q^2+4q+1
       498: q^2+4q+1
       499: 4q^2+4q+1
       500: q^2+4q+1
       501: q+1
       502: q^2+2q+1
       503: q^2+2q+1
       504: q^2+4q+1
       505: 4q+1
       506: 4q+1
       507: 3q^2+4q+1
       508: 3q^2+4q+1
       509: 2q+1
       510: 2q+1
       511: q^2+4q+1
       512: q^2+4q+1
       513: q^2+4q+1
       514: q^2+4q+1
       515: 4q+1
       517: q+1
       518: q+1
       519: 2q+1
       520: q+1
       521: 2q+1
       522: q^2+2q+1
       523: q^2+4q+1
       524: 4q+1
       525: q^2+4q+1
       526: q+1
       527: q+1
       528: 2q+1
       529: q^2+2q+1
       530: q^2+4q+1
       531: 2q^2+4q+1
       532: q^2+4q+1
       533: 2q^2+4q+1
       534: q^2+4q+1
       535: 1
       536: 2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: q^2+2q+1
       542: q^2+2q+1
       543: q+1
       544: 2q+1
       545: q^2+2q+1
       546: 2q^2+4q+1
       547: q^2+4q+1
       548: 2q^2+4q+1
       549: 2q^2+4q+1
       550: 2q^2+4q+1
       551: 2q+1
       552: q+1
       553: q^2+4q+1
       554: 2q+1
       555: 2q^2+4q+1
       556: q^2+2q+1
       557: q^2+2q+1
       558: 4q+1
       559: 4q+1
       560: q^2+4q+1
       561: q^2+4q+1
       562: 2q+1
       564: q+1
       565: q+1
       566: q^2+2q+1
       567: 2q+1
       568: q+1
       569: 2q+1
       570: q^2+4q+1
       571: 4q+1
       572: q^2+4q+1
       573: q+1
       574: q+1
       575: q^2+2q+1
       576: 2q+1
       577: 2q^2+4q+1
       578: q^2+4q+1
       579: q^2+4q+1
       580: 2q^2+4q+1
       581: q^2+4q+1
       582: q+1
       583: q^2+2q+1
       584: 2q+1
       585: 2q^2+4q+1
       586: 2q^2+4q+1
       587: q^2+4q+1
       588: 2q^2+4q+1
       589: 2q^2+4q+1
       590: 1
       591: q+1
       592: 2q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: q^2+2q+1
       597: q^2+2q+1
       598: q+1
       599: 2q+1
       600: q^2+4q+1
       601: 2q+1
       602: q^2+2q+1
       603: 2q^2+4q+1
       604: q^2+2q+1
       605: 4q+1
       606: 4q+1
       607: q^2+4q+1
       608: 2q+1
       609: q^2+4q+1
       610: q+1
       611: q+1
       612: 2q+1
       613: 2q+1
       614: 4q+1
       615: 4q+1
       616: 4q+1
       617: 3q^2+4q+1
       618: 4q+1
       619: q+1
       620: 2q+1
       621: 2q+1
       622: q^2+4q+1
       623: 4q+1
       624: 4q+1
       625: 4q+1
       626: 4q+1
       627: 2q+1
       628: q+1
       629: 4q+1
       630: 2q+1
       631: q^2+4q+1
       632: 2q+1
       633: 2q+1
       634: q+1
       635: 2q+1
       636: 4q+1
       637: 2q+1
       638: 2q+1
       639: q^2+4q+1
       640: 2q+1
       641: 4q+1
       642: 4q+1
       643: 4q+1
       644: 2q+1
       645: 2q+1
       646: 4q+1
       647: 4q+1
       648: 4q+1
       651: q+1
       652: q+1
       653: q+1
       654: 2q+1
       655: 2q+1
       656: q^2+4q+1
       659: q^2+q+1
       660: q+1
       661: q+1
       662: q^2+2q+1
       663: q^2+2q+1
       664: q^2+4q+1
       665: q^2+4q+1
       667: q+1
       668: q+1
       669: q^2+2q+1
       670: 2q+1
       671: q+1
       672: 2q+1
       673: q^2+4q+1
       674: 4q+1
       675: q^2+4q+1
       677: q+1
       678: q+1
       679: 2q+1
       680: q+1
       681: 2q+1
       682: q^2+2q+1
       683: q^2+4q+1
       684: 4q+1
       685: q^2+4q+1
       686: q+1
       687: q+1
       688: 2q+1
       689: 2q+1
       690: 4q+1
       691: 4q+1
       692: 4q+1
       693: 3q^2+4q+1
       694: 4q+1
       695: q+1
       696: 2q+1
       697: 2q+1
       698: q^2+4q+1
       699: 4q+1
       700: 4q+1
       701: 4q+1
       702: 4q+1
       705: q+1
       706: 1
       707: q+1
       708: 2q+1
       709: q+1
       710: 4q+1
       711: 4q+1
       713: q+1
       714: q+1
       715: 2q+1
       716: q+1
       717: 2q+1
       718: q^2+2q+1
       719: q^2+4q+1
       720: 2q+1
       721: q^2+4q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: 2q+1
       727: q+1
       728: q+1
       729: q^2+2q+1
       730: 2q+1
       731: q+1
       732: q+1
       733: 2q+1
       734: q^2+2q+1
       735: q^2+4q+1
       736: 2q^2+4q+1
       737: q^2+4q+1
       738: 2q^2+4q+1
       739: q^2+4q+1
       740: 1
       741: 2q+1
       742: q+1
       743: 2q+1
       744: 2q+1
       745: q+1
       746: q^2+2q+1
       747: q^2+2q+1
       748: 2q+1
       749: q+1
       750: 4q+1
       751: 2q+1
       752: q^2+4q+1
       753: 2q+1
       754: 2q+1
       757: q+1
       758: q+1
       759: 1
       760: q+1
       761: 2q+1
       762: 4q+1
       763: 4q+1
       765: q+1
       766: q+1
       767: q^2+2q+1
       768: 2q+1
       769: q+1
       770: 2q+1
       771: q^2+4q+1
       772: 2q+1
       773: q^2+4q+1
       774: q+1
       775: q+1
       776: q^2+2q+1
       777: 2q+1
       778: 2q^2+4q+1
       779: q^2+4q+1
       780: q^2+4q+1
       781: 2q^2+4q+1
       782: q^2+4q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: 2q+1
       789: q+1
       790: q^2+2q+1
       791: 2q+1
       792: 1
       793: q+1
       794: 2q+1
       795: 2q+1
       796: q+1
       797: 2q+1
       798: q^2+2q+1
       799: q^2+2q+1
       800: q+1
       801: 2q+1
       802: 4q+1
       803: 2q+1
       804: 2q+1
       805: q^2+4q+1
       806: 2q+1
       808: q+1
       809: q+1
       810: 2q+1
       811: q+1
       812: q+1
       813: 2q+1
       814: 4q+1
       815: 4q+1
       816: 4q+1
       817: q+1
       818: q+1
       819: 2q+1
       820: 2q+1
       821: 4q+1
       822: 4q+1
       823: 4q+1
       824: 4q+1
       825: 4q+1
       826: 1
       827: 2q+1
       828: q+1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       834: 1
       835: q+1
       836: 2q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: 2q+1
       841: 2q+1
       842: q+1
       843: q+1
       844: 4q+1
       845: q+1
       846: 2q+1
       847: 2q+1
       848: q+1
       849: 4q+1
       850: 4q+1
       851: 4q+1
       852: 2q+1
       853: 2q+1
       857: q+1
       858: q+1
       859: 2q+1
       860: 2q+1
       863: q+1
       864: q+1
       865: q+1
       866: 2q+1
       867: 2q+1
       868: q^2+4q+1
       871: q+1
       872: q+1
       873: 1
       874: q+1
       875: 2q+1
       876: 4q+1
       877: 4q+1
       880: q+1
       881: 1
       882: q+1
       883: 2q+1
       884: q+1
       885: 4q+1
       886: 4q+1
       888: q+1
       889: q+1
       890: 2q+1
       891: q+1
       892: q+1
       893: 2q+1
       894: 4q+1
       895: 4q+1
       896: 4q+1
       897: q+1
       898: q+1
       899: 2q+1
       900: 2q+1
       901: 4q+1
       902: 4q+1
       903: 4q+1
       904: 4q+1
       905: 4q+1
       908: 1
       909: q+1
       910: 1
       911: 2q+1
       912: q+1
       913: 4q+1
       916: q+1
       917: 1
       918: q+1
       919: 2q+1
       920: q+1
       921: 2q+1
       922: 2q+1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: q+1
       931: q+1
       932: 2q+1
       934: q+1
       935: q+1
       936: 2q+1
       937: q+1
       938: 2q+1
       939: q^2+2q+1
       940: q^2+4q+1
       941: 2q+1
       942: q^2+4q+1
       943: 1
       944: 1
       945: q+1
       946: 1
       947: 2q+1
       948: q+1
       949: q+1
       950: q^2+2q+1
       951: 2q+1
       952: 1
       953: 2q+1
       954: q+1
       955: 2q+1
       956: 2q+1
       957: q+1
       958: 2q+1
       959: 2q+1
       962: q+1
       963: 1
       964: 1
       965: q+1
       966: 2q+1
       967: 4q+1
       970: q+1
       971: q+1
       972: 1
       973: q+1
       974: 2q+1
       975: 2q+1
       976: 2q+1
       978: q+1
       979: q+1
       980: q^2+2q+1
       981: 2q+1
       982: q+1
       983: 2q+1
       984: q^2+4q+1
       985: 2q+1
       986: q^2+4q+1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: q+1
       995: q+1
       996: 2q+1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: q+1
      1002: 2q+1
      1003: q+1
      1004: q^2+2q+1
      1005: 2q+1
      1006: 1
      1007: q+1
      1008: 2q+1
      1009: 2q+1
      1010: q+1
      1011: 2q+1
      1012: 2q+1
      1013: 2q+1
      1016: q+1
      1017: 1
      1018: 1
      1019: q+1
      1020: q+1
      1021: 4q+1
      1022: 4q+1
      1024: q+1
      1025: q+1
      1026: 2q+1
      1027: q+1
      1028: q+1
      1029: 2q+1
      1030: 4q+1
      1031: q+1
      1032: 4q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: 2q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: 2q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: 2q+1
      1048: q+1
      1049: 2q+1
      1050: 2q+1
      1051: 1
      1052: q+1
      1053: q+1
      1054: q+1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: q+1
      1061: 4q+1
      1062: q+1
      1063: 2q+1
      1064: 2q+1
      1065: q+1
      1069: q+1
      1070: q+1
      1074: q+1
      1075: q+1
      1076: 2q+1
      1077: 2q+1
      1080: q+1
      1081: 1
      1082: 1
      1083: q+1
      1084: 2q+1
      1085: 4q+1
      1088: 1
      1089: q+1
      1090: 1
      1091: 2q+1
      1092: q+1
      1093: 4q+1
      1096: q+1
      1097: 1
      1098: 1
      1099: q+1
      1100: q+1
      1101: 4q+1
      1102: 4q+1
      1104: q+1
      1105: q+1
      1106: 2q+1
      1107: q+1
      1108: q+1
      1109: 2q+1
      1110: 4q+1
      1111: q+1
      1112: 4q+1
      1116: 1
      1117: 1
      1118: 2q+1
      1119: q+1
      1122: 1
      1123: q+1
      1124: 1
      1125: q+1
      1126: 1
      1127: 2q+1
      1130: 1
      1131: 1
      1134: 1
      1135: q+1
      1136: q+1
      1139: q+1
      1140: 1
      1141: q+1
      1142: 2q+1
      1143: q+1
      1144: 2q+1
      1145: 2q+1
      1147: 1
      1148: 1
      1149: q+1
      1150: 1
      1152: 1
      1153: q+1
      1154: q+1
      1155: 2q+1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: 2q+1
      1161: q+1
      1162: q+1
      1163: 2q+1
      1164: 2q+1
      1168: 1
      1169: 1
      1170: q+1
      1171: 2q+1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: q+1
      1179: 2q+1
      1182: q+1
      1183: q+1
      1184: 1
      1185: q+1
      1186: 2q+1
      1187: 2q+1
      1188: 2q+1
      1191: 1
      1193: 1
      1194: 1
      1196: q+1
      1197: q+1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: q+1
      1205: q+1
      1206: q+1
      1207: 2q+1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: q+1
      1213: 2q+1
      1214: q+1
      1215: 2q+1
      1216: 2q+1
      1219: 1
      1220: 1
      1221: 1
      1222: q+1
      1223: q+1
      1224: 4q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: q+1
      1231: q+1
      1232: q+1
      1233: q+1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: q+1
      1242: 1
      1243: 2q+1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: q+1
      1252: 1
      1253: 2q+1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: q+1
      1263: 1
      1264: q+1
      1265: q+1
      1266: q+1
      1267: 1
      1268: 1
      1269: q+1
      1270: q+1
      1273: q+1
      1277: q+1
      1278: q+1
      1282: 1
      1283: 1
      1284: q+1
      1285: 2q+1
      1289: 1
      1290: 1
      1291: 2q+1
      1292: q+1
      1295: 1
      1296: 1
      1297: 1
      1298: q+1
      1299: q+1
      1300: 4q+1
      1303: q+1
      1304: 1
      1305: 1
      1306: q+1
      1307: q+1
      1308: q+1
      1309: q+1
      1313: 1
      1314: 1
      1318: 1
      1319: 1
      1320: q+1
      1321: 1
      1324: 1
      1328: 1
      1329: q+1
      1332: 1
      1333: q+1
      1334: 1
      1335: q+1
      1336: 1
      1337: 2q+1
      1340: 1
      1341: 1
      1344: 1
      1345: q+1
      1346: q+1
      1348: 1
      1349: 1
      1350: q+1
      1351: 1
      1353: 1
      1354: q+1
      1355: 1
      1356: 2q+1
      1360: 1
      1361: 1
      1365: 1
      1366: 1
      1367: 1
      1368: q+1
      1371: q+1
      1372: 1
      1373: 1
      1374: 1
      1375: q+1
      1376: 2q+1
      1380: 1
      1382: 1
      1384: q+1
      1387: 1
      1389: 1
      1390: 1
      1392: q+1
      1393: q+1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: q+1
      1401: q+1
      1402: 1
      1403: 2q+1
      1407: 1
      1408: 1
      1409: q+1
      1410: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: q+1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1446: q+1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q+1
      1455: q+1
      1460: q+1
      1464: 1
      1465: 1
      1469: 1
      1470: 1
      1474: 1
      1475: 1
      1476: q+1
      1477: q+1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: q+1
      1488: 1
      1492: 1
      1493: 1
      1500: 1
      1504: 1
      1505: 1
      1506: q+1
      1507: 1
      1510: 1
      1514: 1
      1515: q+1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1527: 1
      1531: 1
      1532: 1
      1536: 1
      1537: 1
      1538: 1
      1539: q+1
      1545: 1
      1550: 1
      1552: 1
      1554: q+1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1567: 1
      1568: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1578: 1
      1582: 1
      1583: 1
      1587: 1
      1589: 1
      1591: 1
      1594: 1
      1599: 1
      1600: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1609: 1
      1610: q+1
      1616: 1
      1619: 1
      1623: 1
      1624: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1636: 1
      1645: 1
      1646: 1
      1653: 1
      1656: 1
      1660: 1
      1661: 1
      1666: 1
      1670: 1
      1671: 1
      1682: 1
      1687: 1
      1689: 1
      1691: 1
      1694: 1
      1698: 1
      1699: 1
      1706: 1
      1712: 1
      1721: 1
      1724: 1
      1729: 1
      1730: 1
      1738: 1
      1742: 1
      1743: 1
      1752: 1
      1764: 1
      1770: 1
      1784: 1
      1790: 1
      1815: 1
      1822: 1

1823:    0: q^4+2q^2+q+1
         1: q^4+2q^2+q+1
         2: q^4+2q^2+q+1
         3: q^4+2q^2+q+1
         4: q^4+2q^2+q+1
         5: q^2+q+1
         6: q^4+2q^2+q+1
         7: q^4+2q^2+q+1
         8: q^4+2q^2+q+1
         9: q^4+2q^2+q+1
        10: q^4+2q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^4+2q^2+q+1
        14: q^4+2q^2+q+1
        15: q^4+2q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^4+2q^2+q+1
        21: q^4+2q^2+q+1
        22: q^4+2q^2+q+1
        23: q+1
        24: q^2+q+1
        25: q^4+2q^2+q+1
        26: q^4+2q^2+q+1
        27: q^4+2q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^4+2q^2+q+1
        34: q^4+2q^2+q+1
        35: q^4+2q^2+q+1
        36: q^4+2q^2+q+1
        37: q^4+2q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q+1
        51: q^2+q+1
        52: q^4+2q^2+q+1
        53: q^4+2q^2+q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q^4+2q^2+q+1
        58: q^4+2q^2+q+1
        59: q^4+2q^2+q+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^4+2q^2+q+1
        72: q^4+2q^2+q+1
        73: q^4+2q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q^4+2q^2+q+1
        77: q^4+2q^2+q+1
        78: q^4+2q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q+1
        88: q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q^2+q+1
       107: q^4+2q^2+q+1
       108: q+1
       109: q^2+q+1
       110: q+1
       111: q+1
       112: q+1
       113: q^2+q+1
       114: q^4+2q^2+q+1
       115: q^4+2q^2+q+1
       116: q+1
       117: q^2+q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: 1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q^2+q+1
       136: q^4+2q^2+q+1
       137: q^4+2q^2+q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q^4+2q^2+q+1
       142: q^4+2q^2+q+1
       143: q^4+2q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q+1
       160: q+1
       161: q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q+1
       180: q+1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^2+q+1
       193: q+1
       194: q^2+q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q^2+q+1
       201: q^4+2q^2+q+1
       202: q+1
       203: q^2+q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: 1
       214: q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: 1
       218: q^2+q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+q+1
       231: q^4+2q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+q+1
       238: q^4+2q^2+q+1
       239: q^4+2q^2+q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: 1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q^2+q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q+1
       293: q+1
       294: q+1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q^2+q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q^2+q+1
       323: q+1
       324: q^2+q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+q+1
       339: q^2+q+1
       340: 1
       341: q^2+q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q^2+q+1
       368: q^4+2q^2+q+1
       369: q+1
       370: q^2+q+1
       371: q+1
       372: q+1
       373: q+1
       374: 1
       375: q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       380: 1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+q+1
       384: 1
       385: q^2+q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q^2+q+1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       420: q+1
       421: q+1
       422: q+1
       424: q+1
       426: q+1
       427: q+1
       428: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q^2+q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q+1
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: 1
       478: 1
       479: q^2+q+1
       480: q+1
       481: q+1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q^2+q+1
       496: 1
       497: q^2+q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: 1
       521: 1
       522: q^2+q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q^2+q+1
       530: q+1
       531: q^2+q+1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+q+1
       546: q^2+q+1
       547: 1
       548: q^2+q+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: q+1
       554: q+1
       555: 1
       556: 1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: 1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       592: q+1
       593: q+1
       595: q+1
       599: 1
       600: q+1
       601: q+1
       603: 1
       605: q+1
       606: q+1
       607: q+1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q^2+q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q+1
       628: 1
       629: q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       635: q+1
       636: q+1
       637: q+1
       639: q+1
       641: q+1
       642: q+1
       643: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q^2+q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: q+1
       706: 1
       707: 1
       708: 1
       709: 1
       710: q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       716: 1
       717: 1
       718: q^2+q+1
       719: q+1
       720: q+1
       721: q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q^2+q+1
       735: 1
       736: q^2+q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: q+1
       751: q+1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: q+1
       758: 1
       761: 1
       762: q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q+1
       768: 1
       770: q+1
       771: q+1
       772: q+1
       773: q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       786: q+1
       788: q+1
       794: 1
       795: q+1
       797: 1
       801: 1
       802: q+1
       803: q+1
       805: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: 1
       813: q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 1
       836: q+1
       837: q+1
       839: q+1
       843: 1
       844: q+1
       845: q+1
       847: 1
       849: q+1
       850: q+1
       851: q+1
       853: 1
       854: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: q+1
       914: q+1
       915: q+1
       916: q+1
       917: 1
       918: 1
       919: 1
       920: 1
       921: q+1
       922: q+1
       923: 1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q^2+q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: 1
       966: 1
       967: q+1
       968: q+1
       969: q+1
       970: q+1
       971: 1
       974: 1
       975: q+1
       976: q+1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: q+1
      1000: 1
      1002: 1
      1008: 1
      1009: q+1
      1011: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1017: 1
      1020: 1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 1
      1029: q+1
      1030: q+1
      1031: q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: q+1
      1047: q+1
      1053: 1
      1054: q+1
      1056: 1
      1060: 1
      1061: q+1
      1062: q+1
      1064: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: q+1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: q+1
      1121: q+1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: q+1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: 1
      1171: 1
      1172: q+1
      1173: q+1
      1174: 1
      1178: 1
      1179: q+1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1217: q+1
      1218: q+1
      1219: 1
      1223: 1
      1224: q+1
      1225: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1231: 1
      1232: q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1250: q+1
      1257: 1
      1259: 1
      1265: 1
      1266: q+1
      1268: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: q+1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1362: q+1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1404: q+1
      1405: 1
      1410: 1
      1411: q+1
      1412: q+1
      1413: 1
      1417: 1
      1418: q+1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1443: 1
      1450: 1
      1452: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1467: 1
      1471: 1
      1478: 1
      1479: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1503: 1
      1506: 1
      1508: 1
      1509: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1523: 1
      1524: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1564: 1
      1569: q+1
      1570: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1607: 1
      1611: 1
      1612: 1
      1613: 1
      1625: 1
      1632: 1
      1633: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1643: 1
      1647: 1
      1654: 1
      1655: 1
      1661: 1
      1667: 1
      1695: 1
      1700: 1
      1701: 1
      1706: 1
      1731: 1
      1744: 1
      1745: 1
      1746: 1
      1758: 1
      1791: 1
      1823: 1

1824:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^2+2q+1
        25: q^3+q^2+2q+1
        26: q^3+q^2+2q+1
        27: q^3+q^2+2q+1
        28: q^3+2q^2+2q+1
        29: q^3+q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^3+2q^2+2q+1
        37: q^3+q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^2+2q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: q^3+2q^2+2q+1
        44: q^2+q+1
        45: q^3+2q^2+2q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^3+2q^2+2q+1
        51: q^2+2q+1
        52: q^3+2q^2+2q+1
        53: q^3+q^2+2q+1
        54: q^3+2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^3+q^2+2q+1
        58: q^3+q^2+2q+1
        59: q^3+q^2+2q+1
        60: q^3+q^2+2q+1
        61: 2q+1
        62: q^3+q^2+2q+1
        63: q^3+q^2+2q+1
        64: q^3+q^2+2q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^3+2q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^3+2q^2+2q+1
        74: q^3+2q^2+2q+1
        75: q^2+2q+1
        76: q^3+q^2+2q+1
        77: q^3+q^2+2q+1
        78: q^3+q^2+2q+1
        79: q^3+2q^2+2q+1
        80: q^3+q^2+2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^3+2q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^3+2q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^2+2q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^3+2q^2+2q+1
        93: q^2+q+1
        94: q^2+2q+1
        95: q+1
        96: q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^3+2q^2+2q+1
       100: q^3+2q^2+2q+1
       101: q^2+q+1
       102: q^3+2q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: q^3+2q^2+2q+1
       106: q^2+2q+1
       107: q^3+q^2+2q+1
       108: q^3+q^2+2q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: q^3+q^2+2q+1
       113: 2q+1
       114: q^3+q^2+2q+1
       115: q^3+q^2+2q+1
       116: q^3+q^2+2q+1
       117: 2q+1
       118: 2q+1
       119: q^3+q^2+2q+1
       120: q^3+q^2+2q+1
       121: q^3+q^2+2q+1
       122: q^3+q^2+2q+1
       123: q+1
       124: 2q+1
       125: 2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q^3+2q^2+2q+1
       135: q^2+2q+1
       136: q^3+2q^2+2q+1
       137: q^3+q^2+2q+1
       138: q^3+2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q^3+q^2+2q+1
       142: q^3+q^2+2q+1
       143: q^3+q^2+2q+1
       144: q^3+q^2+2q+1
       145: 2q+1
       146: q^3+q^2+2q+1
       147: q^3+q^2+2q+1
       148: q^3+q^2+2q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q^3+2q^2+2q+1
       156: q^2+2q+1
       157: q^3+2q^2+2q+1
       158: q^2+q+1
       159: q^3+2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q+1
       175: q^2+2q+1
       176: q^3+2q^2+2q+1
       177: q^3+2q^2+2q+1
       178: q^3+2q^2+2q+1
       179: q^3+2q^2+2q+1
       180: q^2+2q+1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q^3+2q^2+2q+1
       185: q^2+q+1
       186: q^2+2q+1
       187: q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: q^3+q^2+2q+1
       192: 2q+1
       193: q^3+q^2+2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: q^3+q^2+2q+1
       200: 2q+1
       201: q^3+q^2+2q+1
       202: q^3+q^2+2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: q^3+q^2+2q+1
       207: q+1
       208: q^3+q^2+2q+1
       209: q^2+1
       210: q^3+q^2+2q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^3+2q^2+2q+1
       230: q^2+2q+1
       231: q^3+q^2+2q+1
       232: q^3+q^2+2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q^3+q^2+2q+1
       237: 2q+1
       238: q^3+q^2+2q+1
       239: q^3+q^2+2q+1
       240: q^3+q^2+2q+1
       241: 2q+1
       242: 2q+1
       243: q^3+q^2+2q+1
       244: q^3+q^2+2q+1
       245: q^3+q^2+2q+1
       246: q^3+q^2+2q+1
       247: q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q^2+2q+1
       259: q^3+2q^2+2q+1
       260: q^2+2q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: q^2+q+1
       267: q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q+1
       288: q^3+2q^2+2q+1
       289: q^2+2q+1
       290: q^3+2q^2+2q+1
       291: q^2+q+1
       292: q^3+2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q^2+q+1
       299: q+1
       300: q^2+q+1
       301: q^2+q+1
       302: q^2+q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: q^2+2q+1
       311: 2q+1
       312: q^3+q^2+2q+1
       313: q+1
       314: 2q+1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q^3+q^2+2q+1
       322: 2q+1
       323: q^3+q^2+2q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: q^3+q^2+2q+1
       330: q+1
       331: q^2+1
       332: q^2+1
       333: 1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: q+1
       346: 2q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q^3+q^2+2q+1
       359: 2q+1
       360: q^3+q^2+2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: q^3+q^2+2q+1
       367: 2q+1
       368: q^3+q^2+2q+1
       369: q^3+q^2+2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^3+q^2+2q+1
       374: q+1
       375: q^3+q^2+2q+1
       376: q^2+1
       377: q^3+q^2+2q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: q^2+q+1
       398: q+1
       399: q^2+q+1
       400: q+1
       401: q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: q^2+q+1
       406: q+1
       407: q^2+q+1
       408: q^2+q+1
       409: q+1
       410: q+1
       411: q+1
       412: q^2+q+1
       413: 1
       414: q^2+q+1
       415: q^2+1
       416: q^2+q+1
       417: 1
       418: 1
       419: q+1
       420: q+1
       421: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q^2+2q+1
       435: q^3+2q^2+2q+1
       436: q^2+2q+1
       437: q^2+q+1
       438: q^2+q+1
       439: q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q^2+q+1
       443: q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q^2+q+1
       447: q+1
       448: q+1
       449: q^2+q+1
       450: q^2+q+1
       451: q^2+q+1
       452: q^2+q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: q+1
       466: 2q+1
       467: q+1
       468: 2q+1
       469: 2q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: 2q+1
       475: 2q+1
       476: q^3+q^2+2q+1
       477: q+1
       478: 2q+1
       479: 2q+1
       480: 2q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: q^2+1
       486: 1
       487: q^2+1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: 2q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: q^3+q^2+2q+1
       520: q+1
       521: 2q+1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: q^3+q^2+2q+1
       529: 2q+1
       530: q^3+q^2+2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: q+1
       536: q^3+q^2+2q+1
       537: q+1
       538: q^2+1
       539: q^2+1
       540: 1
       541: q+1
       542: q+1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: q+1
       553: 2q+1
       554: 1
       555: 2q+1
       556: q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       563: q+1
       564: q^2+2q+1
       565: q+1
       566: q^2+q+1
       567: 1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: q^2+q+1
       576: q+1
       577: q^2+q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: q^2+q+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       596: q+1
       597: q+1
       598: q+1
       599: 1
       600: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q^2+2q+1
       611: q^2+2q+1
       612: q^2+q+1
       613: q+1
       614: q^2+q+1
       615: q+1
       616: q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: q^2+q+1
       621: q+1
       622: q^2+q+1
       623: q^2+q+1
       624: q+1
       625: q+1
       626: q+1
       627: q^2+q+1
       628: 1
       629: q^2+q+1
       630: q^2+1
       631: q^2+q+1
       632: 1
       633: 1
       634: q+1
       635: q+1
       636: q+1
       638: q+1
       639: q+1
       640: q+1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: q+1
       652: 2q+1
       653: q+1
       654: q+1
       655: 1
       656: q+1
       657: q+1
       658: 1
       659: 2q+1
       660: q+1
       661: 2q+1
       662: 2q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: q^2+1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: 2q+1
       706: q+1
       707: 2q+1
       708: 2q+1
       709: q+1
       710: q+1
       711: q+1
       712: q+1
       713: 2q+1
       714: 2q+1
       715: q^3+q^2+2q+1
       716: q+1
       717: 2q+1
       718: 2q+1
       719: 2q+1
       720: 1
       721: q+1
       722: q+1
       723: q+1
       724: q^2+1
       725: 1
       726: q^2+1
       727: 1
       728: 1
       729: q+1
       730: 1
       731: 2q+1
       732: 2q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: q+1
       741: 2q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       750: q+1
       751: 1
       752: q+1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: q+1
       758: 1
       759: q+1
       760: q+1
       761: 1
       762: q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q^2+q+1
       768: 1
       769: q+1
       770: q+1
       771: q+1
       773: q+1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: q+1
       784: q+1
       790: q+1
       791: q+1
       792: 1
       793: q+1
       794: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       804: q+1
       805: 1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: q+1
       810: q^2+q+1
       811: 1
       812: q+1
       813: q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q^2+q+1
       820: q+1
       821: q^2+q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: q^2+q+1
       828: 1
       829: q^2+1
       830: q^2+1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       840: q+1
       841: q+1
       842: q+1
       843: 1
       844: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       854: q+1
       855: 1
       856: q+1
       857: q+1
       858: 1
       859: q+1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: 2q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: q+1
       882: q+1
       883: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: q+1
       909: 2q+1
       910: q+1
       911: q+1
       912: 1
       913: q+1
       914: q+1
       915: 1
       916: 2q+1
       917: q+1
       918: 2q+1
       919: 2q+1
       920: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: 1
       926: q^2+1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: q+1
       934: 2q+1
       935: q+1
       936: q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       967: q+1
       968: q+1
       970: q+1
       971: 1
       972: q+1
       973: q+1
       974: 1
       977: 1
       978: 1
       979: 1
       980: q^2+1
       981: 1
       982: 1
       983: 1
       984: 1
       986: 1
       987: q+1
       988: q+1
       996: q+1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1017: 1
      1018: q+1
      1019: q+1
      1020: 1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q^2+q+1
      1027: 1
      1028: q+1
      1029: q+1
      1030: q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q^2+1
      1036: 1
      1037: q^2+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: q+1
      1043: q+1
      1049: q+1
      1050: q+1
      1051: 1
      1052: q+1
      1053: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1063: q+1
      1064: 1
      1065: 1
      1066: 1
      1067: q+1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: q+1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: q+1
      1114: 1
      1115: q+1
      1116: q+1
      1117: 1
      1118: q+1
      1119: 1
      1120: 1
      1121: 1
      1122: q+1
      1123: 2q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: q+1
      1141: q+1
      1142: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: 1
      1167: q+1
      1168: 1
      1169: 1
      1170: q+1
      1171: 1
      1174: 1
      1175: q+1
      1176: 1
      1180: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1189: q+1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1224: q+1
      1225: q+1
      1227: q+1
      1228: 1
      1229: q+1
      1230: q+1
      1231: 1
      1234: 1
      1235: 1
      1236: 1
      1237: q^2+1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1243: 1
      1244: q+1
      1245: q+1
      1253: q+1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1303: 1
      1305: 1
      1306: 1
      1310: 1
      1311: q+1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1333: q+1
      1335: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1352: 1
      1353: 1
      1354: 1
      1356: 1
      1357: 1
      1358: q+1
      1359: 1
      1360: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1404: q+1
      1405: 1
      1406: q+1
      1407: 1
      1408: 1
      1409: q+1
      1410: 1
      1413: 1
      1414: q+1
      1415: 1
      1419: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1428: q+1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1481: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1503: 1
      1506: 1
      1508: 1
      1509: 1
      1511: 1
      1513: 1
      1515: 1
      1516: 1
      1518: 1
      1520: 1
      1521: 1
      1525: 1
      1526: 1
      1527: 1
      1536: 1
      1555: 1
      1564: 1
      1565: q+1
      1566: 1
      1567: 1
      1568: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1621: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1643: 1
      1647: 1
      1649: 1
      1652: 1
      1657: 1
      1662: 1
      1692: 1
      1693: 1
      1694: 1
      1703: 1
      1722: 1
      1732: 1
      1745: 1
      1747: 1
      1748: 1
      1749: 1
      1754: 1
      1786: 1
      1824: 1

1825:    0: 2q^4+7q^3+8q^2+4q+1
         1: q^4+5q^3+8q^2+4q+1
         2: 2q^4+7q^3+8q^2+4q+1
         3: q^4+5q^3+8q^2+4q+1
         4: 2q^4+7q^3+8q^2+4q+1
         5: 2q^4+7q^3+8q^2+4q+1
         6: q^4+5q^3+8q^2+4q+1
         7: q^4+5q^3+8q^2+4q+1
         8: q^4+5q^3+8q^2+4q+1
         9: 3q^3+8q^2+4q+1
        10: q^4+5q^3+8q^2+4q+1
        11: q^4+5q^3+8q^2+4q+1
        12: 3q^3+7q^2+4q+1
        13: q^4+5q^3+8q^2+4q+1
        14: 2q^4+7q^3+8q^2+4q+1
        15: q^4+5q^3+8q^2+4q+1
        16: q^4+5q^3+8q^2+4q+1
        17: 2q^4+7q^3+8q^2+4q+1
        18: 3q^3+7q^2+4q+1
        19: 2q^4+7q^3+8q^2+4q+1
        20: 2q^3+6q^2+4q+1
        21: q^4+5q^3+8q^2+4q+1
        22: 3q^3+8q^2+4q+1
        23: q^4+5q^3+8q^2+4q+1
        24: 3q^3+7q^2+4q+1
        25: 3q^3+8q^2+4q+1
        26: 2q^3+6q^2+4q+1
        27: q^4+5q^3+8q^2+4q+1
        28: 3q^3+8q^2+4q+1
        29: q^4+5q^3+8q^2+4q+1
        30: 2q^3+7q^2+4q+1
        31: 3q^3+7q^2+4q+1
        32: 3q^3+7q^2+4q+1
        33: q^4+5q^3+8q^2+4q+1
        34: q^4+5q^3+8q^2+4q+1
        35: q^4+5q^3+8q^2+4q+1
        36: 3q^3+8q^2+4q+1
        37: q^4+5q^3+8q^2+4q+1
        38: q^4+5q^3+8q^2+4q+1
        39: 3q^3+7q^2+4q+1
        40: q^4+5q^3+8q^2+4q+1
        41: q^4+5q^3+8q^2+4q+1
        42: 3q^3+7q^2+4q+1
        43: 2q^3+7q^2+4q+1
        44: 3q^3+7q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: q^3+5q^2+4q+1
        47: q^4+5q^3+8q^2+4q+1
        48: 2q^4+7q^3+8q^2+4q+1
        49: 3q^3+7q^2+4q+1
        50: 2q^3+6q^2+4q+1
        51: 3q^2+3q+1
        52: 2q^3+6q^2+4q+1
        53: 3q^3+8q^2+4q+1
        54: 3q^3+8q^2+4q+1
        55: 2q^3+7q^2+4q+1
        56: 3q^3+7q^2+4q+1
        57: 2q^3+6q^2+4q+1
        58: 2q^3+6q^2+4q+1
        59: 2q^3+6q^2+4q+1
        60: q^4+5q^3+8q^2+4q+1
        61: 3q^3+7q^2+4q+1
        62: 3q^3+8q^2+4q+1
        63: 2q^3+6q^2+4q+1
        64: 2q^3+5q^2+4q+1
        65: 2q^3+7q^2+4q+1
        66: q^3+5q^2+4q+1
        67: 2q^3+5q^2+4q+1
        68: 2q^3+7q^2+4q+1
        69: 3q^3+7q^2+4q+1
        70: q^3+5q^2+4q+1
        71: 2q^3+6q^2+4q+1
        72: q^4+5q^3+8q^2+4q+1
        73: 3q^3+8q^2+4q+1
        74: q^4+5q^3+8q^2+4q+1
        75: 3q^3+7q^2+4q+1
        76: 3q^3+8q^2+4q+1
        77: 2q^3+6q^2+4q+1
        78: q^4+5q^3+8q^2+4q+1
        79: 3q^3+8q^2+4q+1
        80: q^4+5q^3+8q^2+4q+1
        81: 2q^3+7q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: 3q^3+7q^2+4q+1
        84: q^3+5q^2+4q+1
        85: q^4+5q^3+8q^2+4q+1
        86: 2q^3+7q^2+4q+1
        87: 3q^3+7q^2+4q+1
        88: q^3+5q^2+4q+1
        89: 2q^3+7q^2+4q+1
        90: 3q^2+3q+1
        91: 3q^3+7q^2+4q+1
        92: 2q^3+7q^2+4q+1
        93: 3q^3+7q^2+4q+1
        94: q^3+5q^2+4q+1
        95: q^3+5q^2+4q+1
        96: q^3+5q^2+4q+1
        97: q^4+5q^3+8q^2+4q+1
        98: q^4+5q^3+8q^2+4q+1
        99: 3q^3+7q^2+4q+1
       100: 2q^3+7q^2+4q+1
       101: 3q^3+7q^2+4q+1
       102: 3q^3+7q^2+4q+1
       103: q^3+5q^2+4q+1
       104: 3q^2+3q+1
       105: 2q^3+6q^2+4q+1
       106: 3q^2+3q+1
       107: 2q^3+6q^2+4q+1
       108: 3q^3+8q^2+4q+1
       109: 2q^3+7q^2+4q+1
       110: 2q^3+7q^2+4q+1
       111: q^3+5q^2+4q+1
       112: 2q^3+6q^2+4q+1
       113: 3q^2+3q+1
       114: q^3+4q^2+4q+1
       115: 2q^3+6q^2+4q+1
       116: 2q^3+6q^2+4q+1
       117: q^3+5q^2+4q+1
       118: 3q^3+7q^2+4q+1
       119: 3q^2+4q+1
       120: 2q^3+6q^2+4q+1
       121: q^3+4q^2+4q+1
       122: 2q^3+5q^2+4q+1
       123: 2q^2+3q+1
       124: q^3+4q^2+4q+1
       125: q^3+5q^2+4q+1
       126: 3q^2+4q+1
       127: 2q^3+5q^2+4q+1
       128: 2q^3+5q^2+4q+1
       129: 2q^3+7q^2+4q+1
       130: q^3+5q^2+4q+1
       131: 3q^2+4q+1
       132: q^3+5q^2+4q+1
       133: q^3+5q^2+4q+1
       134: 2q^3+6q^2+4q+1
       135: 3q^2+3q+1
       136: 2q^3+6q^2+4q+1
       137: 3q^3+8q^2+4q+1
       138: 3q^3+8q^2+4q+1
       139: 2q^3+7q^2+4q+1
       140: 3q^3+7q^2+4q+1
       141: 2q^3+6q^2+4q+1
       142: 2q^3+6q^2+4q+1
       143: 2q^3+6q^2+4q+1
       144: q^4+5q^3+8q^2+4q+1
       145: 3q^3+7q^2+4q+1
       146: 3q^3+8q^2+4q+1
       147: 2q^3+6q^2+4q+1
       148: 2q^3+5q^2+4q+1
       149: 2q^3+7q^2+4q+1
       150: q^3+5q^2+4q+1
       151: 2q^3+5q^2+4q+1
       152: 2q^3+7q^2+4q+1
       153: 3q^3+7q^2+4q+1
       154: q^3+5q^2+4q+1
       155: q^3+5q^2+4q+1
       156: 2q^2+3q+1
       157: q^3+5q^2+4q+1
       158: 2q^3+7q^2+4q+1
       159: 2q^3+7q^2+4q+1
       160: q^3+5q^2+4q+1
       161: q^3+5q^2+4q+1
       162: q^3+5q^2+4q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: 3q^3+7q^2+4q+1
       166: q^3+5q^2+4q+1
       167: 2q^3+7q^2+4q+1
       168: 3q^2+3q+1
       169: 2q^3+5q^2+4q+1
       170: q^3+5q^2+4q+1
       171: 2q^2+3q+1
       172: 2q^2+3q+1
       173: q^3+5q^2+4q+1
       174: q^3+5q^2+4q+1
       175: q^3+4q^2+4q+1
       176: q^3+5q^2+4q+1
       177: q^4+5q^3+8q^2+4q+1
       178: 2q^3+7q^2+4q+1
       179: 3q^3+7q^2+4q+1
       180: q^3+5q^2+4q+1
       181: 2q^3+7q^2+4q+1
       182: 3q^2+3q+1
       183: 3q^3+7q^2+4q+1
       184: 2q^3+7q^2+4q+1
       185: 3q^3+7q^2+4q+1
       186: q^3+5q^2+4q+1
       187: q^3+5q^2+4q+1
       188: q^3+5q^2+4q+1
       189: q^2+2q+1
       190: 3q^2+3q+1
       191: 2q^3+6q^2+4q+1
       192: 3q^2+3q+1
       193: 3q^2+4q+1
       194: q^3+4q^2+4q+1
       195: 2q^3+7q^2+4q+1
       196: q^3+5q^2+4q+1
       197: q^3+5q^2+4q+1
       198: 3q^2+3q+1
       199: q^3+4q^2+4q+1
       200: 2q^2+3q+1
       201: q^3+4q^2+4q+1
       202: 2q^3+6q^2+4q+1
       203: q^3+5q^2+4q+1
       204: q^3+5q^2+4q+1
       205: 3q^2+4q+1
       206: 3q^2+4q+1
       207: 2q+1
       208: 2q^2+4q+1
       209: q^3+4q^2+4q+1
       210: q^3+4q^2+4q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: q^3+4q^2+4q+1
       214: 2q^2+3q+1
       215: 2q^2+4q+1
       216: 3q^2+4q+1
       217: 3q^2+4q+1
       218: 3q^2+4q+1
       219: 2q^3+5q^2+4q+1
       220: 2q^2+4q+1
       221: q^3+5q^2+4q+1
       222: 2q^2+4q+1
       223: 3q^2+4q+1
       224: q^2+3q+1
       225: q^3+5q^2+4q+1
       226: q^2+2q+1
       227: 3q^2+4q+1
       228: 3q^2+3q+1
       229: 2q^3+6q^2+4q+1
       230: 3q^2+3q+1
       231: 2q^3+6q^2+4q+1
       232: 3q^3+8q^2+4q+1
       233: 2q^3+7q^2+4q+1
       234: 2q^3+7q^2+4q+1
       235: q^3+5q^2+4q+1
       236: 2q^3+6q^2+4q+1
       237: 3q^2+3q+1
       238: q^3+4q^2+4q+1
       239: 2q^3+6q^2+4q+1
       240: 2q^3+6q^2+4q+1
       241: q^3+5q^2+4q+1
       242: 3q^3+7q^2+4q+1
       243: 3q^2+4q+1
       244: 2q^3+6q^2+4q+1
       245: q^3+4q^2+4q+1
       246: 2q^3+5q^2+4q+1
       247: 2q^2+3q+1
       248: q^3+4q^2+4q+1
       249: q^3+5q^2+4q+1
       250: 3q^2+4q+1
       251: 2q^3+5q^2+4q+1
       252: 2q^3+5q^2+4q+1
       253: 2q^3+7q^2+4q+1
       254: q^3+5q^2+4q+1
       255: 3q^2+4q+1
       256: q^3+5q^2+4q+1
       257: q^3+5q^2+4q+1
       258: 2q^2+3q+1
       259: q^3+5q^2+4q+1
       260: 2q^2+3q+1
       261: q^3+5q^2+4q+1
       262: 2q^3+7q^2+4q+1
       263: q^3+5q^2+4q+1
       264: q^3+5q^2+4q+1
       265: q^3+4q^2+4q+1
       266: q^3+5q^2+4q+1
       267: 2q^2+3q+1
       268: 2q^2+3q+1
       269: 3q^2+3q+1
       270: 3q^2+3q+1
       271: 2q^2+3q+1
       272: q^3+5q^2+4q+1
       273: 3q^2+4q+1
       274: 3q^2+3q+1
       275: 2q^2+3q+1
       276: 2q^3+5q^2+4q+1
       277: 2q^2+3q+1
       278: 2q^2+3q+1
       279: 2q^2+3q+1
       280: 2q+1
       281: 2q^2+3q+1
       282: 2q^2+3q+1
       283: q^3+5q^2+4q+1
       284: 2q^2+3q+1
       285: q^2+3q+1
       286: q^3+4q^2+4q+1
       287: q^3+4q^2+4q+1
       288: q^3+5q^2+4q+1
       289: 2q^2+3q+1
       290: q^3+5q^2+4q+1
       291: 2q^3+7q^2+4q+1
       292: 2q^3+7q^2+4q+1
       293: q^3+5q^2+4q+1
       294: q^3+5q^2+4q+1
       295: q^3+5q^2+4q+1
       296: 3q^2+3q+1
       297: 3q^2+3q+1
       298: 3q^3+7q^2+4q+1
       299: q^3+5q^2+4q+1
       300: 2q^3+7q^2+4q+1
       301: 3q^2+3q+1
       302: 2q^3+5q^2+4q+1
       303: q^3+5q^2+4q+1
       304: 2q^2+3q+1
       305: 2q^2+3q+1
       306: q^3+5q^2+4q+1
       307: q^3+5q^2+4q+1
       308: q^3+4q^2+4q+1
       309: q^2+2q+1
       310: q^2+2q+1
       311: 3q^2+3q+1
       312: 3q^2+4q+1
       313: 2q+1
       314: q^3+4q^2+4q+1
       315: 2q^2+3q+1
       316: 2q^2+4q+1
       317: q^3+5q^2+4q+1
       318: q^2+2q+1
       319: 2q+1
       320: 2q^2+3q+1
       321: q^3+4q^2+4q+1
       322: 2q^2+3q+1
       323: 2q^2+4q+1
       324: 2q^2+4q+1
       325: q^3+5q^2+4q+1
       326: 2q^2+4q+1
       327: 3q^2+4q+1
       328: 2q+1
       329: 2q^2+4q+1
       330: 2q+1
       331: 2q^2+4q+1
       332: q^3+4q^2+4q+1
       333: 2q^2+3q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: 2q^2+3q+1
       337: 2q^2+4q+1
       338: q^2+3q+1
       339: 2q^2+4q+1
       340: 3q^2+4q+1
       341: 3q^2+4q+1
       342: 3q^2+4q+1
       343: 3q^2+4q+1
       344: 2q^2+4q+1
       345: 2q+1
       346: q^2+4q+1
       347: 2q^2+4q+1
       348: 2q^2+4q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: 2q^2+4q+1
       352: q^2+2q+1
       353: 2q+1
       354: 3q^2+4q+1
       355: q^2+3q+1
       356: q^2+2q+1
       357: 3q^2+3q+1
       358: 2q^3+6q^2+4q+1
       359: 3q^2+3q+1
       360: 3q^2+4q+1
       361: q^3+4q^2+4q+1
       362: 2q^3+7q^2+4q+1
       363: q^3+5q^2+4q+1
       364: q^3+5q^2+4q+1
       365: 3q^2+3q+1
       366: q^3+4q^2+4q+1
       367: 2q^2+3q+1
       368: q^3+4q^2+4q+1
       369: 2q^3+6q^2+4q+1
       370: q^3+5q^2+4q+1
       371: q^3+5q^2+4q+1
       372: 3q^2+4q+1
       373: 3q^2+4q+1
       374: 2q+1
       375: 2q^2+4q+1
       376: q^3+4q^2+4q+1
       377: q^3+4q^2+4q+1
       378: 2q^2+3q+1
       379: 2q^2+3q+1
       380: q^3+4q^2+4q+1
       381: 2q^2+3q+1
       382: 2q^2+4q+1
       383: 3q^2+4q+1
       384: 3q^2+4q+1
       385: 3q^2+4q+1
       386: 2q^3+5q^2+4q+1
       387: 2q^2+4q+1
       388: q^3+5q^2+4q+1
       389: 2q^2+4q+1
       390: 3q^2+4q+1
       391: q^2+3q+1
       392: q^3+5q^2+4q+1
       393: q^2+2q+1
       394: 3q^2+4q+1
       395: q^2+2q+1
       396: 2q^2+3q+1
       397: q^3+5q^2+4q+1
       398: 2q^2+3q+1
       399: 3q^2+4q+1
       400: 2q^2+3q+1
       401: q^3+5q^2+4q+1
       402: q^3+4q^2+4q+1
       403: q^3+4q^2+4q+1
       404: 2q^2+3q+1
       405: 2q^2+3q+1
       406: q^2+2q+1
       407: 2q^2+3q+1
       408: 3q^2+3q+1
       409: 2q^2+3q+1
       410: 2q^2+3q+1
       411: q^2+3q+1
       412: 3q^2+4q+1
       413: 2q+1
       414: q^2+3q+1
       415: 2q^2+3q+1
       416: 2q^2+3q+1
       417: q^2+2q+1
       418: 2q^2+3q+1
       419: 2q^2+3q+1
       420: q^2+2q+1
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q^2+3q+1
       426: q^2+3q+1
       427: 2q^2+3q+1
       428: 2q+1
       429: q^2+3q+1
       430: 2q+1
       431: q^3+4q^2+4q+1
       432: q^2+2q+1
       433: q^2+3q+1
       434: 2q^2+3q+1
       435: q^3+5q^2+4q+1
       436: 2q^2+3q+1
       437: q^3+5q^2+4q+1
       438: 2q^3+7q^2+4q+1
       439: q^3+5q^2+4q+1
       440: q^3+5q^2+4q+1
       441: q^3+4q^2+4q+1
       442: q^3+5q^2+4q+1
       443: 2q^2+3q+1
       444: 2q^2+3q+1
       445: 3q^2+3q+1
       446: 3q^2+3q+1
       447: 2q^2+3q+1
       448: q^3+5q^2+4q+1
       449: 3q^2+4q+1
       450: 3q^2+3q+1
       451: 2q^2+3q+1
       452: 2q^3+5q^2+4q+1
       453: 2q^2+3q+1
       454: 2q^2+3q+1
       455: 2q^2+3q+1
       456: 2q+1
       457: 2q^2+3q+1
       458: 2q^2+3q+1
       459: q^3+5q^2+4q+1
       460: 2q^2+3q+1
       461: q^2+3q+1
       462: q^3+4q^2+4q+1
       463: q^3+4q^2+4q+1
       465: q^2+2q+1
       466: 2q+1
       467: 2q+1
       468: 2q^2+3q+1
       469: 2q^2+4q+1
       470: 2q+1
       471: 2q^2+4q+1
       472: q^2+2q+1
       473: 2q+1
       474: 2q+1
       475: 2q^2+3q+1
       476: 2q^2+4q+1
       477: 2q+1
       478: 2q^2+4q+1
       479: q^2+3q+1
       480: q^2+4q+1
       481: 2q^2+4q+1
       482: 2q+1
       483: q+1
       484: 2q+1
       485: 2q^2+4q+1
       486: 2q+1
       487: 2q^2+4q+1
       488: 2q+1
       489: 2q^2+3q+1
       490: q^2+3q+1
       491: q^2+3q+1
       492: 2q+1
       493: q^2+3q+1
       494: 2q^2+4q+1
       495: q^2+3q+1
       496: 2q+1
       497: 2q^2+4q+1
       498: 3q^2+4q+1
       499: 2q^2+4q+1
       500: 3q^2+4q+1
       501: 2q+1
       502: q^2+4q+1
       503: 2q+1
       504: q^2+4q+1
       505: 2q^2+4q+1
       506: q^2+3q+1
       507: q^2+3q+1
       508: q^2+3q+1
       509: 2q^2+4q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       515: q^2+3q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: 3q^2+3q+1
       519: 3q^2+4q+1
       520: 2q+1
       521: q^3+4q^2+4q+1
       522: 2q^2+3q+1
       523: 2q^2+4q+1
       524: q^3+5q^2+4q+1
       525: q^2+2q+1
       526: 2q+1
       527: 2q^2+3q+1
       528: q^3+4q^2+4q+1
       529: 2q^2+3q+1
       530: 2q^2+4q+1
       531: 2q^2+4q+1
       532: q^3+5q^2+4q+1
       533: 2q^2+4q+1
       534: 3q^2+4q+1
       535: 2q+1
       536: 2q^2+4q+1
       537: 2q+1
       538: 2q^2+4q+1
       539: q^3+4q^2+4q+1
       540: 2q^2+3q+1
       541: 2q^2+3q+1
       542: q^2+3q+1
       543: 2q^2+3q+1
       544: 2q^2+4q+1
       545: q^2+3q+1
       546: 2q^2+4q+1
       547: 3q^2+4q+1
       548: 3q^2+4q+1
       549: 3q^2+4q+1
       550: 3q^2+4q+1
       551: 2q^2+4q+1
       552: 2q+1
       553: q^2+4q+1
       554: 2q^2+4q+1
       555: 2q^2+4q+1
       556: q^2+3q+1
       557: q^2+3q+1
       558: 2q^2+4q+1
       559: q^2+2q+1
       560: 2q+1
       561: 3q^2+4q+1
       562: q^2+3q+1
       563: q^2+2q+1
       564: q^2+2q+1
       565: 2q^2+3q+1
       566: 3q^2+4q+1
       567: 2q+1
       568: 2q^2+3q+1
       569: q^2+2q+1
       570: q^2+3q+1
       571: q^3+4q^2+4q+1
       572: q^2+2q+1
       573: q+1
       574: q^2+2q+1
       575: 2q^2+3q+1
       576: q^2+2q+1
       577: q^2+3q+1
       578: 2q+1
       579: 2q^2+3q+1
       580: 2q+1
       581: q^2+3q+1
       582: 2q+1
       583: q^2+3q+1
       584: q+1
       585: q^2+3q+1
       586: 2q^2+3q+1
       587: q^2+2q+1
       588: q^2+2q+1
       589: 2q+1
       590: q^2+2q+1
       591: 2q+1
       592: q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q^2+3q+1
       598: q^2+3q+1
       599: q+1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: q+1
       604: 2q+1
       605: q^2+3q+1
       606: q^2+2q+1
       607: q+1
       608: q^2+3q+1
       609: 2q+1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: q^3+5q^2+4q+1
       613: 2q^2+3q+1
       614: 3q^2+4q+1
       615: 2q^2+3q+1
       616: q^3+5q^2+4q+1
       617: q^3+4q^2+4q+1
       618: q^3+4q^2+4q+1
       619: 2q^2+3q+1
       620: 2q^2+3q+1
       621: q^2+2q+1
       622: 2q^2+3q+1
       623: 3q^2+3q+1
       624: 2q^2+3q+1
       625: 2q^2+3q+1
       626: q^2+3q+1
       627: 3q^2+4q+1
       628: 2q+1
       629: q^2+3q+1
       630: 2q^2+3q+1
       631: 2q^2+3q+1
       632: q^2+2q+1
       633: 2q^2+3q+1
       634: 2q^2+3q+1
       635: q^2+2q+1
       636: 2q+1
       637: 2q+1
       638: 2q+1
       639: 2q+1
       640: 2q^2+3q+1
       641: q^2+3q+1
       642: 2q^2+3q+1
       643: 2q+1
       644: q^2+3q+1
       645: 2q+1
       646: q^3+4q^2+4q+1
       647: q^2+2q+1
       648: q^2+3q+1
       650: 2q+1
       651: q+1
       652: 2q+1
       653: 2q+1
       654: 2q^2+4q+1
       655: 2q+1
       656: 2q+1
       658: 2q+1
       659: 2q+1
       660: 2q+1
       661: q^2+3q+1
       662: q^2+4q+1
       663: 2q+1
       664: q^2+4q+1
       665: 2q+1
       666: q+1
       667: q+1
       668: 2q+1
       669: 2q^2+4q+1
       670: 2q+1
       671: 2q+1
       672: q+1
       673: 2q+1
       674: q^2+3q+1
       675: q+1
       676: 2q+1
       677: 2q+1
       678: q^2+3q+1
       679: 2q+1
       681: 2q^2+4q+1
       682: q^2+3q+1
       683: 2q+1
       684: 2q^2+4q+1
       685: 2q+1
       686: q+1
       687: 2q+1
       688: q^2+4q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: q^2+3q+1
       693: q^2+3q+1
       694: q^2+3q+1
       695: 2q+1
       696: 2q+1
       697: q+1
       698: 2q+1
       699: 2q+1
       700: q+1
       701: q+1
       702: q+1
       704: q^2+2q+1
       705: 2q+1
       706: 2q+1
       707: 2q^2+3q+1
       708: 2q^2+4q+1
       709: 2q+1
       710: 2q^2+4q+1
       711: q^2+2q+1
       712: 2q+1
       713: 2q+1
       714: 2q^2+3q+1
       715: 2q^2+4q+1
       716: 2q+1
       717: 2q^2+4q+1
       718: q^2+3q+1
       719: q^2+4q+1
       720: 2q^2+4q+1
       721: 2q+1
       722: q+1
       723: 2q+1
       724: 2q^2+4q+1
       725: 2q+1
       726: 2q^2+4q+1
       727: 2q+1
       728: 2q^2+3q+1
       729: q^2+3q+1
       730: q^2+3q+1
       731: 2q+1
       732: q^2+3q+1
       733: 2q^2+4q+1
       734: q^2+3q+1
       735: 2q+1
       736: 2q^2+4q+1
       737: 3q^2+4q+1
       738: 2q^2+4q+1
       739: 3q^2+4q+1
       740: 2q+1
       741: q^2+4q+1
       742: 2q+1
       743: q^2+4q+1
       744: 2q^2+4q+1
       745: q^2+3q+1
       746: q^2+3q+1
       747: q^2+3q+1
       748: 2q^2+4q+1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: q+1
       754: q^2+3q+1
       756: q^2+2q+1
       757: q+1
       758: 2q+1
       759: q^2+2q+1
       760: q^2+3q+1
       761: q+1
       762: q^2+3q+1
       763: q^2+2q+1
       764: q+1
       765: q+1
       766: q^2+2q+1
       767: q^2+3q+1
       768: q+1
       769: 2q+1
       770: q+1
       771: 2q+1
       772: 2q+1
       773: q+1
       774: 1
       775: q+1
       776: q^2+3q+1
       777: q+1
       778: q^2+3q+1
       779: q+1
       780: q^2+2q+1
       781: q+1
       782: 2q+1
       783: q+1
       784: q+1
       785: 2q+1
       786: q+1
       788: 2q+1
       789: 2q+1
       790: 2q+1
       791: q^2+3q+1
       792: q+1
       793: 2q+1
       794: 1
       795: 2q+1
       796: 2q+1
       797: q+1
       798: q+1
       799: 2q+1
       800: q^2+3q+1
       801: q+1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 2q+1
       807: q^2+2q+1
       808: q^2+2q+1
       809: 2q^2+3q+1
       810: 3q^2+4q+1
       811: 2q+1
       812: 2q^2+3q+1
       813: q^2+2q+1
       814: q^2+3q+1
       815: q^3+4q^2+4q+1
       816: q^2+2q+1
       817: q+1
       818: q^2+2q+1
       819: 2q^2+3q+1
       820: q^2+2q+1
       821: q^2+3q+1
       822: 2q+1
       823: 2q^2+3q+1
       824: 2q+1
       825: q^2+3q+1
       826: 2q+1
       827: q^2+3q+1
       828: q+1
       829: q^2+3q+1
       830: 2q^2+3q+1
       831: q^2+2q+1
       832: q^2+2q+1
       833: 2q+1
       834: q^2+2q+1
       835: 2q+1
       836: q+1
       837: 2q+1
       838: 2q+1
       839: 2q+1
       840: 2q+1
       841: q^2+3q+1
       842: q^2+3q+1
       843: q+1
       844: 2q+1
       845: 2q+1
       846: 2q+1
       847: q+1
       848: 2q+1
       849: q^2+3q+1
       850: q^2+2q+1
       851: q+1
       852: q^2+3q+1
       853: 2q+1
       855: q+1
       856: 2q+1
       857: q+1
       858: 2q+1
       859: 2q+1
       860: q+1
       862: 2q+1
       863: q+1
       864: 2q+1
       865: 2q+1
       866: q^2+4q+1
       867: 2q+1
       868: 2q+1
       870: q+1
       871: 1
       872: 2q+1
       873: q+1
       874: 2q+1
       875: q+1
       876: 2q+1
       877: q+1
       879: 2q+1
       880: q+1
       882: q^2+3q+1
       883: 2q+1
       885: 2q+1
       886: 2q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: 2q+1
       892: 2q+1
       893: q+1
       894: q+1
       895: q^2+3q+1
       896: q+1
       897: 1
       898: q+1
       899: 2q+1
       900: q+1
       901: q+1
       902: 1
       903: q+1
       904: 1
       905: q+1
       907: 2q+1
       908: q+1
       909: 2q+1
       910: 2q+1
       911: 2q^2+4q+1
       912: 2q+1
       913: 2q+1
       915: 2q+1
       916: 2q+1
       917: 2q+1
       918: q^2+3q+1
       919: q^2+4q+1
       920: 2q+1
       921: q^2+4q+1
       922: 2q+1
       923: q+1
       924: q+1
       925: 2q+1
       926: 2q^2+4q+1
       927: 2q+1
       928: 2q+1
       929: q+1
       930: 2q+1
       931: q^2+3q+1
       932: q+1
       933: 2q+1
       934: 2q+1
       935: q^2+3q+1
       936: 2q+1
       938: 2q^2+4q+1
       939: q^2+3q+1
       940: 2q+1
       941: 2q^2+4q+1
       942: 2q+1
       943: q+1
       944: 2q+1
       945: q^2+4q+1
       946: 2q+1
       947: 2q+1
       948: 2q+1
       949: q^2+3q+1
       950: q^2+3q+1
       951: q^2+3q+1
       952: 2q+1
       953: 2q+1
       954: q+1
       955: 2q+1
       956: 2q+1
       957: q+1
       958: q+1
       959: q+1
       961: q+1
       962: 1
       963: q+1
       964: q+1
       965: q^2+3q+1
       966: q+1
       967: q+1
       969: q+1
       970: q+1
       971: q+1
       972: q+1
       973: 2q+1
       974: 1
       975: 2q+1
       976: q+1
       977: 1
       978: 1
       979: q+1
       980: q^2+3q+1
       981: q+1
       982: q+1
       983: 1
       984: q+1
       985: q+1
       986: 1
       987: q+1
       988: q+1
       989: q+1
       992: 2q+1
       993: q+1
       995: 2q+1
       996: q+1
       997: 1
       998: 1
       999: 2q+1
      1000: 1
      1002: q+1
      1003: q+1
      1004: q+1
      1005: 2q+1
      1006: q+1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: q+1
      1015: q^2+2q+1
      1016: q+1
      1017: 2q+1
      1018: q^2+2q+1
      1019: q^2+3q+1
      1020: q+1
      1021: q^2+3q+1
      1022: q^2+2q+1
      1023: q+1
      1024: q+1
      1025: q^2+2q+1
      1026: q^2+3q+1
      1027: q+1
      1028: 2q+1
      1029: q+1
      1030: 2q+1
      1031: 2q+1
      1032: q+1
      1033: 1
      1034: q+1
      1035: q^2+3q+1
      1036: q+1
      1037: q^2+3q+1
      1038: q+1
      1039: q^2+2q+1
      1040: q+1
      1041: 2q+1
      1042: q+1
      1043: q+1
      1044: 2q+1
      1045: q+1
      1047: 2q+1
      1048: 2q+1
      1049: 2q+1
      1050: q^2+3q+1
      1051: q+1
      1052: 2q+1
      1053: 1
      1054: 2q+1
      1055: 2q+1
      1056: q+1
      1057: q+1
      1058: 2q+1
      1059: q^2+3q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: 1
      1065: 2q+1
      1068: q+1
      1069: 1
      1070: q+1
      1072: q+1
      1073: 2q+1
      1074: q+1
      1075: 2q+1
      1076: 2q+1
      1077: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: q+1
      1083: 2q+1
      1084: q+1
      1085: 1
      1087: q+1
      1089: q+1
      1091: 2q+1
      1093: q+1
      1095: q+1
      1096: 1
      1098: q+1
      1099: q+1
      1101: q+1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: q+1
      1115: 2q+1
      1116: q+1
      1117: 2q+1
      1118: 2q+1
      1119: q+1
      1121: 2q+1
      1122: q+1
      1123: 2q+1
      1124: 2q+1
      1125: q^2+4q+1
      1126: 2q+1
      1127: 2q+1
      1129: q+1
      1130: 1
      1131: 2q+1
      1132: q+1
      1133: 2q+1
      1134: q+1
      1135: 2q+1
      1136: q+1
      1138: 2q+1
      1139: q+1
      1141: q^2+3q+1
      1142: 2q+1
      1144: 2q+1
      1145: 2q+1
      1146: q+1
      1147: q+1
      1148: 2q+1
      1149: 2q+1
      1151: 2q+1
      1152: q+1
      1153: q+1
      1154: q^2+3q+1
      1155: q+1
      1156: 1
      1157: q+1
      1158: 2q+1
      1159: q+1
      1160: q+1
      1161: 1
      1162: q+1
      1163: 1
      1164: q+1
      1166: 1
      1167: q+1
      1168: 1
      1169: q+1
      1170: q+1
      1171: 1
      1173: q+1
      1174: 1
      1175: q+1
      1176: 1
      1177: 2q+1
      1178: 1
      1179: q+1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: q+1
      1186: 1
      1187: q+1
      1188: 1
      1190: q+1
      1193: q+1
      1197: q+1
      1198: 1
      1199: 1
      1200: 1
      1203: q+1
      1204: 1
      1206: q+1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: q+1
      1219: 1
      1220: q+1
      1221: q+1
      1222: q^2+3q+1
      1223: q+1
      1224: q+1
      1226: q+1
      1227: q+1
      1228: q+1
      1229: q+1
      1230: 2q+1
      1231: 1
      1232: 2q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: q+1
      1237: q^2+3q+1
      1238: q+1
      1239: q+1
      1240: 1
      1241: q+1
      1242: q+1
      1243: 1
      1244: q+1
      1245: q+1
      1246: q+1
      1249: 2q+1
      1250: q+1
      1252: 2q+1
      1253: q+1
      1254: 1
      1255: 1
      1256: 2q+1
      1257: 1
      1259: q+1
      1260: q+1
      1261: q+1
      1262: 2q+1
      1263: q+1
      1264: q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1270: q+1
      1272: 1
      1273: 1
      1276: q+1
      1277: 1
      1278: q+1
      1280: 1
      1281: 1
      1282: 1
      1283: q+1
      1284: 1
      1285: 1
      1288: q+1
      1291: q+1
      1294: 1
      1296: 1
      1298: q+1
      1300: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1312: q+1
      1313: 1
      1314: q+1
      1316: q+1
      1317: 2q+1
      1318: q+1
      1319: 2q+1
      1320: 2q+1
      1321: q+1
      1323: 1
      1324: 1
      1325: 1
      1326: q+1
      1327: 2q+1
      1328: q+1
      1329: 1
      1331: q+1
      1333: q+1
      1335: 2q+1
      1337: q+1
      1339: q+1
      1340: 1
      1342: q+1
      1343: q+1
      1345: q+1
      1346: q+1
      1347: 1
      1348: 1
      1349: q+1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: q+1
      1365: 1
      1366: 1
      1367: q+1
      1368: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: q+1
      1375: 1
      1376: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1405: 1
      1406: q+1
      1407: 1
      1408: q+1
      1409: q+1
      1410: 1
      1412: q+1
      1413: 1
      1414: q+1
      1415: 1
      1416: 2q+1
      1417: 1
      1418: q+1
      1420: 1
      1421: 1
      1422: q+1
      1423: 1
      1424: q+1
      1425: 1
      1426: q+1
      1427: 1
      1429: q+1
      1432: q+1
      1436: q+1
      1437: 1
      1438: 1
      1439: 1
      1442: q+1
      1443: 1
      1445: q+1
      1446: 1
      1447: 1
      1448: 1
      1449: q+1
      1450: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q+1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1473: 1
      1476: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1487: 1
      1488: 1
      1491: q+1
      1492: 1
      1493: q+1
      1495: 1
      1496: 1
      1497: 1
      1498: q+1
      1499: 1
      1500: 1
      1503: q+1
      1506: q+1
      1509: 1
      1511: 1
      1513: q+1
      1515: 1
      1517: 1
      1518: 1
      1520: 1
      1521: 1
      1523: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1532: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1556: 1
      1559: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: q+1
      1572: 1
      1573: 1
      1574: q+1
      1575: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: q+1
      1582: 1
      1583: 1
      1593: 1
      1596: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1606: 1
      1607: 1
      1609: 1
      1610: 1
      1613: 1
      1615: 1
      1616: 1
      1627: 1
      1630: 1
      1633: 1
      1635: 1
      1636: 1
      1639: 1
      1640: 1
      1641: 1
      1649: 1
      1652: 1
      1655: 1
      1657: 1
      1659: 1
      1661: 1
      1663: 1
      1669: 1
      1671: 1
      1693: 1
      1694: 1
      1697: 1
      1699: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1723: 1
      1726: 1
      1730: 1
      1733: 1
      1746: 1
      1748: 1
      1749: 1
      1760: 1
      1763: 1
      1787: 1
      1793: 1
      1795: 1
      1825: 1

1826:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: 1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
        90: 1
        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q+1
       109: q^2+q+1
       110: q+1
       111: q+1
       112: q+1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q^2+q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q+1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^2+q+1
       193: q+1
       194: q^2+q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q^2+q+1
       201: q^2+q+1
       202: q+1
       203: q^2+q+1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q^2+q+1
       231: q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q^2+q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q^2+q+1
       323: q+1
       324: q^2+q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q^2+q+1
       339: q^2+q+1
       340: q+1
       341: q^2+q+1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q+1
       363: q+1
       364: 1
       365: q+1
       366: q+1
       367: q^2+q+1
       368: q^2+q+1
       369: q+1
       370: q^2+q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q^2+q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q^2+q+1
       496: q+1
       497: q^2+q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q^2+q+1
       523: q+1
       524: 1
       525: 1
       526: q+1
       527: q+1
       528: q+1
       529: q^2+q+1
       530: q+1
       531: q^2+q+1
       532: q+1
       533: q+1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: q^2+q+1
       546: q^2+q+1
       547: q+1
       548: q^2+q+1
       549: q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       599: 1
       600: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       681: q+1
       682: q^2+q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: 1
       711: 1
       712: 1
       713: q+1
       714: q+1
       715: q+1
       716: q+1
       717: q+1
       718: q^2+q+1
       719: q+1
       720: 1
       721: 1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       731: q+1
       732: q+1
       733: q+1
       734: q^2+q+1
       735: q+1
       736: q^2+q+1
       737: q+1
       738: q+1
       739: 1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       794: 1
       801: 1
       802: 1
       805: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       843: 1
       844: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: q+1
       909: q+1
       910: q+1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: q+1
       917: q+1
       918: q+1
       919: q+1
       920: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: q+1
       935: q+1
       936: q+1
       937: q+1
       938: q+1
       939: q^2+q+1
       940: q+1
       941: 1
       942: 1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       986: 1
      1008: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1053: 1
      1060: 1
      1061: 1
      1064: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: q+1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: q+1
      1123: q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: q+1
      1140: q+1
      1141: q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1174: 1
      1180: 1
      1182: 1
      1183: 1
      1186: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1231: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1243: 1
      1265: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1307: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1356: 1
      1357: 1
      1371: 1
      1404: 1
      1405: 1
      1410: 1
      1413: 1
      1419: 1
      1421: 1
      1422: 1
      1425: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1477: 1
      1480: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1518: 1
      1519: 1
      1522: 1
      1564: 1
      1578: 1
      1612: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1653: 1
      1656: 1
      1734: 1
      1745: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1826: 1

1827:    0: q^3+q^2+q+1
         1: q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^3+q^2+q+1
         9: q^2+q+1
        10: q^3+q^2+q+1
        11: q+1
        12: q^3+q^2+q+1
        13: q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q^3+q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^3+q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^3+q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^3+q^2+q+1
        36: q^2+q+1
        37: q^3+q^2+q+1
        38: q+1
        39: q^3+q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q+1
        61: q^3+q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^3+q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q+1
        75: q^3+q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^3+q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^3+q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q^2+q+1
       107: q^2+q+1
       108: q+1
       109: q^2+q+1
       110: q+1
       111: q+1
       112: 1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q^2+q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q+1
       128: q^3+q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q+1
       145: q^3+q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^3+q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: q+1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q^2+q+1
       193: q+1
       194: q^2+q+1
       195: q+1
       196: q+1
       197: q+1
       198: 1
       199: 1
       200: q^2+q+1
       201: q^2+q+1
       202: q+1
       203: q^2+q+1
       204: q+1
       205: q+1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: 1
       227: q+1
       228: 1
       229: 1
       230: q^2+q+1
       231: q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q+1
       235: q+1
       236: 1
       237: q^2+q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: q+1
       252: q^3+q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: 1
       280: 1
       282: q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       313: q+1
       314: 1
       315: q^2+q+1
       316: q+1
       317: q+1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q^2+q+1
       323: q+1
       324: q^2+q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: 1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: 1
       338: q^2+q+1
       339: q^2+q+1
       340: q+1
       341: q^2+q+1
       342: q+1
       343: q+1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q+1
       363: q+1
       364: q+1
       365: 1
       366: 1
       367: q^2+q+1
       368: q^2+q+1
       369: q+1
       370: q^2+q+1
       371: q+1
       372: q+1
       373: 1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: 1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: 1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       420: q+1
       421: 1
       422: 1
       424: 1
       426: q+1
       427: 1
       428: 1
       430: q+1
       431: q+1
       432: 1
       433: q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: 1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: 1
       456: 1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: q+1
       471: q+1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: q+1
       478: 1
       479: q^2+q+1
       480: q+1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q^2+q+1
       496: q+1
       497: q^2+q+1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: 1
       517: 1
       518: 1
       519: 1
       520: q+1
       521: 1
       522: q^2+q+1
       523: q+1
       524: q+1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q^2+q+1
       530: q+1
       531: q^2+q+1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: 1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: q^2+q+1
       546: q^2+q+1
       547: q+1
       548: q^2+q+1
       549: q+1
       550: q+1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: q+1
       556: q+1
       557: q+1
       558: q+1
       559: 1
       560: 1
       561: q+1
       562: q+1
       563: 1
       564: 1
       565: 1
       566: 1
       567: q+1
       569: q+1
       570: q+1
       571: q+1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q+1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       592: 1
       593: 1
       595: 1
       599: q+1
       600: 1
       601: 1
       603: 1
       605: q+1
       606: 1
       607: 1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q+1
       627: 1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       635: q+1
       636: 1
       637: 1
       639: 1
       641: q+1
       642: 1
       643: 1
       645: q+1
       646: q+1
       647: 1
       648: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: q+1
       656: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: q+1
       664: q+1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: q+1
       672: q+1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q^2+q+1
       683: q+1
       684: q+1
       685: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: q+1
       710: q+1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: q+1
       717: 1
       718: q^2+q+1
       719: q+1
       720: q+1
       721: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: q+1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q^2+q+1
       735: q+1
       736: q^2+q+1
       737: q+1
       738: q+1
       739: q+1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: 1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       756: 1
       757: 1
       758: 1
       761: q+1
       762: q+1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: q+1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: q+1
       813: q+1
       814: q+1
       815: q+1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: q+1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       836: 1
       837: 1
       839: 1
       843: q+1
       844: 1
       845: 1
       847: 1
       849: q+1
       850: 1
       851: 1
       853: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: q+1
       868: 1
       870: 1
       871: 1
       872: 1
       875: q+1
       876: q+1
       877: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: q+1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: q+1
       893: q+1
       894: q+1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: q+1
       913: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       921: q+1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: q+1
       929: q+1
       930: q+1
       931: q+1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q^2+q+1
       940: q+1
       941: q+1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: q+1
       948: q+1
       949: q+1
       950: q+1
       951: q+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q+1
       961: 1
       962: 1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1015: 1
      1016: 1
      1017: 1
      1020: q+1
      1021: q+1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q+1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: q+1
      1061: 1
      1062: 1
      1064: 1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1079: 1
      1080: 1
      1084: q+1
      1085: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: q+1
      1093: 1
      1095: 1
      1096: 1
      1097: 1
      1100: q+1
      1101: q+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: q+1
      1127: 1
      1129: 1
      1130: 1
      1131: 1
      1134: q+1
      1135: q+1
      1136: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1144: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: q+1
      1152: q+1
      1153: q+1
      1154: q+1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 1
      1171: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1218: 1
      1219: 1
      1223: q+1
      1224: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1250: 1
      1257: 1
      1259: 1
      1265: 1
      1266: 1
      1268: 1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1294: 1
      1295: 1
      1299: q+1
      1300: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1323: 1
      1324: 1
      1328: q+1
      1329: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: q+1
      1337: 1
      1339: 1
      1340: 1
      1341: 1
      1344: q+1
      1345: q+1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1363: 1
      1368: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1405: 1
      1410: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1443: 1
      1450: 1
      1452: 1
      1457: 1
      1459: 1
      1460: 1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1477: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1492: 1
      1493: 1
      1495: 1
      1500: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1509: 1
      1510: 1
      1514: q+1
      1515: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1534: 1
      1539: 1
      1570: 1
      1575: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1607: 1
      1613: 1
      1618: 1
      1619: 1
      1626: 1
      1631: 1
      1633: 1
      1635: 1
      1636: 1
      1644: 1
      1645: 1
      1646: 1
      1648: 1
      1653: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1701: 1
      1706: 1
      1735: 1
      1746: 1
      1751: 1
      1752: 1
      1759: 1
      1764: 1
      1827: 1

1828:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: 3q^2+3q+1
         9: 2q^3+4q^2+3q+1
        10: q^3+4q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 2q^3+4q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: q^3+4q^2+3q+1
        18: q^3+3q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: 3q^2+3q+1
        28: 2q^3+4q^2+3q+1
        29: q^3+4q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: 2q^3+4q^2+3q+1
        33: q^3+4q^2+3q+1
        34: q^3+4q^2+3q+1
        35: 3q^2+3q+1
        36: 2q^3+4q^2+3q+1
        37: q^3+4q^2+3q+1
        38: 2q^3+4q^2+3q+1
        39: 2q^3+4q^2+3q+1
        40: q^3+4q^2+3q+1
        41: q^3+4q^2+3q+1
        42: 2q^2+3q+1
        43: q^3+3q^2+3q+1
        44: q^2+2q+1
        45: q^3+3q^2+3q+1
        46: q^3+3q^2+3q+1
        47: 2q^3+4q^2+3q+1
        48: q^3+4q^2+3q+1
        49: q^3+3q^2+3q+1
        50: 3q^2+3q+1
        51: 3q^2+3q+1
        52: 3q^2+3q+1
        53: 2q^2+3q+1
        54: 3q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: q^3+4q^2+3q+1
        59: 3q^2+3q+1
        60: 3q^2+3q+1
        61: 3q^2+3q+1
        62: q^3+4q^2+3q+1
        63: q^3+4q^2+3q+1
        64: 2q^2+3q+1
        65: q^3+4q^2+3q+1
        66: q^3+4q^2+3q+1
        67: 3q^2+3q+1
        68: 2q^3+4q^2+3q+1
        69: q^3+4q^2+3q+1
        70: q^3+3q^2+3q+1
        71: 3q^2+3q+1
        72: q^3+4q^2+3q+1
        73: 3q^2+3q+1
        74: 3q^2+3q+1
        75: 3q^2+3q+1
        76: q^3+4q^2+3q+1
        77: q^3+4q^2+3q+1
        78: 3q^2+3q+1
        79: 2q^3+4q^2+3q+1
        80: q^3+4q^2+3q+1
        81: 2q^3+4q^2+3q+1
        82: q^3+4q^2+3q+1
        83: 2q^3+4q^2+3q+1
        84: 2q^2+3q+1
        85: q^3+4q^2+3q+1
        86: 2q^2+3q+1
        87: 2q^2+3q+1
        88: 2q^2+3q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^3+3q^2+3q+1
        93: q^2+2q+1
        94: q^3+3q^2+3q+1
        95: q^2+2q+1
        96: q^3+3q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^2+3q+1
       100: q^3+3q^2+3q+1
       101: q^2+2q+1
       102: q^3+3q^2+3q+1
       103: q^3+3q^2+3q+1
       104: 3q^2+3q+1
       105: 3q^2+3q+1
       106: 3q^2+3q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: 3q^2+3q+1
       111: q^2+2q+1
       112: 3q^2+3q+1
       113: 3q^2+3q+1
       114: 3q^2+3q+1
       115: 2q^2+3q+1
       116: 3q^2+3q+1
       117: 3q^2+3q+1
       118: 3q^2+3q+1
       119: 2q^2+3q+1
       120: q^3+4q^2+3q+1
       121: 2q^2+3q+1
       122: 2q^2+3q+1
       123: 2q^2+3q+1
       124: 3q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 3q^2+3q+1
       127: 3q^2+3q+1
       128: 3q^2+3q+1
       129: q^3+4q^2+3q+1
       130: q^3+4q^2+3q+1
       131: 2q^2+3q+1
       132: q^3+3q^2+3q+1
       133: q^2+2q+1
       134: 3q^2+3q+1
       135: 3q^2+3q+1
       136: 3q^2+3q+1
       137: 2q^2+3q+1
       138: 3q^2+3q+1
       139: 3q^2+3q+1
       140: 3q^2+3q+1
       141: 3q^2+3q+1
       142: q^3+4q^2+3q+1
       143: 3q^2+3q+1
       144: 3q^2+3q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: q^3+4q^2+3q+1
       148: 2q^2+3q+1
       149: q^3+4q^2+3q+1
       150: q^3+4q^2+3q+1
       151: 3q^2+3q+1
       152: 2q^3+4q^2+3q+1
       153: q^3+4q^2+3q+1
       154: q^3+3q^2+3q+1
       155: 2q^2+3q+1
       156: 2q^2+3q+1
       157: 2q^2+3q+1
       158: 2q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 2q^2+3q+1
       162: 2q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q^3+3q^2+3q+1
       174: q^2+2q+1
       175: q^3+3q^2+3q+1
       176: 2q^2+3q+1
       177: q^3+4q^2+3q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: 2q+1
       184: q^3+3q^2+3q+1
       185: q^2+2q+1
       186: q^3+3q^2+3q+1
       187: q^2+2q+1
       188: q^3+3q^2+3q+1
       189: q^2+2q+1
       190: 3q^2+3q+1
       191: 2q^2+3q+1
       192: 2q^2+3q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: 2q^2+3q+1
       196: q^2+2q+1
       197: q+1
       198: 3q^2+3q+1
       199: 3q^2+3q+1
       200: 3q^2+3q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q^2+3q+1
       204: 3q^2+3q+1
       205: q^2+2q+1
       206: 2q^2+3q+1
       207: 2q^2+3q+1
       208: 2q^2+3q+1
       209: 2q+1
       210: 2q^2+3q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: 3q^2+3q+1
       214: 3q^2+3q+1
       215: 3q^2+3q+1
       216: 2q^2+3q+1
       217: 3q^2+3q+1
       218: 3q^2+3q+1
       219: 3q^2+3q+1
       220: 2q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q^2+3q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 3q^2+3q+1
       229: 3q^2+3q+1
       230: 3q^2+3q+1
       231: 2q^2+3q+1
       232: 2q^2+3q+1
       233: 2q^2+3q+1
       234: 3q^2+3q+1
       235: q^2+2q+1
       236: 3q^2+3q+1
       237: 3q^2+3q+1
       238: 3q^2+3q+1
       239: 2q^2+3q+1
       240: 3q^2+3q+1
       241: 3q^2+3q+1
       242: 3q^2+3q+1
       243: 2q^2+3q+1
       244: q^3+4q^2+3q+1
       245: 2q^2+3q+1
       246: 2q^2+3q+1
       247: 2q^2+3q+1
       248: 3q^2+3q+1
       249: q^3+4q^2+3q+1
       250: 3q^2+3q+1
       251: 3q^2+3q+1
       252: 3q^2+3q+1
       253: q^3+4q^2+3q+1
       254: q^3+4q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+3q^2+3q+1
       257: q^2+2q+1
       258: 2q^2+3q+1
       259: 2q^2+3q+1
       260: 2q^2+3q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q^2+3q+1
       265: q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: q+1
       279: q^2+2q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q+1
       286: q^3+3q^2+3q+1
       287: q^2+2q+1
       288: 2q^2+3q+1
       289: 2q^2+3q+1
       290: 2q^2+3q+1
       291: 2q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: 2q^2+3q+1
       295: 2q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: 2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q+1
       306: q^3+3q^2+3q+1
       307: q^2+2q+1
       308: q^3+3q^2+3q+1
       309: q+1
       310: q^2+2q+1
       311: 2q^2+3q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: q+1
       317: q+1
       318: q+1
       319: q^2+2q+1
       320: 3q^2+3q+1
       321: 2q^2+3q+1
       322: 2q^2+3q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: 2q^2+3q+1
       326: q^2+2q+1
       327: q+1
       328: 2q^2+3q+1
       329: 2q^2+3q+1
       330: 2q^2+3q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q^2+3q+1
       335: q^2+2q+1
       336: 3q^2+3q+1
       337: 3q^2+3q+1
       338: 3q^2+3q+1
       339: 2q^2+3q+1
       340: 2q^2+3q+1
       341: 2q^2+3q+1
       342: 3q^2+3q+1
       343: q^2+2q+1
       344: 2q^2+3q+1
       345: 2q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: 2q^2+3q+1
       349: 2q^2+3q+1
       350: 2q^2+3q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       356: q^2+2q+1
       357: 3q^2+3q+1
       358: 2q^2+3q+1
       359: 2q^2+3q+1
       360: q^2+2q+1
       361: q^2+2q+1
       362: 2q^2+3q+1
       363: q^2+2q+1
       364: q+1
       365: 3q^2+3q+1
       366: 3q^2+3q+1
       367: 3q^2+3q+1
       368: 2q^2+3q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 3q^2+3q+1
       372: q^2+2q+1
       373: 2q^2+3q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: 2q+1
       377: 2q^2+3q+1
       378: 2q^2+3q+1
       379: 2q^2+3q+1
       380: 3q^2+3q+1
       381: 3q^2+3q+1
       382: 3q^2+3q+1
       383: 2q^2+3q+1
       384: 3q^2+3q+1
       385: 3q^2+3q+1
       386: 3q^2+3q+1
       387: 2q^2+3q+1
       388: q^3+4q^2+3q+1
       389: 2q^2+3q+1
       390: 2q^2+3q+1
       391: 2q^2+3q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: 2q+1
       395: q^2+2q+1
       396: 2q^2+3q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: q+1
       421: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q+1
       434: 2q^2+3q+1
       435: 2q^2+3q+1
       436: 2q^2+3q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: q^2+2q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: q+1
       455: q^2+2q+1
       456: q+1
       457: q+1
       458: q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^3+3q^2+3q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: q+1
       467: q^2+2q+1
       468: q^2+2q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       473: q+1
       474: q^2+2q+1
       475: 2q^2+3q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: q+1
       481: q+1
       482: q+1
       483: q^2+2q+1
       484: 2q^2+3q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q^2+2q+1
       491: q+1
       492: q^2+2q+1
       493: 3q^2+3q+1
       494: 2q^2+3q+1
       495: 2q^2+3q+1
       496: q^2+2q+1
       497: q^2+2q+1
       498: 2q^2+3q+1
       499: q^2+2q+1
       500: q+1
       501: 2q^2+3q+1
       502: 2q^2+3q+1
       503: 2q^2+3q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q^2+3q+1
       508: q^2+2q+1
       509: 2q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: q+1
       517: q^2+2q+1
       518: 2q^2+3q+1
       519: q^2+2q+1
       520: q^2+2q+1
       521: q^2+2q+1
       522: q^2+2q+1
       523: q+1
       524: q+1
       525: q+1
       526: q^2+2q+1
       527: 3q^2+3q+1
       528: 2q^2+3q+1
       529: 2q^2+3q+1
       530: q^2+2q+1
       531: q^2+2q+1
       532: 2q^2+3q+1
       533: q^2+2q+1
       534: q+1
       535: 2q^2+3q+1
       536: 2q^2+3q+1
       537: 2q^2+3q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q^2+3q+1
       542: q^2+2q+1
       543: 3q^2+3q+1
       544: 3q^2+3q+1
       545: 3q^2+3q+1
       546: 2q^2+3q+1
       547: 2q^2+3q+1
       548: 2q^2+3q+1
       549: 3q^2+3q+1
       550: q^2+2q+1
       551: 2q^2+3q+1
       552: 2q^2+3q+1
       553: 2q^2+3q+1
       554: 2q+1
       555: 2q^2+3q+1
       556: 2q^2+3q+1
       557: 2q^2+3q+1
       558: 2q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q+1
       562: 2q+1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       596: q+1
       597: 1
       598: q+1
       599: q+1
       600: q+1
       602: q+1
       603: q+1
       604: q+1
       605: q+1
       606: q^2+2q+1
       607: q+1
       608: q+1
       609: q+1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: 2q+1
       628: 2q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: q+1
       635: q+1
       636: q+1
       638: q+1
       639: q+1
       640: q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: q+1
       658: q+1
       659: q+1
       660: q^2+2q+1
       661: q^2+2q+1
       662: q+1
       663: q+1
       664: 1
       665: q+1
       666: q+1
       667: q^2+2q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q^2+2q+1
       678: 2q^2+3q+1
       679: q^2+2q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: q^2+2q+1
       683: q+1
       684: q+1
       685: q+1
       686: q^2+2q+1
       687: 2q^2+3q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q^2+2q+1
       694: q+1
       695: 2q+1
       696: 2q+1
       697: 2q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: 2q+1
       702: 1
       703: q+1
       704: q+1
       705: q+1
       706: q^2+2q+1
       707: q^2+2q+1
       708: q+1
       709: q+1
       710: 1
       711: q+1
       712: q+1
       713: q^2+2q+1
       714: 2q^2+3q+1
       715: q^2+2q+1
       716: q^2+2q+1
       717: q^2+2q+1
       718: q^2+2q+1
       719: q+1
       720: q+1
       721: q+1
       722: q^2+2q+1
       723: 2q^2+3q+1
       724: 2q+1
       725: 2q+1
       726: q+1
       727: q+1
       728: 2q+1
       729: q^2+2q+1
       730: q+1
       731: q^2+2q+1
       732: 3q^2+3q+1
       733: 2q^2+3q+1
       734: 2q^2+3q+1
       735: q^2+2q+1
       736: q^2+2q+1
       737: 2q^2+3q+1
       738: q^2+2q+1
       739: q+1
       740: 2q^2+3q+1
       741: 2q^2+3q+1
       742: 2q^2+3q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 2q^2+3q+1
       747: q^2+2q+1
       748: 2q+1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: 2q+1
       754: 2q+1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       773: 1
       774: 1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       790: 1
       791: 1
       792: q+1
       793: q+1
       794: q+1
       798: q+1
       799: 1
       800: q+1
       801: q+1
       802: q+1
       804: q+1
       805: q+1
       806: q+1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: 2q+1
       827: 2q+1
       828: 2q+1
       829: 2q+1
       830: 2q+1
       831: 2q+1
       832: 2q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       840: q+1
       841: 1
       842: q+1
       843: q+1
       844: q+1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       853: q+1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: q+1
       881: q^2+2q+1
       882: q^2+2q+1
       883: q+1
       884: q+1
       885: 1
       886: q+1
       887: q+1
       888: q^2+2q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: 2q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: q+1
       909: q+1
       910: q+1
       911: 1
       912: 1
       913: 1
       914: q+1
       915: q+1
       916: q+1
       917: q^2+2q+1
       918: q^2+2q+1
       919: q+1
       920: q+1
       921: 1
       922: q+1
       923: q+1
       924: q^2+2q+1
       925: 2q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: 1
       931: q+1
       932: q+1
       933: q+1
       934: q^2+2q+1
       935: 2q^2+3q+1
       936: q^2+2q+1
       937: q^2+2q+1
       938: q^2+2q+1
       939: q^2+2q+1
       940: q+1
       941: q+1
       942: q+1
       943: q^2+2q+1
       944: 2q^2+3q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: q^2+2q+1
       951: q+1
       952: 2q+1
       953: 2q+1
       954: 2q+1
       955: 2q+1
       956: 2q+1
       957: 2q+1
       958: 2q+1
       959: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       977: 1
       978: 1
       979: 2q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: q+1
      1004: 1
      1005: 1
      1006: q+1
      1007: q+1
      1008: q+1
      1012: q+1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1032: 1
      1033: 1
      1034: 2q+1
      1035: 2q+1
      1036: 2q+1
      1037: q+1
      1038: q+1
      1039: 2q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1049: 1
      1050: 1
      1051: q+1
      1052: q+1
      1053: q+1
      1057: q+1
      1058: 1
      1059: q+1
      1060: q+1
      1061: q+1
      1063: q+1
      1064: q+1
      1065: q+1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: 2q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: q+1
      1117: 1
      1118: 1
      1119: 1
      1120: q+1
      1121: 1
      1122: q+1
      1123: q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1128: q+1
      1129: q+1
      1130: 1
      1131: q+1
      1132: q+1
      1133: 1
      1134: 1
      1135: 1
      1136: q+1
      1137: q+1
      1138: q+1
      1139: q+1
      1140: q^2+2q+1
      1141: q^2+2q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: q+1
      1146: q+1
      1147: q^2+2q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1155: q+1
      1156: 1
      1157: 2q+1
      1158: 2q+1
      1159: 2q+1
      1160: q+1
      1161: q+1
      1162: 2q+1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1182: 1
      1183: q+1
      1184: q+1
      1185: 1
      1186: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: q+1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1234: 1
      1235: 1
      1236: 2q+1
      1237: q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: q+1
      1261: 1
      1262: 1
      1263: q+1
      1264: q+1
      1265: q+1
      1269: q+1
      1270: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: q+1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: q+1
      1331: 1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1338: q+1
      1339: q+1
      1340: 1
      1341: q+1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1346: q+1
      1347: 1
      1348: 1
      1349: 2q+1
      1350: q+1
      1351: q+1
      1352: q+1
      1353: q+1
      1354: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1421: 1
      1422: q+1
      1423: q+1
      1424: 1
      1425: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: q+1
      1454: 1
      1455: 1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1508: q+1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: 1
      1518: 1
      1519: q+1
      1520: q+1
      1521: 1
      1522: 1
      1525: 1
      1536: 1
      1555: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1614: 1
      1617: 1
      1620: 1
      1621: 1
      1622: 1
      1624: 1
      1628: 1
      1634: 1
      1637: 1
      1638: 1
      1639: 1
      1641: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1656: 1
      1657: 1
      1658: 1
      1692: 1
      1703: 1
      1722: 1
      1736: 1
      1747: 1
      1750: 1
      1753: 1
      1754: 1
      1755: 1
      1757: 1
      1761: 1
      1828: 1

1829:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       165: 1
       166: 1
       167: 1
       169: 1
       170: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       272: 1
       273: 1
       276: 1
       277: 1
       278: 1
       281: 1
       282: 1
       283: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       298: 1
       299: 1
       300: 1
       302: 1
       303: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       411: 1
       412: 1
       413: 1
       418: 1
       419: 1
       420: 1
       425: 1
       426: 1
       429: 1
       430: 1
       431: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       448: 1
       449: 1
       452: 1
       453: 1
       454: 1
       457: 1
       458: 1
       459: 1
       461: 1
       462: 1
       463: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       581: 1
       582: 1
       589: 1
       590: 1
       597: 1
       598: 1
       599: 1
       604: 1
       605: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       626: 1
       627: 1
       628: 1
       633: 1
       634: 1
       635: 1
       640: 1
       641: 1
       644: 1
       645: 1
       646: 1
       648: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       754: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       764: 1
       774: 1
       782: 1
       783: 1
       791: 1
       792: 1
       799: 1
       800: 1
       801: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       825: 1
       826: 1
       833: 1
       834: 1
       841: 1
       842: 1
       843: 1
       848: 1
       849: 1
       852: 1
       853: 1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       977: 1
       987: 1
       997: 1
      1005: 1
      1006: 1
      1013: 1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
      1051: 1
      1058: 1
      1059: 1
      1060: 1
      1065: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1103: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1198: 1
      1208: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1312: 1
      1313: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1347: 1
      1359: 1
      1360: 1
      1394: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1447: 1
      1455: 1
      1459: 1
      1463: 1
      1464: 1
      1468: 1
      1469: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1526: 1
      1566: 1
      1567: 1
      1601: 1
      1615: 1
      1618: 1
      1622: 1
      1623: 1
      1635: 1
      1639: 1
      1640: 1
      1644: 1
      1645: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1693: 1
      1737: 1
      1748: 1
      1751: 1
      1755: 1
      1756: 1
      1829: 1

1830:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: 1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q^2+q+1
        76: q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: 1
        90: 1
        91: 1
        92: q^2+q+1
        93: 1
        94: q^2+q+1
        95: 1
        96: q^2+q+1
        97: q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: 1
       102: q^2+q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+q+1
       111: q^2+q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q+1
       120: q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q^2+q+1
       124: q+1
       125: q+1
       126: q^2+q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q+1
       130: q^2+q+1
       131: q^2+q+1
       132: q^2+q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q^2+q+1
       139: q^2+q+1
       140: q^2+q+1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q+1
       147: q^2+q+1
       148: q^2+q+1
       149: q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q^2+q+1
       153: q^2+q+1
       154: q^2+q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q^2+q+1
       174: 1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q^2+q+1
       179: q^2+q+1
       180: q^2+q+1
       181: 1
       182: 1
       183: 1
       184: q^2+q+1
       185: 1
       186: q^2+q+1
       187: 1
       188: q^2+q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q^2+q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q^2+q+1
       205: q^2+q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q^2+q+1
       211: q^2+q+1
       212: q^2+q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+q+1
       220: q+1
       221: q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q^2+q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q^2+q+1
       235: q^2+q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q^2+q+1
       241: q^2+q+1
       242: q^2+q+1
       243: q+1
       244: q+1
       245: q^2+q+1
       246: q^2+q+1
       247: q^2+q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q+1
       254: q^2+q+1
       255: q^2+q+1
       256: q^2+q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q^2+q+1
       265: q^2+q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q^2+q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q^2+q+1
       293: q^2+q+1
       294: q^2+q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+q+1
       307: 1
       308: q^2+q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q^2+q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q^2+q+1
       335: q^2+q+1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q^2+q+1
       349: q^2+q+1
       350: q^2+q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q^2+q+1
       364: 1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q^2+q+1
       372: q^2+q+1
       373: q+1
       374: q+1
       375: q+1
       376: 1
       377: q^2+q+1
       378: q^2+q+1
       379: q^2+q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q^2+q+1
       385: q^2+q+1
       386: q^2+q+1
       387: q+1
       388: q+1
       389: q^2+q+1
       390: q^2+q+1
       391: q^2+q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q^2+q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q^2+q+1
       441: q^2+q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+q+1
       463: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q^2+q+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q^2+q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q^2+q+1
       508: q^2+q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       524: 1
       525: 1
       526: q+1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q^2+q+1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q^2+q+1
       542: q^2+q+1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q^2+q+1
       550: q^2+q+1
       551: q+1
       552: q+1
       553: q+1
       554: 1
       555: q^2+q+1
       556: q^2+q+1
       557: q^2+q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: 1
       711: 1
       713: q+1
       714: q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: q+1
       720: 1
       721: 1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q^2+q+1
       730: 1
       731: q+1
       732: q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q^2+q+1
       739: 1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q^2+q+1
       747: q^2+q+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       885: 1
       886: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: q+1
       909: q+1
       910: q+1
       911: 1
       912: 1
       913: 1
       916: q+1
       917: q+1
       918: q+1
       919: q+1
       920: q+1
       921: 1
       922: 1
       924: q+1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       934: q+1
       935: q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: 1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q^2+q+1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       986: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1069: 1
      1070: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1116: q+1
      1117: 1
      1118: 1
      1119: 1
      1122: q+1
      1123: q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1139: q+1
      1140: q+1
      1141: q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1243: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1273: 1
      1277: 1
      1278: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1313: 1
      1314: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1356: 1
      1360: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1395: 1
      1403: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1460: 1
      1464: 1
      1465: 1
      1469: 1
      1470: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1488: 1
      1492: 1
      1493: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1527: 1
      1536: 1
      1567: 1
      1568: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1602: 1
      1610: 1
      1616: 1
      1619: 1
      1623: 1
      1624: 1
      1628: 1
      1636: 1
      1640: 1
      1641: 1
      1645: 1
      1646: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1656: 1
      1657: 1
      1658: 1
      1694: 1
      1703: 1
      1738: 1
      1749: 1
      1752: 1
      1756: 1
      1757: 1
      1761: 1
      1830: 1

1831:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: 1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: 1
        55: q^2+q+1
        56: 1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: 1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: 1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: q^2+q+1
       107: q^2+q+1
       108: 1
       109: q^2+q+1
       110: 1
       111: 1
       112: 1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: 1
       117: q^2+q+1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: q+1
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: 1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: 1
       139: q^2+q+1
       140: 1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: 1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: q^2+q+1
       193: 1
       194: q^2+q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q^2+q+1
       201: q^2+q+1
       202: 1
       203: q^2+q+1
       204: 1
       205: 1
       206: 1
       207: q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: 1
       218: q^2+q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: q^2+q+1
       231: q^2+q+1
       232: 1
       233: q^2+q+1
       234: 1
       235: 1
       236: 1
       237: q^2+q+1
       238: q^2+q+1
       239: q^2+q+1
       240: 1
       241: q^2+q+1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: q+1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: 1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q^2+q+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q^2+q+1
       323: 1
       324: q^2+q+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+q+1
       339: q^2+q+1
       340: 1
       341: q^2+q+1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: 1
       357: 1
       358: 1
       359: q^2+q+1
       360: 1
       361: q^2+q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q^2+q+1
       368: q^2+q+1
       369: 1
       370: q^2+q+1
       371: 1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+q+1
       384: 1
       385: q^2+q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       412: 1
       413: q+1
       414: q+1
       415: q+1
       416: 1
       417: q+1
       418: 1
       420: q+1
       421: q+1
       422: q+1
       424: q+1
       426: q+1
       427: q+1
       428: q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: q^2+q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q^2+q+1
       496: 1
       497: q^2+q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q^2+q+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q^2+q+1
       530: 1
       531: q^2+q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+q+1
       546: q^2+q+1
       547: 1
       548: q^2+q+1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: q+1
       585: q+1
       586: 1
       587: q+1
       588: 1
       589: 1
       592: q+1
       593: q+1
       595: q+1
       599: q+1
       600: q+1
       601: q+1
       603: q+1
       605: q+1
       606: q+1
       607: q+1
       609: q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: q+1
       629: q+1
       630: q+1
       631: 1
       632: q+1
       633: 1
       635: q+1
       636: q+1
       637: q+1
       639: q+1
       641: q+1
       642: q+1
       643: q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       651: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: q^2+q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: q^2+q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       727: q+1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q^2+q+1
       735: 1
       736: q^2+q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: q+1
       778: 1
       779: q+1
       780: 1
       781: 1
       782: 1
       786: q+1
       788: q+1
       794: q+1
       795: q+1
       797: q+1
       801: q+1
       802: q+1
       803: q+1
       805: q+1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: q+1
       829: q+1
       830: 1
       831: q+1
       832: 1
       833: 1
       836: q+1
       837: q+1
       839: q+1
       843: q+1
       844: q+1
       845: q+1
       847: q+1
       849: q+1
       850: q+1
       851: q+1
       853: q+1
       854: 1
       855: 1
       860: 1
       861: 1
       862: 1
       863: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       902: q+1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: q+1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: q^2+q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: q+1
       984: 1
       985: 1
       986: 1
       993: q+1
      1000: q+1
      1002: q+1
      1008: q+1
      1009: q+1
      1011: q+1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: q+1
      1037: 1
      1038: q+1
      1039: 1
      1040: 1
      1041: 1
      1045: q+1
      1047: q+1
      1053: q+1
      1054: q+1
      1056: q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1064: q+1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: q+1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1161: q+1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1204: q+1
      1211: q+1
      1213: q+1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: q+1
      1241: 1
      1242: 1
      1243: 1
      1250: q+1
      1257: q+1
      1259: q+1
      1265: q+1
      1266: q+1
      1268: q+1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: q+1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: q+1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1443: q+1
      1450: q+1
      1452: q+1
      1461: 1
      1466: 1
      1471: 1
      1472: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1489: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1502: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1607: q+1
      1620: 1
      1625: 1
      1626: 1
      1631: 1
      1637: 1
      1642: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1667: 1
      1695: 1
      1700: 1
      1701: 1
      1706: 1
      1739: 1
      1753: 1
      1758: 1
      1759: 1
      1764: 1
      1791: 1
      1831: 1

1832:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+q^2+2q+1
        23: q^3+q^2+2q+1
        24: q^2+q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+q^2+2q+1
        28: q^3+2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^3+q^2+2q+1
        36: q^3+2q^2+2q+1
        37: q^3+2q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^3+q^2+2q+1
        51: q^2+q+1
        52: q^3+q^2+2q+1
        53: q^3+q^2+2q+1
        54: q^3+q^2+2q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^3+q^2+2q+1
        58: q^3+2q^2+2q+1
        59: q^3+q^2+2q+1
        60: q^3+q^2+2q+1
        61: q^2+q+1
        62: q^3+2q^2+2q+1
        63: q^3+2q^2+2q+1
        64: 2q+1
        65: q^3+2q^2+2q+1
        66: q^3+2q^2+2q+1
        67: q^3+q^2+2q+1
        68: q^3+2q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^3+q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^3+q^2+2q+1
        74: q^3+q^2+2q+1
        75: q^2+q+1
        76: q^3+2q^2+2q+1
        77: q^3+2q^2+2q+1
        78: q^3+q^2+2q+1
        79: q^3+2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: q^3+2q^2+2q+1
        82: q^3+2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q+1
        85: q^3+2q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+q+1
       105: q^3+q^2+2q+1
       106: q^2+q+1
       107: q^3+q^2+2q+1
       108: q^3+q^2+2q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q+1
       112: q^3+q^2+2q+1
       113: q^2+q+1
       114: q^3+q^2+2q+1
       115: q^3+q^2+2q+1
       116: q^3+q^2+2q+1
       117: q^2+q+1
       118: q^2+q+1
       119: 2q+1
       120: q^3+2q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: q+1
       124: q^3+q^2+2q+1
       125: q^3+2q^2+2q+1
       126: q^3+q^2+2q+1
       127: q^3+q^2+2q+1
       128: q^2+q+1
       129: q^3+2q^2+2q+1
       130: q^3+2q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q^3+q^2+2q+1
       135: q^2+q+1
       136: q^3+q^2+2q+1
       137: q^3+q^2+2q+1
       138: q^3+q^2+2q+1
       139: q^2+q+1
       140: q^2+q+1
       141: q^3+q^2+2q+1
       142: q^3+2q^2+2q+1
       143: q^3+q^2+2q+1
       144: q^3+q^2+2q+1
       145: q^2+q+1
       146: q^3+2q^2+2q+1
       147: q^3+2q^2+2q+1
       148: 2q+1
       149: q^3+2q^2+2q+1
       150: q^3+2q^2+2q+1
       151: q^3+q^2+2q+1
       152: q^3+2q^2+2q+1
       153: q^3+2q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: q+1
       161: q+1
       162: 2q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q+1
       166: q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^3+2q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q^2+q+1
       191: q^3+q^2+2q+1
       192: q^2+q+1
       193: q+1
       194: q^2+1
       195: q^2+q+1
       196: q+1
       197: q+1
       198: q^2+q+1
       199: q^3+q^2+2q+1
       200: q^2+q+1
       201: q^3+q^2+2q+1
       202: q^3+q^2+2q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q+1
       206: 2q+1
       207: q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q+1
       213: q^3+q^2+2q+1
       214: q^2+q+1
       215: q^3+q^2+2q+1
       216: q^3+q^2+2q+1
       217: q^3+q^2+2q+1
       218: q^2+q+1
       219: q^2+q+1
       220: 2q+1
       221: q^3+2q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+q+1
       229: q^3+q^2+2q+1
       230: q^2+q+1
       231: q^3+q^2+2q+1
       232: q^3+q^2+2q+1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q^3+q^2+2q+1
       237: q^2+q+1
       238: q^3+q^2+2q+1
       239: q^3+q^2+2q+1
       240: q^3+q^2+2q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 2q+1
       244: q^3+2q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: q+1
       248: q^3+q^2+2q+1
       249: q^3+2q^2+2q+1
       250: q^3+q^2+2q+1
       251: q^3+q^2+2q+1
       252: q^2+q+1
       253: q^3+2q^2+2q+1
       254: q^3+2q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q+1
       259: 2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q+1
       272: q+1
       273: 2q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q+1
       277: q+1
       278: q+1
       279: q^2+2q+1
       280: q+1
       281: q+1
       282: 1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: q+1
       294: q+1
       295: 2q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q+1
       299: q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: 2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q^2+q+1
       312: q+1
       314: q^2+1
       315: q^2+1
       316: 1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+q+1
       321: q^3+q^2+2q+1
       322: q^2+q+1
       323: q+1
       324: q^2+1
       325: q^2+q+1
       326: q+1
       327: q+1
       328: q+1
       329: 2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q+1
       335: q+1
       336: q^2+q+1
       337: q^3+q^2+2q+1
       338: q^2+q+1
       339: q^3+q^2+2q+1
       340: q^3+q^2+2q+1
       341: q^2+q+1
       342: q^2+q+1
       343: q+1
       344: 2q+1
       345: q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: q+1
       350: q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: q+1
       356: q+1
       357: q^2+q+1
       358: q^3+q^2+2q+1
       359: q^2+q+1
       360: q+1
       361: q^2+1
       362: q^2+q+1
       363: q+1
       364: q+1
       365: q^2+q+1
       366: q^3+q^2+2q+1
       367: q^2+q+1
       368: q^3+q^2+2q+1
       369: q^3+q^2+2q+1
       370: q^2+q+1
       371: q^2+q+1
       372: q+1
       373: 2q+1
       374: q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: q+1
       379: q+1
       380: q^3+q^2+2q+1
       381: q^2+q+1
       382: q^3+q^2+2q+1
       383: q^3+q^2+2q+1
       384: q^3+q^2+2q+1
       385: q^2+q+1
       386: q^2+q+1
       387: 2q+1
       388: q^3+2q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: 2q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: q+1
       410: q+1
       411: 1
       412: 2q+1
       413: q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: 1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q+1
       434: q+1
       435: 2q+1
       436: q+1
       437: 2q+1
       438: 2q+1
       439: q+1
       440: q+1
       441: q+1
       442: 2q+1
       443: q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: q+1
       448: q+1
       449: 2q+1
       450: q^2+2q+1
       451: 2q+1
       452: 2q+1
       453: q+1
       454: q+1
       455: q^2+2q+1
       456: q+1
       457: q+1
       458: 1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: 1
       468: q^2+1
       469: 1
       471: 1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+q+1
       476: q+1
       478: q^2+1
       479: q^2+1
       480: 1
       481: q+1
       482: q+1
       483: q+1
       484: q+1
       485: 2q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       492: q+1
       493: q^2+q+1
       494: q^3+q^2+2q+1
       495: q^2+q+1
       496: q+1
       497: q^2+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: q+1
       502: 2q+1
       503: q+1
       504: 2q+1
       505: 2q+1
       506: q+1
       507: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q^2+q+1
       519: q+1
       521: q^2+1
       522: q^2+1
       523: 1
       524: q+1
       525: q+1
       526: q+1
       527: q^2+q+1
       528: q^3+q^2+2q+1
       529: q^2+q+1
       530: q+1
       531: q^2+1
       532: q^2+q+1
       533: q+1
       534: q+1
       535: q+1
       536: 2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: q+1
       542: q+1
       543: q^2+q+1
       544: q^3+q^2+2q+1
       545: q^2+q+1
       546: q^3+q^2+2q+1
       547: q^3+q^2+2q+1
       548: q^2+q+1
       549: q^2+q+1
       550: q+1
       551: 2q+1
       552: q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: q+1
       557: q+1
       558: 2q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q+1
       562: q+1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: 2q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: 2q+1
       584: q+1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q^2+2q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: 2q+1
       613: q+1
       614: q+1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: 2q+1
       621: q+1
       622: 2q+1
       623: 2q+1
       624: q+1
       625: q+1
       626: 1
       627: 2q+1
       628: q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: q+1
       633: q+1
       634: q+1
       635: 1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: q+1
       645: 1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       652: 1
       654: 1
       656: 1
       657: q+1
       658: q+1
       659: 1
       661: q^2+1
       662: 1
       664: 1
       665: q+1
       666: q+1
       667: q+1
       668: q+1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: q^2+q+1
       679: q+1
       681: q^2+1
       682: q^2+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: 2q+1
       689: q+1
       690: q+1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: 2q+1
       697: q+1
       698: 2q+1
       699: 2q+1
       700: q+1
       701: q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       707: q^2+1
       708: 1
       710: 1
       711: q+1
       712: q+1
       713: q+1
       714: q^2+q+1
       715: q+1
       717: q^2+1
       718: q^2+1
       719: 1
       720: q+1
       721: q+1
       722: q+1
       723: q+1
       724: 2q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: q+1
       730: q+1
       731: q+1
       732: q^2+q+1
       733: q^3+q^2+2q+1
       734: q^2+q+1
       735: q+1
       736: q^2+1
       737: q^2+q+1
       738: q+1
       739: q+1
       740: q+1
       741: 2q+1
       742: q+1
       743: 2q+1
       744: 2q+1
       745: q+1
       746: q+1
       747: q+1
       748: 2q+1
       749: q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: q+1
       754: q+1
       755: q+1
       756: q+1
       757: 1
       759: 1
       760: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: 2q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: 2q+1
       820: q+1
       821: q+1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 2q+1
       828: q+1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       841: 1
       842: q+1
       843: 1
       844: q+1
       845: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       853: 1
       854: 1
       856: 1
       859: 1
       861: q+1
       862: 1
       864: 1
       866: 1
       868: 1
       869: q+1
       870: q+1
       871: 1
       873: 1
       874: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       882: q^2+1
       883: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: 2q+1
       900: q+1
       901: q+1
       902: 1
       903: q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       909: 1
       911: 1
       913: 1
       914: q+1
       915: q+1
       916: 1
       918: q^2+1
       919: 1
       921: 1
       922: q+1
       923: q+1
       924: q+1
       925: q+1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: q+1
       932: q+1
       933: q+1
       934: q+1
       935: q^2+q+1
       936: q+1
       938: q^2+1
       939: q^2+1
       940: 1
       941: q+1
       942: q+1
       943: q+1
       944: q+1
       945: 2q+1
       946: q+1
       947: q+1
       948: 1
       949: q+1
       950: q+1
       951: q+1
       952: q+1
       953: 2q+1
       954: q+1
       955: 2q+1
       956: 2q+1
       957: q+1
       958: q+1
       959: 1
       960: q+1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: 2q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: q+1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: q+1
      1053: 1
      1054: q+1
      1055: q+1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: 1
      1065: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: q+1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: q+1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: q+1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1128: q+1
      1129: q+1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1136: q+1
      1137: q+1
      1138: q+1
      1139: 1
      1141: q^2+1
      1142: 1
      1144: 1
      1145: q+1
      1146: q+1
      1147: q+1
      1148: q+1
      1149: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1155: q+1
      1156: 1
      1157: q+1
      1158: 2q+1
      1159: q+1
      1160: q+1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: 1
      1177: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: q+1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1270: 1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1291: 1
      1293: q+1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1322: q+1
      1323: 1
      1325: 1
      1327: 1
      1329: 1
      1330: q+1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1338: q+1
      1339: q+1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: q+1
      1347: 1
      1348: 1
      1349: q+1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1369: 1
      1370: 1
      1372: 1
      1374: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1423: 1
      1424: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1432: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: q+1
      1450: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1462: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1478: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1490: 1
      1494: 1
      1496: 1
      1499: 1
      1501: 1
      1503: 1
      1506: 1
      1508: q+1
      1509: 1
      1511: 1
      1513: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1520: 1
      1521: 1
      1523: 1
      1524: 1
      1529: 1
      1533: 1
      1535: 1
      1538: 1
      1547: 1
      1555: 1
      1556: 1
      1559: 1
      1563: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1576: 1
      1577: 1
      1579: 1
      1581: 1
      1583: 1
      1584: 1
      1592: 1
      1593: 1
      1596: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1606: 1
      1607: 1
      1609: 1
      1610: 1
      1621: 1
      1625: 1
      1627: 1
      1630: 1
      1638: 1
      1643: 1
      1647: 1
      1649: 1
      1652: 1
      1654: 1
      1655: 1
      1657: 1
      1659: 1
      1661: 1
      1668: 1
      1684: 1
      1696: 1
      1700: 1
      1702: 1
      1705: 1
      1714: 1
      1722: 1
      1723: 1
      1726: 1
      1730: 1
      1740: 1
      1754: 1
      1758: 1
      1760: 1
      1763: 1
      1792: 1
      1808: 1
      1832: 1

1833:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 2q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: 2q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: 2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: 2q+1
       149: 2q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+2q+1
       153: 2q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: 2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q+1
       169: 2q+1
       170: q^2+2q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       182: q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q^2+2q+1
       214: q^2+2q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: q^2+2q+1
       220: 2q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q+1
       227: 2q+1
       228: q^2+2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q^2+2q+1
       237: q^2+2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: q^2+2q+1
       243: 2q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: 2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 2q^2+2q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: 2q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: 2q+1
       277: 2q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: q^2+2q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q+1
       302: 2q+1
       303: q^2+2q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: q^2+2q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+1
       352: q+1
       353: q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: q^2+2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q^2+2q+1
       381: q^2+2q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: q^2+2q+1
       387: 2q+1
       388: q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q^2+2q+1
       393: q+1
       394: 2q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 2q+1
       413: 2q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: 2q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q+1
       427: q+1
       428: 1
       429: q+1
       430: q+1
       431: q^2+2q+1
       432: q+1
       433: q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: 2q+1
       450: q+1
       451: q+1
       452: 2q+1
       453: 2q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: q^2+2q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: q+1
       474: q+1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: 2q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       543: q^2+2q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 2q+1
       559: q+1
       560: q+1
       561: 2q+1
       562: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 2q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q+1
       605: q+1
       606: q+1
       607: 1
       608: q+1
       609: q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 2q+1
       628: 2q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: 2q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: q+1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: q+1
       713: q+1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       722: q+1
       723: 2q+1
       724: 2q+1
       725: 2q+1
       726: q+1
       727: q+1
       728: 2q+1
       729: q+1
       730: q+1
       731: q+1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: 2q+1
       749: 2q+1
       750: q+1
       751: q+1
       752: q+1
       753: q+1
       754: 2q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 2q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: q+1
       902: 1
       903: q+1
       904: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: q+1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       921: 1
       923: q+1
       924: q+1
       925: 2q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: 1
       931: q+1
       933: q+1
       934: q+1
       935: 2q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       943: q+1
       944: 2q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: q+1
       951: q+1
       952: 2q+1
       953: q+1
       954: q+1
       955: q+1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: q+1
      1027: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1103: 1
      1104: 1
      1105: q+1
      1106: q+1
      1107: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: q+1
      1130: 1
      1131: q+1
      1132: q+1
      1133: 1
      1134: 1
      1135: 1
      1138: q+1
      1139: 1
      1140: q+1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1146: q+1
      1147: q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1156: 1
      1157: q+1
      1158: q+1
      1159: q+1
      1160: q+1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1190: 1
      1193: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1302: 1
      1303: 1
      1304: q+1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: q+1
      1340: 1
      1341: q+1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1347: 1
      1348: 1
      1349: q+1
      1350: q+1
      1351: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1386: 1
      1389: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: q+1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1429: 1
      1432: 1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1463: 1
      1468: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1491: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1517: 1
      1518: 1
      1519: q+1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1530: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1556: 1
      1559: 1
      1566: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1593: 1
      1596: 1
      1601: 1
      1602: 1
      1603: 1
      1606: 1
      1607: 1
      1609: 1
      1622: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1639: 1
      1644: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1669: 1
      1697: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1723: 1
      1726: 1
      1741: 1
      1755: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1793: 1
      1833: 1

1834:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: q^3+3q^2+2q+1
         5: q^3+3q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+3q^2+2q+1
        10: 3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: 3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: q^3+3q^2+2q+1
        17: 3q^2+2q+1
        18: q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: 2q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 3q^2+2q+1
        24: 2q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: 3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: 3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: 3q^2+2q+1
        36: q^3+3q^2+2q+1
        37: 3q^2+2q+1
        38: q^3+3q^2+2q+1
        39: q^3+3q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: 3q^2+2q+1
        43: q^3+3q^2+2q+1
        44: 2q^2+2q+1
        45: q^3+3q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+3q^2+2q+1
        48: 3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: 2q^2+2q+1
        51: q^2+q+1
        52: q^2+2q+1
        53: 2q+1
        54: 2q^2+2q+1
        55: q^2+2q+1
        56: 2q^2+2q+1
        57: 2q^2+2q+1
        58: q^2+2q+1
        59: 2q^2+2q+1
        60: 3q^2+2q+1
        61: 2q^2+2q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: 3q^2+2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: 3q^2+2q+1
        68: q^3+3q^2+2q+1
        69: 3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: 3q^2+2q+1
        75: 2q^2+2q+1
        76: 2q^2+2q+1
        77: 2q^2+2q+1
        78: 3q^2+2q+1
        79: q^3+3q^2+2q+1
        80: 3q^2+2q+1
        81: q^3+3q^2+2q+1
        82: 3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: 2q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 3q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+q+1
        91: 2q^2+2q+1
        92: q^3+3q^2+2q+1
        93: 2q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^2+2q+1
        96: q^3+2q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 3q^2+2q+1
       100: q^3+3q^2+2q+1
       101: 2q^2+2q+1
       102: q^3+3q^2+2q+1
       103: q^3+2q^2+2q+1
       104: q^2+q+1
       105: q^2+2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: 2q^2+2q+1
       112: 2q^2+2q+1
       113: q^2+q+1
       114: q^2+2q+1
       115: 2q+1
       116: 2q^2+2q+1
       117: q^2+2q+1
       118: 2q^2+2q+1
       119: 2q^2+2q+1
       120: q^2+2q+1
       121: 2q^2+2q+1
       122: 3q^2+2q+1
       123: q^2+2q+1
       124: 2q^2+2q+1
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: 3q^2+2q+1
       128: 2q^2+2q+1
       129: 2q^2+2q+1
       130: 2q^2+2q+1
       131: 3q^2+2q+1
       132: q^3+3q^2+2q+1
       133: 2q^2+2q+1
       134: 2q^2+2q+1
       135: q^2+q+1
       136: q^2+2q+1
       137: 2q+1
       138: 2q^2+2q+1
       139: q^2+2q+1
       140: 2q^2+2q+1
       141: 2q^2+2q+1
       142: q^2+2q+1
       143: 2q^2+2q+1
       144: 3q^2+2q+1
       145: 2q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^2+2q+1
       148: 3q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 3q^2+2q+1
       152: q^3+3q^2+2q+1
       153: 3q^2+2q+1
       154: q^3+3q^2+2q+1
       155: 2q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: 2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q+1
       164: q^2+q+1
       165: 2q^2+2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q^2+q+1
       169: 2q^2+2q+1
       170: q^2+2q+1
       171: q+1
       172: q^2+2q+1
       173: q^3+2q^2+2q+1
       174: q^2+2q+1
       175: q^3+2q^2+2q+1
       176: 2q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: 3q^2+2q+1
       180: q^2+2q+1
       181: q^2+2q+1
       182: q^2+q+1
       183: 2q^2+2q+1
       184: q^3+3q^2+2q+1
       185: 2q^2+2q+1
       186: q^3+2q^2+2q+1
       187: q^2+2q+1
       188: q^3+2q^2+2q+1
       189: q^2+q+1
       190: q+1
       191: 2q+1
       192: q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q^2+q+1
       198: q^2+q+1
       199: q^2+2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: q^2+2q+1
       205: 2q^2+2q+1
       206: 2q^2+2q+1
       207: q+1
       208: q^2+2q+1
       209: 2q+1
       210: 2q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: 2q^2+2q+1
       214: q^2+q+1
       215: q^2+2q+1
       216: 2q+1
       217: 2q^2+2q+1
       218: q^2+2q+1
       219: 2q^2+2q+1
       220: 2q^2+2q+1
       221: q^2+2q+1
       222: 2q^2+2q+1
       223: 3q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q^2+q+1
       227: 2q^2+2q+1
       228: q^2+q+1
       229: q^2+2q+1
       230: q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: 2q^2+2q+1
       236: 2q^2+2q+1
       237: q^2+q+1
       238: q^2+2q+1
       239: 2q+1
       240: 2q^2+2q+1
       241: q^2+2q+1
       242: 2q^2+2q+1
       243: 2q^2+2q+1
       244: q^2+2q+1
       245: 2q^2+2q+1
       246: 3q^2+2q+1
       247: q^2+2q+1
       248: 2q^2+2q+1
       249: q^2+2q+1
       250: 2q^2+2q+1
       251: 3q^2+2q+1
       252: 2q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 3q^2+2q+1
       256: q^3+3q^2+2q+1
       257: 2q^2+2q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: q^2+2q+1
       267: q+1
       268: q+1
       269: q+1
       270: q^2+q+1
       271: q+1
       272: 2q+1
       273: q^2+2q+1
       274: q+1
       275: q^2+q+1
       276: 2q^2+2q+1
       277: 2q+1
       278: q^2+2q+1
       279: q+1
       280: q+1
       281: q^2+2q+1
       282: 2q+1
       283: q^2+2q+1
       284: q+1
       285: q^2+2q+1
       286: q^3+2q^2+2q+1
       287: q^2+2q+1
       288: 2q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: 2q+1
       292: 2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: q^2+2q+1
       296: q+1
       297: q^2+q+1
       298: 2q^2+2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q^2+q+1
       302: 2q^2+2q+1
       303: q^2+2q+1
       304: q+1
       305: q^2+2q+1
       306: q^3+2q^2+2q+1
       307: q^2+2q+1
       308: q^3+2q^2+2q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: 1
       314: 2q+1
       315: q+1
       316: 2q+1
       317: q+1
       319: q^2+q+1
       320: q+1
       321: 2q+1
       322: q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: q^2+2q+1
       327: q^2+q+1
       328: q+1
       329: q^2+2q+1
       330: q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: q^2+q+1
       337: q^2+2q+1
       338: q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+2q+1
       343: 2q^2+2q+1
       344: 2q^2+2q+1
       345: q+1
       346: q^2+2q+1
       347: 2q+1
       348: 2q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q^2+2q+1
       352: q+1
       353: q^2+q+1
       354: 2q^2+2q+1
       355: 2q+1
       356: q^2+q+1
       357: q+1
       358: 2q+1
       359: q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q^2+q+1
       365: q^2+q+1
       366: q^2+2q+1
       367: q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: q^2+2q+1
       372: 2q^2+2q+1
       373: 2q^2+2q+1
       374: q+1
       375: q^2+2q+1
       376: 2q+1
       377: 2q^2+2q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: 2q^2+2q+1
       381: q^2+q+1
       382: q^2+2q+1
       383: 2q+1
       384: 2q^2+2q+1
       385: q^2+2q+1
       386: 2q^2+2q+1
       387: 2q^2+2q+1
       388: q^2+2q+1
       389: 2q^2+2q+1
       390: 3q^2+2q+1
       391: q^2+2q+1
       392: q^2+2q+1
       393: q^2+q+1
       394: 2q^2+2q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 2q+1
       412: q^2+2q+1
       413: q+1
       414: q+1
       415: q+1
       416: q^2+q+1
       417: q+1
       418: 2q+1
       419: q^2+2q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: 2q+1
       426: q^2+2q+1
       427: q+1
       428: q+1
       429: q^2+2q+1
       430: 2q+1
       431: q^2+2q+1
       432: q+1
       433: q^2+2q+1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q^2+2q+1
       443: q+1
       444: q+1
       445: q+1
       446: q^2+q+1
       447: q+1
       448: 2q+1
       449: q^2+2q+1
       450: q+1
       451: q^2+q+1
       452: 2q^2+2q+1
       453: 2q+1
       454: q^2+2q+1
       455: q+1
       456: q+1
       457: q^2+2q+1
       458: 2q+1
       459: q^2+2q+1
       460: q+1
       461: q^2+2q+1
       462: q^3+2q^2+2q+1
       463: q^2+2q+1
       466: q+1
       467: 1
       468: q+1
       469: 2q+1
       470: 1
       471: q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: 1
       478: 2q+1
       479: q+1
       480: 2q+1
       481: q+1
       483: q+1
       484: q+1
       485: 2q+1
       486: q+1
       487: 2q+1
       488: 2q+1
       489: 2q+1
       490: q^2+2q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: 2q+1
       495: q+1
       496: 2q+1
       497: 2q+1
       498: 2q+1
       499: q^2+2q+1
       500: q^2+q+1
       501: q+1
       502: q^2+2q+1
       503: q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: q^2+2q+1
       508: q^2+2q+1
       509: q^2+2q+1
       510: q+1
       511: q+1
       512: q+1
       513: q^2+q+1
       514: q+1
       515: 2q+1
       517: q+1
       518: q+1
       519: 2q+1
       520: 1
       521: 2q+1
       522: q+1
       523: 2q+1
       524: q+1
       526: q^2+q+1
       527: q+1
       528: 2q+1
       529: q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: q^2+2q+1
       534: q^2+q+1
       535: q+1
       536: q^2+2q+1
       537: q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: q^2+2q+1
       542: q^2+2q+1
       543: q^2+q+1
       544: q^2+2q+1
       545: q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: q^2+2q+1
       550: 2q^2+2q+1
       551: 2q^2+2q+1
       552: q+1
       553: q^2+2q+1
       554: 2q+1
       555: 2q^2+2q+1
       556: q^2+2q+1
       557: q^2+2q+1
       558: q^2+2q+1
       559: q+1
       560: q^2+q+1
       561: 2q^2+2q+1
       562: 2q+1
       564: q+1
       565: q+1
       566: 2q+1
       567: 1
       568: 2q+1
       569: q+1
       570: 2q+1
       571: q+1
       573: q+1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: q+1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: 2q+1
       598: q^2+2q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: 2q+1
       605: q^2+2q+1
       606: q+1
       607: q+1
       608: q^2+2q+1
       609: 2q+1
       610: q+1
       611: q+1
       612: 2q+1
       613: q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 2q+1
       627: q^2+2q+1
       628: q+1
       629: q+1
       630: q+1
       631: q^2+q+1
       632: q+1
       633: 2q+1
       634: q^2+2q+1
       635: q+1
       636: q+1
       637: 1
       638: q+1
       639: q+1
       640: 2q+1
       641: q^2+2q+1
       642: q+1
       643: q+1
       644: q^2+2q+1
       645: 2q+1
       646: q^2+2q+1
       647: q+1
       648: q^2+2q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       659: q+1
       660: 1
       661: q+1
       662: 2q+1
       663: 1
       664: q+1
       667: q+1
       668: q+1
       669: 2q+1
       670: 1
       671: 2q+1
       672: q+1
       673: 2q+1
       674: q+1
       677: q+1
       678: q+1
       679: 2q+1
       680: 1
       681: 2q+1
       682: q+1
       683: 2q+1
       684: q+1
       686: q+1
       687: q+1
       688: 2q+1
       689: q+1
       690: 2q+1
       691: 2q+1
       692: 2q+1
       693: q^2+2q+1
       694: q+1
       695: q+1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 2q+1
       705: q+1
       706: 1
       707: q+1
       708: 2q+1
       709: 1
       710: q+1
       713: q+1
       714: q+1
       715: 2q+1
       716: 1
       717: 2q+1
       718: q+1
       719: 2q+1
       720: q+1
       722: q+1
       723: q+1
       724: 2q+1
       725: q+1
       726: 2q+1
       727: 2q+1
       728: 2q+1
       729: q^2+2q+1
       730: q+1
       731: q^2+q+1
       732: q+1
       733: 2q+1
       734: q+1
       735: 2q+1
       736: 2q+1
       737: 2q+1
       738: q^2+2q+1
       739: q^2+q+1
       740: q+1
       741: q^2+2q+1
       742: q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: q^2+2q+1
       747: q^2+2q+1
       748: q^2+2q+1
       749: q+1
       750: q+1
       751: q+1
       752: q^2+q+1
       753: q+1
       754: 2q+1
       757: q+1
       758: 1
       759: q+1
       760: 2q+1
       761: 1
       762: q+1
       765: 1
       766: 1
       767: q+1
       768: 1
       769: q+1
       770: 1
       771: q+1
       772: 1
       774: q+1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: q+1
       783: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: q+1
       792: q+1
       793: q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: 2q+1
       800: q^2+2q+1
       801: q+1
       802: q+1
       803: 1
       804: q+1
       805: q+1
       806: 2q+1
       808: q+1
       809: q+1
       810: 2q+1
       811: 1
       812: 2q+1
       813: q+1
       814: 2q+1
       815: q+1
       817: q+1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: q+1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 2q+1
       834: q+1
       835: q+1
       836: 1
       837: 1
       838: 1
       839: 1
       840: q+1
       841: 2q+1
       842: q^2+2q+1
       843: q+1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: 2q+1
       849: q^2+2q+1
       850: q+1
       851: q+1
       852: q^2+2q+1
       853: 2q+1
       857: 1
       858: 1
       863: 1
       864: q+1
       865: 1
       866: q+1
       867: 1
       871: q+1
       872: 1
       873: q+1
       874: 2q+1
       875: 1
       876: q+1
       880: q+1
       881: 1
       882: q+1
       883: 2q+1
       884: 1
       885: q+1
       888: q+1
       889: q+1
       890: 2q+1
       891: 1
       892: 2q+1
       893: q+1
       894: 2q+1
       895: q+1
       897: q+1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: q+1
       903: q+1
       904: q+1
       905: q+1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       916: q+1
       917: 1
       918: q+1
       919: 2q+1
       920: 1
       921: q+1
       924: q+1
       925: q+1
       926: 2q+1
       927: 1
       928: 2q+1
       929: q+1
       930: 2q+1
       931: q+1
       934: q+1
       935: q+1
       936: 2q+1
       937: 1
       938: 2q+1
       939: q+1
       940: 2q+1
       941: q+1
       943: q+1
       944: q+1
       945: 2q+1
       946: q+1
       947: 2q+1
       948: 2q+1
       949: 2q+1
       950: q^2+2q+1
       951: q+1
       952: q+1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: q+1
       958: q+1
       959: 2q+1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       970: 1
       971: 1
       972: 1
       973: q+1
       974: 1
       975: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       985: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: q+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: q+1
      1006: q+1
      1007: q+1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: q+1
      1013: 2q+1
      1016: q+1
      1017: 1
      1018: q+1
      1019: 2q+1
      1020: 1
      1021: q+1
      1024: 1
      1025: 1
      1026: q+1
      1027: 1
      1028: q+1
      1029: 1
      1030: q+1
      1031: 1
      1033: q+1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: q+1
      1042: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: q+1
      1050: q+1
      1051: q+1
      1052: q+1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: 2q+1
      1059: q^2+2q+1
      1060: q+1
      1061: q+1
      1062: 1
      1063: q+1
      1064: q+1
      1065: 2q+1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1081: q+1
      1082: 1
      1083: q+1
      1084: 1
      1088: 1
      1089: q+1
      1090: 1
      1091: q+1
      1092: 1
      1096: q+1
      1097: 1
      1098: q+1
      1099: 2q+1
      1100: 1
      1101: q+1
      1104: 1
      1105: 1
      1106: q+1
      1107: 1
      1108: q+1
      1109: 1
      1110: q+1
      1111: 1
      1116: 1
      1117: 1
      1122: 1
      1123: q+1
      1124: 1
      1125: q+1
      1126: 1
      1130: q+1
      1131: 1
      1132: q+1
      1133: 2q+1
      1134: 1
      1135: q+1
      1139: q+1
      1140: 1
      1141: q+1
      1142: 2q+1
      1143: 1
      1144: q+1
      1147: q+1
      1148: q+1
      1149: 2q+1
      1150: 1
      1151: 2q+1
      1152: q+1
      1153: 2q+1
      1154: q+1
      1156: q+1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: q+1
      1162: q+1
      1163: q+1
      1164: q+1
      1168: 1
      1169: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1187: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: q+1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: q+1
      1216: q+1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1227: 1
      1228: 1
      1229: 1
      1230: q+1
      1231: 1
      1232: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1239: q+1
      1240: 1
      1241: q+1
      1242: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: q+1
      1263: q+1
      1264: q+1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: q+1
      1270: 2q+1
      1277: 1
      1282: 1
      1283: 1
      1289: 1
      1290: 1
      1295: 1
      1296: q+1
      1297: 1
      1298: q+1
      1299: 1
      1303: 1
      1304: 1
      1305: 1
      1306: q+1
      1307: 1
      1308: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1325: q+1
      1326: 1
      1327: q+1
      1328: 1
      1332: 1
      1333: q+1
      1334: 1
      1335: q+1
      1336: 1
      1340: q+1
      1341: 1
      1342: q+1
      1343: 2q+1
      1344: 1
      1345: q+1
      1348: 1
      1349: 1
      1350: q+1
      1351: 1
      1352: q+1
      1353: 1
      1354: q+1
      1355: 1
      1360: 1
      1365: 1
      1366: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1380: 1
      1382: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1407: 1
      1408: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1421: 1
      1422: 1
      1423: 1
      1424: q+1
      1425: 1
      1426: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q+1
      1455: q+1
      1464: 1
      1469: 1
      1474: 1
      1475: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1492: 1
      1497: 1
      1498: 1
      1504: 1
      1505: 1
      1510: 1
      1511: q+1
      1512: 1
      1513: q+1
      1514: 1
      1518: 1
      1519: 1
      1520: 1
      1521: q+1
      1522: 1
      1523: 1
      1531: 1
      1536: 1
      1537: 1
      1550: 1
      1552: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1567: 1
      1572: 1
      1573: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1587: 1
      1589: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1602: 1
      1603: 1
      1604: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1623: 1
      1628: 1
      1629: 1
      1640: 1
      1645: 1
      1650: 1
      1651: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1670: 1
      1687: 1
      1689: 1
      1698: 1
      1703: 1
      1704: 1
      1717: 1
      1719: 1
      1724: 1
      1726: 1
      1727: 1
      1729: 1
      1742: 1
      1756: 1
      1761: 1
      1762: 1
      1794: 1
      1811: 1
      1813: 1
      1834: 1

1835:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: q^2+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q^2+1
        51: q^2+1
        52: q^2+1
        53: q^2+q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q+1
        71: q^2+1
        72: q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: 1
        85: q^2+q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+1
       105: q^2+1
       106: q^2+1
       107: q^2+1
       108: q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q+1
       112: q^2+1
       113: q^2+1
       114: q^2+1
       115: q^2+q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: 1
       120: q^2+q+1
       121: q+1
       122: q+1
       123: q+1
       124: q^2+1
       125: q^2+q+1
       126: q^2+q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q+1
       132: q+1
       133: q+1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: q^2+q+1
       141: q^2+1
       142: q^2+q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q^2+q+1
       153: q^2+q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: q^2+1
       191: q^2+1
       192: q^2+1
       193: 1
       194: q^2+1
       195: q^2+q+1
       196: q+1
       197: q+1
       198: q^2+1
       199: q^2+1
       200: q^2+1
       201: q^2+1
       202: q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q+1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q^2+1
       214: q^2+1
       215: q^2+1
       216: q^2+q+1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+q+1
       220: 1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: q^2+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q^2+1
       237: q^2+1
       238: q^2+1
       239: q^2+q+1
       240: q^2+q+1
       241: q^2+q+1
       242: q^2+q+1
       243: 1
       244: q^2+q+1
       245: q+1
       246: q+1
       247: q+1
       248: q^2+1
       249: q^2+q+1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q^2+q+1
       254: q^2+q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       311: q^2+1
       312: 1
       313: 1
       314: q^2+1
       315: q^2+1
       316: 1
       317: q+1
       318: q+1
       320: q^2+1
       321: q^2+1
       322: q^2+1
       323: 1
       324: q^2+1
       325: q^2+q+1
       326: q+1
       327: q+1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: q^2+1
       337: q^2+1
       338: q^2+1
       339: q^2+1
       340: q^2+q+1
       341: q^2+q+1
       342: q^2+q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       357: q^2+1
       358: q^2+1
       359: q^2+1
       360: 1
       361: q^2+1
       362: q^2+q+1
       363: q+1
       364: q+1
       365: q^2+1
       366: q^2+1
       367: q^2+1
       368: q^2+1
       369: q^2+q+1
       370: q^2+q+1
       371: q^2+q+1
       372: q+1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q^2+1
       381: q^2+1
       382: q^2+1
       383: q^2+q+1
       384: q^2+q+1
       385: q^2+q+1
       386: q^2+q+1
       387: 1
       388: q^2+q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       467: 1
       468: q^2+1
       469: 1
       470: 1
       471: 1
       472: q+1
       475: q^2+1
       476: 1
       477: 1
       478: q^2+1
       479: q^2+1
       480: 1
       481: q+1
       482: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       493: q^2+1
       494: q^2+1
       495: q^2+1
       496: 1
       497: q^2+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       518: q^2+1
       519: 1
       520: 1
       521: q^2+1
       522: q^2+1
       523: 1
       524: q+1
       525: q+1
       527: q^2+1
       528: q^2+1
       529: q^2+1
       530: 1
       531: q^2+1
       532: q^2+q+1
       533: q+1
       534: q+1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: q^2+1
       544: q^2+1
       545: q^2+1
       546: q^2+1
       547: q^2+q+1
       548: q^2+q+1
       549: q^2+q+1
       550: q+1
       551: 1
       552: 1
       553: 1
       554: q+1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: q^2+1
       662: 1
       663: 1
       664: 1
       665: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       678: q^2+1
       679: 1
       680: 1
       681: q^2+1
       682: q^2+1
       683: 1
       684: q+1
       685: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       706: 1
       707: q^2+1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: q^2+1
       715: 1
       716: 1
       717: q^2+1
       718: q^2+1
       719: 1
       720: q+1
       721: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       730: q+1
       732: q^2+1
       733: q^2+1
       734: q^2+1
       735: 1
       736: q^2+1
       737: q^2+q+1
       738: q+1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: 1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: 1
       782: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       881: 1
       882: q^2+1
       883: 1
       884: 1
       885: 1
       886: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: q^2+1
       919: 1
       920: 1
       921: 1
       922: q+1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: q+1
       932: q+1
       935: q^2+1
       936: 1
       937: 1
       938: q^2+1
       939: q^2+1
       940: 1
       941: q+1
       942: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       951: q+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: q+1
      1140: 1
      1141: q^2+1
      1142: 1
      1143: 1
      1144: 1
      1145: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1155: q+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1193: 1
      1197: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1290: 1
      1291: 1
      1292: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: q+1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1389: 1
      1393: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1432: 1
      1436: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1465: 1
      1470: 1
      1475: 1
      1476: 1
      1477: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1493: 1
      1498: 1
      1499: 1
      1500: 1
      1505: 1
      1506: 1
      1507: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1524: 1
      1532: 1
      1537: 1
      1538: 1
      1539: 1
      1559: 1
      1563: 1
      1568: 1
      1573: 1
      1574: 1
      1575: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1596: 1
      1600: 1
      1603: 1
      1606: 1
      1607: 1
      1609: 1
      1610: 1
      1624: 1
      1629: 1
      1630: 1
      1631: 1
      1641: 1
      1646: 1
      1651: 1
      1652: 1
      1653: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1671: 1
      1699: 1
      1704: 1
      1705: 1
      1706: 1
      1726: 1
      1730: 1
      1743: 1
      1757: 1
      1762: 1
      1763: 1
      1764: 1
      1795: 1
      1835: 1

1836:    0: q^4+2q^2+q+1
         1: q^4+2q^2+q+1
         2: q^4+2q^2+q+1
         3: q^4+2q^2+q+1
         4: q^2+q+1
         5: q^4+2q^2+q+1
         6: q^4+2q^2+q+1
         7: q^4+2q^2+q+1
         8: q^4+2q^2+q+1
         9: q^4+2q^2+q+1
        10: q^4+2q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^4+2q^2+q+1
        17: q^4+2q^2+q+1
        18: q^4+2q^2+q+1
        19: q^2+q+1
        20: q^4+2q^2+q+1
        21: q^4+2q^2+q+1
        22: q^4+2q^2+q+1
        23: q^2+q+1
        24: q+1
        25: q^4+2q^2+q+1
        26: q^4+2q^2+q+1
        27: q^4+2q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q+1
        40: q^4+2q^2+q+1
        41: q^4+2q^2+q+1
        42: q^4+2q^2+q+1
        43: q^4+2q^2+q+1
        44: q^4+2q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q+1
        52: q^4+2q^2+q+1
        53: q^4+2q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q^4+2q^2+q+1
        58: q^4+2q^2+q+1
        59: q^4+2q^2+q+1
        60: q^2+q+1
        61: q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q+1
        75: q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^4+2q^2+q+1
        85: q^4+2q^2+q+1
        86: q^4+2q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q^4+2q^2+q+1
        90: q^4+2q^2+q+1
        91: q^4+2q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q+1
       103: q+1
       104: q+1
       105: q^2+q+1
       106: q+1
       107: q^4+2q^2+q+1
       108: q^2+q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^2+q+1
       113: q+1
       114: q^4+2q^2+q+1
       115: q^4+2q^2+q+1
       116: q^2+q+1
       117: q+1
       118: q+1
       119: q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: q+1
       157: q^4+2q^2+q+1
       158: q^4+2q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q^4+2q^2+q+1
       163: q^4+2q^2+q+1
       164: q^4+2q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q+1
       180: q+1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q^2+q+1
       192: q+1
       193: q^2+q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q^2+q+1
       200: q+1
       201: q^4+2q^2+q+1
       202: q^2+q+1
       203: q+1
       204: q+1
       205: q+1
       206: q^2+q+1
       207: 1
       208: q^2+q+1
       209: q^2+q+1
       210: q^2+q+1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: q^2+q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q+1
       260: q+1
       261: q^4+2q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+q+1
       267: q+1
       268: q^4+2q^2+q+1
       269: q^4+2q^2+q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q+1
       293: q+1
       294: q+1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q^2+q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q^2+q+1
       322: q+1
       323: q^2+q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q^2+q+1
       330: 1
       331: q^2+q+1
       332: q^2+q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q^2+q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       375: q+1
       376: q+1
       377: q+1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q+1
       399: q^2+q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q^2+q+1
       406: q+1
       407: q^4+2q^2+q+1
       408: q^2+q+1
       409: q+1
       410: q+1
       411: q+1
       412: q^2+q+1
       413: 1
       414: q^2+q+1
       415: q^2+q+1
       416: q^2+q+1
       417: 1
       418: 1
       419: 1
       420: q+1
       421: q+1
       422: q+1
       423: 1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q^2+q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q+1
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q^2+q+1
       477: 1
       478: 1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: 1
       484: 1
       485: q^2+q+1
       486: 1
       487: q^2+q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       521: 1
       522: q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: q+1
       536: q+1
       538: q+1
       539: q+1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       553: q+1
       554: q+1
       555: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: 1
       568: 1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: q^2+q+1
       576: q+1
       577: q^2+q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: q^2+q+1
       584: 1
       585: q^2+q+1
       586: q^2+q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: q+1
       596: 1
       597: 1
       598: 1
       599: 1
       600: q+1
       601: q+1
       602: 1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q^2+q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q+1
       629: q+1
       630: q+1
       631: q+1
       634: 1
       635: q+1
       636: q+1
       637: q+1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q^2+q+1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: q+1
       707: 1
       708: 1
       710: q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       717: 1
       718: q+1
       719: q+1
       720: q+1
       721: q+1
       724: q+1
       726: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       741: 1
       743: q+1
       744: 1
       748: 1
       750: q+1
       751: q+1
       752: 1
       755: q+1
       756: q+1
       757: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q^2+q+1
       768: 1
       769: 1
       770: q+1
       771: q+1
       772: q+1
       773: q+1
       774: 1
       775: 1
       776: q^2+q+1
       777: 1
       778: q^2+q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: q+1
       803: q+1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       812: 1
       813: q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       827: q+1
       829: q+1
       830: q+1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: 1
       842: 1
       844: q+1
       845: q+1
       846: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       854: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       909: 1
       911: 1
       913: q+1
       914: q+1
       915: q+1
       916: q+1
       918: 1
       919: 1
       921: q+1
       922: q+1
       926: q+1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: q+1
       956: 1
       960: q+1
       961: q+1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: q+1
       968: q+1
       969: q+1
       970: q+1
       971: 1
       972: 1
       973: 1
       974: 1
       975: q+1
       976: q+1
       977: 1
       978: 1
       979: 1
       980: q^2+q+1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1018: 1
      1019: 1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1028: 1
      1029: q+1
      1030: q+1
      1031: q+1
      1032: q+1
      1035: q+1
      1037: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: q+1
      1055: 1
      1059: 1
      1061: q+1
      1062: q+1
      1063: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: q+1
      1115: 1
      1118: 1
      1120: q+1
      1121: q+1
      1123: 1
      1125: 1
      1127: q+1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1165: q+1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: q+1
      1173: q+1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: q+1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1220: 1
      1222: 1
      1224: q+1
      1225: q+1
      1226: q+1
      1227: q+1
      1229: 1
      1230: 1
      1232: q+1
      1233: q+1
      1237: q+1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1256: 1
      1258: 1
      1264: 1
      1266: q+1
      1267: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1311: 1
      1315: q+1
      1317: 1
      1320: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: q+1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1404: q+1
      1406: 1
      1409: 1
      1411: q+1
      1412: q+1
      1414: 1
      1416: 1
      1418: q+1
      1428: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1440: 1
      1449: 1
      1451: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1467: 1
      1471: 1
      1478: 1
      1479: 1
      1485: 1
      1490: 1
      1501: 1
      1503: 1
      1506: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1562: 1
      1563: 1
      1565: 1
      1569: q+1
      1571: 1
      1574: 1
      1584: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1604: 1
      1611: 1
      1612: 1
      1613: 1
      1625: 1
      1643: 1
      1662: 1
      1663: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1673: 1
      1677: 1
      1684: 1
      1685: 1
      1691: 1
      1696: 1
      1707: 1
      1709: 1
      1712: 1
      1731: 1
      1765: 1
      1766: 1
      1767: 1
      1779: 1
      1797: 1
      1836: 1

1837:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q^2+q+1
       106: q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^2+q+1
       113: q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q^2+q+1
       117: q+1
       118: q+1
       119: q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q^2+q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q^2+q+1
       192: q+1
       193: q^2+q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q^2+q+1
       200: q+1
       201: q^2+q+1
       202: q^2+q+1
       203: q+1
       204: q+1
       205: q+1
       206: q^2+q+1
       207: q+1
       208: q^2+q+1
       209: q^2+q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q^2+q+1
       260: q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+q+1
       267: q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q^2+q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q^2+q+1
       322: q+1
       323: q^2+q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q^2+q+1
       330: q+1
       331: q^2+q+1
       332: q^2+q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q+1
       399: q^2+q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       404: q+1
       405: q^2+q+1
       406: q+1
       407: q^2+q+1
       408: q^2+q+1
       409: q+1
       410: q+1
       411: q+1
       412: q^2+q+1
       413: q+1
       414: q^2+q+1
       415: q^2+q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q^2+q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: q^2+q+1
       486: q+1
       487: q^2+q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: 1
       572: 1
       573: q+1
       574: q+1
       575: q^2+q+1
       576: q+1
       577: q^2+q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       582: q+1
       583: q^2+q+1
       584: q+1
       585: q^2+q+1
       586: q^2+q+1
       587: q+1
       588: q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       631: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q^2+q+1
       670: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       721: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       748: 1
       750: 1
       752: 1
       755: 1
       756: 1
       757: q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: 1
       763: 1
       764: 1
       765: q+1
       766: q+1
       767: q^2+q+1
       768: q+1
       769: q+1
       770: q+1
       771: q+1
       772: 1
       773: 1
       774: q+1
       775: q+1
       776: q^2+q+1
       777: q+1
       778: q^2+q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: q+1
       872: q+1
       873: q+1
       874: q+1
       875: q+1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       916: 1
       918: 1
       919: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       942: 1
       953: 1
       960: 1
       961: 1
       962: q+1
       963: q+1
       964: q+1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: q+1
       971: q+1
       972: q+1
       973: q+1
       974: q+1
       975: 1
       976: 1
       977: 1
       978: q+1
       979: q+1
       980: q^2+q+1
       981: q+1
       982: q+1
       983: q+1
       984: q+1
       985: 1
       986: 1
       987: 1
       988: q+1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1059: 1
      1061: 1
      1063: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1123: 1
      1137: 1
      1139: 1
      1141: 1
      1142: 1
      1165: 1
      1166: 1
      1167: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: q+1
      1183: q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1227: 1
      1229: 1
      1230: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1253: 1
      1264: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1303: 1
      1305: 1
      1306: 1
      1311: 1
      1333: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1414: 1
      1428: 1
      1430: 1
      1432: 1
      1433: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1481: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1557: 1
      1559: 1
      1560: 1
      1565: 1
      1587: 1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1621: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1687: 1
      1732: 1
      1766: 1
      1768: 1
      1769: 1
      1770: 1
      1775: 1
      1837: 1

1838:    0: q^3+q^2+q+1
         1: q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q+1
         5: q^3+q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^3+q^2+q+1
         9: q^2+q+1
        10: q^3+q^2+q+1
        11: q^3+q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^3+q^2+q+1
        18: q^3+q^2+q+1
        19: q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^3+q^2+q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^3+q^2+q+1
        28: q^2+q+1
        29: q^3+q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^3+q^2+q+1
        43: q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: 1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^3+q^2+q+1
        61: q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q^3+q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: 1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^3+q^2+q+1
        88: q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^3+q^2+q+1
        92: q^2+q+1
        93: q^3+q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: q^2+q+1
       106: 1
       107: q^2+q+1
       108: q^2+q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^2+q+1
       113: 1
       114: q^2+q+1
       115: q^2+q+1
       116: q^2+q+1
       117: q+1
       118: q+1
       119: q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^3+q^2+q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^3+q^2+q+1
       166: q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^3+q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q^2+q+1
       192: 1
       193: q^2+q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: 1
       199: q^2+q+1
       200: 1
       201: q^2+q+1
       202: q^2+q+1
       203: q+1
       204: q+1
       205: q+1
       206: q^2+q+1
       207: 1
       208: q^2+q+1
       209: q^2+q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: q+1
       214: 1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: 1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       248: q+1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: q^2+q+1
       260: 1
       261: q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+q+1
       267: 1
       268: q^2+q+1
       269: q^2+q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^3+q^2+q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: q^2+q+1
       313: 1
       314: q+1
       315: 1
       316: q+1
       317: q+1
       318: 1
       319: 1
       320: 1
       321: q^2+q+1
       322: 1
       323: q^2+q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q^2+q+1
       330: 1
       331: q^2+q+1
       332: q^2+q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: 1
       353: 1
       354: q+1
       355: q+1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: q+1
       375: 1
       376: 1
       377: 1
       380: q+1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: q+1
       388: 1
       389: 1
       390: q+1
       392: q+1
       393: 1
       394: q+1
       395: 1
       396: 1
       397: q^2+q+1
       398: 1
       399: q^2+q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: 1
       405: q^2+q+1
       406: 1
       407: q^2+q+1
       408: q^2+q+1
       409: q+1
       410: q+1
       411: q+1
       412: q^2+q+1
       413: 1
       414: q^2+q+1
       415: q^2+q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: 1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: 1
       451: 1
       452: q+1
       454: q+1
       455: 1
       456: 1
       457: q+1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       465: 1
       466: 1
       467: 1
       468: 1
       469: q+1
       470: 1
       471: q+1
       472: 1
       473: 1
       474: 1
       475: 1
       476: q^2+q+1
       477: 1
       478: q+1
       479: 1
       480: q+1
       481: q+1
       482: 1
       483: 1
       484: 1
       485: q^2+q+1
       486: 1
       487: q^2+q+1
       488: q+1
       489: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q+1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: q+1
       522: 1
       523: q+1
       524: q+1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q+1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: q+1
       553: 1
       554: 1
       555: 1
       558: q+1
       559: 1
       560: 1
       561: q+1
       563: 1
       564: 1
       565: 1
       566: q^2+q+1
       567: 1
       568: q+1
       569: 1
       570: q+1
       571: q+1
       572: 1
       573: 1
       574: 1
       575: q^2+q+1
       576: 1
       577: q^2+q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: q^2+q+1
       584: 1
       585: q^2+q+1
       586: q^2+q+1
       587: q+1
       588: q+1
       589: q+1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: q+1
       604: q+1
       605: q+1
       606: 1
       607: 1
       608: q+1
       609: q+1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q+1
       627: q+1
       629: 1
       630: 1
       631: 1
       634: q+1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: 1
       643: 1
       644: q+1
       646: q+1
       647: 1
       648: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: q+1
       655: 1
       656: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: q+1
       663: 1
       664: q+1
       665: 1
       666: 1
       667: 1
       668: 1
       669: q^2+q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       681: q+1
       682: 1
       683: q+1
       684: q+1
       685: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: 1
       705: 1
       707: 1
       708: q+1
       710: q+1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       741: 1
       743: 1
       744: 1
       748: q+1
       750: 1
       751: 1
       752: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: q+1
       761: 1
       762: q+1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q^2+q+1
       768: 1
       769: q+1
       770: 1
       771: q+1
       772: q+1
       773: 1
       774: 1
       775: 1
       776: q^2+q+1
       777: 1
       778: q^2+q+1
       779: q+1
       780: q+1
       781: q+1
       782: q+1
       783: 1
       784: 1
       785: q+1
       786: 1
       787: q+1
       788: q+1
       789: q+1
       790: q+1
       791: q+1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       800: q+1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: q+1
       813: 1
       814: q+1
       815: q+1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: q+1
       827: 1
       829: 1
       830: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: q+1
       844: 1
       845: 1
       846: 1
       849: q+1
       850: 1
       851: 1
       852: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: q+1
       867: 1
       868: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: q+1
       877: 1
       879: 1
       880: 1
       882: 1
       883: q+1
       885: q+1
       886: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: q+1
       893: 1
       894: q+1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: q+1
       907: 1
       909: 1
       911: q+1
       913: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: q+1
       966: 1
       967: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: q+1
       974: 1
       975: q+1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q^2+q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       985: q+1
       986: 1
       987: 1
       988: 1
       989: 1
       990: q+1
       992: q+1
       993: 1
       994: q+1
       995: q+1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: q+1
      1002: q+1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q+1
      1015: 1
      1016: 1
      1018: 1
      1019: q+1
      1021: q+1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1052: 1
      1054: 1
      1055: 1
      1059: q+1
      1061: 1
      1062: 1
      1063: 1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: q+1
      1084: 1
      1085: 1
      1087: 1
      1089: 1
      1091: q+1
      1093: 1
      1095: 1
      1096: 1
      1098: 1
      1099: q+1
      1101: q+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1115: 1
      1118: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: q+1
      1178: 1
      1179: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1187: q+1
      1188: 1
      1190: 1
      1191: 1
      1193: 1
      1194: q+1
      1196: q+1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1203: q+1
      1204: 1
      1205: q+1
      1206: q+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: 1
      1220: 1
      1222: q+1
      1224: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1267: 1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1288: 1
      1291: 1
      1294: 1
      1296: 1
      1298: q+1
      1300: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1317: 1
      1320: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: q+1
      1375: 1
      1376: 1
      1378: 1
      1380: 1
      1382: q+1
      1384: 1
      1386: 1
      1387: 1
      1389: 1
      1390: q+1
      1392: q+1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1406: 1
      1409: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1440: 1
      1449: 1
      1451: 1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1473: 1
      1476: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1503: 1
      1506: 1
      1526: 1
      1527: 1
      1530: 1
      1531: 1
      1532: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1542: 1
      1545: 1
      1548: 1
      1550: 1
      1552: q+1
      1554: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1571: 1
      1574: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1604: 1
      1613: 1
      1615: 1
      1616: 1
      1627: 1
      1630: 1
      1663: 1
      1665: 1
      1666: 1
      1669: 1
      1670: 1
      1671: 1
      1679: 1
      1682: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1709: 1
      1712: 1
      1733: 1
      1767: 1
      1769: 1
      1770: 1
      1781: 1
      1784: 1
      1838: 1

1839:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+q^2+2q+1
        11: q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^2+2q+1
        24: q^3+2q^2+2q+1
        25: q^3+q^2+2q+1
        26: q^3+q^2+2q+1
        27: q^3+q^2+2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q^3+2q^2+2q+1
        31: q^3+q^2+2q+1
        32: q^2+2q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^3+2q^2+2q+1
        37: q^2+q+1
        38: q^2+2q+1
        39: q^3+2q^2+2q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: q^3+2q^2+2q+1
        44: q^3+q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^2+2q+1
        51: q^3+2q^2+2q+1
        52: q^3+2q^2+2q+1
        53: q^3+q^2+2q+1
        54: q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^2+2q+1
        57: q^3+q^2+2q+1
        58: q^3+q^2+2q+1
        59: q^3+q^2+2q+1
        60: 2q+1
        61: q^3+q^2+2q+1
        62: 2q+1
        63: 2q+1
        64: 2q+1
        65: q^3+q^2+2q+1
        66: q^3+q^2+2q+1
        67: q^3+q^2+2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^3+2q^2+2q+1
        72: q^3+2q^2+2q+1
        73: q^3+2q^2+2q+1
        74: q^2+2q+1
        75: q^3+2q^2+2q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q^2+2q+1
        80: q+1
        81: q^3+2q^2+2q+1
        82: q^2+q+1
        83: q^2+2q+1
        84: q^3+2q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^3+2q^2+2q+1
        87: q^2+2q+1
        88: q^3+2q^2+2q+1
        89: q^3+q^2+2q+1
        90: q^3+q^2+2q+1
        91: q^3+q^2+2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^3+2q^2+2q+1
        95: q^3+q^2+2q+1
        96: q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^3+2q^2+2q+1
       100: q^3+2q^2+2q+1
       101: q^2+q+1
       102: q^2+2q+1
       103: q^3+2q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^3+2q^2+2q+1
       107: q^3+q^2+2q+1
       108: 2q+1
       109: q^3+q^2+2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 2q+1
       113: q^3+q^2+2q+1
       114: q^3+q^2+2q+1
       115: q^3+q^2+2q+1
       116: 2q+1
       117: q^3+q^2+2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q^3+q^2+2q+1
       125: q^3+q^2+2q+1
       126: q^3+q^2+2q+1
       127: q+1
       128: q^3+q^2+2q+1
       129: 2q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^3+2q^2+2q+1
       136: q^3+2q^2+2q+1
       137: q^2+q+1
       138: q^2+2q+1
       139: q^3+2q^2+2q+1
       140: q^2+2q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q^2+2q+1
       153: q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q^3+2q^2+2q+1
       157: q^3+2q^2+2q+1
       158: q^3+q^2+2q+1
       159: q^2+2q+1
       160: q^3+2q^2+2q+1
       161: q^2+2q+1
       162: q^3+q^2+2q+1
       163: q^3+q^2+2q+1
       164: q^3+q^2+2q+1
       165: 2q+1
       166: q^3+q^2+2q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q^3+q^2+2q+1
       171: q^3+q^2+2q+1
       172: q^3+q^2+2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^3+2q^2+2q+1
       177: q^3+2q^2+2q+1
       178: q^3+2q^2+2q+1
       179: q^2+2q+1
       180: q^3+2q^2+2q+1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q^2+2q+1
       185: q+1
       186: q^3+2q^2+2q+1
       187: q^2+q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: 2q+1
       192: q^3+q^2+2q+1
       193: 2q+1
       194: q^3+q^2+2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: q^3+q^2+2q+1
       201: q^3+q^2+2q+1
       202: 2q+1
       203: q^3+q^2+2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: q^3+q^2+2q+1
       215: q^3+q^2+2q+1
       216: q^2+1
       217: q+1
       218: q^3+q^2+2q+1
       219: q+1
       220: 2q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^3+2q^2+2q+1
       231: q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: q^2+q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: 1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^3+2q^2+2q+1
       261: q^3+q^2+2q+1
       262: 2q+1
       263: q^3+q^2+2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: q^3+q^2+2q+1
       268: q^3+q^2+2q+1
       269: q^3+q^2+2q+1
       270: 2q+1
       271: q^3+q^2+2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: q^3+q^2+2q+1
       279: q^3+q^2+2q+1
       280: q^3+q^2+2q+1
       281: q+1
       282: q^3+q^2+2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q^3+2q^2+2q+1
       290: q^3+2q^2+2q+1
       291: q^2+q+1
       292: q^2+2q+1
       293: q^3+2q^2+2q+1
       294: q^2+2q+1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q+1
       299: q^2+q+1
       300: q+1
       301: q+1
       302: q+1
       303: q^2+q+1
       304: q^2+q+1
       305: q^2+q+1
       306: q^2+2q+1
       307: q+1
       308: q^2+2q+1
       309: q+1
       310: q^2+2q+1
       311: 2q+1
       312: 2q+1
       313: 2q+1
       314: q+1
       315: q^3+q^2+2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: q^3+q^2+2q+1
       323: 2q+1
       324: q^3+q^2+2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: q^3+q^2+2q+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: q+1
       343: q+1
       344: q+1
       345: 2q+1
       346: 2q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q+1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: q+1
       367: q^2+q+1
       368: q^2+q+1
       369: q+1
       370: q^2+q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+1
       384: 1
       385: q^2+q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q+1
       398: q^3+q^2+2q+1
       399: 2q+1
       400: q^3+q^2+2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: q^3+q^2+2q+1
       407: q^3+q^2+2q+1
       408: 2q+1
       409: q^3+q^2+2q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: q^3+q^2+2q+1
       421: q^3+q^2+2q+1
       422: q^2+1
       423: q+1
       424: q^3+q^2+2q+1
       425: q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: q+1
       432: q+1
       433: q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^3+2q^2+2q+1
       437: q^2+q+1
       438: q+1
       439: q^2+q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q+1
       443: q^2+q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q+1
       447: q^2+q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: q^2+q+1
       455: q^2+q+1
       456: q^2+q+1
       457: 1
       458: q^2+q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: q+1
       466: 2q+1
       467: 2q+1
       468: q+1
       469: q+1
       470: 2q+1
       471: q+1
       472: q+1
       473: q+1
       474: 2q+1
       475: 2q+1
       476: 2q+1
       477: 2q+1
       478: q+1
       479: q^3+q^2+2q+1
       480: 2q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: q+1
       493: q+1
       494: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: 2q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       511: q+1
       512: 1
       513: 1
       514: q+1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: q^2+q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q^2+q+1
       530: q+1
       531: q^2+q+1
       532: q+1
       533: q+1
       534: q+1
       535: q+1
       536: q+1
       537: q+1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: q^2+q+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       568: q+1
       569: q^3+q^2+2q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: q^3+q^2+2q+1
       577: 2q+1
       578: q^3+q^2+2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: q^3+q^2+2q+1
       593: q^2+1
       594: 1
       595: q^2+1
       596: q+1
       597: q+1
       598: q+1
       599: 2q+1
       600: 2q+1
       601: 1
       602: q+1
       603: 2q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: q+1
       613: q^2+q+1
       614: q+1
       615: q^2+q+1
       616: q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: q+1
       621: q^2+q+1
       622: q^2+q+1
       623: q+1
       624: q^2+q+1
       625: q+1
       626: q+1
       627: q+1
       628: q+1
       629: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: q^2+q+1
       636: q^2+q+1
       637: q^2+1
       638: 1
       639: q^2+q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: 2q+1
       652: q+1
       653: q+1
       654: 1
       655: q+1
       656: q+1
       657: q+1
       658: 1
       659: 2q+1
       660: 2q+1
       661: q+1
       662: q+1
       663: 2q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: q+1
       669: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       676: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: q+1
       710: q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       716: q+1
       717: 1
       718: q^2+q+1
       719: q+1
       721: q+1
       722: q+1
       723: q+1
       729: q+1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       752: 1
       753: q+1
       754: 1
       755: q+1
       756: q+1
       757: 2q+1
       758: 2q+1
       759: q+1
       760: q+1
       761: 2q+1
       762: q+1
       763: q+1
       764: q+1
       765: 2q+1
       766: 2q+1
       767: 2q+1
       768: 2q+1
       769: q+1
       770: q^3+q^2+2q+1
       771: 2q+1
       772: 1
       773: q+1
       774: 2q+1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: q+1
       784: q+1
       785: 1
       786: q^2+1
       787: 1
       788: q^2+1
       789: 1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: 2q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       802: q+1
       803: 1
       804: 1
       805: q+1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: q^2+q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q^2+q+1
       821: q+1
       822: q^2+q+1
       823: q+1
       824: q+1
       825: q+1
       826: q+1
       827: q+1
       828: q+1
       832: q+1
       833: q+1
       834: 1
       835: 1
       836: q^2+q+1
       837: q^2+1
       838: 1
       839: q^2+1
       840: 1
       841: 1
       842: 1
       843: q+1
       844: q+1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       854: q+1
       855: q+1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: q+1
       861: 1
       862: 1
       863: 2q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: q+1
       870: 1
       871: q+1
       872: q+1
       875: q+1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       913: q+1
       914: q+1
       916: q+1
       917: q+1
       918: 1
       919: 1
       920: q+1
       923: q+1
       924: q+1
       932: q+1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: q^2+1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: 2q+1
       963: q+1
       964: q+1
       965: 1
       966: q+1
       967: q+1
       968: q+1
       969: 1
       970: 2q+1
       971: 2q+1
       972: q+1
       973: q+1
       974: 2q+1
       975: 1
       976: 1
       977: q+1
       978: 2q+1
       979: q+1
       980: q+1
       981: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       987: 1
       988: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: q^2+1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: q+1
      1028: 1
      1029: q^2+q+1
      1030: q+1
      1032: q+1
      1033: q+1
      1034: q+1
      1040: q+1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q^2+1
      1046: 1
      1047: q^2+1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1061: q+1
      1063: 1
      1064: q+1
      1065: 1
      1066: q+1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1113: q+1
      1114: q+1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: q+1
      1122: q+1
      1123: 1
      1124: 1
      1128: q+1
      1137: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: q+1
      1167: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: q+1
      1172: 1
      1173: 1
      1174: 2q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1180: q+1
      1181: 1
      1182: q+1
      1183: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1224: q+1
      1225: q+1
      1227: q+1
      1228: q+1
      1229: 1
      1230: 1
      1231: q+1
      1234: q+1
      1235: q+1
      1243: q+1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: q^2+1
      1251: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1307: 1
      1310: q+1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1357: q+1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: 1
      1401: 1
      1403: 1
      1404: q+1
      1405: q+1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: q+1
      1413: q+1
      1414: 1
      1415: 1
      1419: q+1
      1428: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1477: 1
      1480: 1
      1486: 1
      1487: 1
      1488: 1
      1504: 1
      1516: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1553: 1
      1554: 1
      1555: 1
      1557: 1
      1558: 1
      1561: 1
      1564: q+1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1572: 1
      1586: 1
      1587: 1
      1588: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1612: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1632: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1683: 1
      1686: 1
      1692: 1
      1693: 1
      1694: 1
      1710: 1
      1722: 1
      1734: 1
      1766: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1786: 1
      1839: 1

1840:    0: 2q^4+7q^3+8q^2+4q+1
         1: q^4+5q^3+8q^2+4q+1
         2: 2q^4+7q^3+8q^2+4q+1
         3: q^4+5q^3+8q^2+4q+1
         4: 2q^4+7q^3+8q^2+4q+1
         5: 2q^4+7q^3+8q^2+4q+1
         6: q^4+5q^3+8q^2+4q+1
         7: q^4+5q^3+8q^2+4q+1
         8: q^4+5q^3+8q^2+4q+1
         9: 3q^3+8q^2+4q+1
        10: q^4+5q^3+8q^2+4q+1
        11: 3q^3+7q^2+4q+1
        12: q^4+5q^3+8q^2+4q+1
        13: q^4+5q^3+8q^2+4q+1
        14: 2q^4+7q^3+8q^2+4q+1
        15: 3q^3+7q^2+4q+1
        16: q^4+5q^3+8q^2+4q+1
        17: 2q^4+7q^3+8q^2+4q+1
        18: q^4+5q^3+8q^2+4q+1
        19: 2q^4+7q^3+8q^2+4q+1
        20: 2q^3+6q^2+4q+1
        21: q^4+5q^3+8q^2+4q+1
        22: 3q^3+8q^2+4q+1
        23: 3q^3+7q^2+4q+1
        24: q^4+5q^3+8q^2+4q+1
        25: 3q^3+8q^2+4q+1
        26: 2q^3+6q^2+4q+1
        27: q^4+5q^3+8q^2+4q+1
        28: 2q^3+7q^2+4q+1
        29: 3q^3+7q^2+4q+1
        30: 3q^3+8q^2+4q+1
        31: q^4+5q^3+8q^2+4q+1
        32: 3q^3+7q^2+4q+1
        33: q^4+5q^3+8q^2+4q+1
        34: q^4+5q^3+8q^2+4q+1
        35: 3q^3+7q^2+4q+1
        36: 2q^3+7q^2+4q+1
        37: 3q^3+7q^2+4q+1
        38: q^3+5q^2+4q+1
        39: 3q^3+7q^2+4q+1
        40: q^4+5q^3+8q^2+4q+1
        41: q^4+5q^3+8q^2+4q+1
        42: q^4+5q^3+8q^2+4q+1
        43: 3q^3+8q^2+4q+1
        44: q^4+5q^3+8q^2+4q+1
        45: 3q^3+7q^2+4q+1
        46: q^4+5q^3+8q^2+4q+1
        47: q^4+5q^3+8q^2+4q+1
        48: 2q^4+7q^3+8q^2+4q+1
        49: 3q^3+7q^2+4q+1
        50: 3q^2+3q+1
        51: 2q^3+6q^2+4q+1
        52: 2q^3+6q^2+4q+1
        53: 3q^3+8q^2+4q+1
        54: 2q^3+7q^2+4q+1
        55: 3q^3+8q^2+4q+1
        56: 3q^3+7q^2+4q+1
        57: 2q^3+6q^2+4q+1
        58: 2q^3+6q^2+4q+1
        59: 2q^3+6q^2+4q+1
        60: 3q^3+7q^2+4q+1
        61: q^4+5q^3+8q^2+4q+1
        62: 2q^3+7q^2+4q+1
        63: q^3+5q^2+4q+1
        64: 2q^3+5q^2+4q+1
        65: 3q^3+8q^2+4q+1
        66: 2q^3+6q^2+4q+1
        67: 2q^3+5q^2+4q+1
        68: 2q^3+7q^2+4q+1
        69: 3q^3+7q^2+4q+1
        70: q^3+5q^2+4q+1
        71: q^3+5q^2+4q+1
        72: q^4+5q^3+8q^2+4q+1
        73: 2q^3+7q^2+4q+1
        74: q^3+5q^2+4q+1
        75: 3q^3+7q^2+4q+1
        76: 2q^3+7q^2+4q+1
        77: 3q^2+3q+1
        78: 3q^3+7q^2+4q+1
        79: q^3+5q^2+4q+1
        80: q^3+5q^2+4q+1
        81: 2q^3+7q^2+4q+1
        82: 3q^3+7q^2+4q+1
        83: q^3+5q^2+4q+1
        84: 2q^3+6q^2+4q+1
        85: q^4+5q^3+8q^2+4q+1
        86: 3q^3+8q^2+4q+1
        87: 3q^3+7q^2+4q+1
        88: q^4+5q^3+8q^2+4q+1
        89: 3q^3+8q^2+4q+1
        90: 2q^3+6q^2+4q+1
        91: q^4+5q^3+8q^2+4q+1
        92: 2q^3+7q^2+4q+1
        93: 3q^3+7q^2+4q+1
        94: 3q^3+8q^2+4q+1
        95: q^4+5q^3+8q^2+4q+1
        96: 3q^3+7q^2+4q+1
        97: q^4+5q^3+8q^2+4q+1
        98: q^4+5q^3+8q^2+4q+1
        99: 3q^3+7q^2+4q+1
       100: 2q^3+7q^2+4q+1
       101: 3q^3+7q^2+4q+1
       102: q^3+5q^2+4q+1
       103: 3q^3+7q^2+4q+1
       104: 3q^2+3q+1
       105: 3q^2+3q+1
       106: 2q^3+6q^2+4q+1
       107: 2q^3+6q^2+4q+1
       108: 2q^3+7q^2+4q+1
       109: 3q^3+8q^2+4q+1
       110: 2q^3+7q^2+4q+1
       111: q^3+5q^2+4q+1
       112: 3q^2+3q+1
       113: 2q^3+6q^2+4q+1
       114: q^3+4q^2+4q+1
       115: 2q^3+6q^2+4q+1
       116: q^3+5q^2+4q+1
       117: 2q^3+6q^2+4q+1
       118: 3q^3+7q^2+4q+1
       119: q^3+4q^2+4q+1
       120: q^3+5q^2+4q+1
       121: 3q^2+4q+1
       122: 2q^3+5q^2+4q+1
       123: 2q^3+5q^2+4q+1
       124: 3q^2+4q+1
       125: 2q^3+6q^2+4q+1
       126: q^3+4q^2+4q+1
       127: 2q^2+3q+1
       128: 2q^3+5q^2+4q+1
       129: 2q^3+7q^2+4q+1
       130: q^3+5q^2+4q+1
       131: 3q^2+4q+1
       132: q^3+5q^2+4q+1
       133: q^3+5q^2+4q+1
       134: 2q^2+3q+1
       135: q^3+5q^2+4q+1
       136: q^3+5q^2+4q+1
       137: 2q^3+7q^2+4q+1
       138: q^3+5q^2+4q+1
       139: 2q^3+7q^2+4q+1
       140: q^3+5q^2+4q+1
       141: q^3+5q^2+4q+1
       142: 3q^2+3q+1
       143: 3q^2+3q+1
       144: q^3+5q^2+4q+1
       145: 3q^3+7q^2+4q+1
       146: q^3+5q^2+4q+1
       147: 2q^2+3q+1
       148: 2q^2+3q+1
       149: 2q^3+7q^2+4q+1
       150: 3q^2+3q+1
       151: 2q^3+5q^2+4q+1
       152: q^3+5q^2+4q+1
       153: q^3+5q^2+4q+1
       154: q^3+4q^2+4q+1
       155: 3q^2+3q+1
       156: 2q^3+6q^2+4q+1
       157: 2q^3+6q^2+4q+1
       158: 3q^3+8q^2+4q+1
       159: 2q^3+7q^2+4q+1
       160: 3q^3+8q^2+4q+1
       161: 3q^3+7q^2+4q+1
       162: 2q^3+6q^2+4q+1
       163: 2q^3+6q^2+4q+1
       164: 2q^3+6q^2+4q+1
       165: 3q^3+7q^2+4q+1
       166: q^4+5q^3+8q^2+4q+1
       167: 2q^3+7q^2+4q+1
       168: q^3+5q^2+4q+1
       169: 2q^3+5q^2+4q+1
       170: 3q^3+8q^2+4q+1
       171: 2q^3+6q^2+4q+1
       172: 2q^3+5q^2+4q+1
       173: 2q^3+7q^2+4q+1
       174: 3q^3+7q^2+4q+1
       175: q^3+5q^2+4q+1
       176: q^3+5q^2+4q+1
       177: q^4+5q^3+8q^2+4q+1
       178: 2q^3+7q^2+4q+1
       179: q^3+5q^2+4q+1
       180: 3q^3+7q^2+4q+1
       181: 2q^3+7q^2+4q+1
       182: 3q^2+3q+1
       183: 3q^3+7q^2+4q+1
       184: q^3+5q^2+4q+1
       185: q^3+5q^2+4q+1
       186: 2q^3+7q^2+4q+1
       187: 3q^3+7q^2+4q+1
       188: q^3+5q^2+4q+1
       189: q^2+2q+1
       190: 3q^2+3q+1
       191: 3q^2+3q+1
       192: 2q^3+6q^2+4q+1
       193: q^3+4q^2+4q+1
       194: 3q^2+4q+1
       195: 2q^3+7q^2+4q+1
       196: q^3+5q^2+4q+1
       197: q^3+5q^2+4q+1
       198: 3q^2+3q+1
       199: 2q^2+3q+1
       200: q^3+4q^2+4q+1
       201: q^3+4q^2+4q+1
       202: q^3+5q^2+4q+1
       203: 2q^3+6q^2+4q+1
       204: q^3+5q^2+4q+1
       205: 3q^2+4q+1
       206: 2q^2+3q+1
       207: q^3+4q^2+4q+1
       208: 2q^2+4q+1
       209: 3q^2+4q+1
       210: 3q^2+4q+1
       211: 3q^2+4q+1
       212: 2q^3+5q^2+4q+1
       213: 2q+1
       214: 3q^2+4q+1
       215: 2q^2+4q+1
       216: q^3+4q^2+4q+1
       217: 2q^2+3q+1
       218: q^3+4q^2+4q+1
       219: 2q^2+3q+1
       220: 2q^2+4q+1
       221: q^3+5q^2+4q+1
       222: 2q^2+4q+1
       223: q^2+3q+1
       224: 3q^2+4q+1
       225: q^3+5q^2+4q+1
       226: q^2+2q+1
       227: 3q^2+4q+1
       228: 2q^2+3q+1
       229: 2q^2+3q+1
       230: q^3+5q^2+4q+1
       231: q^3+5q^2+4q+1
       232: q^3+5q^2+4q+1
       233: 2q^3+7q^2+4q+1
       234: q^3+5q^2+4q+1
       235: q^3+4q^2+4q+1
       236: 2q^2+3q+1
       237: q^3+5q^2+4q+1
       238: 2q^2+3q+1
       239: 3q^2+3q+1
       240: 2q^2+3q+1
       241: 3q^2+3q+1
       242: q^3+5q^2+4q+1
       243: 2q^2+3q+1
       244: 2q^2+3q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2q^2+3q+1
       248: 3q^2+4q+1
       249: 3q^2+3q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^3+5q^2+4q+1
       253: q^3+5q^2+4q+1
       254: 2q^2+3q+1
       255: q^2+3q+1
       256: q^3+4q^2+4q+1
       257: q^3+4q^2+4q+1
       258: 3q^2+3q+1
       259: 3q^2+3q+1
       260: 2q^3+6q^2+4q+1
       261: 2q^3+6q^2+4q+1
       262: 2q^3+7q^2+4q+1
       263: 3q^3+8q^2+4q+1
       264: 2q^3+7q^2+4q+1
       265: q^3+5q^2+4q+1
       266: 3q^2+3q+1
       267: 2q^3+6q^2+4q+1
       268: q^3+4q^2+4q+1
       269: 2q^3+6q^2+4q+1
       270: q^3+5q^2+4q+1
       271: 2q^3+6q^2+4q+1
       272: 3q^3+7q^2+4q+1
       273: q^3+4q^2+4q+1
       274: q^3+5q^2+4q+1
       275: 3q^2+4q+1
       276: 2q^3+5q^2+4q+1
       277: 2q^3+5q^2+4q+1
       278: 3q^2+4q+1
       279: 2q^3+6q^2+4q+1
       280: q^3+4q^2+4q+1
       281: 2q^2+3q+1
       282: 2q^3+5q^2+4q+1
       283: 2q^3+7q^2+4q+1
       284: q^3+5q^2+4q+1
       285: 3q^2+4q+1
       286: q^3+5q^2+4q+1
       287: q^3+5q^2+4q+1
       288: 2q^2+3q+1
       289: q^3+5q^2+4q+1
       290: q^3+5q^2+4q+1
       291: 2q^3+7q^2+4q+1
       292: q^3+5q^2+4q+1
       293: 2q^3+7q^2+4q+1
       294: q^3+5q^2+4q+1
       295: q^3+5q^2+4q+1
       296: 3q^2+3q+1
       297: 3q^2+3q+1
       298: q^3+5q^2+4q+1
       299: 3q^3+7q^2+4q+1
       300: q^3+5q^2+4q+1
       301: 2q^2+3q+1
       302: 2q^2+3q+1
       303: 2q^3+7q^2+4q+1
       304: 3q^2+3q+1
       305: 2q^3+5q^2+4q+1
       306: q^3+5q^2+4q+1
       307: q^3+5q^2+4q+1
       308: q^3+4q^2+4q+1
       309: q^2+2q+1
       310: q^2+2q+1
       311: 3q^2+3q+1
       312: 2q^2+3q+1
       313: q^3+4q^2+4q+1
       314: 2q+1
       315: 3q^2+4q+1
       316: 2q^2+4q+1
       317: q^3+5q^2+4q+1
       318: q^2+2q+1
       319: 2q+1
       320: 2q^2+3q+1
       321: 2q^2+3q+1
       322: q^3+4q^2+4q+1
       323: 2q^2+4q+1
       324: 2q^2+4q+1
       325: q^3+5q^2+4q+1
       326: 2q^2+4q+1
       327: 3q^2+4q+1
       328: 2q^2+3q+1
       329: q^2+3q+1
       330: 2q^2+4q+1
       331: 2q^2+4q+1
       332: 3q^2+4q+1
       333: 3q^2+4q+1
       334: 3q^2+4q+1
       335: 3q^2+4q+1
       336: 2q+1
       337: 2q+1
       338: 2q^2+4q+1
       339: 2q^2+4q+1
       340: 2q^2+3q+1
       341: q^3+4q^2+4q+1
       342: 2q^2+3q+1
       343: q^2+3q+1
       344: 2q+1
       345: 2q^2+4q+1
       346: q^2+4q+1
       347: 2q^2+4q+1
       348: q^2+3q+1
       349: 2q^2+4q+1
       350: q^2+3q+1
       351: 2q^2+4q+1
       352: q^2+2q+1
       353: 2q+1
       354: q^2+3q+1
       355: 3q^2+4q+1
       356: q^2+2q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: q^3+5q^2+4q+1
       360: 2q^2+3q+1
       361: 3q^2+4q+1
       362: q^3+5q^2+4q+1
       363: q^3+4q^2+4q+1
       364: q^3+4q^2+4q+1
       365: 2q^2+3q+1
       366: q^2+2q+1
       367: 2q^2+3q+1
       368: 2q^2+3q+1
       369: 2q^2+3q+1
       370: 3q^2+3q+1
       371: 2q^2+3q+1
       372: q^2+3q+1
       373: q^2+2q+1
       374: 2q^2+3q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q^2+3q+1
       380: 2q+1
       381: 3q^2+4q+1
       382: q^2+3q+1
       383: 2q^2+3q+1
       384: q^2+2q+1
       385: 2q^2+3q+1
       386: 2q^2+3q+1
       387: q^2+3q+1
       388: 2q^2+3q+1
       389: 2q+1
       390: 2q+1
       391: q^2+3q+1
       392: q^3+4q^2+4q+1
       393: q^2+2q+1
       394: q^2+3q+1
       395: q^2+2q+1
       396: 3q^2+3q+1
       397: 3q^2+3q+1
       398: 2q^3+6q^2+4q+1
       399: q^3+4q^2+4q+1
       400: 3q^2+4q+1
       401: 2q^3+7q^2+4q+1
       402: q^3+5q^2+4q+1
       403: q^3+5q^2+4q+1
       404: 3q^2+3q+1
       405: 2q^2+3q+1
       406: q^3+4q^2+4q+1
       407: q^3+4q^2+4q+1
       408: q^3+5q^2+4q+1
       409: 2q^3+6q^2+4q+1
       410: q^3+5q^2+4q+1
       411: 3q^2+4q+1
       412: 2q^2+3q+1
       413: q^3+4q^2+4q+1
       414: 2q^2+4q+1
       415: 3q^2+4q+1
       416: 3q^2+4q+1
       417: 3q^2+4q+1
       418: 2q^3+5q^2+4q+1
       419: 2q+1
       420: 3q^2+4q+1
       421: 2q^2+4q+1
       422: q^3+4q^2+4q+1
       423: 2q^2+3q+1
       424: q^3+4q^2+4q+1
       425: 2q^2+3q+1
       426: 2q^2+4q+1
       427: q^3+5q^2+4q+1
       428: 2q^2+4q+1
       429: q^2+3q+1
       430: 3q^2+4q+1
       431: q^3+5q^2+4q+1
       432: q^2+2q+1
       433: 3q^2+4q+1
       434: 2q^2+3q+1
       435: 2q^2+3q+1
       436: q^3+5q^2+4q+1
       437: q^3+5q^2+4q+1
       438: q^3+5q^2+4q+1
       439: 2q^3+7q^2+4q+1
       440: q^3+5q^2+4q+1
       441: q^3+4q^2+4q+1
       442: 2q^2+3q+1
       443: q^3+5q^2+4q+1
       444: 2q^2+3q+1
       445: 3q^2+3q+1
       446: 2q^2+3q+1
       447: 3q^2+3q+1
       448: q^3+5q^2+4q+1
       449: 2q^2+3q+1
       450: 2q^2+3q+1
       451: 2q+1
       452: 2q^2+3q+1
       453: 2q^2+3q+1
       454: 3q^2+4q+1
       455: 3q^2+3q+1
       456: 2q^2+3q+1
       457: 2q^2+3q+1
       458: 2q^3+5q^2+4q+1
       459: q^3+5q^2+4q+1
       460: 2q^2+3q+1
       461: q^2+3q+1
       462: q^3+4q^2+4q+1
       463: q^3+4q^2+4q+1
       465: q^2+2q+1
       466: 2q+1
       467: 2q^2+3q+1
       468: 2q+1
       469: 2q+1
       470: 2q^2+4q+1
       471: 2q^2+4q+1
       472: q^2+2q+1
       473: 2q+1
       474: 2q+1
       475: 2q^2+3q+1
       476: q^2+3q+1
       477: 2q^2+4q+1
       478: 2q+1
       479: 2q^2+4q+1
       480: q^2+4q+1
       481: 2q^2+4q+1
       482: 2q+1
       483: 2q+1
       484: q^2+3q+1
       485: q^2+3q+1
       486: 2q^2+4q+1
       487: 2q^2+4q+1
       488: 2q+1
       489: 3q^2+4q+1
       490: 2q^2+4q+1
       491: 3q^2+4q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q^2+4q+1
       496: 2q+1
       497: 2q^2+4q+1
       498: 2q^2+3q+1
       499: q^2+3q+1
       500: q^2+3q+1
       501: 2q+1
       502: 2q+1
       503: q^2+4q+1
       504: q^2+4q+1
       505: q^2+3q+1
       506: 2q^2+4q+1
       507: q^2+3q+1
       508: q^2+3q+1
       509: 2q+1
       510: 2q^2+4q+1
       511: 2q+1
       512: 2q+1
       513: q+1
       514: 2q+1
       515: q^2+3q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: 2q^2+3q+1
       519: q^2+2q+1
       520: 2q^2+3q+1
       521: 2q+1
       522: 3q^2+4q+1
       523: q^2+3q+1
       524: q^3+4q^2+4q+1
       525: q^2+2q+1
       526: q+1
       527: q^2+2q+1
       528: q^2+2q+1
       529: 2q^2+3q+1
       530: 2q+1
       531: q^2+3q+1
       532: 2q^2+3q+1
       533: 2q+1
       534: q^2+3q+1
       535: q^2+2q+1
       536: q+1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q^2+3q+1
       543: 2q+1
       544: q+1
       545: q^2+3q+1
       546: q^2+3q+1
       547: q^2+2q+1
       548: 2q^2+3q+1
       549: q^2+2q+1
       550: 2q+1
       551: q+1
       552: q^2+3q+1
       553: 2q+1
       554: 2q+1
       555: q+1
       556: 2q+1
       557: 2q+1
       558: q^2+3q+1
       559: q^2+2q+1
       560: q+1
       561: 2q+1
       562: q^2+3q+1
       563: q^2+2q+1
       564: q^2+2q+1
       565: 3q^2+3q+1
       566: 2q^2+3q+1
       567: q^3+4q^2+4q+1
       568: 2q+1
       569: 3q^2+4q+1
       570: 2q^2+4q+1
       571: q^3+5q^2+4q+1
       572: q^2+2q+1
       573: 2q+1
       574: 2q^2+3q+1
       575: 2q^2+3q+1
       576: q^3+4q^2+4q+1
       577: 2q^2+4q+1
       578: 2q^2+4q+1
       579: q^3+5q^2+4q+1
       580: 2q^2+4q+1
       581: 3q^2+4q+1
       582: 2q^2+3q+1
       583: q^2+3q+1
       584: 2q^2+4q+1
       585: 2q^2+4q+1
       586: 3q^2+4q+1
       587: 3q^2+4q+1
       588: 3q^2+4q+1
       589: 3q^2+4q+1
       590: 2q+1
       591: 2q+1
       592: 2q^2+4q+1
       593: 2q^2+4q+1
       594: 2q^2+3q+1
       595: q^3+4q^2+4q+1
       596: 2q^2+3q+1
       597: q^2+3q+1
       598: 2q+1
       599: 2q^2+4q+1
       600: q^2+4q+1
       601: 2q^2+4q+1
       602: q^2+3q+1
       603: 2q^2+4q+1
       604: q^2+3q+1
       605: 2q^2+4q+1
       606: q^2+2q+1
       607: 2q+1
       608: q^2+3q+1
       609: 3q^2+4q+1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: 2q^2+3q+1
       613: q^3+5q^2+4q+1
       614: 2q^2+3q+1
       615: 3q^2+4q+1
       616: q^3+5q^2+4q+1
       617: q^3+4q^2+4q+1
       618: q^3+4q^2+4q+1
       619: 2q^2+3q+1
       620: q^2+2q+1
       621: 2q^2+3q+1
       622: 2q^2+3q+1
       623: 2q^2+3q+1
       624: 3q^2+3q+1
       625: 2q^2+3q+1
       626: q^2+3q+1
       627: q^2+2q+1
       628: 2q^2+3q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: 2q+1
       633: 2q^2+3q+1
       634: 2q+1
       635: 3q^2+4q+1
       636: q^2+3q+1
       637: 2q^2+3q+1
       638: q^2+2q+1
       639: 2q^2+3q+1
       640: 2q^2+3q+1
       641: q^2+3q+1
       642: 2q^2+3q+1
       643: 2q+1
       644: 2q+1
       645: q^2+3q+1
       646: q^3+4q^2+4q+1
       647: q^2+2q+1
       648: q^2+3q+1
       650: 2q+1
       651: 2q+1
       652: q+1
       653: 2q+1
       654: 2q+1
       655: 2q^2+4q+1
       656: 2q+1
       658: 2q+1
       659: 2q+1
       660: q^2+3q+1
       661: 2q+1
       662: 2q+1
       663: q^2+4q+1
       664: q^2+4q+1
       665: 2q+1
       666: 2q+1
       667: 2q+1
       668: q^2+3q+1
       669: q^2+3q+1
       670: 2q^2+4q+1
       672: 2q+1
       673: 2q+1
       674: 2q^2+4q+1
       675: 2q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: 2q+1
       681: 2q+1
       682: 2q^2+4q+1
       683: 2q+1
       684: q^2+3q+1
       685: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: q^2+4q+1
       690: 2q+1
       691: 2q+1
       692: q^2+3q+1
       693: q^2+3q+1
       694: q^2+3q+1
       695: 2q+1
       696: q+1
       697: 2q+1
       698: 2q+1
       699: q+1
       700: 2q+1
       701: q+1
       702: q+1
       704: q^2+2q+1
       705: q+1
       706: q^2+2q+1
       707: 2q+1
       708: q+1
       709: q^2+3q+1
       710: q^2+3q+1
       711: q^2+2q+1
       712: q+1
       713: q+1
       714: q^2+2q+1
       715: q+1
       716: 2q+1
       717: q+1
       718: q^2+3q+1
       719: 2q+1
       720: 2q+1
       721: q+1
       722: q+1
       723: q+1
       724: q+1
       725: 2q+1
       726: 2q+1
       728: 2q+1
       729: 2q+1
       730: q^2+3q+1
       731: 1
       732: q+1
       733: q+1
       734: q^2+3q+1
       735: q+1
       736: q^2+3q+1
       737: q^2+2q+1
       738: q+1
       739: 2q+1
       740: q+1
       741: 1
       742: 2q+1
       743: 2q+1
       744: q+1
       745: 2q+1
       746: q+1
       747: 2q+1
       748: q+1
       749: q^2+3q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 2q+1
       756: q^2+2q+1
       757: 2q+1
       758: 2q^2+3q+1
       759: 2q+1
       760: 2q+1
       761: 2q^2+4q+1
       762: 2q^2+4q+1
       763: q^2+2q+1
       764: 2q+1
       765: 2q+1
       766: 2q^2+3q+1
       767: q^2+3q+1
       768: 2q^2+4q+1
       769: 2q+1
       770: 2q^2+4q+1
       771: q^2+4q+1
       772: 2q^2+4q+1
       773: 2q+1
       774: 2q+1
       775: q^2+3q+1
       776: q^2+3q+1
       777: 2q^2+4q+1
       778: 2q^2+4q+1
       779: 2q+1
       780: 3q^2+4q+1
       781: 2q^2+4q+1
       782: 3q^2+4q+1
       783: q+1
       784: 2q+1
       785: 2q+1
       786: 2q^2+4q+1
       787: 2q+1
       788: 2q^2+4q+1
       789: 2q^2+3q+1
       790: q^2+3q+1
       791: q^2+3q+1
       792: 2q+1
       793: 2q+1
       794: q^2+4q+1
       795: q^2+4q+1
       796: q^2+3q+1
       797: 2q^2+4q+1
       798: q^2+3q+1
       799: q^2+3q+1
       800: 2q+1
       801: 2q^2+4q+1
       802: 2q+1
       803: 2q+1
       804: q+1
       805: 2q+1
       806: q^2+3q+1
       807: q^2+2q+1
       808: q^2+2q+1
       809: 2q^2+3q+1
       810: q^2+2q+1
       811: 2q^2+3q+1
       812: 2q+1
       813: 3q^2+4q+1
       814: q^2+3q+1
       815: q^3+4q^2+4q+1
       816: q^2+2q+1
       817: q+1
       818: q^2+2q+1
       819: q^2+2q+1
       820: 2q^2+3q+1
       821: 2q+1
       822: q^2+3q+1
       823: 2q^2+3q+1
       824: 2q+1
       825: q^2+3q+1
       826: q^2+2q+1
       827: q+1
       828: 2q+1
       829: 2q+1
       830: 2q+1
       831: 2q+1
       832: 2q+1
       833: q^2+3q+1
       834: 2q+1
       835: q+1
       836: q^2+3q+1
       837: q^2+3q+1
       838: q^2+2q+1
       839: 2q^2+3q+1
       840: q^2+2q+1
       841: 2q+1
       842: q+1
       843: q^2+3q+1
       844: 2q+1
       845: 2q+1
       846: q+1
       847: 2q+1
       848: 2q+1
       849: q^2+3q+1
       850: q^2+2q+1
       851: q+1
       852: 2q+1
       853: q^2+3q+1
       855: 2q+1
       856: q+1
       857: q+1
       858: 2q+1
       859: q+1
       860: 2q+1
       862: 2q+1
       863: 2q+1
       864: q+1
       865: 2q+1
       866: 2q+1
       867: q^2+4q+1
       868: 2q+1
       870: 2q+1
       871: q+1
       872: q^2+3q+1
       875: 2q+1
       876: 2q+1
       877: 2q+1
       879: q+1
       880: 1
       881: q+1
       882: 2q+1
       883: q+1
       884: 2q+1
       885: 2q+1
       886: q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: 2q+1
       893: 2q+1
       894: q+1
       895: q^2+3q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: 2q+1
       901: 1
       902: q+1
       903: q+1
       904: 1
       905: q+1
       907: q+1
       908: q+1
       909: 1
       910: q+1
       911: q+1
       912: q^2+3q+1
       913: q+1
       915: q+1
       916: q+1
       917: q+1
       918: q+1
       919: 1
       920: 2q+1
       921: 2q+1
       922: q+1
       923: q+1
       924: q+1
       925: q+1
       926: q+1
       927: 2q+1
       931: 2q+1
       932: q+1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: q+1
       938: q+1
       939: q^2+3q+1
       940: q+1
       941: q+1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 2q+1
       947: q+1
       949: q+1
       950: q+1
       951: 2q+1
       952: q+1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: q+1
       961: 2q+1
       962: 2q+1
       963: q+1
       964: 2q+1
       965: 2q+1
       966: 2q^2+4q+1
       967: 2q+1
       969: 2q+1
       970: 2q+1
       971: q^2+3q+1
       972: 2q+1
       973: 2q+1
       974: q^2+4q+1
       975: q^2+4q+1
       976: 2q+1
       977: 2q+1
       978: 2q+1
       979: q^2+3q+1
       980: q^2+3q+1
       981: 2q^2+4q+1
       983: 2q+1
       984: 2q+1
       985: 2q^2+4q+1
       986: 2q+1
       987: q+1
       988: q+1
       989: 2q+1
       990: q+1
       991: 2q+1
       992: 2q+1
       993: 2q^2+4q+1
       994: 2q+1
       995: q^2+3q+1
       996: q+1
       997: q+1
       998: 2q+1
       999: 2q+1
      1000: q^2+4q+1
      1001: 2q+1
      1002: 2q+1
      1003: q^2+3q+1
      1004: q^2+3q+1
      1005: q^2+3q+1
      1006: 2q+1
      1007: q+1
      1008: 2q+1
      1009: 2q+1
      1010: q+1
      1011: 2q+1
      1012: q+1
      1013: q+1
      1015: q^2+2q+1
      1016: q+1
      1017: q^2+2q+1
      1018: 2q+1
      1019: q+1
      1020: q^2+3q+1
      1021: q^2+3q+1
      1022: q^2+2q+1
      1023: q+1
      1024: q+1
      1025: q^2+2q+1
      1026: q+1
      1027: 2q+1
      1028: q+1
      1029: q^2+3q+1
      1030: 2q+1
      1031: 2q+1
      1032: q+1
      1033: q+1
      1034: q+1
      1035: q+1
      1036: 2q+1
      1037: 2q+1
      1039: 2q+1
      1040: 2q+1
      1041: q^2+3q+1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q^2+3q+1
      1046: q+1
      1047: q^2+3q+1
      1048: q^2+2q+1
      1049: q+1
      1050: 2q+1
      1051: q+1
      1052: 1
      1053: 2q+1
      1054: 2q+1
      1055: q+1
      1056: 2q+1
      1057: q+1
      1058: 2q+1
      1059: q+1
      1060: q^2+3q+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: q+1
      1065: 2q+1
      1068: q+1
      1069: 1
      1070: q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: 2q+1
      1079: q+1
      1080: q+1
      1084: 2q+1
      1085: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: q+1
      1091: q+1
      1092: 2q+1
      1093: 1
      1095: q+1
      1096: 1
      1097: q+1
      1100: q+1
      1101: q+1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1114: q+1
      1115: 1
      1116: 1
      1117: q+1
      1118: 1
      1119: q+1
      1121: q+1
      1122: q+1
      1123: 1
      1124: 1
      1125: 1
      1126: 2q+1
      1127: q+1
      1129: q+1
      1131: q+1
      1136: q+1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: q+1
      1144: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: q+1
      1154: q+1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 2q+1
      1167: q+1
      1168: q+1
      1169: 2q+1
      1170: q+1
      1171: 2q+1
      1173: 2q+1
      1174: 2q+1
      1175: q+1
      1176: 2q+1
      1177: 2q+1
      1178: q^2+4q+1
      1179: 2q+1
      1181: 2q+1
      1182: q+1
      1183: q^2+3q+1
      1186: 2q+1
      1187: 2q+1
      1188: 2q+1
      1190: q+1
      1191: 1
      1192: q+1
      1193: 2q+1
      1194: q+1
      1195: 2q+1
      1196: 2q+1
      1197: q+1
      1198: q+1
      1199: q+1
      1200: 2q+1
      1201: q+1
      1202: 2q+1
      1204: 2q+1
      1205: q+1
      1206: q^2+3q+1
      1207: q+1
      1208: 1
      1209: q+1
      1210: q+1
      1211: 2q+1
      1212: 1
      1213: q+1
      1214: q+1
      1215: 1
      1216: q+1
      1218: q+1
      1219: q+1
      1220: 1
      1221: q+1
      1222: q+1
      1223: q^2+3q+1
      1224: q+1
      1226: q+1
      1227: q+1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 2q+1
      1232: 2q+1
      1233: q+1
      1234: q+1
      1235: q+1
      1236: q+1
      1237: q+1
      1238: 2q+1
      1242: 2q+1
      1243: q+1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: q+1
      1249: q+1
      1250: q^2+3q+1
      1251: q+1
      1252: q+1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 2q+1
      1258: q+1
      1260: q+1
      1261: q+1
      1262: 2q+1
      1263: q+1
      1264: 1
      1265: q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1270: q+1
      1272: 1
      1273: 1
      1276: q+1
      1277: 1
      1278: q+1
      1280: q+1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: q+1
      1291: 1
      1292: 1
      1294: 1
      1295: 1
      1299: q+1
      1300: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: q+1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: q+1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: q+1
      1337: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1359: q+1
      1360: 1
      1361: q+1
      1363: 2q+1
      1364: q+1
      1365: q+1
      1366: 2q+1
      1367: q+1
      1368: 2q+1
      1370: q+1
      1371: q+1
      1375: 2q+1
      1376: q+1
      1378: 1
      1379: 1
      1380: 1
      1381: q+1
      1382: q+1
      1383: 2q+1
      1384: 1
      1386: q+1
      1387: 1
      1388: q+1
      1391: q+1
      1392: q+1
      1393: q+1
      1394: 1
      1395: 1
      1396: q+1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1405: q+1
      1406: 1
      1407: 1
      1408: q+1
      1409: 1
      1410: q+1
      1412: q+1
      1413: q+1
      1414: 1
      1415: 1
      1416: 1
      1417: 2q+1
      1418: q+1
      1420: q+1
      1422: q+1
      1427: q+1
      1429: 1
      1430: 1
      1431: 1
      1432: q+1
      1433: 1
      1434: q+1
      1435: q+1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: q+1
      1445: q+1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1453: 1
      1454: 1
      1455: q+1
      1457: 1
      1459: 1
      1460: 1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1477: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1493: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1517: 1
      1519: 1
      1524: 1
      1526: 1
      1527: 1
      1530: q+1
      1531: 1
      1532: q+1
      1534: q+1
      1539: q+1
      1541: 1
      1542: 1
      1543: 1
      1544: q+1
      1545: 1
      1546: 1
      1548: 1
      1549: 1
      1553: q+1
      1554: 1
      1556: 1
      1557: 1
      1558: 1
      1561: 1
      1562: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: q+1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: q+1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: q+1
      1591: 1
      1593: 1
      1595: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1609: 1
      1610: 1
      1613: 1
      1618: 1
      1619: 1
      1626: 1
      1631: 1
      1633: 1
      1644: 1
      1646: 1
      1663: 1
      1665: 1
      1666: 1
      1674: 1
      1675: 1
      1676: 1
      1678: 1
      1683: 1
      1685: 1
      1686: 1
      1690: 1
      1691: 1
      1693: 1
      1694: 1
      1697: 1
      1699: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1723: 1
      1725: 1
      1730: 1
      1735: 1
      1767: 1
      1772: 1
      1773: 1
      1780: 1
      1785: 1
      1787: 1
      1798: 1
      1800: 1
      1840: 1

1841:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: 3q^2+3q+1
         9: 2q^3+4q^2+3q+1
        10: q^3+4q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: q^3+3q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: q^3+4q^2+3q+1
        18: 2q^3+4q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+4q^2+3q+1
        22: 3q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^3+4q^2+3q+1
        27: 3q^2+3q+1
        28: 2q^3+4q^2+3q+1
        29: q^3+4q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: 2q^3+4q^2+3q+1
        33: q^3+4q^2+3q+1
        34: q^3+4q^2+3q+1
        35: 2q^2+3q+1
        36: q^3+3q^2+3q+1
        37: q^2+2q+1
        38: q^3+3q^2+3q+1
        39: q^3+3q^2+3q+1
        40: q^3+4q^2+3q+1
        41: q^3+4q^2+3q+1
        42: 3q^2+3q+1
        43: 2q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: 2q^3+4q^2+3q+1
        46: 2q^3+4q^2+3q+1
        47: 2q^3+4q^2+3q+1
        48: q^3+4q^2+3q+1
        49: q^3+3q^2+3q+1
        50: 3q^2+3q+1
        51: 3q^2+3q+1
        52: 3q^2+3q+1
        53: 2q^2+3q+1
        54: 3q^2+3q+1
        55: 3q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: q^3+4q^2+3q+1
        59: 3q^2+3q+1
        60: 3q^2+3q+1
        61: 3q^2+3q+1
        62: q^3+4q^2+3q+1
        63: q^3+4q^2+3q+1
        64: 3q^2+3q+1
        65: q^3+4q^2+3q+1
        66: q^3+4q^2+3q+1
        67: 2q^2+3q+1
        68: 2q^3+4q^2+3q+1
        69: q^3+4q^2+3q+1
        70: q^3+3q^2+3q+1
        71: 2q^2+3q+1
        72: q^3+4q^2+3q+1
        73: 2q^2+3q+1
        74: 2q^2+3q+1
        75: 2q^2+3q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: q^3+3q^2+3q+1
        80: q^2+2q+1
        81: q^3+3q^2+3q+1
        82: q^2+2q+1
        83: q^3+3q^2+3q+1
        84: 3q^2+3q+1
        85: q^3+4q^2+3q+1
        86: 3q^2+3q+1
        87: 3q^2+3q+1
        88: 3q^2+3q+1
        89: q^3+4q^2+3q+1
        90: q^3+4q^2+3q+1
        91: 3q^2+3q+1
        92: 2q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: 2q^3+4q^2+3q+1
        95: q^3+4q^2+3q+1
        96: 2q^3+4q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: 2q^2+3q+1
       100: q^3+3q^2+3q+1
       101: q^2+2q+1
       102: q^3+3q^2+3q+1
       103: q^3+3q^2+3q+1
       104: 3q^2+3q+1
       105: 3q^2+3q+1
       106: 3q^2+3q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: 3q^2+3q+1
       111: q^2+2q+1
       112: 3q^2+3q+1
       113: 3q^2+3q+1
       114: 3q^2+3q+1
       115: 2q^2+3q+1
       116: 3q^2+3q+1
       117: 3q^2+3q+1
       118: 3q^2+3q+1
       119: 3q^2+3q+1
       120: q^3+4q^2+3q+1
       121: 3q^2+3q+1
       122: 3q^2+3q+1
       123: 3q^2+3q+1
       124: 2q^2+3q+1
       125: q^3+4q^2+3q+1
       126: 2q^2+3q+1
       127: 2q^2+3q+1
       128: 2q^2+3q+1
       129: q^3+4q^2+3q+1
       130: q^3+4q^2+3q+1
       131: 2q^2+3q+1
       132: q^3+3q^2+3q+1
       133: q^2+2q+1
       134: 2q^2+3q+1
       135: 2q^2+3q+1
       136: 2q^2+3q+1
       137: 2q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: 2q^2+3q+1
       141: 2q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: 2q+1
       152: q^3+3q^2+3q+1
       153: q^2+2q+1
       154: q^3+3q^2+3q+1
       155: 3q^2+3q+1
       156: 3q^2+3q+1
       157: 3q^2+3q+1
       158: 2q^2+3q+1
       159: 3q^2+3q+1
       160: 3q^2+3q+1
       161: 3q^2+3q+1
       162: 3q^2+3q+1
       163: q^3+4q^2+3q+1
       164: 3q^2+3q+1
       165: 3q^2+3q+1
       166: 3q^2+3q+1
       167: q^3+4q^2+3q+1
       168: q^3+4q^2+3q+1
       169: 3q^2+3q+1
       170: q^3+4q^2+3q+1
       171: q^3+4q^2+3q+1
       172: 2q^2+3q+1
       173: 2q^3+4q^2+3q+1
       174: q^3+4q^2+3q+1
       175: q^3+3q^2+3q+1
       176: 2q^2+3q+1
       177: q^3+4q^2+3q+1
       178: 2q^2+3q+1
       179: 2q^2+3q+1
       180: 2q^2+3q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: 2q+1
       184: q^3+3q^2+3q+1
       185: q^2+2q+1
       186: q^3+3q^2+3q+1
       187: q^2+2q+1
       188: q^3+3q^2+3q+1
       189: q^2+2q+1
       190: 3q^2+3q+1
       191: 2q^2+3q+1
       192: 2q^2+3q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: 2q^2+3q+1
       196: q^2+2q+1
       197: q+1
       198: 3q^2+3q+1
       199: 3q^2+3q+1
       200: 3q^2+3q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q^2+3q+1
       204: 3q^2+3q+1
       205: q^2+2q+1
       206: 3q^2+3q+1
       207: 3q^2+3q+1
       208: 3q^2+3q+1
       209: 2q^2+3q+1
       210: 3q^2+3q+1
       211: 3q^2+3q+1
       212: 3q^2+3q+1
       213: 2q^2+3q+1
       214: 2q^2+3q+1
       215: 2q^2+3q+1
       216: 2q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 2q^2+3q+1
       220: 2q^2+3q+1
       221: q^3+4q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: 2q^2+3q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 2q^2+3q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q^2+3q+1
       235: q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       247: q+1
       248: 2q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q+1
       256: q^3+3q^2+3q+1
       257: q^2+2q+1
       258: 3q^2+3q+1
       259: 3q^2+3q+1
       260: 3q^2+3q+1
       261: 2q^2+3q+1
       262: 2q^2+3q+1
       263: 2q^2+3q+1
       264: 3q^2+3q+1
       265: q^2+2q+1
       266: 3q^2+3q+1
       267: 3q^2+3q+1
       268: 3q^2+3q+1
       269: 2q^2+3q+1
       270: 3q^2+3q+1
       271: 3q^2+3q+1
       272: 3q^2+3q+1
       273: 3q^2+3q+1
       274: q^3+4q^2+3q+1
       275: 3q^2+3q+1
       276: 3q^2+3q+1
       277: 3q^2+3q+1
       278: 2q^2+3q+1
       279: q^3+4q^2+3q+1
       280: 2q^2+3q+1
       281: 2q^2+3q+1
       282: 2q^2+3q+1
       283: q^3+4q^2+3q+1
       284: q^3+4q^2+3q+1
       285: 2q^2+3q+1
       286: q^3+3q^2+3q+1
       287: q^2+2q+1
       288: 2q^2+3q+1
       289: 2q^2+3q+1
       290: 2q^2+3q+1
       291: 2q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: 2q^2+3q+1
       295: 2q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: 2q+1
       306: q^3+3q^2+3q+1
       307: q^2+2q+1
       308: q^3+3q^2+3q+1
       309: q+1
       310: q^2+2q+1
       311: 2q^2+3q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: q+1
       317: q+1
       318: q+1
       319: q^2+2q+1
       320: 3q^2+3q+1
       321: 2q^2+3q+1
       322: 2q^2+3q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: 2q^2+3q+1
       326: q^2+2q+1
       327: q+1
       328: 3q^2+3q+1
       329: 3q^2+3q+1
       330: 3q^2+3q+1
       331: 2q^2+3q+1
       332: 2q^2+3q+1
       333: 2q^2+3q+1
       334: 3q^2+3q+1
       335: q^2+2q+1
       336: 2q^2+3q+1
       337: 2q^2+3q+1
       338: 2q^2+3q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q^2+3q+1
       343: q^2+2q+1
       344: 2q^2+3q+1
       345: 2q^2+3q+1
       346: 2q^2+3q+1
       347: 2q+1
       348: 2q^2+3q+1
       349: 2q^2+3q+1
       350: 2q^2+3q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q^2+3q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: q+1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q+1
       395: q^2+2q+1
       396: 3q^2+3q+1
       397: 2q^2+3q+1
       398: 2q^2+3q+1
       399: q^2+2q+1
       400: q^2+2q+1
       401: 2q^2+3q+1
       402: q^2+2q+1
       403: q+1
       404: 3q^2+3q+1
       405: 3q^2+3q+1
       406: 3q^2+3q+1
       407: 2q^2+3q+1
       408: 2q^2+3q+1
       409: 2q^2+3q+1
       410: 3q^2+3q+1
       411: q^2+2q+1
       412: 3q^2+3q+1
       413: 3q^2+3q+1
       414: 3q^2+3q+1
       415: 2q^2+3q+1
       416: 3q^2+3q+1
       417: 3q^2+3q+1
       418: 3q^2+3q+1
       419: 2q^2+3q+1
       420: 2q^2+3q+1
       421: 2q^2+3q+1
       422: 2q+1
       423: 2q^2+3q+1
       424: 2q^2+3q+1
       425: 2q^2+3q+1
       426: 2q^2+3q+1
       427: q^3+4q^2+3q+1
       428: 2q^2+3q+1
       429: 2q^2+3q+1
       430: 2q^2+3q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: 2q+1
       434: 2q^2+3q+1
       435: 2q^2+3q+1
       436: 2q^2+3q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q^2+2q+1
       451: q+1
       452: q+1
       453: q+1
       454: 2q+1
       455: q^2+2q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^3+3q^2+3q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: q+1
       467: q^2+2q+1
       468: q^2+2q+1
       469: q+1
       470: q+1
       471: 1
       472: q+1
       473: q+1
       474: q^2+2q+1
       475: 2q^2+3q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: q+1
       481: q+1
       482: q+1
       483: q^2+2q+1
       484: 3q^2+3q+1
       485: 2q^2+3q+1
       486: 2q^2+3q+1
       487: q^2+2q+1
       488: q^2+2q+1
       489: 2q^2+3q+1
       490: q^2+2q+1
       491: q+1
       492: q^2+2q+1
       493: 2q^2+3q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q^2+2q+1
       500: q+1
       501: 2q^2+3q+1
       502: 2q^2+3q+1
       503: 2q^2+3q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q^2+3q+1
       508: q^2+2q+1
       509: 2q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       541: q+1
       542: 1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: 1
       551: q+1
       552: q+1
       553: q+1
       555: q+1
       556: q+1
       557: q+1
       558: q+1
       559: q^2+2q+1
       560: q+1
       561: q+1
       562: q+1
       563: q+1
       564: q^2+2q+1
       565: 2q^2+3q+1
       566: q^2+2q+1
       567: q^2+2q+1
       568: q^2+2q+1
       569: q^2+2q+1
       570: q+1
       571: q+1
       572: q+1
       573: q^2+2q+1
       574: 3q^2+3q+1
       575: 2q^2+3q+1
       576: 2q^2+3q+1
       577: q^2+2q+1
       578: q^2+2q+1
       579: 2q^2+3q+1
       580: q^2+2q+1
       581: q+1
       582: 3q^2+3q+1
       583: 3q^2+3q+1
       584: 3q^2+3q+1
       585: 2q^2+3q+1
       586: 2q^2+3q+1
       587: 2q^2+3q+1
       588: 3q^2+3q+1
       589: q^2+2q+1
       590: 2q^2+3q+1
       591: 2q^2+3q+1
       592: 2q^2+3q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q^2+3q+1
       597: q^2+2q+1
       598: 2q^2+3q+1
       599: 2q^2+3q+1
       600: 2q^2+3q+1
       601: 2q+1
       602: 2q^2+3q+1
       603: 2q^2+3q+1
       604: 2q^2+3q+1
       605: 2q+1
       606: q^2+2q+1
       607: 2q+1
       608: 2q+1
       609: 2q+1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 2q+1
       635: 2q+1
       636: 2q+1
       637: 2q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: q+1
       658: q+1
       659: q+1
       660: q^2+2q+1
       661: q^2+2q+1
       662: q+1
       663: q+1
       664: 1
       665: q+1
       666: q+1
       667: q^2+2q+1
       668: 2q^2+3q+1
       669: q^2+2q+1
       670: q^2+2q+1
       671: q^2+2q+1
       672: q^2+2q+1
       673: q+1
       674: q+1
       675: q+1
       676: q+1
       677: q^2+2q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: q^2+2q+1
       687: 2q^2+3q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q^2+2q+1
       694: q+1
       695: 2q+1
       696: 2q+1
       697: 2q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: 2q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       721: 1
       722: 1
       723: q+1
       729: 1
       730: 1
       731: 1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: 1
       739: 1
       740: q+1
       741: q+1
       742: q+1
       746: q+1
       747: 1
       748: q+1
       749: q+1
       750: q+1
       752: q+1
       753: q+1
       754: q+1
       755: q+1
       756: q+1
       757: q+1
       758: q^2+2q+1
       759: q^2+2q+1
       760: q+1
       761: q+1
       762: 1
       763: q+1
       764: q+1
       765: q^2+2q+1
       766: 2q^2+3q+1
       767: q^2+2q+1
       768: q^2+2q+1
       769: q^2+2q+1
       770: q^2+2q+1
       771: q+1
       772: q+1
       773: q+1
       774: q^2+2q+1
       775: 3q^2+3q+1
       776: 2q^2+3q+1
       777: 2q^2+3q+1
       778: q^2+2q+1
       779: q^2+2q+1
       780: 2q^2+3q+1
       781: q^2+2q+1
       782: q+1
       783: q^2+2q+1
       784: 2q^2+3q+1
       785: 2q+1
       786: 2q+1
       787: q+1
       788: q+1
       789: 2q+1
       790: q^2+2q+1
       791: q+1
       792: 2q^2+3q+1
       793: 2q^2+3q+1
       794: 2q^2+3q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 2q^2+3q+1
       799: q^2+2q+1
       800: 2q+1
       801: 2q+1
       802: 2q+1
       803: 2q+1
       804: 2q+1
       805: 2q+1
       806: 2q+1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       832: q+1
       833: 1
       834: 2q+1
       835: 2q+1
       836: 2q+1
       837: 2q+1
       838: 2q+1
       839: 2q+1
       840: 2q+1
       841: 1
       842: q+1
       843: q+1
       844: q+1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       853: q+1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: q+1
       870: q+1
       871: q+1
       872: q^2+2q+1
       873: q^2+2q+1
       874: q+1
       875: q+1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q^2+2q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: 2q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: 2q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: 1
       942: 1
       943: 1
       944: q+1
       950: 1
       951: 1
       952: q+1
       953: q+1
       954: q+1
       958: q+1
       959: 1
       960: q+1
       961: 1
       962: q+1
       963: q+1
       964: q+1
       965: 1
       966: 1
       967: 1
       968: q+1
       969: q+1
       970: q+1
       971: q^2+2q+1
       972: q^2+2q+1
       973: q+1
       974: q+1
       975: 1
       976: q+1
       977: q+1
       978: q^2+2q+1
       979: 2q^2+3q+1
       980: q^2+2q+1
       981: q^2+2q+1
       982: q^2+2q+1
       983: q^2+2q+1
       984: q+1
       985: q+1
       986: q+1
       987: q+1
       988: q^2+2q+1
       989: 2q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: 1
       995: q+1
       996: q+1
       997: q^2+2q+1
       998: 2q^2+3q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: q^2+2q+1
      1005: q+1
      1006: 2q+1
      1007: 2q+1
      1008: 2q+1
      1009: 2q+1
      1010: 2q+1
      1011: 2q+1
      1012: 2q+1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1032: 1
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      1042: 1
      1043: 2q+1
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      1047: q+1
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      1050: 1
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      1117: 1
      1118: 1
      1119: 1
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      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1139: 1
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      1142: 1
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      1146: 1
      1147: 1
      1155: 1
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      1171: 1
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      1178: 1
      1179: 1
      1180: q+1
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      1182: q+1
      1183: q^2+2q+1
      1184: q^2+2q+1
      1185: q+1
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      1188: q+1
      1189: q+1
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      1191: 1
      1192: q+1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1197: q+1
      1198: q+1
      1199: q^2+2q+1
      1200: 2q+1
      1201: q+1
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      1203: q+1
      1204: q+1
      1205: 1
      1206: q+1
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      1209: 2q+1
      1210: 2q+1
      1211: 2q+1
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      1216: 1
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      1218: 1
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      1220: 1
      1221: 1
      1222: 1
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      1227: 1
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      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 2q+1
      1247: q+1
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      1253: 1
      1254: 1
      1255: q+1
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      1278: 1
      1279: 1
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      1286: 1
      1287: 1
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      1289: 1
      1290: 1
      1291: 1
      1292: 1
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      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
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      1303: 1
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      1332: 1
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      1338: 1
      1347: 1
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      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
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      1366: 1
      1367: 1
      1368: 1
      1369: q+1
      1370: 1
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      1372: q+1
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      1374: 1
      1375: 1
      1376: 1
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      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: q+1
      1386: q+1
      1387: 1
      1388: q+1
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      1391: 1
      1392: 1
      1393: q+1
      1394: 1
      1395: 1
      1396: 2q+1
      1397: q+1
      1398: q+1
      1399: q+1
      1400: q+1
      1401: 1
      1403: 1
      1404: 1
      1405: 1
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      1408: 1
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      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1428: 1
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      1433: 1
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      1437: 1
      1438: 1
      1446: 1
      1447: 1
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      1454: 1
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      1458: 1
      1461: 1
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      1463: 1
      1465: 1
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      1467: 1
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      1470: 1
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      1472: 1
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      1480: 1
      1481: 1
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      1486: 1
      1504: 1
      1516: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
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      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
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      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: 1
      1557: 1
      1558: q+1
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      1560: 1
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      1564: 1
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      1568: 1
      1572: 1
      1586: 1
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      1592: 1
      1601: 1
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      1628: 1
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      1667: 1
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      1692: 1
      1710: 1
      1722: 1
      1736: 1
      1768: 1
      1771: 1
      1774: 1
      1775: 1
      1776: 1
      1778: 1
      1782: 1
      1841: 1

1842:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
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        10: 1
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       365: 1
       372: 1
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       386: 1
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       390: 1
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       534: 1
       535: 1
       542: 1
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       550: 1
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       557: 1
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       565: 1
       566: 1
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       568: 1
       569: 1
       570: 1
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       573: 1
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       581: 1
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       618: 1
       619: 1
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       633: 1
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       644: 1
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       664: 1
       666: 1
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       668: 1
       669: 1
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       674: 1
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       702: 1
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       712: 1
       722: 1
       730: 1
       731: 1
       739: 1
       740: 1
       747: 1
       748: 1
       749: 1
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       762: 1
       764: 1
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       769: 1
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       833: 1
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       890: 1
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       912: 1
       923: 1
       933: 1
       943: 1
       951: 1
       952: 1
       959: 1
       961: 1
       962: 1
       963: 1
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       965: 1
       966: 1
       969: 1
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       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
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       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
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       998: 1
       999: 1
      1000: 1
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      1002: 1
      1003: 1
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      1013: 1
      1015: 1
      1016: 1
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      1020: 1
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      1023: 1
      1033: 1
      1041: 1
      1042: 1
      1050: 1
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      1058: 1
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      1065: 1
      1068: 1
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      1072: 1
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      1079: 1
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      1114: 1
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      1146: 1
      1156: 1
      1164: 1
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      1181: 1
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      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1234: 1
      1244: 1
      1254: 1
      1262: 1
      1263: 1
      1270: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1312: 1
      1313: 1
      1347: 1
      1359: 1
      1360: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1394: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1437: 1
      1447: 1
      1455: 1
      1459: 1
      1463: 1
      1464: 1
      1468: 1
      1469: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1487: 1
      1526: 1
      1530: 1
      1531: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1566: 1
      1567: 1
      1601: 1
      1615: 1
      1618: 1
      1622: 1
      1623: 1
      1665: 1
      1669: 1
      1670: 1
      1674: 1
      1675: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1693: 1
      1737: 1
      1769: 1
      1772: 1
      1776: 1
      1777: 1
      1842: 1

1843:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q+1
        21: q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: 1
        38: q^2+q+1
        39: q^2+q+1
        40: q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q+1
        58: q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q+1
        72: q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q^2+q+1
        76: 1
        77: 1
        78: 1
        79: q^2+q+1
        80: 1
        81: q^2+q+1
        82: 1
        83: q^2+q+1
        84: q+1
        85: q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: 1
       102: q^2+q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+q+1
       111: q^2+q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q+1
       120: q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q^2+q+1
       124: q+1
       125: q+1
       126: q^2+q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q+1
       130: q^2+q+1
       131: q^2+q+1
       132: q^2+q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q^2+q+1
       139: q^2+q+1
       140: q^2+q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q^2+q+1
       153: 1
       154: q^2+q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q+1
       163: q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q^2+q+1
       167: q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q^2+q+1
       172: q^2+q+1
       173: q^2+q+1
       174: q^2+q+1
       175: q^2+q+1
       176: q+1
       177: q+1
       178: q^2+q+1
       179: q^2+q+1
       180: q^2+q+1
       181: 1
       182: 1
       183: 1
       184: q^2+q+1
       185: 1
       186: q^2+q+1
       187: 1
       188: q^2+q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q^2+q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q^2+q+1
       205: q^2+q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q^2+q+1
       211: q^2+q+1
       212: q^2+q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+q+1
       220: q+1
       221: q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q^2+q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q^2+q+1
       235: q^2+q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q^2+q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q^2+q+1
       265: q^2+q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q^2+q+1
       271: q^2+q+1
       272: q^2+q+1
       273: q+1
       274: q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q^2+q+1
       278: q+1
       279: q+1
       280: q^2+q+1
       281: q^2+q+1
       282: q^2+q+1
       283: q+1
       284: q^2+q+1
       285: q^2+q+1
       286: q^2+q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q^2+q+1
       293: q^2+q+1
       294: q^2+q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q^2+q+1
       307: 1
       308: q^2+q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q^2+q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+q+1
       335: q^2+q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q^2+q+1
       343: q^2+q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q^2+q+1
       349: q^2+q+1
       350: q^2+q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q^2+q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q^2+q+1
       403: 1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q^2+q+1
       411: q^2+q+1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q^2+q+1
       417: q^2+q+1
       418: q^2+q+1
       419: q+1
       420: q+1
       421: q+1
       422: 1
       423: q^2+q+1
       424: q^2+q+1
       425: q^2+q+1
       426: q+1
       427: q+1
       428: q^2+q+1
       429: q^2+q+1
       430: q^2+q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q^2+q+1
       441: q^2+q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q^2+q+1
       463: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: q^2+q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q^2+q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q^2+q+1
       508: q^2+q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: 1
       572: 1
       573: q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q^2+q+1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q^2+q+1
       589: q^2+q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q^2+q+1
       597: q^2+q+1
       598: q+1
       599: q+1
       600: q+1
       601: 1
       602: q^2+q+1
       603: q^2+q+1
       604: q^2+q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       757: q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: 1
       763: 1
       765: q+1
       766: q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: q+1
       772: 1
       773: 1
       774: q+1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: q^2+q+1
       782: 1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q^2+q+1
       791: 1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q^2+q+1
       799: q^2+q+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       871: q+1
       872: q+1
       873: q+1
       874: q+1
       875: q+1
       876: 1
       877: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: 1
       932: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       962: q+1
       963: q+1
       964: q+1
       965: 1
       966: 1
       967: 1
       970: q+1
       971: q+1
       972: q+1
       973: q+1
       974: q+1
       975: 1
       976: 1
       978: q+1
       979: q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: q+1
       985: 1
       986: 1
       988: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q^2+q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1069: 1
      1070: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: 1
      1174: q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1182: q+1
      1183: q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: 1
      1243: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1273: 1
      1277: 1
      1278: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1313: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1348: 1
      1356: 1
      1360: 1
      1361: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1403: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1460: 1
      1464: 1
      1465: 1
      1469: 1
      1470: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1488: 1
      1504: 1
      1527: 1
      1531: 1
      1532: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1567: 1
      1568: 1
      1572: 1
      1586: 1
      1587: 1
      1588: 1
      1602: 1
      1610: 1
      1616: 1
      1619: 1
      1623: 1
      1624: 1
      1628: 1
      1666: 1
      1670: 1
      1671: 1
      1675: 1
      1676: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1686: 1
      1687: 1
      1688: 1
      1694: 1
      1710: 1
      1738: 1
      1770: 1
      1773: 1
      1777: 1
      1778: 1
      1782: 1
      1843: 1

1844:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^3+q^2+2q+1
        21: q^3+2q^2+2q+1
        22: q^3+q^2+2q+1
        23: q^2+q+1
        24: q^3+q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^3+2q^2+2q+1
        27: q^3+q^2+2q+1
        28: q^3+2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: q^3+q^2+2q+1
        43: q^3+2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+q+1
        51: q^3+q^2+2q+1
        52: q^3+q^2+2q+1
        53: q^3+q^2+2q+1
        54: q^2+q+1
        55: q^3+q^2+2q+1
        56: q^2+q+1
        57: q^3+q^2+2q+1
        58: q^3+2q^2+2q+1
        59: q^3+q^2+2q+1
        60: q^2+q+1
        61: q^3+q^2+2q+1
        62: q^3+2q^2+2q+1
        63: q^3+2q^2+2q+1
        64: q^3+q^2+2q+1
        65: q^3+2q^2+2q+1
        66: q^3+2q^2+2q+1
        67: 2q+1
        68: q^3+2q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: 2q+1
        72: q^3+2q^2+2q+1
        73: 2q+1
        74: q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^3+q^2+2q+1
        85: q^3+2q^2+2q+1
        86: q^3+q^2+2q+1
        87: q^2+q+1
        88: q^3+q^2+2q+1
        89: q^3+2q^2+2q+1
        90: q^3+2q^2+2q+1
        91: q^3+q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: q^3+2q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+q+1
       105: q^2+q+1
       106: q^3+q^2+2q+1
       107: q^3+q^2+2q+1
       108: q^2+q+1
       109: q^3+q^2+2q+1
       110: q^2+q+1
       111: q+1
       112: q^2+q+1
       113: q^3+q^2+2q+1
       114: q^3+q^2+2q+1
       115: q^3+q^2+2q+1
       116: q^2+q+1
       117: q^3+q^2+2q+1
       118: q^2+q+1
       119: q^3+q^2+2q+1
       120: q^3+2q^2+2q+1
       121: q^3+q^2+2q+1
       122: q^2+q+1
       123: q^3+q^2+2q+1
       124: 2q+1
       125: q^3+2q^2+2q+1
       126: 2q+1
       127: q+1
       128: 2q+1
       129: q^3+2q^2+2q+1
       130: q^3+2q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: q+1
       139: 2q+1
       140: q+1
       141: 2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q^2+q+1
       156: q^3+q^2+2q+1
       157: q^3+q^2+2q+1
       158: q^3+q^2+2q+1
       159: q^2+q+1
       160: q^3+q^2+2q+1
       161: q^2+q+1
       162: q^3+q^2+2q+1
       163: q^3+2q^2+2q+1
       164: q^3+q^2+2q+1
       165: q^2+q+1
       166: q^3+q^2+2q+1
       167: q^3+2q^2+2q+1
       168: q^3+2q^2+2q+1
       169: q^3+q^2+2q+1
       170: q^3+2q^2+2q+1
       171: q^3+2q^2+2q+1
       172: 2q+1
       173: q^3+2q^2+2q+1
       174: q^3+2q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^3+2q^2+2q+1
       178: 2q+1
       179: q+1
       180: 2q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q^2+q+1
       191: q^2+q+1
       192: q^3+q^2+2q+1
       193: q^2+1
       194: q+1
       195: q^2+q+1
       196: q+1
       197: q+1
       198: q^2+q+1
       199: q^2+q+1
       200: q^3+q^2+2q+1
       201: q^3+q^2+2q+1
       202: q^2+q+1
       203: q^3+q^2+2q+1
       204: q^2+q+1
       205: q+1
       206: q^2+q+1
       207: q^3+q^2+2q+1
       208: q^3+q^2+2q+1
       209: q^3+q^2+2q+1
       210: q^2+q+1
       211: q^3+q^2+2q+1
       212: q^2+q+1
       213: q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: q+1
       218: 2q+1
       219: q+1
       220: 2q+1
       221: q^3+2q^2+2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q+1
       229: q+1
       230: 2q+1
       231: 2q+1
       232: q+1
       233: 2q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: q+1
       241: 2q+1
       242: q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: 1
       247: q+1
       248: 2q+1
       249: q^2+2q+1
       250: 2q+1
       251: q+1
       252: 2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+q+1
       259: q^2+q+1
       260: q^3+q^2+2q+1
       261: q^3+q^2+2q+1
       262: q^2+q+1
       263: q^3+q^2+2q+1
       264: q^2+q+1
       265: q+1
       266: q^2+q+1
       267: q^3+q^2+2q+1
       268: q^3+q^2+2q+1
       269: q^3+q^2+2q+1
       270: q^2+q+1
       271: q^3+q^2+2q+1
       272: q^2+q+1
       273: q^3+q^2+2q+1
       274: q^3+2q^2+2q+1
       275: q^3+q^2+2q+1
       276: q^2+q+1
       277: q^3+q^2+2q+1
       278: 2q+1
       279: q^3+2q^2+2q+1
       280: 2q+1
       281: q+1
       282: 2q+1
       283: q^3+2q^2+2q+1
       284: q^3+2q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: q+1
       293: 2q+1
       294: q+1
       295: 2q+1
       296: q^2+2q+1
       297: 2q+1
       298: q+1
       299: 2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q^2+q+1
       312: q^2+1
       313: q^2+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+q+1
       321: q^2+q+1
       322: q^3+q^2+2q+1
       323: q^2+1
       324: q+1
       325: q^2+q+1
       326: q+1
       327: q+1
       328: q^2+q+1
       329: q^2+q+1
       330: q^3+q^2+2q+1
       331: q^3+q^2+2q+1
       332: q^2+q+1
       333: q^3+q^2+2q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: q+1
       338: 2q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q+1
       343: q+1
       344: q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: q+1
       370: 2q+1
       371: q+1
       372: 1
       373: 1
       374: q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       380: q+1
       381: 2q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: 1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q+1
       395: q+1
       396: q^2+q+1
       397: q^2+q+1
       398: q^3+q^2+2q+1
       399: q^2+1
       400: q+1
       401: q^2+q+1
       402: q+1
       403: q+1
       404: q^2+q+1
       405: q^2+q+1
       406: q^3+q^2+2q+1
       407: q^3+q^2+2q+1
       408: q^2+q+1
       409: q^3+q^2+2q+1
       410: q^2+q+1
       411: q+1
       412: q^2+q+1
       413: q^3+q^2+2q+1
       414: q^3+q^2+2q+1
       415: q^3+q^2+2q+1
       416: q^2+q+1
       417: q^3+q^2+2q+1
       418: q^2+q+1
       419: q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: q+1
       424: 2q+1
       425: q+1
       426: 2q+1
       427: q^3+2q^2+2q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: 2q+1
       434: q+1
       435: q+1
       436: 2q+1
       437: 2q+1
       438: q+1
       439: 2q+1
       440: q+1
       441: q+1
       442: q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: q+1
       447: 2q+1
       448: q+1
       449: q+1
       450: q^2+2q+1
       451: q+1
       452: 1
       453: q+1
       454: 2q+1
       455: q^2+2q+1
       456: 2q+1
       457: q+1
       458: 2q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: 1
       467: q^2+1
       470: 1
       471: 1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+q+1
       476: q^2+1
       477: q^2+1
       479: q+1
       480: 1
       481: q+1
       482: q+1
       483: q+1
       484: q^2+q+1
       485: q^2+q+1
       486: q^3+q^2+2q+1
       487: q^2+1
       488: q+1
       489: q^2+q+1
       490: q+1
       491: q+1
       492: q+1
       493: q+1
       494: q+1
       495: 2q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: 2q+1
       504: 2q+1
       505: q+1
       506: 2q+1
       507: q+1
       508: q+1
       509: q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: q+1
       514: 2q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: 2q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: 2q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q^2+2q+1
       560: q+1
       561: 1
       562: q+1
       563: q+1
       564: q+1
       565: q^2+q+1
       566: q^2+1
       567: q^2+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: q+1
       574: q^2+q+1
       575: q^2+q+1
       576: q^3+q^2+2q+1
       577: q^2+1
       578: q+1
       579: q^2+q+1
       580: q+1
       581: q+1
       582: q^2+q+1
       583: q^2+q+1
       584: q^3+q^2+2q+1
       585: q^3+q^2+2q+1
       586: q^2+q+1
       587: q^3+q^2+2q+1
       588: q^2+q+1
       589: q+1
       590: q+1
       591: q+1
       592: 2q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: q+1
       597: q+1
       598: q+1
       599: 2q+1
       600: 2q+1
       601: 2q+1
       602: q+1
       603: 2q+1
       604: q+1
       605: 2q+1
       606: q^2+2q+1
       607: 2q+1
       608: q+1
       609: 2q+1
       610: q+1
       611: q+1
       612: q+1
       613: 2q+1
       614: 1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: 2q+1
       622: 2q+1
       623: q+1
       624: 2q+1
       625: q+1
       626: 1
       627: 1
       628: q+1
       629: q+1
       630: q+1
       631: 1
       632: q+1
       633: 1
       634: q+1
       635: 2q+1
       636: 2q+1
       637: 2q+1
       638: q+1
       639: 2q+1
       640: q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: 1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       651: 1
       655: 1
       656: 1
       657: q+1
       658: q+1
       659: 1
       660: q^2+1
       663: 1
       664: 1
       665: q+1
       666: q+1
       667: q+1
       668: q^2+q+1
       669: q^2+1
       670: q^2+1
       672: q+1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: q+1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: 2q+1
       690: 1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q+1
       697: 2q+1
       698: 2q+1
       699: q+1
       700: 2q+1
       701: q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: 2q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 1
       755: q+1
       756: q+1
       757: 1
       758: q^2+1
       761: 1
       762: 1
       763: q+1
       764: q+1
       765: q+1
       766: q^2+q+1
       767: q^2+1
       768: q^2+1
       770: q+1
       771: 1
       772: q+1
       773: q+1
       774: q+1
       775: q^2+q+1
       776: q^2+q+1
       777: q^3+q^2+2q+1
       778: q^2+1
       779: q+1
       780: q^2+q+1
       781: q+1
       782: q+1
       783: q+1
       784: q+1
       785: q+1
       786: 2q+1
       787: 1
       788: q+1
       789: q+1
       790: q+1
       791: q+1
       792: q+1
       793: q+1
       794: 2q+1
       795: 2q+1
       796: q+1
       797: 2q+1
       798: q+1
       799: q+1
       800: q+1
       801: 2q+1
       802: 2q+1
       803: 2q+1
       804: q+1
       805: 2q+1
       806: q+1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: 2q+1
       821: 1
       822: q+1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: q+1
       829: q+1
       830: 1
       831: q+1
       832: 1
       833: 1
       834: q+1
       835: q+1
       836: 2q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: q+1
       841: 1
       842: 1
       843: q+1
       844: q+1
       845: q+1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: 1
       853: q+1
       854: 1
       855: 1
       860: 1
       861: q+1
       862: 1
       863: 1
       867: 1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q^2+1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       881: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: 2q+1
       901: 1
       902: q+1
       903: q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: 1
       960: q+1
       961: 1
       962: 1
       966: 1
       967: 1
       968: q+1
       969: q+1
       970: 1
       971: q^2+1
       974: 1
       975: 1
       976: q+1
       977: q+1
       978: q+1
       979: q^2+q+1
       980: q^2+1
       981: q^2+1
       983: q+1
       984: 1
       985: q+1
       986: q+1
       987: q+1
       988: q+1
       989: q+1
       990: 1
       991: 1
       993: q+1
       994: 1
       995: q+1
       996: q+1
       997: q+1
       998: q+1
       999: q+1
      1000: 2q+1
      1001: 1
      1002: q+1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: q+1
      1007: q+1
      1008: 2q+1
      1009: 2q+1
      1010: q+1
      1011: 2q+1
      1012: q+1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: q+1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: 2q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: q+1
      1055: 1
      1056: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: q+1
      1065: 1
      1066: 1
      1071: 1
      1072: 1
      1077: 1
      1078: q+1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1172: q+1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: q+1
      1181: q+1
      1182: 1
      1183: q^2+1
      1186: 1
      1187: 1
      1188: q+1
      1189: q+1
      1190: q+1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1197: q+1
      1198: q+1
      1199: q+1
      1200: q+1
      1201: 1
      1202: 1
      1204: q+1
      1205: 1
      1206: q+1
      1207: q+1
      1208: 1
      1209: q+1
      1210: q+1
      1211: 2q+1
      1212: 1
      1213: q+1
      1214: q+1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: q+1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1270: 1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: q+1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1377: q+1
      1378: 1
      1379: 1
      1383: 1
      1384: 1
      1385: q+1
      1386: q+1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: q+1
      1394: 1
      1395: 1
      1396: q+1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: 1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1431: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1453: 1
      1454: 1
      1455: 1
      1461: 1
      1466: 1
      1471: 1
      1472: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1489: 1
      1501: 1
      1502: 1
      1507: 1
      1508: 1
      1516: 1
      1517: 1
      1519: 1
      1524: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1541: 1
      1546: 1
      1547: q+1
      1548: 1
      1549: 1
      1553: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1558: 1
      1561: 1
      1562: 1
      1563: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1584: 1
      1585: 1
      1586: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1595: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1609: 1
      1610: 1
      1620: 1
      1625: 1
      1626: 1
      1631: 1
      1642: 1
      1654: 1
      1667: 1
      1672: 1
      1677: 1
      1678: 1
      1683: 1
      1684: 1
      1685: 1
      1686: 1
      1690: 1
      1691: 1
      1695: 1
      1707: 1
      1708: 1
      1713: 1
      1714: 1
      1722: 1
      1723: 1
      1725: 1
      1730: 1
      1739: 1
      1774: 1
      1779: 1
      1780: 1
      1785: 1
      1796: 1
      1808: 1
      1844: 1

1845:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: 1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q^2+q+1
        51: 1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: 1
        56: 1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: 1
        62: q^2+q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: 1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: q^2+q+1
       106: 1
       107: q^2+q+1
       108: q^2+q+1
       109: 1
       110: 1
       111: 1
       112: q^2+q+1
       113: 1
       114: q^2+q+1
       115: q^2+q+1
       116: q^2+q+1
       117: 1
       118: 1
       119: q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: 1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: 1
       161: 1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q^2+q+1
       192: 1
       193: q^2+q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q^2+q+1
       200: 1
       201: q^2+q+1
       202: q^2+q+1
       203: 1
       204: 1
       205: 1
       206: q^2+q+1
       207: 1
       208: q^2+q+1
       209: q^2+q+1
       210: q^2+q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: q^2+q+1
       260: 1
       261: q^2+q+1
       262: q^2+q+1
       263: 1
       264: 1
       265: 1
       266: q^2+q+1
       267: 1
       268: q^2+q+1
       269: q^2+q+1
       270: q^2+q+1
       271: 1
       272: 1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: q^2+q+1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q^2+q+1
       322: 1
       323: q^2+q+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q^2+q+1
       330: 1
       331: q^2+q+1
       332: q^2+q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       375: q+1
       376: q+1
       377: q+1
       380: q+1
       381: 1
       382: q+1
       383: q+1
       384: q+1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: q^2+q+1
       398: 1
       399: q^2+q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q^2+q+1
       406: 1
       407: q^2+q+1
       408: q^2+q+1
       409: 1
       410: 1
       411: 1
       412: q^2+q+1
       413: 1
       414: q^2+q+1
       415: q^2+q+1
       416: q^2+q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: q^2+q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q^2+q+1
       486: 1
       487: q^2+q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       511: q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       536: q+1
       538: q+1
       539: q+1
       543: 1
       544: q+1
       545: 1
       546: q+1
       547: q+1
       548: 1
       549: 1
       550: 1
       551: q+1
       553: q+1
       554: q+1
       555: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       563: 1
       564: 1
       565: 1
       566: q^2+q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q^2+q+1
       576: 1
       577: q^2+q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q^2+q+1
       584: 1
       585: q^2+q+1
       586: q^2+q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       629: q+1
       630: q+1
       631: q+1
       634: q+1
       635: 1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: q^2+q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: q+1
       726: q+1
       731: 1
       732: 1
       733: q+1
       734: 1
       735: q+1
       736: 1
       737: 1
       738: 1
       739: 1
       741: q+1
       743: q+1
       744: q+1
       748: q+1
       750: q+1
       751: q+1
       752: q+1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q^2+q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q^2+q+1
       777: 1
       778: q^2+q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       787: q+1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       827: q+1
       829: q+1
       830: q+1
       834: 1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       841: 1
       842: q+1
       844: q+1
       845: q+1
       846: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       869: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: q+1
       933: 1
       934: 1
       935: 1
       936: q+1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       945: q+1
       947: q+1
       953: q+1
       955: q+1
       956: q+1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q^2+q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: q+1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: q+1
      1037: q+1
      1042: 1
      1043: 1
      1044: q+1
      1045: 1
      1046: q+1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: q+1
      1054: q+1
      1055: q+1
      1059: q+1
      1061: q+1
      1062: q+1
      1063: q+1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1149: q+1
      1158: q+1
      1160: q+1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: 1
      1177: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1212: q+1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: q+1
      1244: 1
      1245: 1
      1246: 1
      1247: q+1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1256: q+1
      1258: q+1
      1264: q+1
      1266: q+1
      1267: q+1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: q+1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1369: 1
      1370: 1
      1372: 1
      1374: 1
      1376: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: q+1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1428: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1440: q+1
      1449: q+1
      1451: q+1
      1462: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1478: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1490: 1
      1501: 1
      1503: 1
      1506: 1
      1529: 1
      1533: 1
      1535: 1
      1538: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1584: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1604: q+1
      1621: 1
      1625: 1
      1627: 1
      1630: 1
      1643: 1
      1668: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1684: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1696: 1
      1707: 1
      1709: 1
      1712: 1
      1740: 1
      1775: 1
      1779: 1
      1781: 1
      1784: 1
      1797: 1
      1845: 1

1846:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 2q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q+1
        78: 2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 2q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: 2q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: 2q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q+1
       148: q+1
       149: q^2+2q+1
       150: q+1
       151: 2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: 2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: 2q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q^2+2q+1
       171: q^2+2q+1
       172: 2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       182: q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: q^2+2q+1
       207: q^2+2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: q^2+2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q+1
       227: 2q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: 2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: 2q+1
       252: 2q+1
       253: q^2+2q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q^2+2q+1
       267: q^2+2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: q^2+2q+1
       273: q^2+2q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 2q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q^2+2q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q+1
       302: q+1
       303: q^2+2q+1
       304: q+1
       305: 2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       328: q^2+2q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+1
       352: q+1
       353: q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: 2q+1
       381: 2q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: 2q+1
       387: q+1
       388: q+1
       389: 1
       390: q+1
       391: q+1
       392: q^2+2q+1
       393: q+1
       394: q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: q^2+2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q+1
       412: q^2+2q+1
       413: q^2+2q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: q^2+2q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q^2+2q+1
       432: q+1
       433: 2q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: 2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: 2q+1
       455: q+1
       456: q+1
       457: 2q+1
       458: 2q+1
       459: q^2+2q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: q+1
       474: q+1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: 2q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 2q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: q+1
       552: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q+1
       558: q+1
       559: q+1
       560: 1
       561: q+1
       562: q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: q+1
       581: q+1
       582: q^2+2q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 2q+1
       606: q+1
       607: q+1
       608: 2q+1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: 2q+1
       635: 2q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: 2q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: q+1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       772: q+1
       774: q+1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: q+1
       782: q+1
       783: q+1
       784: 2q+1
       785: 2q+1
       786: 2q+1
       787: q+1
       788: q+1
       789: 2q+1
       790: q+1
       791: q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: q+1
       800: 2q+1
       801: 2q+1
       802: q+1
       803: q+1
       804: q+1
       805: q+1
       806: 2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: q+1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 2q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: q+1
       903: q+1
       904: 1
       905: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: q+1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       977: q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: 1
       985: q+1
       987: q+1
       988: q+1
       989: 2q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: 1
       995: q+1
       997: q+1
       998: 2q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1006: 2q+1
      1007: q+1
      1008: q+1
      1009: q+1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1108: q+1
      1109: q+1
      1110: 1
      1111: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1131: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: q+1
      1182: 1
      1183: q+1
      1184: q+1
      1185: 1
      1186: 1
      1187: 1
      1190: q+1
      1191: 1
      1192: q+1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1198: q+1
      1199: q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1203: q+1
      1204: q+1
      1205: 1
      1206: q+1
      1208: 1
      1209: q+1
      1210: q+1
      1211: q+1
      1212: 1
      1213: q+1
      1214: q+1
      1215: 1
      1216: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1249: q+1
      1250: q+1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1302: 1
      1303: 1
      1304: 1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: 1
      1341: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: q+1
      1387: 1
      1388: q+1
      1389: q+1
      1390: 1
      1391: 1
      1392: 1
      1394: 1
      1395: 1
      1396: q+1
      1397: 1
      1398: 1
      1399: q+1
      1400: q+1
      1401: 1
      1402: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1422: 1
      1429: 1
      1430: 1
      1431: 1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1453: 1
      1454: 1
      1455: 1
      1463: 1
      1468: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1491: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1517: 1
      1519: 1
      1530: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1556: 1
      1557: 1
      1558: 1
      1559: q+1
      1560: 1
      1561: 1
      1562: 1
      1566: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1593: 1
      1595: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1609: 1
      1622: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1644: 1
      1669: 1
      1674: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1697: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1723: 1
      1725: 1
      1741: 1
      1776: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1798: 1
      1846: 1

1847:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: q^3+3q^2+2q+1
         5: q^3+3q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+3q^2+2q+1
        10: 3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: 3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: q^3+3q^2+2q+1
        17: 3q^2+2q+1
        18: q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: 2q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: 3q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: 3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: 3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: 3q^2+2q+1
        36: q^3+3q^2+2q+1
        37: 2q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^3+3q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: 3q^2+2q+1
        43: q^3+3q^2+2q+1
        44: 3q^2+2q+1
        45: q^3+3q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: 3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: q^2+q+1
        51: 2q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: 2q^2+2q+1
        58: q^2+2q+1
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: 3q^2+2q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: 3q^2+2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: 3q^2+2q+1
        68: q^3+3q^2+2q+1
        69: 3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: 2q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        75: 3q^2+2q+1
        76: q^2+2q+1
        77: q^2+q+1
        78: 2q^2+2q+1
        79: q^3+2q^2+2q+1
        80: q^2+2q+1
        81: q^3+3q^2+2q+1
        82: 2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 3q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: 3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: 3q^2+2q+1
        94: q^3+3q^2+2q+1
        95: 3q^2+2q+1
        96: q^3+3q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 3q^2+2q+1
       100: q^3+3q^2+2q+1
       101: 2q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^3+3q^2+2q+1
       104: q^2+q+1
       105: q+1
       106: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: 2q^2+2q+1
       112: q^2+q+1
       113: 2q^2+2q+1
       114: q^2+2q+1
       115: 2q+1
       116: q^2+2q+1
       117: 2q^2+2q+1
       118: 2q^2+2q+1
       119: 2q^2+2q+1
       120: q^2+2q+1
       121: 2q^2+2q+1
       122: 2q^2+2q+1
       123: 3q^2+2q+1
       124: 2q^2+2q+1
       125: q^2+2q+1
       126: 2q^2+2q+1
       127: q^2+2q+1
       128: 3q^2+2q+1
       129: 2q^2+2q+1
       130: 2q^2+2q+1
       131: 3q^2+2q+1
       132: q^3+3q^2+2q+1
       133: 2q^2+2q+1
       134: q+1
       135: 2q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q+1
       143: q^2+q+1
       144: 2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: q^2+2q+1
       149: q^2+2q+1
       150: q^2+q+1
       151: 2q^2+2q+1
       152: q^3+2q^2+2q+1
       153: q^2+2q+1
       154: q^3+2q^2+2q+1
       155: q^2+q+1
       156: 2q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 2q^2+2q+1
       163: q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 3q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: 3q^2+2q+1
       170: 2q^2+2q+1
       171: 2q^2+2q+1
       172: 3q^2+2q+1
       173: q^3+3q^2+2q+1
       174: 3q^2+2q+1
       175: q^3+3q^2+2q+1
       176: 2q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: q^2+2q+1
       180: 3q^2+2q+1
       181: q^2+2q+1
       182: q^2+q+1
       183: 2q^2+2q+1
       184: q^3+2q^2+2q+1
       185: q^2+2q+1
       186: q^3+3q^2+2q+1
       187: 2q^2+2q+1
       188: q^3+2q^2+2q+1
       189: q^2+q+1
       190: q+1
       191: q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q^2+q+1
       198: q^2+q+1
       199: q+1
       200: q^2+2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: q^2+2q+1
       205: 2q^2+2q+1
       206: q^2+q+1
       207: 2q^2+2q+1
       208: q^2+2q+1
       209: 2q+1
       210: q^2+2q+1
       211: 2q^2+2q+1
       212: 2q^2+2q+1
       213: q+1
       214: 2q^2+2q+1
       215: q^2+2q+1
       216: 2q+1
       217: q^2+2q+1
       218: 2q^2+2q+1
       219: q^2+2q+1
       220: 2q^2+2q+1
       221: q^2+2q+1
       222: 2q^2+2q+1
       223: q^2+2q+1
       224: 3q^2+2q+1
       225: q^2+2q+1
       226: q^2+q+1
       227: 2q^2+2q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: q^2+2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q^2+q+1
       242: 2q+1
       243: q^2+2q+1
       244: q+1
       245: q+1
       246: 2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q+1
       250: q^2+q+1
       251: 2q+1
       252: 2q^2+2q+1
       253: q^2+2q+1
       254: q+1
       255: q^2+2q+1
       256: q^3+2q^2+2q+1
       257: q^2+2q+1
       258: q^2+q+1
       259: q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: 2q^2+2q+1
       266: q^2+q+1
       267: 2q^2+2q+1
       268: q^2+2q+1
       269: 2q+1
       270: q^2+2q+1
       271: 2q^2+2q+1
       272: 2q^2+2q+1
       273: 2q^2+2q+1
       274: q^2+2q+1
       275: 2q^2+2q+1
       276: 2q^2+2q+1
       277: 3q^2+2q+1
       278: 2q^2+2q+1
       279: q^2+2q+1
       280: 2q^2+2q+1
       281: q^2+2q+1
       282: 3q^2+2q+1
       283: 2q^2+2q+1
       284: 2q^2+2q+1
       285: 3q^2+2q+1
       286: q^3+3q^2+2q+1
       287: 2q^2+2q+1
       288: q+1
       289: 2q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q^2+2q+1
       295: q^2+2q+1
       296: q+1
       297: q^2+q+1
       298: 2q+1
       299: 2q^2+2q+1
       300: q^2+2q+1
       301: q+1
       302: q^2+2q+1
       303: q^2+2q+1
       304: q^2+q+1
       305: 2q^2+2q+1
       306: q^3+2q^2+2q+1
       307: q^2+2q+1
       308: q^3+2q^2+2q+1
       310: q+1
       311: q+1
       312: q+1
       313: 2q+1
       314: 1
       315: 2q+1
       316: 2q+1
       317: q+1
       319: q^2+q+1
       320: q+1
       321: q+1
       322: 2q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: q^2+2q+1
       327: q^2+q+1
       328: q^2+q+1
       329: q+1
       330: q^2+2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: q^2+2q+1
       335: 2q^2+2q+1
       336: q+1
       337: q+1
       338: q^2+2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: q^2+2q+1
       343: q^2+2q+1
       344: q+1
       345: 2q^2+2q+1
       346: q^2+2q+1
       347: 2q+1
       348: q^2+2q+1
       349: 2q^2+2q+1
       350: q^2+2q+1
       351: q^2+2q+1
       352: q+1
       353: q^2+q+1
       354: 2q+1
       355: 2q^2+2q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: 1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 2q+1
       373: q+1
       374: q^2+2q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: 2q+1
       380: q+1
       381: q^2+2q+1
       382: q+1
       383: q+1
       384: q+1
       385: q^2+q+1
       386: 2q+1
       387: q^2+2q+1
       388: q+1
       389: q+1
       390: 2q+1
       391: q^2+2q+1
       392: q^2+2q+1
       393: q+1
       394: q^2+2q+1
       395: q^2+q+1
       396: q+1
       397: q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q^2+q+1
       404: q^2+q+1
       405: q+1
       406: q^2+2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: q^2+2q+1
       411: 2q^2+2q+1
       412: q^2+q+1
       413: 2q^2+2q+1
       414: q^2+2q+1
       415: 2q+1
       416: q^2+2q+1
       417: 2q^2+2q+1
       418: 2q^2+2q+1
       419: q+1
       420: 2q^2+2q+1
       421: q^2+2q+1
       422: 2q+1
       423: q^2+2q+1
       424: 2q^2+2q+1
       425: q^2+2q+1
       426: 2q^2+2q+1
       427: q^2+2q+1
       428: 2q^2+2q+1
       429: q^2+2q+1
       430: 3q^2+2q+1
       431: q^2+2q+1
       432: q^2+q+1
       433: 2q^2+2q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q+1
       443: q^2+2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q^2+q+1
       448: 2q+1
       449: q^2+2q+1
       450: q+1
       451: q+1
       452: 2q+1
       453: q^2+2q+1
       454: q^2+2q+1
       455: q+1
       456: q^2+q+1
       457: 2q+1
       458: 2q^2+2q+1
       459: q^2+2q+1
       460: q+1
       461: q^2+2q+1
       462: q^3+2q^2+2q+1
       463: q^2+2q+1
       466: q+1
       467: q+1
       468: 1
       469: 1
       470: 2q+1
       471: q+1
       474: q+1
       475: q+1
       476: q+1
       477: 2q+1
       478: 1
       479: 2q+1
       480: 2q+1
       481: q+1
       483: q^2+q+1
       484: q+1
       485: q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: 2q+1
       490: q^2+2q+1
       491: q^2+q+1
       492: q+1
       493: q+1
       494: q+1
       495: 2q+1
       496: 2q+1
       497: 2q+1
       498: 2q+1
       499: q^2+2q+1
       500: q+1
       501: q+1
       502: q+1
       503: q^2+2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: q^2+2q+1
       508: q^2+2q+1
       509: q+1
       510: q^2+2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q^2+q+1
       515: 2q+1
       517: q+1
       518: q+1
       519: q+1
       520: 2q+1
       521: 1
       522: 2q+1
       523: 2q+1
       524: q+1
       526: q+1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: q+1
       535: q+1
       536: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: 2q+1
       543: q+1
       544: 1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 2q+1
       551: q+1
       552: q^2+2q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: 2q+1
       558: q^2+2q+1
       559: q+1
       560: q+1
       561: 2q+1
       562: q^2+2q+1
       564: q+1
       565: q+1
       566: q+1
       567: 2q+1
       568: 1
       569: 2q+1
       570: 2q+1
       571: q+1
       573: q^2+q+1
       574: q+1
       575: q+1
       576: 2q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: q^2+2q+1
       581: q^2+q+1
       582: q^2+q+1
       583: q+1
       584: q^2+2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: q^2+2q+1
       589: 2q^2+2q+1
       590: q+1
       591: q+1
       592: q^2+2q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: q^2+2q+1
       597: q^2+2q+1
       598: q+1
       599: 2q^2+2q+1
       600: q^2+2q+1
       601: 2q+1
       602: q^2+2q+1
       603: 2q^2+2q+1
       604: q^2+2q+1
       605: q^2+2q+1
       606: q+1
       607: q^2+q+1
       608: 2q+1
       609: 2q^2+2q+1
       610: q+1
       611: q+1
       612: q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: 1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 2q+1
       627: q+1
       628: q^2+2q+1
       629: q+1
       630: 1
       631: q+1
       632: q+1
       633: 2q+1
       634: q+1
       635: q^2+2q+1
       636: q+1
       637: q+1
       638: q+1
       639: q^2+q+1
       640: 2q+1
       641: q^2+2q+1
       642: q+1
       643: q+1
       644: 2q+1
       645: q^2+2q+1
       646: q^2+2q+1
       647: q+1
       648: q^2+2q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       659: q+1
       660: q+1
       661: 1
       662: 1
       663: 2q+1
       664: q+1
       667: q+1
       668: q+1
       669: q+1
       670: 2q+1
       671: 1
       672: 2q+1
       673: 2q+1
       674: q+1
       677: q+1
       678: q+1
       679: q+1
       680: 2q+1
       681: 1
       682: 2q+1
       683: 2q+1
       684: q+1
       686: q+1
       687: q+1
       688: q+1
       689: 2q+1
       690: 2q+1
       691: 2q+1
       692: 2q+1
       693: q^2+2q+1
       694: q+1
       695: q+1
       696: 1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 2q+1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: 2q+1
       710: q+1
       713: 1
       714: 1
       715: 1
       716: q+1
       717: 1
       718: q+1
       719: q+1
       720: 1
       722: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: q+1
       731: q+1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: q+1
       740: q+1
       741: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: 2q+1
       748: q+1
       749: q^2+2q+1
       750: q+1
       751: 1
       752: q+1
       753: q+1
       754: 2q+1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: 2q+1
       762: q+1
       765: q+1
       766: q+1
       767: q+1
       768: 2q+1
       769: 1
       770: 2q+1
       771: 2q+1
       772: q+1
       774: q^2+q+1
       775: q+1
       776: q+1
       777: 2q+1
       778: 2q+1
       779: 2q+1
       780: 2q+1
       781: q^2+2q+1
       782: q^2+q+1
       783: q+1
       784: q+1
       785: q+1
       786: 2q+1
       787: 2q+1
       788: 2q+1
       789: 2q+1
       790: q^2+2q+1
       791: q+1
       792: q+1
       793: q+1
       794: q^2+2q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: q^2+2q+1
       799: q^2+2q+1
       800: q+1
       801: q^2+2q+1
       802: q+1
       803: q+1
       804: q+1
       805: q^2+q+1
       806: 2q+1
       808: q+1
       809: q+1
       810: q+1
       811: 2q+1
       812: 1
       813: 2q+1
       814: 2q+1
       815: q+1
       817: q+1
       818: 1
       819: 1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: q+1
       827: 1
       828: q+1
       829: 1
       830: 1
       831: 1
       832: q+1
       833: 2q+1
       834: q+1
       835: 1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 2q+1
       842: q+1
       843: q^2+2q+1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: 2q+1
       849: q^2+2q+1
       850: q+1
       851: q+1
       852: 2q+1
       853: q^2+2q+1
       857: 1
       858: 1
       863: q+1
       864: 1
       865: 1
       866: 1
       867: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: 2q+1
       876: q+1
       880: q+1
       881: q+1
       882: 1
       883: 1
       884: 2q+1
       885: q+1
       888: q+1
       889: q+1
       890: q+1
       891: 2q+1
       892: 1
       893: 2q+1
       894: 2q+1
       895: q+1
       897: q+1
       898: 1
       899: 1
       900: q+1
       901: q+1
       902: q+1
       903: q+1
       904: q+1
       905: q+1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       921: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q+1
       940: q+1
       941: 1
       943: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: q+1
       952: q+1
       953: 1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: q+1
       959: 2q+1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       970: q+1
       971: q+1
       972: 1
       973: 1
       974: 2q+1
       975: q+1
       978: q+1
       979: q+1
       980: q+1
       981: 2q+1
       982: 1
       983: 2q+1
       984: 2q+1
       985: q+1
       988: q+1
       989: q+1
       990: q+1
       991: 2q+1
       992: 1
       993: 2q+1
       994: 2q+1
       995: q+1
       997: q+1
       998: q+1
       999: q+1
      1000: 2q+1
      1001: 2q+1
      1002: 2q+1
      1003: 2q+1
      1004: q^2+2q+1
      1005: q+1
      1006: q+1
      1007: 1
      1008: q+1
      1009: q+1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 2q+1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: 2q+1
      1021: q+1
      1024: 1
      1025: 1
      1026: 1
      1027: q+1
      1028: 1
      1029: q+1
      1030: q+1
      1031: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: q+1
      1041: q+1
      1042: q+1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: q+1
      1050: q+1
      1051: q+1
      1052: 1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: 2q+1
      1059: q+1
      1060: q^2+2q+1
      1061: q+1
      1062: 1
      1063: q+1
      1064: q+1
      1065: 2q+1
      1069: 1
      1074: 1
      1075: 1
      1080: q+1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1088: q+1
      1089: 1
      1090: 1
      1091: 1
      1092: q+1
      1096: q+1
      1097: q+1
      1098: 1
      1099: 1
      1100: 2q+1
      1101: q+1
      1104: 1
      1105: 1
      1106: 1
      1107: q+1
      1108: 1
      1109: q+1
      1110: q+1
      1111: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1156: q+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: q+1
      1164: q+1
      1168: 1
      1169: 1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: q+1
      1182: q+1
      1183: q+1
      1184: 1
      1185: 1
      1186: 2q+1
      1187: q+1
      1191: q+1
      1192: q+1
      1193: 1
      1194: 1
      1195: 2q+1
      1196: q+1
      1199: q+1
      1200: q+1
      1201: q+1
      1202: 2q+1
      1203: 1
      1204: 2q+1
      1205: 2q+1
      1206: q+1
      1208: q+1
      1209: 1
      1210: 1
      1211: q+1
      1212: q+1
      1213: q+1
      1214: q+1
      1215: q+1
      1216: q+1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: q+1
      1232: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1245: 1
      1246: 1
      1247: 1
      1248: q+1
      1249: 1
      1250: q+1
      1251: q+1
      1252: 1
      1254: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: q+1
      1263: q+1
      1264: 1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: q+1
      1270: 2q+1
      1277: 1
      1282: 1
      1283: 1
      1289: 1
      1290: 1
      1295: q+1
      1296: 1
      1297: 1
      1298: 1
      1299: q+1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: q+1
      1308: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1328: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1360: 1
      1365: 1
      1366: 1
      1371: q+1
      1372: 1
      1373: 1
      1374: 1
      1375: q+1
      1379: q+1
      1380: 1
      1381: 1
      1382: 1
      1383: q+1
      1387: q+1
      1388: q+1
      1389: 1
      1390: 1
      1391: 2q+1
      1392: q+1
      1395: 1
      1396: 1
      1397: 1
      1398: q+1
      1399: 1
      1400: q+1
      1401: q+1
      1402: 1
      1407: 1
      1408: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: q+1
      1435: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q+1
      1455: q+1
      1464: 1
      1469: 1
      1474: 1
      1475: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1492: 1
      1504: 1
      1505: 1
      1510: 1
      1514: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1531: 1
      1536: 1
      1537: 1
      1543: 1
      1544: 1
      1549: q+1
      1550: 1
      1551: 1
      1552: 1
      1553: q+1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: q+1
      1562: 1
      1567: 1
      1572: 1
      1573: 1
      1578: 1
      1582: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: 1
      1608: 1
      1609: 1
      1623: 1
      1628: 1
      1629: 1
      1645: 1
      1656: 1
      1660: 1
      1670: 1
      1675: 1
      1680: 1
      1681: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1698: 1
      1710: 1
      1711: 1
      1716: 1
      1720: 1
      1724: 1
      1725: 1
      1728: 1
      1729: 1
      1742: 1
      1777: 1
      1782: 1
      1783: 1
      1799: 1
      1810: 1
      1814: 1
      1847: 1

1848:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q^2+1
        51: q^2+1
        52: q^2+1
        53: q^2+q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q+1
        71: 1
        72: q^2+q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+1
       105: q^2+1
       106: q^2+1
       107: q^2+1
       108: q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q+1
       112: q^2+1
       113: q^2+1
       114: q^2+1
       115: q^2+q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q^2+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q^2+q+1
       124: 1
       125: q^2+q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+1
       156: q^2+1
       157: q^2+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q^2+q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q^2+q+1
       171: q^2+q+1
       172: q+1
       173: q^2+q+1
       174: q^2+q+1
       175: q+1
       176: 1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: q^2+1
       191: q^2+1
       192: q^2+1
       193: q^2+1
       194: 1
       195: q^2+q+1
       196: q+1
       197: q+1
       198: q^2+1
       199: q^2+1
       200: q^2+1
       201: q^2+1
       202: q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q+1
       206: q^2+1
       207: q^2+1
       208: q^2+1
       209: q^2+q+1
       210: q^2+q+1
       211: q^2+q+1
       212: q^2+q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q^2+1
       259: q^2+1
       260: q^2+1
       261: q^2+1
       262: q^2+q+1
       263: q^2+q+1
       264: q^2+q+1
       265: q+1
       266: q^2+1
       267: q^2+1
       268: q^2+1
       269: q^2+q+1
       270: q^2+q+1
       271: q^2+q+1
       272: q^2+q+1
       273: q^2+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q^2+q+1
       278: 1
       279: q^2+q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+q+1
       284: q^2+q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       311: q^2+1
       312: q^2+1
       313: q^2+1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       320: q^2+1
       321: q^2+1
       322: q^2+1
       323: q^2+1
       324: 1
       325: q^2+q+1
       326: q+1
       327: q+1
       328: q^2+1
       329: q^2+1
       330: q^2+1
       331: q^2+1
       332: q^2+q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       396: q^2+1
       397: q^2+1
       398: q^2+1
       399: q^2+1
       400: 1
       401: q^2+q+1
       402: q+1
       403: q+1
       404: q^2+1
       405: q^2+1
       406: q^2+1
       407: q^2+1
       408: q^2+q+1
       409: q^2+q+1
       410: q^2+q+1
       411: q+1
       412: q^2+1
       413: q^2+1
       414: q^2+1
       415: q^2+q+1
       416: q^2+q+1
       417: q^2+q+1
       418: q^2+q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q^2+q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       467: q^2+1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       475: q^2+1
       476: q^2+1
       477: q^2+1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       484: q^2+1
       485: q^2+1
       486: q^2+1
       487: q^2+1
       488: 1
       489: q^2+q+1
       490: q+1
       491: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       565: q^2+1
       566: q^2+1
       567: q^2+1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       574: q^2+1
       575: q^2+1
       576: q^2+1
       577: q^2+1
       578: 1
       579: q^2+q+1
       580: q+1
       581: q+1
       582: q^2+1
       583: q^2+1
       584: q^2+1
       585: q^2+1
       586: q^2+q+1
       587: q^2+q+1
       588: q^2+q+1
       589: q+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: 1
       599: 1
       600: 1
       601: q+1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       653: 1
       654: 1
       655: 1
       656: 1
       660: q^2+1
       661: 1
       662: 1
       663: 1
       664: 1
       665: q+1
       668: q^2+1
       669: q^2+1
       670: q^2+1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: q+1
       685: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       758: q^2+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: q^2+1
       767: q^2+1
       768: q^2+1
       769: 1
       770: 1
       771: 1
       772: q+1
       773: q+1
       775: q^2+1
       776: q^2+1
       777: q^2+1
       778: q^2+1
       779: 1
       780: q^2+q+1
       781: q+1
       782: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       791: q+1
       792: 1
       793: 1
       794: 1
       795: 1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: q^2+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       964: 1
       965: 1
       966: 1
       967: 1
       971: q^2+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: q+1
       979: q^2+1
       980: q^2+1
       981: q^2+1
       982: 1
       983: 1
       984: 1
       985: q+1
       986: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: q+1
       996: q+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1136: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1183: q^2+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: q+1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: q+1
      1207: q+1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: 1
      1216: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1290: 1
      1291: 1
      1292: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1341: 1
      1346: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: q+1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1422: 1
      1427: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1453: 1
      1454: 1
      1455: 1
      1465: 1
      1470: 1
      1475: 1
      1476: 1
      1477: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1493: 1
      1505: 1
      1506: 1
      1507: 1
      1519: 1
      1524: 1
      1532: 1
      1537: 1
      1538: 1
      1539: 1
      1544: 1
      1545: 1
      1546: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1563: 1
      1568: 1
      1573: 1
      1574: 1
      1575: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1595: 1
      1600: 1
      1603: 1
      1604: 1
      1605: 1
      1609: 1
      1610: 1
      1624: 1
      1629: 1
      1630: 1
      1631: 1
      1646: 1
      1671: 1
      1676: 1
      1681: 1
      1682: 1
      1683: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1699: 1
      1711: 1
      1712: 1
      1713: 1
      1725: 1
      1730: 1
      1743: 1
      1778: 1
      1783: 1
      1784: 1
      1785: 1
      1800: 1
      1848: 1

1849:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: q+1
        21: q^2+q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: 1
        65: q+1
        66: q+1
        67: 1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: 1
       122: 1
       123: 1
       124: 1
       125: q+1
       126: 1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: 1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: 1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: 1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: 1
       249: q+1
       250: 1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: 1
       276: 1
       277: 1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: q+1
       321: q+1
       322: q+1
       323: 1
       324: 1
       325: q+1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: q+1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: 1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: 1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       681: 1
       682: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: 1
       877: 1
       878: 1
       879: 1
       882: 1
       886: 1
       887: 1
       888: 1
       889: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       938: 1
       939: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1094: 1
      1095: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1141: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: 1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1293: 1
      1301: 1
      1302: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1338: 1
      1339: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1355: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1377: 1
      1385: 1
      1386: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: 1
      1427: 1
      1428: 1
      1429: 1
      1432: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: 1
      1478: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1508: 1
      1516: 1
      1517: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1547: 1
      1555: 1
      1556: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1584: 1
      1592: 1
      1593: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1609: 1
      1610: 1
      1611: 1
      1632: 1
      1633: 1
      1634: 1
      1654: 1
      1662: 1
      1663: 1
      1664: 1
      1684: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1714: 1
      1722: 1
      1723: 1
      1730: 1
      1744: 1
      1765: 1
      1786: 1
      1787: 1
      1788: 1
      1808: 1
      1849: 1

1850:    0: 3q^3+6q^2+4q+1
         1: 3q^3+6q^2+4q+1
         2: 3q^3+6q^2+4q+1
         3: 3q^3+6q^2+4q+1
         4: 3q^3+6q^2+4q+1
         5: 3q^3+6q^2+4q+1
         6: 3q^3+6q^2+4q+1
         7: 3q^3+6q^2+4q+1
         8: 3q^3+6q^2+4q+1
         9: 3q^3+6q^2+4q+1
        10: q^3+4q^2+4q+1
        11: q^3+4q^2+4q+1
        12: q^3+4q^2+4q+1
        13: 3q^3+6q^2+4q+1
        14: 3q^3+6q^2+4q+1
        15: 3q^3+6q^2+4q+1
        16: 3q^3+6q^2+4q+1
        17: 3q^3+6q^2+4q+1
        18: 3q^3+6q^2+4q+1
        19: 3q^3+6q^2+4q+1
        20: 3q^3+6q^2+4q+1
        21: 3q^3+6q^2+4q+1
        22: 3q^3+6q^2+4q+1
        23: q^3+4q^2+4q+1
        24: q^3+4q^2+4q+1
        25: q^3+4q^2+4q+1
        26: q^3+4q^2+4q+1
        27: q^3+4q^2+4q+1
        28: q^3+4q^2+4q+1
        29: 2q^2+4q+1
        30: q^3+4q^2+4q+1
        31: 2q^2+4q+1
        32: 3q^2+4q+1
        33: 3q^3+6q^2+4q+1
        34: 3q^3+6q^2+4q+1
        35: 3q^3+6q^2+4q+1
        36: 3q^3+6q^2+4q+1
        37: q^3+4q^2+4q+1
        38: q^3+4q^2+4q+1
        39: q^3+4q^2+4q+1
        40: 3q^3+6q^2+4q+1
        41: 3q^3+6q^2+4q+1
        42: 3q^3+6q^2+4q+1
        43: 3q^3+6q^2+4q+1
        44: q^3+4q^2+4q+1
        45: q^3+4q^2+4q+1
        46: q^3+4q^2+4q+1
        47: 3q^3+6q^2+4q+1
        48: 3q^3+6q^2+4q+1
        49: 3q^3+6q^2+4q+1
        50: q^3+4q^2+4q+1
        51: q^3+4q^2+4q+1
        52: 3q^3+6q^2+4q+1
        53: q^3+4q^2+4q+1
        54: q^3+4q^2+4q+1
        55: q^3+4q^2+4q+1
        56: 3q^2+4q+1
        57: q^3+4q^2+4q+1
        58: q^3+4q^2+4q+1
        59: q^3+4q^2+4q+1
        60: 2q^2+4q+1
        61: 2q^2+4q+1
        62: 2q^2+4q+1
        63: 2q^2+4q+1
        64: 2q^2+4q+1
        65: 2q^2+4q+1
        66: 2q^2+4q+1
        67: 2q^2+4q+1
        68: 3q^2+4q+1
        69: q^2+4q+1
        70: 3q^2+4q+1
        71: 3q^3+6q^2+4q+1
        72: 3q^3+6q^2+4q+1
        73: 3q^3+6q^2+4q+1
        74: q^3+4q^2+4q+1
        75: q^3+4q^2+4q+1
        76: q^3+4q^2+4q+1
        77: q^3+4q^2+4q+1
        78: q^3+4q^2+4q+1
        79: q^3+4q^2+4q+1
        80: 2q^2+4q+1
        81: q^3+4q^2+4q+1
        82: 2q^2+4q+1
        83: 3q^2+4q+1
        84: 3q^3+6q^2+4q+1
        85: 3q^3+6q^2+4q+1
        86: 3q^3+6q^2+4q+1
        87: q^3+4q^2+4q+1
        88: q^3+4q^2+4q+1
        89: q^3+4q^2+4q+1
        90: q^3+4q^2+4q+1
        91: q^3+4q^2+4q+1
        92: q^3+4q^2+4q+1
        93: 2q^2+4q+1
        94: q^3+4q^2+4q+1
        95: 2q^2+4q+1
        96: 3q^2+4q+1
        97: 3q^3+6q^2+4q+1
        98: 3q^3+6q^2+4q+1
        99: 3q^3+6q^2+4q+1
       100: 3q^3+6q^2+4q+1
       101: q^3+4q^2+4q+1
       102: q^3+4q^2+4q+1
       103: q^3+4q^2+4q+1
       104: 3q^2+4q+1
       105: q^3+4q^2+4q+1
       106: q^3+4q^2+4q+1
       107: q^3+4q^2+4q+1
       108: 2q^2+4q+1
       109: 2q^2+4q+1
       110: 3q^2+4q+1
       111: 3q^2+4q+1
       112: 2q^2+4q+1
       113: 2q^2+4q+1
       114: q^3+4q^2+4q+1
       115: q^3+4q^2+4q+1
       116: 2q^2+4q+1
       117: 2q^2+4q+1
       118: q^2+4q+1
       119: 2q^2+4q+1
       120: 2q^2+4q+1
       121: 2q^2+4q+1
       122: 2q^2+4q+1
       123: 2q+1
       124: 2q^2+4q+1
       125: 2q^2+4q+1
       126: 2q^2+4q+1
       127: 2q+1
       128: 2q^2+4q+1
       129: q^2+4q+1
       130: q^2+4q+1
       131: q^2+4q+1
       132: 3q^2+4q+1
       133: 3q+1
       134: q^3+4q^2+4q+1
       135: q^3+4q^2+4q+1
       136: 3q^3+6q^2+4q+1
       137: q^3+4q^2+4q+1
       138: q^3+4q^2+4q+1
       139: q^3+4q^2+4q+1
       140: 3q^2+4q+1
       141: q^3+4q^2+4q+1
       142: q^3+4q^2+4q+1
       143: q^3+4q^2+4q+1
       144: 2q^2+4q+1
       145: 2q^2+4q+1
       146: 2q^2+4q+1
       147: 2q^2+4q+1
       148: 2q^2+4q+1
       149: 2q^2+4q+1
       150: 2q^2+4q+1
       151: 2q^2+4q+1
       152: 3q^2+4q+1
       153: q^2+4q+1
       154: 3q^2+4q+1
       155: q^3+4q^2+4q+1
       156: q^3+4q^2+4q+1
       157: 3q^3+6q^2+4q+1
       158: q^3+4q^2+4q+1
       159: q^3+4q^2+4q+1
       160: q^3+4q^2+4q+1
       161: 3q^2+4q+1
       162: q^3+4q^2+4q+1
       163: q^3+4q^2+4q+1
       164: q^3+4q^2+4q+1
       165: 2q^2+4q+1
       166: 2q^2+4q+1
       167: 2q^2+4q+1
       168: 2q^2+4q+1
       169: 2q^2+4q+1
       170: 2q^2+4q+1
       171: 2q^2+4q+1
       172: 2q^2+4q+1
       173: 3q^2+4q+1
       174: q^2+4q+1
       175: 3q^2+4q+1
       176: 3q^3+6q^2+4q+1
       177: 3q^3+6q^2+4q+1
       178: 3q^3+6q^2+4q+1
       179: q^3+4q^2+4q+1
       180: q^3+4q^2+4q+1
       181: q^3+4q^2+4q+1
       182: q^3+4q^2+4q+1
       183: q^3+4q^2+4q+1
       184: q^3+4q^2+4q+1
       185: 2q^2+4q+1
       186: q^3+4q^2+4q+1
       187: 2q^2+4q+1
       188: 3q^2+4q+1
       189: 3q^2+4q+1
       190: 3q^2+4q+1
       191: 2q^2+4q+1
       192: 2q^2+4q+1
       193: 2q^2+4q+1
       194: 2q^2+4q+1
       195: q^2+4q+1
       196: 3q^2+4q+1
       197: 3q+1
       198: q^2+4q+1
       199: 2q^2+4q+1
       200: 2q^2+4q+1
       201: q^3+4q^2+4q+1
       202: 2q^2+4q+1
       203: 2q^2+4q+1
       204: q^2+4q+1
       205: q^2+4q+1
       206: 2q^2+4q+1
       207: 2q+1
       208: 2q^2+4q+1
       209: q^2+2q+1
       210: 2q^2+4q+1
       211: 2q+1
       212: 2q+1
       213: 2q+1
       214: 2q^2+4q+1
       215: 2q^2+4q+1
       216: q^2+2q+1
       217: 2q+1
       218: 2q^2+4q+1
       219: 2q+1
       220: q^2+4q+1
       221: q^2+4q+1
       222: q^2+4q+1
       223: 2q+1
       224: 2q+1
       225: 3q+1
       226: 3q+1
       227: 3q+1
       228: 3q^2+4q+1
       229: q^3+4q^2+4q+1
       230: q^3+4q^2+4q+1
       231: q^3+4q^2+4q+1
       232: 2q^2+4q+1
       233: 2q^2+4q+1
       234: 3q^2+4q+1
       235: 3q^2+4q+1
       236: 2q^2+4q+1
       237: 2q^2+4q+1
       238: q^3+4q^2+4q+1
       239: q^3+4q^2+4q+1
       240: 2q^2+4q+1
       241: 2q^2+4q+1
       242: q^2+4q+1
       243: 2q^2+4q+1
       244: 2q^2+4q+1
       245: 2q^2+4q+1
       246: 2q^2+4q+1
       247: 2q+1
       248: 2q^2+4q+1
       249: 2q^2+4q+1
       250: 2q^2+4q+1
       251: 2q+1
       252: 2q^2+4q+1
       253: q^2+4q+1
       254: q^2+4q+1
       255: q^2+4q+1
       256: 3q^2+4q+1
       257: 3q+1
       258: 3q^2+4q+1
       259: q^3+4q^2+4q+1
       260: q^3+4q^2+4q+1
       261: q^3+4q^2+4q+1
       262: 2q^2+4q+1
       263: 2q^2+4q+1
       264: 3q^2+4q+1
       265: 3q^2+4q+1
       266: 2q^2+4q+1
       267: 2q^2+4q+1
       268: q^3+4q^2+4q+1
       269: q^3+4q^2+4q+1
       270: 2q^2+4q+1
       271: 2q^2+4q+1
       272: q^2+4q+1
       273: 2q^2+4q+1
       274: 2q^2+4q+1
       275: 2q^2+4q+1
       276: 2q^2+4q+1
       277: 2q+1
       278: 2q^2+4q+1
       279: 2q^2+4q+1
       280: 2q^2+4q+1
       281: 2q+1
       282: 2q^2+4q+1
       283: q^2+4q+1
       284: q^2+4q+1
       285: q^2+4q+1
       286: 3q^2+4q+1
       287: 3q+1
       288: q^3+4q^2+4q+1
       289: q^3+4q^2+4q+1
       290: 3q^3+6q^2+4q+1
       291: q^3+4q^2+4q+1
       292: q^3+4q^2+4q+1
       293: q^3+4q^2+4q+1
       294: 3q^2+4q+1
       295: q^3+4q^2+4q+1
       296: q^3+4q^2+4q+1
       297: q^3+4q^2+4q+1
       298: 2q^2+4q+1
       299: 2q^2+4q+1
       300: 2q^2+4q+1
       301: 2q^2+4q+1
       302: 2q^2+4q+1
       303: 2q^2+4q+1
       304: 2q^2+4q+1
       305: 2q^2+4q+1
       306: 3q^2+4q+1
       307: q^2+4q+1
       308: 3q^2+4q+1
       309: 3q+1
       310: 3q^2+4q+1
       311: q^2+4q+1
       312: 2q^2+4q+1
       313: 2q+1
       314: 2q+1
       315: 2q^2+4q+1
       316: q^2+4q+1
       317: 3q+1
       318: 3q+1
       319: q^2+4q+1
       320: q^2+4q+1
       321: 2q^2+4q+1
       322: 2q^2+4q+1
       323: 2q^2+4q+1
       324: 2q^2+4q+1
       325: q^2+4q+1
       326: q^2+4q+1
       327: 3q+1
       328: 2q+1
       329: 2q^2+4q+1
       330: 2q+1
       331: q^2+2q+1
       332: q^2+2q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: 2q+1
       338: 2q^2+4q+1
       339: q^2+2q+1
       340: q+1
       341: q^2+2q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: 2q+1
       346: q^2+4q+1
       347: q+1
       348: 2q+1
       349: 2q+1
       350: q+1
       351: 3q+1
       352: 3q+1
       353: 3q+1
       354: q+1
       355: q+1
       356: 3q^2+4q+1
       357: 3q^2+4q+1
       358: 2q^2+4q+1
       359: 2q^2+4q+1
       360: 2q^2+4q+1
       361: 2q^2+4q+1
       362: q^2+4q+1
       363: 3q^2+4q+1
       364: 3q+1
       365: q^2+4q+1
       366: 2q^2+4q+1
       367: 2q^2+4q+1
       368: q^3+4q^2+4q+1
       369: 2q^2+4q+1
       370: 2q^2+4q+1
       371: q^2+4q+1
       372: q^2+4q+1
       373: 2q^2+4q+1
       374: 2q+1
       375: 2q^2+4q+1
       376: q^2+2q+1
       377: 2q^2+4q+1
       378: 2q+1
       379: 2q+1
       380: 2q+1
       381: 2q^2+4q+1
       382: 2q^2+4q+1
       383: q^2+2q+1
       384: 2q+1
       385: 2q^2+4q+1
       386: 2q+1
       387: q^2+4q+1
       388: q^2+4q+1
       389: q^2+4q+1
       390: 2q+1
       391: 2q+1
       392: 3q+1
       393: 3q+1
       394: 3q+1
       395: 3q^2+4q+1
       396: 3q^2+4q+1
       397: 2q^2+4q+1
       398: 2q^2+4q+1
       399: 2q^2+4q+1
       400: 2q^2+4q+1
       401: q^2+4q+1
       402: 3q^2+4q+1
       403: 3q+1
       404: q^2+4q+1
       405: 2q^2+4q+1
       406: 2q^2+4q+1
       407: q^3+4q^2+4q+1
       408: 2q^2+4q+1
       409: 2q^2+4q+1
       410: q^2+4q+1
       411: q^2+4q+1
       412: 2q^2+4q+1
       413: 2q+1
       414: 2q^2+4q+1
       415: q^2+2q+1
       416: 2q^2+4q+1
       417: 2q+1
       418: 2q+1
       419: 2q+1
       420: 2q^2+4q+1
       421: 2q^2+4q+1
       422: q^2+2q+1
       423: 2q+1
       424: 2q^2+4q+1
       425: 2q+1
       426: q^2+4q+1
       427: q^2+4q+1
       428: q^2+4q+1
       429: 2q+1
       430: 2q+1
       431: 3q+1
       432: 3q+1
       433: 3q+1
       434: 3q^2+4q+1
       435: q^3+4q^2+4q+1
       436: q^3+4q^2+4q+1
       437: q^3+4q^2+4q+1
       438: 2q^2+4q+1
       439: 2q^2+4q+1
       440: 3q^2+4q+1
       441: 3q^2+4q+1
       442: 2q^2+4q+1
       443: 2q^2+4q+1
       444: q^3+4q^2+4q+1
       445: q^3+4q^2+4q+1
       446: 2q^2+4q+1
       447: 2q^2+4q+1
       448: q^2+4q+1
       449: 2q^2+4q+1
       450: 2q^2+4q+1
       451: 2q^2+4q+1
       452: 2q^2+4q+1
       453: 2q+1
       454: 2q^2+4q+1
       455: 2q^2+4q+1
       456: 2q^2+4q+1
       457: 2q+1
       458: 2q^2+4q+1
       459: q^2+4q+1
       460: q^2+4q+1
       461: q^2+4q+1
       462: 3q^2+4q+1
       463: 3q+1
       464: 3q+1
       465: 3q+1
       466: q^2+4q+1
       467: 2q+1
       468: 2q+1
       469: 2q+1
       470: 2q+1
       471: 3q+1
       472: 3q+1
       473: 3q+1
       474: q^2+4q+1
       475: q^2+4q+1
       476: 2q^2+4q+1
       477: 2q+1
       478: 2q+1
       479: 2q^2+4q+1
       480: q^2+4q+1
       481: q+1
       482: 3q+1
       483: 2q+1
       484: 2q+1
       485: q^2+2q+1
       486: q+1
       487: q^2+2q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: q^2+2q+1
       496: q+1
       497: q^2+2q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: 2q+1
       503: 2q+1
       504: q+1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: 3q+1
       512: q+1
       513: q+1
       514: q+1
       515: 1
       516: 3q+1
       517: 3q^2+4q+1
       518: q^2+4q+1
       519: 2q^2+4q+1
       520: 2q+1
       521: 2q+1
       522: 2q^2+4q+1
       523: q^2+4q+1
       524: 3q+1
       525: 3q+1
       526: q^2+4q+1
       527: q^2+4q+1
       528: 2q^2+4q+1
       529: 2q^2+4q+1
       530: 2q^2+4q+1
       531: 2q^2+4q+1
       532: q^2+4q+1
       533: q^2+4q+1
       534: 3q+1
       535: 2q+1
       536: 2q^2+4q+1
       537: 2q+1
       538: q^2+2q+1
       539: q^2+2q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: 2q+1
       544: 2q+1
       545: 2q^2+4q+1
       546: q^2+2q+1
       547: q+1
       548: q^2+2q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: 2q+1
       553: q^2+4q+1
       554: q+1
       555: 2q+1
       556: 2q+1
       557: q+1
       558: 3q+1
       559: 3q+1
       560: 3q+1
       561: q+1
       562: q+1
       563: 3q+1
       564: 3q^2+4q+1
       565: q^2+4q+1
       566: 2q^2+4q+1
       567: 2q+1
       568: 2q+1
       569: 2q^2+4q+1
       570: q^2+4q+1
       571: 3q+1
       572: 3q+1
       573: q^2+4q+1
       574: q^2+4q+1
       575: 2q^2+4q+1
       576: 2q^2+4q+1
       577: 2q^2+4q+1
       578: 2q^2+4q+1
       579: q^2+4q+1
       580: q^2+4q+1
       581: 3q+1
       582: 2q+1
       583: 2q^2+4q+1
       584: 2q+1
       585: q^2+2q+1
       586: q^2+2q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: 2q+1
       591: 2q+1
       592: 2q^2+4q+1
       593: q^2+2q+1
       594: q+1
       595: q^2+2q+1
       596: 2q+1
       597: 2q+1
       598: 2q+1
       599: 2q+1
       600: q^2+4q+1
       601: q+1
       602: 2q+1
       603: 2q+1
       604: q+1
       605: 3q+1
       606: 3q+1
       607: 3q+1
       608: q+1
       609: q+1
       610: 3q^2+4q+1
       611: 3q^2+4q+1
       612: 2q^2+4q+1
       613: 2q^2+4q+1
       614: 2q^2+4q+1
       615: 2q^2+4q+1
       616: q^2+4q+1
       617: 3q^2+4q+1
       618: 3q+1
       619: q^2+4q+1
       620: 2q^2+4q+1
       621: 2q^2+4q+1
       622: q^3+4q^2+4q+1
       623: 2q^2+4q+1
       624: 2q^2+4q+1
       625: q^2+4q+1
       626: q^2+4q+1
       627: 2q^2+4q+1
       628: 2q+1
       629: 2q^2+4q+1
       630: q^2+2q+1
       631: 2q^2+4q+1
       632: 2q+1
       633: 2q+1
       634: 2q+1
       635: 2q^2+4q+1
       636: 2q^2+4q+1
       637: q^2+2q+1
       638: 2q+1
       639: 2q^2+4q+1
       640: 2q+1
       641: q^2+4q+1
       642: q^2+4q+1
       643: q^2+4q+1
       644: 2q+1
       645: 2q+1
       646: 3q+1
       647: 3q+1
       648: 3q+1
       649: 3q+1
       650: 3q+1
       651: 2q+1
       652: 2q+1
       653: q+1
       654: q+1
       655: q+1
       656: 3q+1
       657: 3q+1
       658: q+1
       659: q^2+4q+1
       660: 2q+1
       661: 2q+1
       662: 2q+1
       663: 2q+1
       664: q+1
       665: q+1
       666: q+1
       667: 2q+1
       668: q+1
       669: q^2+2q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       681: q+1
       682: q^2+2q+1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: q+1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 3q+1
       704: 3q+1
       705: q^2+4q+1
       706: 2q+1
       707: 2q+1
       708: 2q+1
       709: 2q+1
       710: 3q+1
       711: 3q+1
       712: 3q+1
       713: q^2+4q+1
       714: q^2+4q+1
       715: 2q^2+4q+1
       716: 2q+1
       717: 2q+1
       718: 2q^2+4q+1
       719: q^2+4q+1
       720: q+1
       721: 3q+1
       722: 2q+1
       723: 2q+1
       724: q^2+2q+1
       725: q+1
       726: q^2+2q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       731: 2q+1
       732: 2q+1
       733: q+1
       734: q^2+2q+1
       735: q+1
       736: q^2+2q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: q+1
       741: 2q+1
       742: 2q+1
       743: q+1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: q+1
       750: 3q+1
       751: q+1
       752: q+1
       753: q+1
       754: 1
       755: 3q+1
       756: 3q+1
       757: q^2+4q+1
       758: 2q+1
       759: 2q+1
       760: 2q+1
       761: 2q+1
       762: 3q+1
       763: 3q+1
       764: 3q+1
       765: q^2+4q+1
       766: q^2+4q+1
       767: 2q^2+4q+1
       768: 2q+1
       769: 2q+1
       770: 2q^2+4q+1
       771: q^2+4q+1
       772: q+1
       773: 3q+1
       774: 2q+1
       775: 2q+1
       776: q^2+2q+1
       777: q+1
       778: q^2+2q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: 2q+1
       784: 2q+1
       785: q+1
       786: q^2+2q+1
       787: q+1
       788: q^2+2q+1
       789: q+1
       790: 2q+1
       791: q+1
       792: q+1
       793: 2q+1
       794: 2q+1
       795: q+1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: q+1
       802: 3q+1
       803: q+1
       804: q+1
       805: q+1
       806: 1
       807: 3q+1
       808: 3q^2+4q+1
       809: q^2+4q+1
       810: 2q^2+4q+1
       811: 2q+1
       812: 2q+1
       813: 2q^2+4q+1
       814: q^2+4q+1
       815: 3q+1
       816: 3q+1
       817: q^2+4q+1
       818: q^2+4q+1
       819: 2q^2+4q+1
       820: 2q^2+4q+1
       821: 2q^2+4q+1
       822: 2q^2+4q+1
       823: q^2+4q+1
       824: q^2+4q+1
       825: 3q+1
       826: 2q+1
       827: 2q^2+4q+1
       828: 2q+1
       829: q^2+2q+1
       830: q^2+2q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       834: 2q+1
       835: 2q+1
       836: 2q^2+4q+1
       837: q^2+2q+1
       838: q+1
       839: q^2+2q+1
       840: 2q+1
       841: 2q+1
       842: 2q+1
       843: 2q+1
       844: q^2+4q+1
       845: q+1
       846: 2q+1
       847: 2q+1
       848: q+1
       849: 3q+1
       850: 3q+1
       851: 3q+1
       852: q+1
       853: q+1
       854: 3q+1
       855: q+1
       856: q+1
       857: q+1
       858: 1
       859: q+1
       860: q+1
       861: q+1
       862: q+1
       863: 2q+1
       864: 2q+1
       865: q+1
       866: 1
       867: 1
       868: q+1
       869: q+1
       870: 1
       871: q+1
       872: q+1
       875: q+1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: q+1
       882: q+1
       883: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 3q+1
       907: 3q+1
       908: 2q+1
       909: 2q+1
       910: q+1
       911: q+1
       912: q+1
       913: 3q+1
       914: 3q+1
       915: q+1
       916: q^2+4q+1
       917: 2q+1
       918: 2q+1
       919: 2q+1
       920: 2q+1
       921: q+1
       922: q+1
       923: q+1
       924: 2q+1
       925: q+1
       926: q^2+2q+1
       927: q+1
       929: q+1
       930: q+1
       931: 1
       932: q+1
       933: q+1
       934: 2q+1
       935: q+1
       936: q+1
       938: q+1
       939: q^2+2q+1
       940: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q+1
       954: q+1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       960: 3q+1
       961: 3q+1
       962: 2q+1
       963: 2q+1
       964: q+1
       965: q+1
       966: q+1
       967: 3q+1
       968: 3q+1
       969: q+1
       970: q^2+4q+1
       971: 2q+1
       972: 2q+1
       973: 2q+1
       974: 2q+1
       975: q+1
       976: q+1
       977: q+1
       978: 2q+1
       979: q+1
       980: q^2+2q+1
       981: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       987: q+1
       988: 2q+1
       989: q+1
       990: q+1
       992: q+1
       993: q^2+2q+1
       994: q+1
       995: 1
       996: q+1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: q+1
      1008: q+1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 3q+1
      1015: 3q+1
      1016: q^2+4q+1
      1017: 2q+1
      1018: 2q+1
      1019: 2q+1
      1020: 2q+1
      1021: 3q+1
      1022: 3q+1
      1023: 3q+1
      1024: q^2+4q+1
      1025: q^2+4q+1
      1026: 2q^2+4q+1
      1027: 2q+1
      1028: 2q+1
      1029: 2q^2+4q+1
      1030: q^2+4q+1
      1031: q+1
      1032: 3q+1
      1033: 2q+1
      1034: 2q+1
      1035: q^2+2q+1
      1036: q+1
      1037: q^2+2q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1042: 2q+1
      1043: 2q+1
      1044: q+1
      1045: q^2+2q+1
      1046: q+1
      1047: q^2+2q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1051: q+1
      1052: 2q+1
      1053: 2q+1
      1054: q+1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: q+1
      1061: 3q+1
      1062: q+1
      1063: q+1
      1064: q+1
      1065: 1
      1066: q+1
      1067: q+1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: q+1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 3q+1
      1114: q+1
      1115: q+1
      1116: q+1
      1117: 1
      1118: q+1
      1119: q+1
      1120: q+1
      1121: q+1
      1122: 2q+1
      1123: 2q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: q+1
      1128: q+1
      1129: 1
      1130: q+1
      1131: q+1
      1134: q+1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: q+1
      1141: q+1
      1142: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 3q+1
      1166: q+1
      1167: q+1
      1168: q+1
      1169: 1
      1170: q+1
      1171: q+1
      1172: q+1
      1173: q+1
      1174: 2q+1
      1175: 2q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: q+1
      1180: q+1
      1181: 1
      1182: q+1
      1183: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: q+1
      1190: 1
      1191: q+1
      1193: q+1
      1194: q+1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 3q+1
      1218: 3q+1
      1219: 2q+1
      1220: 2q+1
      1221: q+1
      1222: q+1
      1223: q+1
      1224: 3q+1
      1225: 3q+1
      1226: q+1
      1227: q^2+4q+1
      1228: 2q+1
      1229: 2q+1
      1230: 2q+1
      1231: 2q+1
      1232: q+1
      1233: q+1
      1234: q+1
      1235: 2q+1
      1236: q+1
      1237: q^2+2q+1
      1238: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: q+1
      1244: q+1
      1245: 2q+1
      1246: q+1
      1247: q+1
      1249: q+1
      1250: q^2+2q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: q+1
      1255: q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: q+1
      1265: q+1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1303: 1
      1310: q+1
      1311: q+1
      1312: 1
      1313: 1
      1314: 1
      1315: q+1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: q+1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1333: q+1
      1335: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1356: 1
      1357: q+1
      1358: q+1
      1359: 1
      1360: 1
      1361: 1
      1362: q+1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1380: q+1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1403: 1
      1404: 3q+1
      1405: q+1
      1406: q+1
      1407: q+1
      1408: 1
      1409: q+1
      1410: q+1
      1411: q+1
      1412: q+1
      1413: 2q+1
      1414: 2q+1
      1415: q+1
      1416: 1
      1417: 1
      1418: q+1
      1419: q+1
      1420: 1
      1421: q+1
      1422: q+1
      1425: q+1
      1426: 1
      1427: 1
      1428: q+1
      1429: 1
      1430: q+1
      1432: q+1
      1433: q+1
      1435: 1
      1436: 1
      1437: 1
      1438: q+1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1467: 1
      1471: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1503: 1
      1506: 1
      1508: 1
      1509: 1
      1515: 1
      1516: 1
      1518: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1554: 1
      1555: 1
      1557: 1
      1564: q+1
      1565: q+1
      1566: 1
      1567: 1
      1568: 1
      1569: q+1
      1570: 1
      1571: 1
      1572: q+1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: q+1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1587: q+1
      1589: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1610: 1
      1612: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1643: 1
      1647: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1673: 1
      1677: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1706: 1
      1707: 1
      1709: 1
      1712: 1
      1714: 1
      1715: 1
      1721: 1
      1722: 1
      1724: 1
      1745: 1
      1766: 1
      1786: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1797: 1
      1801: 1
      1850: 1

1851:    0: 2q^3+3q^2+2q+1
         1: 3q^2+2q+1
         2: 2q^3+3q^2+2q+1
         3: 2q^3+3q^2+2q+1
         4: 2q^3+3q^2+2q+1
         5: 2q^3+3q^2+2q+1
         6: 3q^2+2q+1
         7: 3q^2+2q+1
         8: 2q^3+3q^2+2q+1
         9: 3q^2+2q+1
        10: 2q^3+3q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: 3q^2+2q+1
        14: 2q^3+3q^2+2q+1
        15: 2q^3+3q^2+2q+1
        16: 3q^2+2q+1
        17: 2q^3+3q^2+2q+1
        18: 2q^3+3q^2+2q+1
        19: 2q^3+3q^2+2q+1
        20: 3q^2+2q+1
        21: 3q^2+2q+1
        22: 3q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 3q^2+2q+1
        26: q^2+2q+1
        27: 2q^3+3q^2+2q+1
        28: 2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: 2q^2+2q+1
        31: q^3+2q^2+2q+1
        32: 2q^2+2q+1
        33: 3q^2+2q+1
        34: 3q^2+2q+1
        35: 2q^3+3q^2+2q+1
        36: 3q^2+2q+1
        37: 2q^3+3q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        40: 3q^2+2q+1
        41: 3q^2+2q+1
        42: 2q^3+3q^2+2q+1
        43: 3q^2+2q+1
        44: 2q^3+3q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: 3q^2+2q+1
        48: 2q^3+3q^2+2q+1
        49: 2q^3+3q^2+2q+1
        50: q^2+q+1
        51: q^2+q+1
        52: 3q^2+2q+1
        53: 3q^2+2q+1
        54: 2q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: 3q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^3+2q^2+2q+1
        61: q^3+2q^2+2q+1
        62: 2q^2+2q+1
        63: 2q+1
        64: q^3+2q^2+2q+1
        65: 2q^2+2q+1
        66: 2q+1
        67: q^3+2q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: 2q^2+2q+1
        71: 3q^2+2q+1
        72: 3q^2+2q+1
        73: 3q^2+2q+1
        74: q^3+2q^2+2q+1
        75: q^3+2q^2+2q+1
        76: 3q^2+2q+1
        77: q^2+2q+1
        78: 2q^3+3q^2+2q+1
        79: 2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: 2q^2+2q+1
        82: q^3+2q^2+2q+1
        83: 2q^2+2q+1
        84: 3q^2+2q+1
        85: 3q^2+2q+1
        86: 3q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^3+2q^2+2q+1
        89: 3q^2+2q+1
        90: q^2+2q+1
        91: 2q^3+3q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: 2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: 2q^2+2q+1
        97: 3q^2+2q+1
        98: 3q^2+2q+1
        99: 2q^3+3q^2+2q+1
       100: 3q^2+2q+1
       101: 2q^3+3q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^3+2q^2+2q+1
       104: q+1
       105: q^2+q+1
       106: q^2+q+1
       107: 3q^2+2q+1
       108: 2q^2+2q+1
       109: 2q^2+2q+1
       110: 2q^2+2q+1
       111: 2q^2+2q+1
       112: q^2+q+1
       113: q^2+q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: 2q+1
       117: 2q+1
       118: 2q^2+2q+1
       119: 2q^2+2q+1
       120: 2q+1
       121: 2q+1
       122: q^3+2q^2+2q+1
       123: q^2+q+1
       124: 2q^2+2q+1
       125: 2q+1
       126: 2q+1
       127: q^2+q+1
       128: q^3+2q^2+2q+1
       129: 2q^2+2q+1
       130: 2q+1
       131: 2q^2+2q+1
       132: 2q^2+2q+1
       133: 2q^2+2q+1
       134: q^2+q+1
       135: q^2+q+1
       136: 3q^2+2q+1
       137: 3q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: 2q^2+2q+1
       141: 3q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^3+2q^2+2q+1
       145: q^3+2q^2+2q+1
       146: 2q^2+2q+1
       147: 2q+1
       148: q^3+2q^2+2q+1
       149: 2q^2+2q+1
       150: 2q+1
       151: q^3+2q^2+2q+1
       152: 2q^2+2q+1
       153: 2q^2+2q+1
       154: 2q^2+2q+1
       155: q^2+q+1
       156: q^2+q+1
       157: 3q^2+2q+1
       158: 3q^2+2q+1
       159: 2q^2+2q+1
       160: 2q^2+2q+1
       161: 2q^2+2q+1
       162: 3q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^3+2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q+1
       169: q^3+2q^2+2q+1
       170: 2q^2+2q+1
       171: 2q+1
       172: q^3+2q^2+2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: 2q^2+2q+1
       176: 3q^2+2q+1
       177: 3q^2+2q+1
       178: 3q^2+2q+1
       179: q^3+2q^2+2q+1
       180: q^3+2q^2+2q+1
       181: 3q^2+2q+1
       182: q^2+2q+1
       183: 2q^3+3q^2+2q+1
       184: 2q^2+2q+1
       185: q^3+2q^2+2q+1
       186: 2q^2+2q+1
       187: q^3+2q^2+2q+1
       188: 2q^2+2q+1
       189: q+1
       190: q+1
       191: q^2+q+1
       192: q^2+q+1
       193: 2q^2+2q+1
       194: 2q^2+2q+1
       195: 2q^2+2q+1
       196: 2q^2+2q+1
       197: 2q^2+2q+1
       198: q+1
       199: q+1
       200: q+1
       201: q^2+2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q^2+2q+1
       206: q^2+q+1
       207: q^2+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: q+1
       212: q^2+q+1
       213: q^2+1
       214: q^2+q+1
       215: 2q+1
       216: 2q+1
       217: q+1
       218: 2q+1
       219: q^2+q+1
       220: 2q^2+2q+1
       221: 2q+1
       222: 2q+1
       223: q^2+q+1
       224: q^2+q+1
       225: 2q^2+2q+1
       226: q+1
       227: 2q^2+2q+1
       228: q+1
       229: q^2+q+1
       230: q^2+q+1
       231: 3q^2+2q+1
       232: 2q^2+2q+1
       233: 2q^2+2q+1
       234: 2q^2+2q+1
       235: 2q^2+2q+1
       236: q^2+q+1
       237: q^2+q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: 2q+1
       241: 2q+1
       242: 2q^2+2q+1
       243: 2q^2+2q+1
       244: 2q+1
       245: 2q+1
       246: q^3+2q^2+2q+1
       247: q^2+q+1
       248: 2q^2+2q+1
       249: 2q+1
       250: 2q+1
       251: q^2+q+1
       252: q^3+2q^2+2q+1
       253: 2q^2+2q+1
       254: 2q+1
       255: 2q^2+2q+1
       256: 2q^2+2q+1
       257: 2q^2+2q+1
       258: q+1
       259: q^2+q+1
       260: q^2+q+1
       261: 3q^2+2q+1
       262: 2q^2+2q+1
       263: 2q^2+2q+1
       264: 2q^2+2q+1
       265: 2q^2+2q+1
       266: q^2+q+1
       267: q^2+q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: 2q+1
       271: 2q+1
       272: 2q^2+2q+1
       273: 2q^2+2q+1
       274: 2q+1
       275: 2q+1
       276: q^3+2q^2+2q+1
       277: q^2+q+1
       278: 2q^2+2q+1
       279: 2q+1
       280: 2q+1
       281: q^2+q+1
       282: q^3+2q^2+2q+1
       283: 2q^2+2q+1
       284: 2q+1
       285: 2q^2+2q+1
       286: 2q^2+2q+1
       287: 2q^2+2q+1
       288: q^2+q+1
       289: q^2+q+1
       290: 3q^2+2q+1
       291: 3q^2+2q+1
       292: 2q^2+2q+1
       293: 2q^2+2q+1
       294: 2q^2+2q+1
       295: 3q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q^3+2q^2+2q+1
       299: q^3+2q^2+2q+1
       300: 2q^2+2q+1
       301: 2q+1
       302: q^3+2q^2+2q+1
       303: 2q^2+2q+1
       304: 2q+1
       305: q^3+2q^2+2q+1
       306: 2q^2+2q+1
       307: 2q^2+2q+1
       308: 2q^2+2q+1
       309: q+1
       310: q+1
       311: q+1
       312: q^2+q+1
       313: q^2+1
       314: q^2+1
       315: q^2+q+1
       316: 2q^2+2q+1
       317: 2q^2+2q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: 2q^2+2q+1
       328: 1
       329: q+1
       330: 1
       331: 2q+1
       332: 2q+1
       333: q+1
       334: q+1
       335: q^2+q+1
       336: 1
       337: 1
       338: q+1
       339: 2q+1
       340: q+1
       341: 2q+1
       342: q+1
       343: q^2+q+1
       344: q^2+1
       345: q^2+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: q+1
       350: q+1
       351: 2q^2+2q+1
       352: q+1
       353: q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: q^2+q+1
       360: 2q^2+2q+1
       361: 2q^2+2q+1
       362: 2q^2+2q+1
       363: 2q^2+2q+1
       364: 2q^2+2q+1
       365: q+1
       366: q+1
       367: q+1
       368: q^2+2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q^2+2q+1
       373: q^2+q+1
       374: q^2+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: q+1
       379: q^2+q+1
       380: q^2+1
       381: q^2+q+1
       382: 2q+1
       383: 2q+1
       384: q+1
       385: 2q+1
       386: q^2+q+1
       387: 2q^2+2q+1
       388: 2q+1
       389: 2q+1
       390: q^2+q+1
       391: q^2+q+1
       392: 2q^2+2q+1
       393: q+1
       394: 2q^2+2q+1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q^2+q+1
       399: 2q^2+2q+1
       400: 2q^2+2q+1
       401: 2q^2+2q+1
       402: 2q^2+2q+1
       403: 2q^2+2q+1
       404: q+1
       405: q+1
       406: q+1
       407: q^2+2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q^2+2q+1
       412: q^2+q+1
       413: q^2+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: q+1
       418: q^2+q+1
       419: q^2+1
       420: q^2+q+1
       421: 2q+1
       422: 2q+1
       423: q+1
       424: 2q+1
       425: q^2+q+1
       426: 2q^2+2q+1
       427: 2q+1
       428: 2q+1
       429: q^2+q+1
       430: q^2+q+1
       431: 2q^2+2q+1
       432: q+1
       433: 2q^2+2q+1
       434: q+1
       435: q^2+q+1
       436: q^2+q+1
       437: 3q^2+2q+1
       438: 2q^2+2q+1
       439: 2q^2+2q+1
       440: 2q^2+2q+1
       441: 2q^2+2q+1
       442: q^2+q+1
       443: q^2+q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: 2q+1
       447: 2q+1
       448: 2q^2+2q+1
       449: 2q^2+2q+1
       450: 2q+1
       451: 2q+1
       452: q^3+2q^2+2q+1
       453: q^2+q+1
       454: 2q^2+2q+1
       455: 2q+1
       456: 2q+1
       457: q^2+q+1
       458: q^3+2q^2+2q+1
       459: 2q^2+2q+1
       460: 2q+1
       461: 2q^2+2q+1
       462: 2q^2+2q+1
       463: 2q^2+2q+1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: q^2+1
       470: q^2+1
       471: 2q^2+2q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: 1
       478: 1
       479: q+1
       480: 2q+1
       481: 2q+1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: 2q+1
       488: q+1
       489: q+1
       490: q+1
       491: q^2+q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: 2q+1
       498: q+1
       499: q+1
       500: q^2+q+1
       501: 1
       502: 1
       503: 1
       504: 2q+1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: q^2+1
       510: q^2+1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q^2+q+1
       520: q^2+1
       521: q^2+1
       522: q^2+q+1
       523: 2q^2+2q+1
       524: 2q^2+2q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: 2q^2+2q+1
       535: 1
       536: q+1
       537: 1
       538: 2q+1
       539: 2q+1
       540: q+1
       541: q+1
       542: q^2+q+1
       543: 1
       544: 1
       545: q+1
       546: 2q+1
       547: q+1
       548: 2q+1
       549: q+1
       550: q^2+q+1
       551: q^2+1
       552: q^2+1
       553: 2q+1
       554: 2q+1
       555: q+1
       556: q+1
       557: q+1
       558: 2q^2+2q+1
       559: q+1
       560: q+1
       561: q^2+q+1
       562: q^2+q+1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: q^2+1
       568: q^2+1
       569: q^2+q+1
       570: 2q^2+2q+1
       571: 2q^2+2q+1
       572: q+1
       573: q+1
       574: q+1
       575: q+1
       576: q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: 2q^2+2q+1
       582: 1
       583: q+1
       584: 1
       585: 2q+1
       586: 2q+1
       587: q+1
       588: q+1
       589: q^2+q+1
       590: 1
       591: 1
       592: q+1
       593: 2q+1
       594: q+1
       595: 2q+1
       596: q+1
       597: q^2+q+1
       598: q^2+1
       599: q^2+1
       600: 2q+1
       601: 2q+1
       602: q+1
       603: q+1
       604: q+1
       605: 2q^2+2q+1
       606: q+1
       607: q+1
       608: q^2+q+1
       609: q^2+q+1
       610: q+1
       611: q+1
       612: q^2+q+1
       613: q^2+q+1
       614: 2q^2+2q+1
       615: 2q^2+2q+1
       616: 2q^2+2q+1
       617: 2q^2+2q+1
       618: 2q^2+2q+1
       619: q+1
       620: q+1
       621: q+1
       622: q^2+2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q^2+2q+1
       627: q^2+q+1
       628: q^2+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: q+1
       633: q^2+q+1
       634: q^2+1
       635: q^2+q+1
       636: 2q+1
       637: 2q+1
       638: q+1
       639: 2q+1
       640: q^2+q+1
       641: 2q^2+2q+1
       642: 2q+1
       643: 2q+1
       644: q^2+q+1
       645: q^2+q+1
       646: 2q^2+2q+1
       647: q+1
       648: 2q^2+2q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: q^2+1
       655: q^2+1
       656: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 2q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: q+1
       684: q+1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: q+1
       704: q+1
       705: q+1
       706: 1
       707: 1
       708: q^2+1
       709: q^2+1
       710: 2q^2+2q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       716: 1
       717: 1
       718: q+1
       719: 2q+1
       720: 2q+1
       721: q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: 2q+1
       727: q+1
       728: q+1
       729: q+1
       730: q^2+q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: 2q+1
       737: q+1
       738: q+1
       739: q^2+q+1
       740: 1
       741: 1
       742: 1
       743: 2q+1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: q^2+1
       749: q^2+1
       750: q+1
       751: q+1
       752: 1
       753: 1
       754: q+1
       756: q+1
       757: q+1
       758: 1
       759: 1
       760: q^2+1
       761: q^2+1
       762: 2q^2+2q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q+1
       768: 1
       769: 1
       770: q+1
       771: 2q+1
       772: 2q+1
       773: q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: 2q+1
       779: q+1
       780: q+1
       781: q+1
       782: q^2+q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: 2q+1
       789: q+1
       790: q+1
       791: q^2+q+1
       792: 1
       793: 1
       794: 1
       795: 2q+1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       800: q^2+1
       801: q^2+1
       802: q+1
       803: q+1
       804: 1
       805: 1
       806: q+1
       807: q+1
       808: q+1
       809: q+1
       810: q^2+q+1
       811: q^2+1
       812: q^2+1
       813: q^2+q+1
       814: 2q^2+2q+1
       815: 2q^2+2q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: 2q^2+2q+1
       826: 1
       827: q+1
       828: 1
       829: 2q+1
       830: 2q+1
       831: q+1
       832: q+1
       833: q^2+q+1
       834: 1
       835: 1
       836: q+1
       837: 2q+1
       838: q+1
       839: 2q+1
       840: q+1
       841: q^2+q+1
       842: q^2+1
       843: q^2+1
       844: 2q+1
       845: 2q+1
       846: q+1
       847: q+1
       848: q+1
       849: 2q^2+2q+1
       850: q+1
       851: q+1
       852: q^2+q+1
       853: q^2+q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       870: 1
       871: 1
       872: 1
       875: 1
       876: q+1
       877: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: q+1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: q+1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: q+1
       907: q+1
       908: 1
       909: 1
       910: 1
       911: q^2+1
       912: q^2+1
       913: q+1
       915: q+1
       916: q+1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 2q+1
       922: q+1
       923: 1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: q+1
       931: q+1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: q+1
       941: q+1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: q+1
       948: q+1
       949: q+1
       950: q+1
       951: q+1
       952: 1
       953: 1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: q+1
       961: q+1
       962: 1
       963: 1
       964: 1
       965: q^2+1
       966: q^2+1
       967: q+1
       969: q+1
       970: q+1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 2q+1
       976: q+1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: q+1
       985: q+1
       986: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: q+1
       995: q+1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: q+1
      1002: q+1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: 1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: q+1
      1015: q+1
      1016: q+1
      1017: 1
      1018: 1
      1019: q^2+1
      1020: q^2+1
      1021: 2q^2+2q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 1
      1028: 1
      1029: q+1
      1030: 2q+1
      1031: 2q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: 2q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: q^2+q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: 2q+1
      1048: q+1
      1049: q+1
      1050: q^2+q+1
      1051: 1
      1052: 1
      1053: 1
      1054: 2q+1
      1055: q+1
      1056: q+1
      1057: q+1
      1058: q+1
      1059: q^2+1
      1060: q^2+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: 1
      1065: q+1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1095: 1
      1096: 1
      1101: q+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1121: q+1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: q+1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: q+1
      1136: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: q+1
      1154: q+1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1173: q+1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: q+1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: q+1
      1188: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: q+1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: q+1
      1206: q+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: q+1
      1219: 1
      1220: 1
      1221: 1
      1222: q^2+1
      1223: q^2+1
      1224: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 2q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: q+1
      1242: q+1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: q+1
      1252: q+1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: q+1
      1259: q+1
      1260: q+1
      1261: q+1
      1262: q+1
      1263: 1
      1264: 1
      1265: 1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: q+1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: 1
      1285: 1
      1288: 1
      1291: 1
      1294: 1
      1300: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1339: 1
      1340: 1
      1345: q+1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1386: 1
      1387: 1
      1392: q+1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1412: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: q+1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: q+1
      1427: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: q+1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: q+1
      1445: q+1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q+1
      1457: 1
      1459: 1
      1460: 1
      1479: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1492: 1
      1493: 1
      1495: 1
      1500: 1
      1503: 1
      1506: 1
      1509: 1
      1515: 1
      1517: 1
      1518: 1
      1523: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1531: 1
      1532: 1
      1534: 1
      1539: 1
      1542: 1
      1545: 1
      1548: 1
      1554: 1
      1556: 1
      1557: 1
      1562: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1593: 1
      1594: 1
      1599: q+1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1613: 1
      1633: 1
      1635: 1
      1636: 1
      1655: 1
      1661: 1
      1663: 1
      1665: 1
      1666: 1
      1685: 1
      1691: 1
      1693: 1
      1694: 1
      1697: 1
      1698: 1
      1699: 1
      1701: 1
      1706: 1
      1709: 1
      1712: 1
      1715: 1
      1721: 1
      1723: 1
      1724: 1
      1729: 1
      1730: 1
      1746: 1
      1767: 1
      1787: 1
      1789: 1
      1790: 1
      1809: 1
      1815: 1
      1851: 1

1852:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
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       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
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       678: q+1
       681: q+1
       682: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
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       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
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       784: q+1
       785: q+1
       786: q+1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
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       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
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       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       882: q+1
       886: 1
       887: 1
       888: 1
       889: 1
       892: 1
       893: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       902: 1
       903: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       927: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       938: q+1
       939: q+1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: q+1
       992: q+1
       993: q+1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1094: 1
      1095: 1
      1098: 1
      1102: 1
      1105: 1
      1108: 1
      1109: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: q+1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1141: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1151: 1
      1152: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1161: 1
      1162: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: q+1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1249: q+1
      1250: q+1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1293: 1
      1305: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1338: 1
      1339: 1
      1342: 1
      1346: 1
      1349: 1
      1352: 1
      1353: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1396: 1
      1399: 1
      1400: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1422: q+1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1432: q+1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1452: 1
      1453: 1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1508: 1
      1520: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1547: 1
      1559: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1584: 1
      1592: 1
      1593: 1
      1596: 1
      1600: 1
      1603: 1
      1606: 1
      1607: 1
      1614: 1
      1634: 1
      1637: 1
      1638: 1
      1639: 1
      1641: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1692: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1714: 1
      1726: 1
      1747: 1
      1768: 1
      1788: 1
      1791: 1
      1792: 1
      1793: 1
      1795: 1
      1852: 1

1853:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q+1
        25: q^2+q+1
        26: q^2+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^2+1
        59: q^2+1
        60: q^2+q+1
        61: q+1
        62: q^2+q+1
        63: q^2+1
        64: q^2+q+1
        65: q+1
        66: 1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q+1
        76: q^2+q+1
        77: q^2+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q^2+q+1
        90: q^2+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q^2+q+1
       103: q+1
       104: q+1
       105: q^2+q+1
       106: q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^2+q+1
       113: q+1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: 1
       118: q+1
       119: q^2+q+1
       120: q^2+1
       121: q^2+1
       122: q^2+q+1
       123: 1
       124: q+1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: q+1
       130: 1
       131: q+1
       132: q+1
       133: q+1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q+1
       140: q+1
       141: q^2+q+1
       142: q^2+1
       143: q^2+1
       144: q^2+q+1
       145: q+1
       146: q^2+q+1
       147: q^2+1
       148: q^2+q+1
       149: q+1
       150: 1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q^2+q+1
       163: q^2+1
       164: q^2+1
       165: q^2+q+1
       166: q+1
       167: q^2+q+1
       168: q^2+1
       169: q^2+q+1
       170: q+1
       171: 1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q^2+q+1
       180: q+1
       181: q^2+q+1
       182: q^2+1
       183: q^2+q+1
       184: q^2+q+1
       185: q^2+q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q^2+q+1
       192: q+1
       193: q^2+q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q^2+1
       200: 1
       201: q^2+1
       202: q^2+1
       203: 1
       204: 1
       205: q+1
       206: q^2+q+1
       207: 1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: q+1
       221: 1
       222: 1
       223: q+1
       224: 1
       225: q+1
       227: q+1
       228: q+1
       229: q^2+q+1
       230: q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q+1
       234: q+1
       235: q+1
       236: q^2+q+1
       237: q+1
       238: q^2+1
       239: q^2+1
       240: q^2+1
       241: 1
       242: q+1
       243: q^2+q+1
       244: q^2+1
       245: q^2+1
       246: q^2+q+1
       247: 1
       248: q+1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q+1
       260: q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+q+1
       267: q+1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: q+1
       273: q^2+q+1
       274: q^2+1
       275: q^2+1
       276: q^2+q+1
       277: 1
       278: q+1
       279: 1
       280: 1
       281: q+1
       282: q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       288: q^2+q+1
       289: q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q^2+q+1
       293: q+1
       294: q+1
       295: q^2+q+1
       296: q^2+1
       297: q^2+1
       298: q^2+q+1
       299: q+1
       300: q^2+q+1
       301: q^2+1
       302: q^2+q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q^2+q+1
       313: 1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       319: q+1
       320: 1
       321: q^2+1
       322: 1
       323: q^2+1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: 1
       329: q^2+1
       330: 1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: q+1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: q+1
       360: q^2+q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q^2+1
       367: 1
       368: q^2+1
       369: q^2+1
       370: 1
       371: 1
       372: q+1
       373: q^2+q+1
       374: 1
       375: q^2+1
       376: q^2+1
       377: q^2+1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: q+1
       388: 1
       389: 1
       390: q+1
       391: 1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q+1
       399: q^2+q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q^2+1
       406: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: q+1
       412: q^2+q+1
       413: 1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q+1
       427: 1
       428: 1
       429: q+1
       430: 1
       431: q+1
       433: q+1
       434: q+1
       435: q^2+q+1
       436: q+1
       437: q^2+q+1
       438: q^2+q+1
       439: q+1
       440: q+1
       441: q+1
       442: q^2+q+1
       443: q+1
       444: q^2+1
       445: q^2+1
       446: q^2+1
       447: 1
       448: q+1
       449: q^2+q+1
       450: q^2+1
       451: q^2+1
       452: q^2+q+1
       453: 1
       454: q+1
       455: 1
       456: 1
       457: q+1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       465: q+1
       466: q+1
       467: 1
       468: q+1
       469: q+1
       470: 1
       471: q+1
       473: q+1
       474: 1
       475: 1
       476: q^2+1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q^2+1
       486: 1
       487: q^2+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q^2+q+1
       520: 1
       521: q+1
       522: q+1
       523: q+1
       524: q+1
       526: q+1
       527: 1
       528: q^2+1
       529: 1
       530: q^2+1
       531: 1
       532: 1
       533: 1
       534: q+1
       535: 1
       536: q^2+1
       537: 1
       538: q^2+1
       539: q^2+1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: q+1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: q+1
       561: q+1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: 1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       573: q+1
       574: 1
       575: q^2+1
       576: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: q+1
       582: 1
       583: q^2+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q+1
       598: q+1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: q^2+q+1
       613: q+1
       614: q^2+q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q^2+1
       621: 1
       622: q^2+1
       623: q^2+1
       624: 1
       625: 1
       626: q+1
       627: q^2+q+1
       628: 1
       629: q^2+1
       630: q^2+1
       631: q^2+1
       632: 1
       633: 1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: 1
       643: 1
       644: q+1
       645: 1
       646: q+1
       648: q+1
       650: q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q^2+1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: q+1
       705: q+1
       706: 1
       707: q+1
       708: q+1
       709: 1
       710: q+1
       712: q+1
       713: 1
       714: 1
       715: q^2+1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: q^2+1
       725: 1
       726: q^2+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       754: 1
       756: q+1
       757: q+1
       758: 1
       759: q+1
       760: q+1
       761: 1
       762: q+1
       764: q+1
       765: 1
       766: 1
       767: q^2+1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: q+1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q^2+q+1
       811: 1
       812: q+1
       813: q+1
       814: q+1
       815: q+1
       817: q+1
       818: 1
       819: q^2+1
       820: 1
       821: q^2+1
       822: 1
       823: 1
       824: 1
       825: q+1
       826: 1
       827: q^2+1
       828: 1
       829: q^2+1
       830: q^2+1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: q+1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+1
       852: q+1
       853: 1
       855: 1
       856: q+1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: q+1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: q^2+1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: q+1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: q^2+1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       987: q+1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: q+1
      1016: q+1
      1017: 1
      1018: q+1
      1019: q+1
      1020: 1
      1021: q+1
      1023: q+1
      1024: 1
      1025: 1
      1026: q^2+1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: q^2+1
      1036: 1
      1037: q^2+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1065: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1114: 1
      1115: q+1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1166: 1
      1167: q+1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: q+1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: q^2+1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: q+1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1270: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1312: 1
      1313: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1331: 1
      1333: 1
      1335: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1347: 1
      1359: 1
      1360: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1394: 1
      1405: 1
      1406: q+1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1455: 1
      1459: 1
      1463: 1
      1464: 1
      1473: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1503: 1
      1509: 1
      1511: 1
      1513: 1
      1526: 1
      1530: 1
      1531: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1542: 1
      1548: 1
      1550: 1
      1552: 1
      1566: 1
      1567: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1585: 1
      1587: 1
      1589: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1601: 1
      1615: 1
      1635: 1
      1639: 1
      1640: 1
      1649: 1
      1665: 1
      1669: 1
      1670: 1
      1679: 1
      1693: 1
      1697: 1
      1698: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1709: 1
      1715: 1
      1717: 1
      1719: 1
      1748: 1
      1769: 1
      1789: 1
      1793: 1
      1794: 1
      1803: 1
      1853: 1

1854:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q^2+2q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: 2q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+2q+1
        51: q+1
        52: q^2+2q+1
        53: 2q+1
        54: 2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: 2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: 2q+1
        62: 2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: 2q^2+2q+1
        75: q^2+2q+1
        76: 2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: q^2+2q+1
        89: 2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: q^2+2q+1
       106: q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 2q+1
       113: q+1
       114: 2q+1
       115: 2q+1
       116: q^2+2q+1
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q+1
       124: 2q+1
       125: 2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q+1
       136: q^2+2q+1
       137: 2q+1
       138: 2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       142: 2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q+1
       157: q^2+2q+1
       158: 2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: 2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q+1
       171: 2q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: 2q^2+2q+1
       180: q^2+2q+1
       181: 2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: 2q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: 2q+1
       192: q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: q+1
       199: 2q+1
       200: q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: 1
       208: 2q+1
       209: q+1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: q+1
       215: 2q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q^2+2q+1
       230: q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: q+1
       238: 2q+1
       239: 2q+1
       240: q^2+2q+1
       241: 2q+1
       242: 2q+1
       243: 2q+1
       244: 2q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q^2+2q+1
       260: q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: q+1
       268: 2q+1
       269: 2q+1
       270: q^2+2q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       279: 2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q+1
       290: q^2+2q+1
       291: 2q+1
       292: 2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: 2q+1
       297: q^2+2q+1
       298: q^2+2q+1
       299: 2q+1
       300: 2q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: 2q+1
       313: 1
       314: 2q+1
       315: q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: 2q+1
       322: q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       328: 1
       329: 2q+1
       330: 1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: 1
       346: 2q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: 2q+1
       359: q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: 2q+1
       367: q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: 2q+1
       374: 1
       375: 2q+1
       376: q+1
       377: q^2+2q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: q+1
       382: 2q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: 2q+1
       398: q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: 2q+1
       406: q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       413: 1
       414: 2q+1
       415: q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: 2q+1
       420: q+1
       421: 2q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       429: 2q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q^2+2q+1
       436: q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: q+1
       444: 2q+1
       445: 2q+1
       446: q^2+2q+1
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: q^2+2q+1
       452: q^2+2q+1
       453: q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       466: q+1
       467: 1
       468: q+1
       469: 2q+1
       470: 1
       471: q+1
       472: q+1
       474: q+1
       475: q+1
       476: 2q+1
       477: 1
       478: 2q+1
       479: q+1
       480: 2q+1
       481: 1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: 1
       502: 2q+1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       517: q+1
       518: q+1
       519: 2q+1
       520: 1
       521: 2q+1
       522: q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: 2q+1
       529: q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: 1
       536: 2q+1
       537: 1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: q+1
       544: 2q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: 1
       553: 2q+1
       554: 1
       555: 2q+1
       556: q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       564: q+1
       565: q+1
       566: 2q+1
       567: 1
       568: 2q+1
       569: q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: 2q+1
       576: q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: 1
       583: 2q+1
       584: 1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: q+1
       591: 2q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: 2q+1
       597: 2q+1
       598: 2q+1
       599: 1
       600: 2q+1
       601: 1
       602: 2q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: 2q+1
       613: q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: 2q+1
       621: q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: 2q+1
       628: 1
       629: 2q+1
       630: q+1
       631: q^2+2q+1
       632: q+1
       633: q+1
       634: 2q+1
       635: q+1
       636: 2q+1
       637: q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       656: q+1
       659: q+1
       660: 1
       661: q+1
       662: 2q+1
       663: 1
       664: 1
       665: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: 1
       675: 1
       677: q+1
       678: q+1
       679: q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: q+1
       706: 1
       707: q+1
       708: 2q+1
       709: 1
       710: q+1
       711: q+1
       713: q+1
       714: q+1
       715: 2q+1
       716: 1
       717: 2q+1
       718: q+1
       719: 2q+1
       720: 1
       721: q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: q+1
       728: q+1
       729: q+1
       730: 1
       731: q+1
       732: q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: 1
       741: 2q+1
       742: 1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       750: q+1
       751: 1
       752: q+1
       753: 1
       754: 1
       757: q+1
       758: 1
       759: q+1
       760: 2q+1
       761: 1
       762: q+1
       763: q+1
       765: q+1
       766: q+1
       767: 2q+1
       768: 1
       769: 2q+1
       770: q+1
       771: 2q+1
       772: 1
       773: q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: q+1
       784: q+1
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: 2q+1
       791: q+1
       792: 1
       793: 2q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: 1
       802: q+1
       803: 1
       804: q+1
       805: 1
       806: 1
       808: q+1
       809: q+1
       810: 2q+1
       811: 1
       812: 2q+1
       813: q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: 2q+1
       820: q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: 1
       827: 2q+1
       828: 1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       834: q+1
       835: 2q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: 2q+1
       841: 2q+1
       842: 2q+1
       843: 1
       844: 2q+1
       845: 1
       846: 2q+1
       847: q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       857: 1
       858: 1
       859: q+1
       860: 1
       863: 1
       864: q+1
       865: 1
       866: 1
       867: 1
       868: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: 1
       877: 1
       880: q+1
       882: q+1
       883: q+1
       885: 1
       886: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       913: q+1
       916: q+1
       917: 1
       918: q+1
       919: 2q+1
       920: 1
       921: 1
       922: 1
       924: 1
       925: 1
       926: q+1
       927: 1
       928: q+1
       929: 1
       930: q+1
       931: 1
       932: 1
       934: q+1
       935: q+1
       936: q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       967: q+1
       970: q+1
       971: 1
       972: q+1
       973: 2q+1
       974: 1
       975: 1
       976: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       985: 1
       986: 1
       988: q+1
       989: q+1
       990: q+1
       992: q+1
       993: q+1
       994: q+1
       995: 1
       996: q+1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: q+1
      1017: 1
      1018: q+1
      1019: 2q+1
      1020: 1
      1021: q+1
      1022: q+1
      1024: q+1
      1025: q+1
      1026: 2q+1
      1027: 1
      1028: 2q+1
      1029: q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: 1
      1042: q+1
      1043: q+1
      1044: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1051: 1
      1052: 2q+1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: 1
      1061: q+1
      1062: 1
      1063: q+1
      1064: 1
      1065: 1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1089: q+1
      1091: 1
      1093: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1116: 1
      1117: 1
      1118: q+1
      1119: 1
      1122: 1
      1123: q+1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1130: 1
      1131: 1
      1132: 1
      1133: q+1
      1134: 1
      1135: 1
      1136: 1
      1139: q+1
      1141: q+1
      1142: q+1
      1144: 1
      1145: 1
      1147: 1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1168: 1
      1169: 1
      1170: q+1
      1171: 1
      1174: 1
      1175: q+1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1187: 1
      1188: 1
      1191: q+1
      1193: q+1
      1194: q+1
      1196: 1
      1197: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1224: q+1
      1227: q+1
      1228: 1
      1229: q+1
      1230: 2q+1
      1231: 1
      1232: 1
      1233: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1239: q+1
      1240: 1
      1241: q+1
      1242: 1
      1243: 1
      1245: q+1
      1246: q+1
      1247: q+1
      1249: q+1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1273: 1
      1277: 1
      1278: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1291: 1
      1296: 1
      1298: 1
      1300: 1
      1303: 1
      1305: 1
      1306: 1
      1313: 1
      1314: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1333: q+1
      1335: 1
      1337: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: 1
      1348: 1
      1349: 1
      1350: 1
      1352: 1
      1353: 1
      1354: 1
      1356: 1
      1360: 1
      1361: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1380: q+1
      1382: 1
      1384: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1403: 1
      1407: 1
      1408: 1
      1409: q+1
      1410: 1
      1413: 1
      1414: q+1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1421: 1
      1422: 1
      1423: 1
      1424: q+1
      1425: 1
      1426: 1
      1427: 1
      1430: q+1
      1432: q+1
      1433: q+1
      1435: 1
      1436: 1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1460: 1
      1464: 1
      1465: 1
      1476: 1
      1481: 1
      1488: 1
      1492: 1
      1493: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1506: 1
      1511: 1
      1513: 1
      1515: 1
      1518: 1
      1520: 1
      1521: 1
      1527: 1
      1531: 1
      1532: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1545: 1
      1550: 1
      1552: 1
      1554: 1
      1557: 1
      1559: 1
      1560: 1
      1567: 1
      1568: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1587: q+1
      1589: 1
      1591: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1600: 1
      1602: 1
      1603: 1
      1604: 1
      1606: 1
      1607: 1
      1608: 1
      1610: 1
      1616: 1
      1636: 1
      1640: 1
      1641: 1
      1652: 1
      1657: 1
      1666: 1
      1670: 1
      1671: 1
      1682: 1
      1687: 1
      1694: 1
      1698: 1
      1699: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1712: 1
      1717: 1
      1719: 1
      1721: 1
      1724: 1
      1726: 1
      1727: 1
      1749: 1
      1770: 1
      1790: 1
      1794: 1
      1795: 1
      1806: 1
      1811: 1
      1854: 1

1855:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: 2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: 2q+1
        10: 2q+1
        11: 2q+1
        12: 2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: 2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: 2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: 2q+1
        29: 2q+1
        30: 2q+1
        31: 2q+1
        32: 2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: 2q+1
        37: 2q+1
        38: 2q+1
        39: 2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: 2q+1
        44: 2q+1
        45: 2q+1
        46: 2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: 2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: q+1
        65: 2q+1
        66: 2q+1
        67: q+1
        68: 2q+1
        69: 2q+1
        70: q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: 2q+1
        80: 2q+1
        81: 2q+1
        82: 2q+1
        83: 2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: 2q+1
        93: 2q+1
        94: 2q+1
        95: 2q+1
        96: 2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: 2q+1
       101: 2q+1
       102: 2q+1
       103: 2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: q+1
       120: 2q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: 2q+1
       126: q+1
       127: q+1
       128: q+1
       129: 2q+1
       130: 2q+1
       131: 1
       132: q+1
       133: q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: q+1
       149: 2q+1
       150: 2q+1
       151: q+1
       152: 2q+1
       153: 2q+1
       154: q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: q+1
       170: 2q+1
       171: 2q+1
       172: q+1
       173: 2q+1
       174: 2q+1
       175: q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: 2q+1
       185: 2q+1
       186: 2q+1
       187: 2q+1
       188: 2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: 2q+1
       222: 1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: 1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: 2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: 2q+1
       250: q+1
       251: q+1
       252: q+1
       253: 2q+1
       254: 2q+1
       255: 1
       256: q+1
       257: q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: q+1
       274: 2q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: 2q+1
       280: q+1
       281: q+1
       282: q+1
       283: 2q+1
       284: 2q+1
       285: 1
       286: q+1
       287: q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: q+1
       303: 2q+1
       304: 2q+1
       305: q+1
       306: 2q+1
       307: 2q+1
       308: q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: 1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: 1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: q+1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: 2q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: 2q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: 2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: 2q+1
       456: q+1
       457: q+1
       458: q+1
       459: 2q+1
       460: 2q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: 1
       474: 1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       489: q+1
       490: 1
       491: 1
       492: 1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: 2q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: q+1
       669: q+1
       670: q+1
       674: 1
       675: 1
       676: 1
       677: 1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       785: q+1
       786: q+1
       787: 1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       872: q+1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       895: 1
       896: 1
       898: 1
       899: 1
       900: 1
       901: 1
       903: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       927: q+1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       985: 1
       986: 1
       987: 1
       988: 1
       989: q+1
       990: 1
       991: 1
       992: q+1
       993: q+1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1097: 1
      1102: 1
      1105: 1
      1106: 1
      1107: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: q+1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1183: q+1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1206: 1
      1207: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1214: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1249: q+1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1304: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1349: 1
      1350: 1
      1351: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1377: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1388: 1
      1393: 1
      1396: 1
      1397: 1
      1398: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: q+1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1431: 1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1446: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1453: 1
      1458: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1519: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1558: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1584: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1595: 1
      1600: 1
      1603: 1
      1604: 1
      1605: 1
      1617: 1
      1634: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1664: 1
      1672: 1
      1673: 1
      1674: 1
      1676: 1
      1692: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1707: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1725: 1
      1750: 1
      1771: 1
      1788: 1
      1796: 1
      1797: 1
      1798: 1
      1800: 1
      1855: 1

1856:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q^2+q+1
        58: q^2+1
        59: q^2+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: 1
        64: q+1
        65: q^2+q+1
        66: q^2+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+1
        91: q^2+q+1
        92: q+1
        93: q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q+1
       109: q^2+q+1
       110: q+1
       111: q+1
       112: q+1
       113: q^2+q+1
       114: q^2+1
       115: q^2+1
       116: 1
       117: q^2+1
       118: q+1
       119: q+1
       120: 1
       121: 1
       122: q+1
       123: q+1
       124: q^2+q+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+q+1
       129: q+1
       130: 1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+1
       143: q^2+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: 1
       148: q+1
       149: q^2+q+1
       150: q^2+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q^2+q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q+1
       160: q^2+q+1
       161: q+1
       162: q^2+q+1
       163: q^2+1
       164: q^2+1
       165: q+1
       166: q^2+q+1
       167: q+1
       168: 1
       169: q+1
       170: q^2+q+1
       171: q^2+1
       172: q^2+q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q+1
       180: q^2+q+1
       181: q^2+q+1
       182: q^2+1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: q^2+q+1
       187: q^2+q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^2+q+1
       193: q+1
       194: q^2+q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: 1
       200: q^2+1
       201: q^2+1
       202: 1
       203: q^2+1
       204: 1
       205: q+1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: 1
       214: q^2+q+1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: q+1
       221: 1
       222: 1
       223: 1
       224: q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+q+1
       231: q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+q+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       248: q^2+q+1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+q+1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+q+1
       261: q^2+q+1
       262: q+1
       263: q^2+q+1
       264: q+1
       265: q+1
       266: q+1
       267: q^2+q+1
       268: q^2+1
       269: q^2+1
       270: 1
       271: q^2+1
       272: q+1
       273: q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       278: q^2+q+1
       279: q^2+1
       280: q^2+1
       281: 1
       282: q^2+q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q^2+q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q+1
       293: q^2+q+1
       294: q+1
       295: q^2+q+1
       296: q^2+1
       297: q^2+1
       298: q+1
       299: q^2+q+1
       300: q+1
       301: 1
       302: q+1
       303: q^2+q+1
       304: q^2+1
       305: q^2+q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: q^2+q+1
       316: q+1
       317: q+1
       319: q+1
       320: 1
       321: 1
       322: q^2+1
       323: 1
       324: q^2+1
       325: 1
       326: 1
       327: q+1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: 1
       337: 1
       338: q^2+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: q+1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: 1
       381: q^2+q+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: q+1
       388: 1
       389: 1
       390: 1
       391: q+1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q^2+q+1
       399: q+1
       400: q^2+q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: 1
       406: q^2+1
       407: q^2+1
       408: 1
       409: q^2+1
       410: 1
       411: q+1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: 1
       420: q^2+q+1
       421: q^2+1
       422: q^2+1
       423: 1
       424: q^2+1
       425: 1
       426: q+1
       427: 1
       428: 1
       429: 1
       430: q+1
       431: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q^2+q+1
       437: q^2+q+1
       438: q+1
       439: q^2+q+1
       440: q+1
       441: q+1
       442: q+1
       443: q^2+q+1
       444: q^2+1
       445: q^2+1
       446: 1
       447: q^2+1
       448: q+1
       449: q+1
       450: 1
       451: 1
       452: q+1
       453: q+1
       454: q^2+q+1
       455: q^2+1
       456: q^2+1
       457: 1
       458: q^2+q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       465: q+1
       466: q+1
       467: q+1
       468: 1
       469: 1
       470: q+1
       471: q+1
       473: q+1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: q^2+1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: q+1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: q^2+q+1
       523: q+1
       524: q+1
       526: q+1
       527: 1
       528: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: q+1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q+1
       543: 1
       544: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: q+1
       561: 1
       562: q+1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: q^2+q+1
       570: q+1
       571: q+1
       573: q+1
       574: 1
       575: 1
       576: q^2+1
       577: 1
       578: q^2+1
       579: 1
       580: 1
       581: q+1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       590: 1
       591: 1
       592: q^2+1
       593: q^2+1
       594: 1
       595: q^2+1
       596: 1
       597: 1
       598: 1
       599: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: q^2+q+1
       614: q+1
       615: q^2+q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: 1
       621: q^2+1
       622: q^2+1
       623: 1
       624: q^2+1
       625: 1
       626: q+1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: 1
       635: q^2+q+1
       636: q^2+1
       637: q^2+1
       638: 1
       639: q^2+1
       640: 1
       641: q+1
       642: 1
       643: 1
       644: 1
       645: q+1
       646: q+1
       648: q+1
       650: q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: q^2+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       702: 1
       704: q+1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: q+1
       710: q+1
       712: q+1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: q^2+1
       719: 1
       720: 1
       722: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: q+1
       754: 1
       756: q+1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: q+1
       762: q+1
       764: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: q^2+1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q^2+1
       787: 1
       788: q^2+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: q+1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: q^2+q+1
       814: q+1
       815: q+1
       817: q+1
       818: 1
       819: 1
       820: q^2+1
       821: 1
       822: q^2+1
       823: 1
       824: 1
       825: q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       834: 1
       835: 1
       836: q^2+1
       837: q^2+1
       838: 1
       839: q^2+1
       840: 1
       841: 1
       842: 1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: q+1
       852: 1
       853: q+1
       855: q+1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       897: 1
       905: 1
       907: q+1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: q+1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: q^2+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       959: 1
       961: q+1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: q+1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: q^2+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1013: 1
      1015: q+1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: q+1
      1021: q+1
      1023: q+1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: q^2+1
      1030: 1
      1031: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q^2+1
      1046: 1
      1047: q^2+1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1065: 1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1114: q+1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1164: 1
      1166: q+1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1216: 1
      1218: q+1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: q+1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: q^2+1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1270: 1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1299: 1
      1312: 1
      1313: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1347: 1
      1359: 1
      1360: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1375: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1394: 1
      1405: q+1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1455: 1
      1459: 1
      1468: 1
      1469: 1
      1472: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1514: 1
      1526: 1
      1530: 1
      1531: 1
      1534: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1548: 1
      1549: 1
      1553: 1
      1566: 1
      1567: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1582: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1601: 1
      1618: 1
      1635: 1
      1644: 1
      1645: 1
      1648: 1
      1665: 1
      1674: 1
      1675: 1
      1678: 1
      1693: 1
      1697: 1
      1698: 1
      1701: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1715: 1
      1716: 1
      1720: 1
      1751: 1
      1772: 1
      1789: 1
      1798: 1
      1799: 1
      1802: 1
      1856: 1

1857:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q^2+2q+1
        23: q^2+2q+1
        24: 2q^2+2q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q^2+2q+1
        55: 2q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: 2q+1
        59: q^2+2q+1
        60: 2q+1
        61: q^2+2q+1
        62: 2q+1
        63: 2q+1
        64: 2q+1
        65: 2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        75: 2q^2+2q+1
        76: 2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+2q+1
        89: 2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       104: q+1
       105: q+1
       106: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: q^2+2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+2q+1
       129: 2q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       142: 2q+1
       143: q^2+2q+1
       144: 2q+1
       145: q^2+2q+1
       146: 2q+1
       147: 2q+1
       148: 2q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: q^2+2q+1
       160: 2q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 2q+1
       164: q^2+2q+1
       165: 2q+1
       166: q^2+2q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: 2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q^2+2q+1
       179: q^2+2q+1
       180: 2q^2+2q+1
       181: 2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: 2q+1
       186: 2q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: q+1
       199: q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: 1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: 2q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: q^2+2q+1
       242: 2q+1
       243: 2q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: 2q+1
       249: 2q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: q^2+2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: 2q+1
       279: 2q+1
       280: q^2+2q+1
       281: q+1
       282: q^2+2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: 2q+1
       297: q^2+2q+1
       298: 2q+1
       299: q^2+2q+1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: 2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       310: q+1
       311: q+1
       312: q+1
       313: 2q+1
       314: 1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: 2q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: q+1
       330: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 1
       337: 1
       338: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: 2q+1
       346: 2q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: q+1
       366: q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: 1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: q+1
       391: 2q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: q+1
       405: q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: 1
       420: 2q+1
       421: 2q+1
       422: q+1
       423: q+1
       424: q^2+2q+1
       425: q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q^2+2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: q^2+2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: 2q+1
       456: q^2+2q+1
       457: q+1
       458: q^2+2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       466: q+1
       467: q+1
       468: 1
       469: 1
       470: 2q+1
       471: q+1
       472: q+1
       474: q+1
       475: q+1
       476: q+1
       477: 2q+1
       478: 1
       479: 2q+1
       480: 2q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: 1
       502: 1
       503: 2q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       511: q+1
       512: 1
       513: 1
       514: q+1
       515: 1
       517: q+1
       518: q+1
       519: q+1
       520: 2q+1
       521: 1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: 2q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: q+1
       536: q+1
       537: 2q+1
       538: q+1
       539: q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: 1
       544: 1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: 1
       552: 2q+1
       553: 2q+1
       554: 1
       555: q+1
       556: 2q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       564: q+1
       565: q+1
       566: q+1
       567: 2q+1
       568: 1
       569: 2q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: q+1
       576: 2q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: q+1
       583: q+1
       584: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: 1
       591: 1
       592: 2q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: 1
       599: 2q+1
       600: 2q+1
       601: 1
       602: q+1
       603: 2q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: q+1
       620: q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: q+1
       628: 2q+1
       629: 2q+1
       630: q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: 1
       635: 2q+1
       636: 2q+1
       637: q+1
       638: q+1
       639: q^2+2q+1
       640: q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: q+1
       645: 2q+1
       646: q+1
       647: q+1
       648: q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       656: q+1
       659: q+1
       660: q+1
       661: 1
       662: 1
       663: 2q+1
       664: 1
       665: 1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: 2q+1
       710: q+1
       711: q+1
       713: q+1
       714: q+1
       715: q+1
       716: 2q+1
       717: 1
       718: 2q+1
       719: 2q+1
       720: 1
       721: q+1
       722: q+1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       740: 1
       741: 1
       742: 2q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: q+1
       750: q+1
       751: 1
       752: 1
       753: q+1
       754: 1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: 2q+1
       762: q+1
       763: q+1
       765: q+1
       766: q+1
       767: q+1
       768: 2q+1
       769: 1
       770: 2q+1
       771: 2q+1
       772: 1
       773: q+1
       774: q+1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: q+1
       791: 1
       792: 1
       793: 1
       794: 2q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       802: q+1
       803: 1
       804: 1
       805: q+1
       806: 1
       808: q+1
       809: q+1
       810: q+1
       811: 2q+1
       812: 1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: 2q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: q+1
       827: q+1
       828: 2q+1
       829: q+1
       830: q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       834: 1
       835: 1
       836: 2q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       842: 1
       843: 2q+1
       844: 2q+1
       845: 1
       846: q+1
       847: 2q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       857: 1
       858: 1
       859: 1
       860: q+1
       863: q+1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       871: q+1
       872: q+1
       875: q+1
       876: 1
       877: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: 1
       886: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       913: q+1
       916: q+1
       917: q+1
       918: 1
       919: 1
       920: 2q+1
       921: 1
       922: 1
       924: q+1
       925: q+1
       926: q+1
       927: q+1
       929: q+1
       930: q+1
       931: 1
       932: q+1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q+1
       940: q+1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       967: q+1
       970: q+1
       971: q+1
       972: 1
       973: 1
       974: 2q+1
       975: 1
       976: 1
       978: q+1
       979: q+1
       980: q+1
       981: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       988: 1
       989: 1
       990: 1
       991: q+1
       992: 1
       993: q+1
       994: q+1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: 2q+1
      1021: q+1
      1022: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 2q+1
      1028: 1
      1029: 2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: q+1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: q+1
      1050: 1
      1051: 1
      1052: 1
      1053: 2q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: 1
      1060: q+1
      1061: q+1
      1062: 1
      1063: 1
      1064: q+1
      1065: 1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1080: q+1
      1084: 1
      1085: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1116: 1
      1117: 1
      1118: 1
      1119: q+1
      1122: q+1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1130: q+1
      1131: q+1
      1134: q+1
      1135: 1
      1136: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1144: 1
      1145: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1168: 1
      1169: 1
      1170: 1
      1171: q+1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1182: q+1
      1183: q+1
      1186: q+1
      1187: 1
      1188: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: q+1
      1196: 1
      1197: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1224: q+1
      1227: q+1
      1228: q+1
      1229: 1
      1230: 1
      1231: 2q+1
      1232: 1
      1233: 1
      1235: q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: q+1
      1245: 1
      1246: 1
      1247: 1
      1248: q+1
      1249: 1
      1250: q+1
      1251: q+1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1273: 1
      1277: 1
      1278: 1
      1285: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1295: 1
      1299: 1
      1300: 1
      1303: 1
      1304: 1
      1307: 1
      1313: 1
      1314: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1324: q+1
      1328: 1
      1329: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1356: 1
      1360: 1
      1361: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1371: q+1
      1375: 1
      1376: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: 1
      1401: 1
      1403: 1
      1407: 1
      1408: 1
      1409: 1
      1410: q+1
      1413: q+1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1421: q+1
      1422: q+1
      1425: q+1
      1426: 1
      1427: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: q+1
      1435: 1
      1436: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1460: 1
      1469: 1
      1470: 1
      1477: 1
      1480: 1
      1488: 1
      1492: 1
      1493: 1
      1500: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1510: 1
      1514: 1
      1515: 1
      1518: 1
      1519: 1
      1522: 1
      1527: 1
      1531: 1
      1532: 1
      1539: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1549: 1
      1553: 1
      1554: 1
      1557: 1
      1558: 1
      1561: 1
      1567: 1
      1568: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1578: q+1
      1582: 1
      1583: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1600: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: 1
      1608: 1
      1610: 1
      1619: 1
      1636: 1
      1645: 1
      1646: 1
      1653: 1
      1656: 1
      1666: 1
      1675: 1
      1676: 1
      1683: 1
      1686: 1
      1694: 1
      1698: 1
      1699: 1
      1706: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1716: 1
      1720: 1
      1721: 1
      1724: 1
      1725: 1
      1728: 1
      1752: 1
      1773: 1
      1790: 1
      1799: 1
      1800: 1
      1807: 1
      1810: 1
      1857: 1

1858:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: 2q^3+4q^2+3q+1
        10: 3q^2+3q+1
        11: q^3+3q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 2q^3+4q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: q^3+4q^2+3q+1
        18: 2q^3+4q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^2+2q+1
        24: q^3+4q^2+3q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: q^3+3q^2+3q+1
        29: 2q^2+3q+1
        30: 2q^3+4q^2+3q+1
        31: 3q^2+3q+1
        32: q^3+3q^2+3q+1
        33: q^3+4q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 2q^3+4q^2+3q+1
        37: 3q^2+3q+1
        38: q^3+3q^2+3q+1
        39: 2q^3+4q^2+3q+1
        40: q^3+4q^2+3q+1
        41: q^3+4q^2+3q+1
        42: q^3+4q^2+3q+1
        43: 2q^3+4q^2+3q+1
        44: 3q^2+3q+1
        45: q^3+3q^2+3q+1
        46: 2q^3+4q^2+3q+1
        47: 2q^3+4q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 2q^3+4q^2+3q+1
        50: q^2+2q+1
        51: q^3+4q^2+3q+1
        52: q^3+4q^2+3q+1
        53: 2q^2+3q+1
        54: q^2+2q+1
        55: q^3+4q^2+3q+1
        56: q^2+2q+1
        57: 3q^2+3q+1
        58: 3q^2+3q+1
        59: 3q^2+3q+1
        60: 2q+1
        61: 3q^2+3q+1
        62: 2q^2+3q+1
        63: 2q^2+3q+1
        64: 2q^2+3q+1
        65: 3q^2+3q+1
        66: 3q^2+3q+1
        67: 3q^2+3q+1
        68: q^3+3q^2+3q+1
        69: 2q^2+3q+1
        70: q^3+3q^2+3q+1
        71: q^3+4q^2+3q+1
        72: q^3+4q^2+3q+1
        73: q^3+4q^2+3q+1
        74: q^2+2q+1
        75: q^3+4q^2+3q+1
        76: 3q^2+3q+1
        77: 3q^2+3q+1
        78: 3q^2+3q+1
        79: q^3+3q^2+3q+1
        80: 2q^2+3q+1
        81: 2q^3+4q^2+3q+1
        82: 3q^2+3q+1
        83: q^3+3q^2+3q+1
        84: q^3+4q^2+3q+1
        85: q^3+4q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^2+2q+1
        88: q^3+4q^2+3q+1
        89: 3q^2+3q+1
        90: 3q^2+3q+1
        91: 3q^2+3q+1
        92: q^3+3q^2+3q+1
        93: 2q^2+3q+1
        94: 2q^3+4q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+3q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: q^3+4q^2+3q+1
       100: 2q^3+4q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+3q^2+3q+1
       103: 2q^3+4q^2+3q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^3+4q^2+3q+1
       107: 2q^2+3q+1
       108: 2q+1
       109: 2q^2+3q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 2q+1
       113: 3q^2+3q+1
       114: 3q^2+3q+1
       115: 2q^2+3q+1
       116: 2q+1
       117: 3q^2+3q+1
       118: 2q+1
       119: 2q^2+3q+1
       120: 2q^2+3q+1
       121: 2q^2+3q+1
       122: 2q+1
       123: 2q^2+3q+1
       124: 3q^2+3q+1
       125: 3q^2+3q+1
       126: 3q^2+3q+1
       127: q+1
       128: 3q^2+3q+1
       129: 2q^2+3q+1
       130: 2q^2+3q+1
       131: 2q^2+3q+1
       132: q^3+3q^2+3q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^3+4q^2+3q+1
       136: q^3+4q^2+3q+1
       137: 2q^2+3q+1
       138: q^2+2q+1
       139: q^3+4q^2+3q+1
       140: q^2+2q+1
       141: 3q^2+3q+1
       142: 3q^2+3q+1
       143: 3q^2+3q+1
       144: 2q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 2q^2+3q+1
       148: 2q^2+3q+1
       149: 3q^2+3q+1
       150: 3q^2+3q+1
       151: 3q^2+3q+1
       152: q^3+3q^2+3q+1
       153: 2q^2+3q+1
       154: q^3+3q^2+3q+1
       155: q^2+2q+1
       156: q^3+4q^2+3q+1
       157: q^3+4q^2+3q+1
       158: 2q^2+3q+1
       159: q^2+2q+1
       160: q^3+4q^2+3q+1
       161: q^2+2q+1
       162: 3q^2+3q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: 2q+1
       166: 3q^2+3q+1
       167: 2q^2+3q+1
       168: 2q^2+3q+1
       169: 2q^2+3q+1
       170: 3q^2+3q+1
       171: 3q^2+3q+1
       172: 3q^2+3q+1
       173: q^3+3q^2+3q+1
       174: 2q^2+3q+1
       175: q^3+3q^2+3q+1
       176: q^3+4q^2+3q+1
       177: q^3+4q^2+3q+1
       178: q^3+4q^2+3q+1
       179: q^2+2q+1
       180: q^3+4q^2+3q+1
       181: 3q^2+3q+1
       182: 3q^2+3q+1
       183: 3q^2+3q+1
       184: q^3+3q^2+3q+1
       185: 2q^2+3q+1
       186: 2q^3+4q^2+3q+1
       187: 3q^2+3q+1
       188: q^3+3q^2+3q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: 2q+1
       192: 2q^2+3q+1
       193: 2q+1
       194: 2q^2+3q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 3q^2+3q+1
       201: 2q^2+3q+1
       202: 2q+1
       203: 2q^2+3q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: 2q^2+3q+1
       208: 2q^2+3q+1
       209: q^2+2q+1
       210: 2q+1
       211: 2q^2+3q+1
       212: 2q+1
       213: q+1
       214: 3q^2+3q+1
       215: 3q^2+3q+1
       216: q^2+2q+1
       217: q+1
       218: 3q^2+3q+1
       219: q+1
       220: 2q^2+3q+1
       221: 2q^2+3q+1
       222: 2q^2+3q+1
       223: q+1
       224: 2q^2+3q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^3+4q^2+3q+1
       231: 2q^2+3q+1
       232: 2q+1
       233: 2q^2+3q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: 3q^2+3q+1
       238: 3q^2+3q+1
       239: 2q^2+3q+1
       240: 2q+1
       241: 3q^2+3q+1
       242: 2q+1
       243: 2q^2+3q+1
       244: 2q^2+3q+1
       245: 2q^2+3q+1
       246: 2q+1
       247: 2q^2+3q+1
       248: 3q^2+3q+1
       249: 3q^2+3q+1
       250: 3q^2+3q+1
       251: q+1
       252: 3q^2+3q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+3q^2+3q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^3+4q^2+3q+1
       261: 2q^2+3q+1
       262: 2q+1
       263: 2q^2+3q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: 3q^2+3q+1
       268: 3q^2+3q+1
       269: 2q^2+3q+1
       270: 2q+1
       271: 3q^2+3q+1
       272: 2q+1
       273: 2q^2+3q+1
       274: 2q^2+3q+1
       275: 2q^2+3q+1
       276: 2q+1
       277: 2q^2+3q+1
       278: 3q^2+3q+1
       279: 3q^2+3q+1
       280: 3q^2+3q+1
       281: q+1
       282: 3q^2+3q+1
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: 2q^2+3q+1
       286: q^3+3q^2+3q+1
       287: q^2+2q+1
       288: q^2+2q+1
       289: q^3+4q^2+3q+1
       290: q^3+4q^2+3q+1
       291: 2q^2+3q+1
       292: q^2+2q+1
       293: q^3+4q^2+3q+1
       294: q^2+2q+1
       295: 3q^2+3q+1
       296: 3q^2+3q+1
       297: 3q^2+3q+1
       298: 2q+1
       299: 3q^2+3q+1
       300: 2q^2+3q+1
       301: 2q^2+3q+1
       302: 2q^2+3q+1
       303: 3q^2+3q+1
       304: 3q^2+3q+1
       305: 3q^2+3q+1
       306: q^3+3q^2+3q+1
       307: 2q^2+3q+1
       308: q^3+3q^2+3q+1
       309: q+1
       310: q^2+2q+1
       311: 2q+1
       312: 2q+1
       313: 2q+1
       315: 2q^2+3q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q^2+3q+1
       323: 2q+1
       324: 2q^2+3q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: 2q^2+3q+1
       331: q^2+2q+1
       332: q+1
       333: q^2+2q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: 3q^2+3q+1
       339: q^2+2q+1
       340: q+1
       341: q^2+2q+1
       342: q+1
       343: q+1
       344: q+1
       345: 2q^2+3q+1
       346: 2q^2+3q+1
       347: q+1
       348: q+1
       349: 2q^2+3q+1
       350: q+1
       351: q^2+2q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: 1
       355: q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q+1
       359: 2q^2+3q+1
       360: 2q+1
       361: 2q^2+3q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 3q^2+3q+1
       368: 2q^2+3q+1
       369: 2q+1
       370: 2q^2+3q+1
       371: 2q+1
       372: 2q+1
       373: 2q+1
       374: 2q^2+3q+1
       375: 2q^2+3q+1
       376: q^2+2q+1
       377: 2q+1
       378: 2q^2+3q+1
       379: 2q+1
       380: q+1
       381: 3q^2+3q+1
       382: 3q^2+3q+1
       383: q^2+2q+1
       384: q+1
       385: 3q^2+3q+1
       386: q+1
       387: 2q^2+3q+1
       388: 2q^2+3q+1
       389: 2q^2+3q+1
       390: q+1
       391: 2q^2+3q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q^2+2q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q+1
       398: 2q^2+3q+1
       399: 2q+1
       400: 2q^2+3q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 3q^2+3q+1
       407: 2q^2+3q+1
       408: 2q+1
       409: 2q^2+3q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       413: 2q^2+3q+1
       414: 2q^2+3q+1
       415: q^2+2q+1
       416: 2q+1
       417: 2q^2+3q+1
       418: 2q+1
       419: q+1
       420: 3q^2+3q+1
       421: 3q^2+3q+1
       422: q^2+2q+1
       423: q+1
       424: 3q^2+3q+1
       425: q+1
       426: 2q^2+3q+1
       427: 2q^2+3q+1
       428: 2q^2+3q+1
       429: q+1
       430: 2q^2+3q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q^2+2q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^3+4q^2+3q+1
       437: 2q^2+3q+1
       438: 2q+1
       439: 2q^2+3q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: 3q^2+3q+1
       444: 3q^2+3q+1
       445: 2q^2+3q+1
       446: 2q+1
       447: 3q^2+3q+1
       448: 2q+1
       449: 2q^2+3q+1
       450: 2q^2+3q+1
       451: 2q^2+3q+1
       452: 2q+1
       453: 2q^2+3q+1
       454: 3q^2+3q+1
       455: 3q^2+3q+1
       456: 3q^2+3q+1
       457: q+1
       458: 3q^2+3q+1
       459: 2q^2+3q+1
       460: 2q^2+3q+1
       461: 2q^2+3q+1
       462: q^3+3q^2+3q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: 2q+1
       467: 2q+1
       470: 2q+1
       471: q+1
       472: q+1
       473: q+1
       474: 2q+1
       475: 2q+1
       476: 2q+1
       477: 2q+1
       479: 2q^2+3q+1
       480: 2q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q^2+2q+1
       487: q+1
       488: q^2+2q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: q+1
       493: q+1
       494: q+1
       495: q^2+2q+1
       496: q+1
       497: q^2+2q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: 2q^2+3q+1
       504: q+1
       505: 1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: q^2+2q+1
       511: q^2+2q+1
       512: q+1
       513: 1
       514: q^2+2q+1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: 2q+1
       522: 2q^2+3q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: 2q+1
       529: 2q^2+3q+1
       530: 2q+1
       531: 2q^2+3q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q^2+3q+1
       538: q^2+2q+1
       539: q+1
       540: q^2+2q+1
       541: 2q+1
       542: 2q+1
       543: q+1
       544: q+1
       545: 3q^2+3q+1
       546: q^2+2q+1
       547: q+1
       548: q^2+2q+1
       549: q+1
       550: q+1
       551: q+1
       552: 2q^2+3q+1
       553: 2q^2+3q+1
       554: q+1
       555: q+1
       556: 2q^2+3q+1
       557: q+1
       558: q^2+2q+1
       559: q^2+2q+1
       560: q^2+2q+1
       561: 1
       562: q^2+2q+1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       569: 2q^2+3q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: 2q^2+3q+1
       577: 2q+1
       578: 2q^2+3q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: 2q+1
       583: 2q+1
       584: 2q^2+3q+1
       585: q^2+2q+1
       586: q+1
       587: q^2+2q+1
       588: 2q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: 3q^2+3q+1
       593: q^2+2q+1
       594: q+1
       595: q^2+2q+1
       596: q+1
       597: q+1
       598: q+1
       599: 2q^2+3q+1
       600: 2q^2+3q+1
       601: q+1
       602: q+1
       603: 2q^2+3q+1
       604: q+1
       605: q^2+2q+1
       606: q^2+2q+1
       607: q^2+2q+1
       608: 1
       609: q^2+2q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: 2q+1
       613: 2q^2+3q+1
       614: 2q+1
       615: 2q^2+3q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 3q^2+3q+1
       622: 2q^2+3q+1
       623: 2q+1
       624: 2q^2+3q+1
       625: 2q+1
       626: 2q+1
       627: 2q+1
       628: 2q^2+3q+1
       629: 2q^2+3q+1
       630: q^2+2q+1
       631: 2q+1
       632: 2q^2+3q+1
       633: 2q+1
       634: q+1
       635: 3q^2+3q+1
       636: 3q^2+3q+1
       637: q^2+2q+1
       638: q+1
       639: 3q^2+3q+1
       640: q+1
       641: 2q^2+3q+1
       642: 2q^2+3q+1
       643: 2q^2+3q+1
       644: q+1
       645: 2q^2+3q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q^2+2q+1
       649: q+1
       650: q+1
       651: 2q+1
       655: q+1
       656: q+1
       657: q+1
       658: 1
       659: 2q+1
       660: 2q+1
       663: 2q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: q+1
       669: q+1
       670: q+1
       672: q^2+2q+1
       673: q+1
       674: 1
       675: q+1
       676: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       682: q^2+2q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: q^2+2q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: 2q+1
       706: 2q+1
       709: 2q+1
       710: q+1
       711: q+1
       712: q+1
       713: 2q+1
       714: 2q+1
       715: 2q+1
       716: 2q+1
       718: 2q^2+3q+1
       719: 2q+1
       720: 1
       721: q+1
       722: 2q+1
       723: 2q+1
       724: q+1
       725: q^2+2q+1
       726: q+1
       727: q^2+2q+1
       728: q+1
       729: 2q+1
       730: q+1
       731: q+1
       732: q+1
       733: q+1
       734: q^2+2q+1
       735: q+1
       736: q^2+2q+1
       737: q+1
       738: q+1
       739: 1
       740: q+1
       741: q+1
       742: 2q^2+3q+1
       743: q+1
       744: 1
       745: q+1
       746: q+1
       747: q+1
       748: 1
       749: q^2+2q+1
       750: q^2+2q+1
       751: q+1
       752: 1
       753: q^2+2q+1
       754: 1
       755: q+1
       756: q+1
       757: 2q+1
       758: 2q+1
       761: 2q+1
       762: q+1
       763: q+1
       764: q+1
       765: 2q+1
       766: 2q+1
       767: 2q+1
       768: 2q+1
       770: 2q^2+3q+1
       771: 2q+1
       772: 1
       773: q+1
       774: 2q+1
       775: 2q+1
       776: q+1
       777: q^2+2q+1
       778: q+1
       779: q^2+2q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: q+1
       784: q+1
       785: q+1
       786: q^2+2q+1
       787: q+1
       788: q^2+2q+1
       789: q+1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: 2q^2+3q+1
       795: q+1
       796: 1
       797: q+1
       798: q+1
       799: q+1
       800: 1
       801: q^2+2q+1
       802: q^2+2q+1
       803: q+1
       804: 1
       805: q^2+2q+1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: 2q+1
       811: 2q+1
       813: 2q^2+3q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: 2q+1
       818: 2q+1
       819: 2q+1
       820: 2q^2+3q+1
       821: 2q+1
       822: 2q^2+3q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: 2q+1
       827: 2q+1
       828: 2q^2+3q+1
       829: q^2+2q+1
       830: q+1
       831: q^2+2q+1
       832: 2q+1
       833: 2q+1
       834: q+1
       835: q+1
       836: 3q^2+3q+1
       837: q^2+2q+1
       838: q+1
       839: q^2+2q+1
       840: q+1
       841: q+1
       842: q+1
       843: 2q^2+3q+1
       844: 2q^2+3q+1
       845: q+1
       846: q+1
       847: 2q^2+3q+1
       848: q+1
       849: q^2+2q+1
       850: q^2+2q+1
       851: q^2+2q+1
       852: 1
       853: q^2+2q+1
       854: q+1
       855: q+1
       860: q+1
       861: 1
       862: 1
       863: 2q+1
       867: 1
       868: 1
       869: q+1
       870: 1
       871: q+1
       872: q+1
       875: q+1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       881: q+1
       884: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       902: q+1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: 2q+1
       912: q+1
       913: q+1
       914: q+1
       915: 1
       916: 2q+1
       917: 2q+1
       920: 2q+1
       921: 1
       922: 1
       923: q+1
       924: 2q+1
       925: q+1
       926: q+1
       927: q+1
       929: q^2+2q+1
       930: q+1
       931: 1
       932: q+1
       933: 1
       934: q+1
       935: q+1
       936: q+1
       937: q+1
       939: q^2+2q+1
       940: q+1
       941: 1
       942: 1
       943: q+1
       944: q+1
       945: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: q^2+2q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: 2q+1
       966: q+1
       967: q+1
       968: q+1
       969: 1
       970: 2q+1
       971: 2q+1
       974: 2q+1
       975: 1
       976: 1
       977: q+1
       978: 2q+1
       979: q+1
       980: q+1
       981: q+1
       983: q^2+2q+1
       984: q+1
       985: 1
       986: q+1
       987: 1
       988: q+1
       989: q+1
       990: q+1
       991: q+1
       993: q^2+2q+1
       994: q+1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: q+1
      1001: 1
      1002: q+1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: q^2+2q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 2q+1
      1017: 2q+1
      1020: 2q+1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: 2q+1
      1025: 2q+1
      1026: 2q+1
      1027: 2q+1
      1029: 2q^2+3q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: 2q+1
      1034: 2q+1
      1035: q+1
      1036: q^2+2q+1
      1037: q+1
      1038: q^2+2q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1042: q+1
      1043: q+1
      1044: q+1
      1045: q^2+2q+1
      1046: q+1
      1047: q^2+2q+1
      1048: q+1
      1049: q+1
      1050: 1
      1051: q+1
      1052: q+1
      1053: 2q^2+3q+1
      1054: q+1
      1055: 1
      1056: q+1
      1057: q+1
      1058: q+1
      1059: 1
      1060: q^2+2q+1
      1061: q^2+2q+1
      1062: q+1
      1063: 1
      1064: q^2+2q+1
      1065: 1
      1066: q+1
      1071: 1
      1072: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: q+1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1112: 1
      1113: q+1
      1114: q+1
      1119: q+1
      1120: 1
      1121: 1
      1122: 2q+1
      1126: 1
      1127: 1
      1128: q+1
      1129: 1
      1130: q+1
      1131: q+1
      1134: q+1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: q+1
      1140: q+1
      1143: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1152: q+1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1161: q+1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: q+1
      1171: q+1
      1172: 1
      1173: 1
      1174: 2q+1
      1178: 1
      1179: 1
      1180: q+1
      1181: 1
      1182: q+1
      1183: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: q+1
      1192: q+1
      1195: q+1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1204: q+1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1213: q+1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1219: 2q+1
      1223: q+1
      1224: q+1
      1225: q+1
      1226: 1
      1227: 2q+1
      1228: 2q+1
      1231: 2q+1
      1232: 1
      1233: 1
      1234: q+1
      1235: 2q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1240: q^2+2q+1
      1241: q+1
      1242: 1
      1243: q+1
      1244: 1
      1245: q+1
      1246: q+1
      1247: q+1
      1248: q+1
      1250: q^2+2q+1
      1251: q+1
      1252: 1
      1253: 1
      1254: q+1
      1255: q+1
      1256: 1
      1257: q+1
      1258: 1
      1259: q+1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: 1
      1265: q^2+2q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1270: 1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1307: 1
      1310: q+1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1323: 1
      1324: q+1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: q+1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: q+1
      1354: 1
      1356: 1
      1357: q+1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1379: q+1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1403: 1
      1404: q+1
      1405: q+1
      1410: q+1
      1411: 1
      1412: 1
      1413: 2q+1
      1417: 1
      1418: 1
      1419: q+1
      1420: 1
      1421: q+1
      1422: q+1
      1425: q+1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1430: q+1
      1431: q+1
      1434: q+1
      1435: 1
      1436: 1
      1437: 1
      1438: q+1
      1439: 1
      1440: 1
      1441: 1
      1443: q+1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1452: q+1
      1453: 1
      1454: 1
      1455: 1
      1461: 1
      1466: 1
      1471: 1
      1472: 1
      1477: 1
      1480: 1
      1489: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1502: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1518: 1
      1519: 1
      1522: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1541: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1553: 1
      1554: 1
      1555: 1
      1557: 1
      1558: 1
      1561: 1
      1564: q+1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1577: 1
      1578: q+1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1586: q+1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: q+1
      1608: 1
      1610: 1
      1620: 1
      1637: 1
      1642: 1
      1647: 1
      1648: 1
      1653: 1
      1656: 1
      1667: 1
      1672: 1
      1677: 1
      1678: 1
      1683: 1
      1686: 1
      1695: 1
      1700: 1
      1701: 1
      1706: 1
      1707: 1
      1708: 1
      1713: 1
      1714: 1
      1715: 1
      1716: 1
      1720: 1
      1721: 1
      1722: 1
      1724: 1
      1725: 1
      1728: 1
      1753: 1
      1774: 1
      1791: 1
      1796: 1
      1801: 1
      1802: 1
      1807: 1
      1810: 1
      1858: 1

1859:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: q^3+4q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: q^3+4q^2+3q+1
         7: q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: 2q^3+4q^2+3q+1
        10: 3q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: q^3+3q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: q^3+4q^2+3q+1
        15: 2q^3+4q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: q^3+4q^2+3q+1
        18: 2q^3+4q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: q^3+4q^2+3q+1
        21: q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^2+2q+1
        25: 3q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: 2q^3+4q^2+3q+1
        29: 3q^2+3q+1
        30: q^3+3q^2+3q+1
        31: 2q^2+3q+1
        32: q^3+3q^2+3q+1
        33: q^3+4q^2+3q+1
        34: q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: 2q^3+4q^2+3q+1
        37: 3q^2+3q+1
        38: 2q^3+4q^2+3q+1
        39: q^3+3q^2+3q+1
        40: q^3+4q^2+3q+1
        41: q^3+4q^2+3q+1
        42: q^3+4q^2+3q+1
        43: 2q^3+4q^2+3q+1
        44: 3q^2+3q+1
        45: 2q^3+4q^2+3q+1
        46: q^3+3q^2+3q+1
        47: 2q^3+4q^2+3q+1
        48: q^3+4q^2+3q+1
        49: 2q^3+4q^2+3q+1
        50: q^3+4q^2+3q+1
        51: q^2+2q+1
        52: q^3+4q^2+3q+1
        53: 2q^2+3q+1
        54: q^3+4q^2+3q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 3q^2+3q+1
        58: 3q^2+3q+1
        59: 3q^2+3q+1
        60: 3q^2+3q+1
        61: 2q+1
        62: 3q^2+3q+1
        63: 3q^2+3q+1
        64: 3q^2+3q+1
        65: 2q^2+3q+1
        66: 2q^2+3q+1
        67: 2q^2+3q+1
        68: q^3+3q^2+3q+1
        69: 2q^2+3q+1
        70: q^3+3q^2+3q+1
        71: q^3+4q^2+3q+1
        72: q^3+4q^2+3q+1
        73: q^3+4q^2+3q+1
        74: q^3+4q^2+3q+1
        75: q^2+2q+1
        76: 3q^2+3q+1
        77: 3q^2+3q+1
        78: 3q^2+3q+1
        79: 2q^3+4q^2+3q+1
        80: 3q^2+3q+1
        81: q^3+3q^2+3q+1
        82: 2q^2+3q+1
        83: q^3+3q^2+3q+1
        84: q^3+4q^2+3q+1
        85: q^3+4q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: q^2+2q+1
        89: 3q^2+3q+1
        90: 3q^2+3q+1
        91: 3q^2+3q+1
        92: 2q^3+4q^2+3q+1
        93: 3q^2+3q+1
        94: q^3+3q^2+3q+1
        95: 2q^2+3q+1
        96: q^3+3q^2+3q+1
        97: q^3+4q^2+3q+1
        98: q^3+4q^2+3q+1
        99: q^3+4q^2+3q+1
       100: 2q^3+4q^2+3q+1
       101: 3q^2+3q+1
       102: 2q^3+4q^2+3q+1
       103: q^3+3q^2+3q+1
       104: q^2+2q+1
       105: q^3+4q^2+3q+1
       106: q^2+2q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 3q^2+3q+1
       113: 2q+1
       114: 3q^2+3q+1
       115: 2q^2+3q+1
       116: 3q^2+3q+1
       117: 2q+1
       118: 2q+1
       119: 3q^2+3q+1
       120: 3q^2+3q+1
       121: 3q^2+3q+1
       122: 3q^2+3q+1
       123: q+1
       124: 2q^2+3q+1
       125: 2q^2+3q+1
       126: 2q^2+3q+1
       127: 2q^2+3q+1
       128: 2q+1
       129: 2q^2+3q+1
       130: 2q^2+3q+1
       131: 2q^2+3q+1
       132: q^3+3q^2+3q+1
       133: q^2+2q+1
       134: q^3+4q^2+3q+1
       135: q^2+2q+1
       136: q^3+4q^2+3q+1
       137: 2q^2+3q+1
       138: q^3+4q^2+3q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 3q^2+3q+1
       142: 3q^2+3q+1
       143: 3q^2+3q+1
       144: 3q^2+3q+1
       145: 2q+1
       146: 3q^2+3q+1
       147: 3q^2+3q+1
       148: 3q^2+3q+1
       149: 2q^2+3q+1
       150: 2q^2+3q+1
       151: 2q^2+3q+1
       152: q^3+3q^2+3q+1
       153: 2q^2+3q+1
       154: q^3+3q^2+3q+1
       155: q^3+4q^2+3q+1
       156: q^2+2q+1
       157: q^3+4q^2+3q+1
       158: 2q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 3q^2+3q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: 3q^2+3q+1
       166: 2q+1
       167: 3q^2+3q+1
       168: 3q^2+3q+1
       169: 3q^2+3q+1
       170: 2q^2+3q+1
       171: 2q^2+3q+1
       172: 2q^2+3q+1
       173: q^3+3q^2+3q+1
       174: 2q^2+3q+1
       175: q^3+3q^2+3q+1
       176: q^3+4q^2+3q+1
       177: q^3+4q^2+3q+1
       178: q^3+4q^2+3q+1
       179: q^3+4q^2+3q+1
       180: q^2+2q+1
       181: 3q^2+3q+1
       182: 3q^2+3q+1
       183: 3q^2+3q+1
       184: 2q^3+4q^2+3q+1
       185: 3q^2+3q+1
       186: q^3+3q^2+3q+1
       187: 2q^2+3q+1
       188: q^3+3q^2+3q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: 2q^2+3q+1
       192: 2q+1
       193: 2q^2+3q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: 3q^2+3q+1
       200: 2q+1
       201: 2q^2+3q+1
       202: 2q^2+3q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 3q^2+3q+1
       207: q+1
       208: 3q^2+3q+1
       209: q^2+2q+1
       210: 3q^2+3q+1
       211: q+1
       212: q+1
       213: 2q^2+3q+1
       214: 2q+1
       215: 2q^2+3q+1
       216: q^2+2q+1
       217: 2q^2+3q+1
       218: 2q+1
       219: 2q+1
       220: 2q^2+3q+1
       221: 2q^2+3q+1
       222: 2q^2+3q+1
       223: 2q^2+3q+1
       224: q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q^3+4q^2+3q+1
       230: q^2+2q+1
       231: 2q^2+3q+1
       232: 2q^2+3q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 3q^2+3q+1
       237: 2q+1
       238: 3q^2+3q+1
       239: 2q^2+3q+1
       240: 3q^2+3q+1
       241: 2q+1
       242: 2q+1
       243: 3q^2+3q+1
       244: 3q^2+3q+1
       245: 3q^2+3q+1
       246: 3q^2+3q+1
       247: q+1
       248: 2q^2+3q+1
       249: 2q^2+3q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q+1
       253: 2q^2+3q+1
       254: 2q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+3q^2+3q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^3+4q^2+3q+1
       260: q^2+2q+1
       261: 2q^2+3q+1
       262: 2q^2+3q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 3q^2+3q+1
       267: 2q+1
       268: 3q^2+3q+1
       269: 2q^2+3q+1
       270: 3q^2+3q+1
       271: 2q+1
       272: 2q+1
       273: 3q^2+3q+1
       274: 3q^2+3q+1
       275: 3q^2+3q+1
       276: 3q^2+3q+1
       277: q+1
       278: 2q^2+3q+1
       279: 2q^2+3q+1
       280: 2q^2+3q+1
       281: 2q^2+3q+1
       282: 2q+1
       283: 2q^2+3q+1
       284: 2q^2+3q+1
       285: 2q^2+3q+1
       286: q^3+3q^2+3q+1
       287: q^2+2q+1
       288: q^3+4q^2+3q+1
       289: q^2+2q+1
       290: q^3+4q^2+3q+1
       291: 2q^2+3q+1
       292: q^3+4q^2+3q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 3q^2+3q+1
       296: 3q^2+3q+1
       297: 3q^2+3q+1
       298: 3q^2+3q+1
       299: 2q+1
       300: 3q^2+3q+1
       301: 3q^2+3q+1
       302: 3q^2+3q+1
       303: 2q^2+3q+1
       304: 2q^2+3q+1
       305: 2q^2+3q+1
       306: q^3+3q^2+3q+1
       307: 2q^2+3q+1
       308: q^3+3q^2+3q+1
       309: q+1
       310: q^2+2q+1
       311: 2q+1
       312: 2q^2+3q+1
       314: 2q+1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: 2q^2+3q+1
       322: 2q+1
       323: 2q^2+3q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: 3q^2+3q+1
       330: q+1
       331: q^2+2q+1
       332: q^2+2q+1
       333: q+1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q^2+3q+1
       338: 2q+1
       339: q^2+2q+1
       340: q^2+2q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q^2+3q+1
       345: q+1
       346: 2q^2+3q+1
       347: q+1
       348: 2q^2+3q+1
       349: q+1
       350: q+1
       351: q^2+2q+1
       352: q^2+2q+1
       353: q^2+2q+1
       354: q^2+2q+1
       355: 1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q^2+3q+1
       359: 2q+1
       360: 2q^2+3q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 3q^2+3q+1
       367: 2q+1
       368: 2q^2+3q+1
       369: 2q^2+3q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: 3q^2+3q+1
       374: q+1
       375: 3q^2+3q+1
       376: q^2+2q+1
       377: 3q^2+3q+1
       378: q+1
       379: q+1
       380: 2q^2+3q+1
       381: 2q+1
       382: 2q^2+3q+1
       383: q^2+2q+1
       384: 2q^2+3q+1
       385: 2q+1
       386: 2q+1
       387: 2q^2+3q+1
       388: 2q^2+3q+1
       389: 2q^2+3q+1
       390: 2q^2+3q+1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q^2+2q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q^2+3q+1
       398: 2q+1
       399: 2q^2+3q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 3q^2+3q+1
       406: 2q+1
       407: 2q^2+3q+1
       408: 2q^2+3q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: 3q^2+3q+1
       413: q+1
       414: 3q^2+3q+1
       415: q^2+2q+1
       416: 3q^2+3q+1
       417: q+1
       418: q+1
       419: 2q^2+3q+1
       420: 2q+1
       421: 2q^2+3q+1
       422: q^2+2q+1
       423: 2q^2+3q+1
       424: 2q+1
       425: 2q+1
       426: 2q^2+3q+1
       427: 2q^2+3q+1
       428: 2q^2+3q+1
       429: 2q^2+3q+1
       430: q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q^2+2q+1
       434: q^2+2q+1
       435: q^3+4q^2+3q+1
       436: q^2+2q+1
       437: 2q^2+3q+1
       438: 2q^2+3q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 3q^2+3q+1
       443: 2q+1
       444: 3q^2+3q+1
       445: 2q^2+3q+1
       446: 3q^2+3q+1
       447: 2q+1
       448: 2q+1
       449: 3q^2+3q+1
       450: 3q^2+3q+1
       451: 3q^2+3q+1
       452: 3q^2+3q+1
       453: q+1
       454: 2q^2+3q+1
       455: 2q^2+3q+1
       456: 2q^2+3q+1
       457: 2q^2+3q+1
       458: 2q+1
       459: 2q^2+3q+1
       460: 2q^2+3q+1
       461: 2q^2+3q+1
       462: q^3+3q^2+3q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: 2q+1
       468: 2q+1
       469: 2q+1
       471: q+1
       472: q+1
       473: q+1
       474: 2q+1
       475: 2q+1
       476: 2q^2+3q+1
       478: 2q+1
       479: 2q+1
       480: 2q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: q^2+2q+1
       486: q+1
       487: q^2+2q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: 2q+1
       493: 2q+1
       494: q^2+2q+1
       495: q+1
       496: q^2+2q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: 2q^2+3q+1
       503: q+1
       504: q+1
       505: q+1
       506: 1
       507: q+1
       508: q+1
       509: q^2+2q+1
       510: 1
       511: q^2+2q+1
       512: q+1
       513: q^2+2q+1
       514: 1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: 2q^2+3q+1
       521: 2q+1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: 2q^2+3q+1
       529: 2q+1
       530: 2q^2+3q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: q+1
       536: 3q^2+3q+1
       537: q+1
       538: q^2+2q+1
       539: q^2+2q+1
       540: q+1
       541: q+1
       542: q+1
       543: 2q+1
       544: 2q^2+3q+1
       545: 2q+1
       546: q^2+2q+1
       547: q^2+2q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: 2q^2+3q+1
       552: q+1
       553: 2q^2+3q+1
       554: q+1
       555: 2q^2+3q+1
       556: q+1
       557: q+1
       558: q^2+2q+1
       559: q^2+2q+1
       560: q^2+2q+1
       561: q^2+2q+1
       562: 1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: 2q^2+3q+1
       568: 2q+1
       569: 2q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q^2+3q+1
       576: 2q+1
       577: 2q^2+3q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: q+1
       583: 3q^2+3q+1
       584: q+1
       585: q^2+2q+1
       586: q^2+2q+1
       587: q+1
       588: q+1
       589: q+1
       590: 2q+1
       591: 2q^2+3q+1
       592: 2q+1
       593: q^2+2q+1
       594: q^2+2q+1
       595: q+1
       596: 2q+1
       597: 2q+1
       598: 2q^2+3q+1
       599: q+1
       600: 2q^2+3q+1
       601: q+1
       602: 2q^2+3q+1
       603: q+1
       604: q+1
       605: q^2+2q+1
       606: q^2+2q+1
       607: q^2+2q+1
       608: q^2+2q+1
       609: 1
       610: q^2+2q+1
       611: q^2+2q+1
       612: 2q^2+3q+1
       613: 2q+1
       614: 2q^2+3q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 3q^2+3q+1
       621: 2q+1
       622: 2q^2+3q+1
       623: 2q^2+3q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: 3q^2+3q+1
       628: q+1
       629: 3q^2+3q+1
       630: q^2+2q+1
       631: 3q^2+3q+1
       632: q+1
       633: q+1
       634: 2q^2+3q+1
       635: 2q+1
       636: 2q^2+3q+1
       637: q^2+2q+1
       638: 2q^2+3q+1
       639: 2q+1
       640: 2q+1
       641: 2q^2+3q+1
       642: 2q^2+3q+1
       643: 2q^2+3q+1
       644: 2q^2+3q+1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q^2+2q+1
       649: q+1
       650: q+1
       652: 2q+1
       654: q+1
       656: q+1
       657: q+1
       658: 1
       659: 2q+1
       661: 2q+1
       662: 2q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q^2+2q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q^2+2q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q^2+2q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: 2q+1
       707: 2q+1
       708: 2q+1
       710: q+1
       711: q+1
       712: q+1
       713: 2q+1
       714: 2q+1
       715: 2q^2+3q+1
       717: 2q+1
       718: 2q+1
       719: 2q+1
       720: 1
       721: q+1
       722: q+1
       723: q+1
       724: q^2+2q+1
       725: q+1
       726: q^2+2q+1
       727: q+1
       728: q+1
       729: q+1
       730: 1
       731: 2q+1
       732: 2q+1
       733: q^2+2q+1
       734: q+1
       735: q^2+2q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: q+1
       741: 2q^2+3q+1
       742: q+1
       743: q+1
       744: q+1
       745: 1
       746: q+1
       747: q+1
       748: q^2+2q+1
       749: 1
       750: q^2+2q+1
       751: q+1
       752: q^2+2q+1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 2q+1
       759: 2q+1
       760: 2q+1
       762: q+1
       763: q+1
       764: q+1
       765: 2q+1
       766: 2q+1
       767: 2q^2+3q+1
       769: 2q+1
       770: 2q+1
       771: 2q+1
       772: 1
       773: q+1
       774: q+1
       775: q+1
       776: q^2+2q+1
       777: q+1
       778: q^2+2q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: 2q+1
       784: 2q+1
       785: q^2+2q+1
       786: q+1
       787: q^2+2q+1
       788: q+1
       789: q+1
       790: 2q+1
       791: q+1
       792: q+1
       793: 2q^2+3q+1
       794: q+1
       795: q+1
       796: q+1
       797: 1
       798: q+1
       799: q+1
       800: q^2+2q+1
       801: 1
       802: q^2+2q+1
       803: q+1
       804: q^2+2q+1
       805: 1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: 2q^2+3q+1
       812: 2q+1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: 2q+1
       818: 2q+1
       819: 2q^2+3q+1
       820: 2q+1
       821: 2q^2+3q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: q+1
       827: 3q^2+3q+1
       828: q+1
       829: q^2+2q+1
       830: q^2+2q+1
       831: q+1
       832: q+1
       833: q+1
       834: 2q+1
       835: 2q^2+3q+1
       836: 2q+1
       837: q^2+2q+1
       838: q^2+2q+1
       839: q+1
       840: 2q+1
       841: 2q+1
       842: 2q^2+3q+1
       843: q+1
       844: 2q^2+3q+1
       845: q+1
       846: 2q^2+3q+1
       847: q+1
       848: q+1
       849: q^2+2q+1
       850: q^2+2q+1
       851: q^2+2q+1
       852: q^2+2q+1
       853: 1
       854: q+1
       856: q+1
       859: q+1
       861: 1
       862: 1
       864: 2q+1
       866: 1
       868: 1
       869: 1
       870: 1
       871: q+1
       873: q+1
       874: q+1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: q+1
       882: q+1
       883: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       909: 2q+1
       911: q+1
       913: q+1
       914: q+1
       915: 1
       916: 2q+1
       918: 2q+1
       919: 2q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: q+1
       926: q^2+2q+1
       928: q+1
       929: q+1
       930: q+1
       931: 1
       932: 1
       933: q+1
       934: 2q+1
       935: q+1
       936: q^2+2q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: q+1
       946: 1
       947: q+1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q^2+2q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       963: 2q+1
       965: q+1
       967: q+1
       968: q+1
       969: 1
       970: 2q+1
       972: 2q+1
       973: 2q+1
       975: 1
       976: 1
       977: 1
       978: q+1
       979: q+1
       980: q^2+2q+1
       982: q+1
       983: q+1
       984: q+1
       985: 1
       986: 1
       987: q+1
       988: 2q+1
       989: q+1
       990: q^2+2q+1
       992: q+1
       993: q+1
       994: q+1
       995: 1
       996: q+1
       997: q+1
       998: q+1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: q^2+2q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 2q+1
      1018: 2q+1
      1019: 2q+1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: 2q+1
      1025: 2q+1
      1026: 2q^2+3q+1
      1028: 2q+1
      1029: 2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: q+1
      1034: q+1
      1035: q^2+2q+1
      1036: q+1
      1037: q^2+2q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: 1
      1042: 2q+1
      1043: 2q+1
      1044: q^2+2q+1
      1045: q+1
      1046: q^2+2q+1
      1047: q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1051: q+1
      1052: 2q^2+3q+1
      1053: q+1
      1054: q+1
      1055: q+1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q^2+2q+1
      1060: 1
      1061: q^2+2q+1
      1062: q+1
      1063: q^2+2q+1
      1064: 1
      1065: 1
      1067: q+1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: q+1
      1083: 1
      1085: 1
      1086: 1
      1087: 1
      1089: q+1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: q+1
      1115: q+1
      1118: q+1
      1120: 1
      1121: 1
      1123: 2q+1
      1125: 1
      1127: 1
      1128: 1
      1129: 1
      1130: q+1
      1132: q+1
      1133: q+1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: q+1
      1141: q+1
      1142: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1167: q+1
      1170: q+1
      1172: 1
      1173: 1
      1175: 2q+1
      1177: 1
      1179: 1
      1180: 1
      1181: 1
      1182: q+1
      1184: q+1
      1185: q+1
      1187: 1
      1188: 1
      1189: q+1
      1190: 1
      1191: q+1
      1193: q+1
      1194: q+1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1212: q+1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1220: 2q+1
      1222: q+1
      1224: q+1
      1225: q+1
      1226: 1
      1227: 2q+1
      1229: 2q+1
      1230: 2q+1
      1232: 1
      1233: 1
      1234: 1
      1235: q+1
      1236: q+1
      1237: q^2+2q+1
      1239: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: 1
      1244: q+1
      1245: 2q+1
      1246: q+1
      1247: q^2+2q+1
      1249: q+1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: q+1
      1255: q+1
      1256: q+1
      1257: 1
      1258: q+1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: q^2+2q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1270: 1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1303: 1
      1305: 1
      1306: 1
      1311: q+1
      1315: 1
      1317: 1
      1320: 1
      1322: 1
      1323: 1
      1325: q+1
      1327: 1
      1329: 1
      1330: 1
      1331: 1
      1333: q+1
      1335: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1356: 1
      1358: q+1
      1362: 1
      1364: 1
      1367: 1
      1369: 1
      1370: 1
      1372: q+1
      1374: 1
      1376: 1
      1377: 1
      1378: 1
      1380: q+1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: q+1
      1399: 1
      1400: 1
      1401: 1
      1403: 1
      1404: q+1
      1406: q+1
      1409: q+1
      1411: 1
      1412: 1
      1414: 2q+1
      1416: 1
      1418: 1
      1419: 1
      1420: 1
      1421: q+1
      1423: q+1
      1424: q+1
      1426: 1
      1427: 1
      1428: q+1
      1429: 1
      1430: q+1
      1432: q+1
      1433: q+1
      1435: 1
      1436: 1
      1437: 1
      1438: q+1
      1439: 1
      1440: q+1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: q+1
      1450: 1
      1451: q+1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1462: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1481: 1
      1490: 1
      1494: 1
      1496: 1
      1499: 1
      1501: 1
      1503: 1
      1506: 1
      1508: 1
      1509: 1
      1511: 1
      1513: 1
      1515: 1
      1516: 1
      1518: 1
      1520: 1
      1521: 1
      1529: 1
      1533: 1
      1535: 1
      1538: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1557: 1
      1559: 1
      1560: 1
      1565: q+1
      1569: 1
      1571: 1
      1574: 1
      1576: 1
      1577: 1
      1579: q+1
      1581: 1
      1583: 1
      1584: 1
      1585: 1
      1587: q+1
      1589: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: q+1
      1606: 1
      1607: 1
      1608: 1
      1610: 1
      1621: 1
      1638: 1
      1643: 1
      1647: 1
      1649: 1
      1652: 1
      1657: 1
      1668: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1687: 1
      1696: 1
      1700: 1
      1702: 1
      1705: 1
      1707: 1
      1709: 1
      1712: 1
      1714: 1
      1715: 1
      1717: 1
      1719: 1
      1721: 1
      1722: 1
      1724: 1
      1726: 1
      1727: 1
      1754: 1
      1775: 1
      1792: 1
      1797: 1
      1801: 1
      1803: 1
      1806: 1
      1811: 1
      1859: 1

1860:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: 2q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: q^3+3q^2+3q+1
         8: 3q^2+3q+1
         9: q^3+4q^2+3q+1
        10: q^3+4q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: 2q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: q^3+4q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: 3q^2+3q+1
        21: q^3+3q^2+3q+1
        22: 2q^2+3q+1
        23: 3q^2+3q+1
        24: 3q^2+3q+1
        25: q^3+4q^2+3q+1
        26: q^2+2q+1
        27: 3q^2+3q+1
        28: q^3+4q^2+3q+1
        29: q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: q^3+4q^2+3q+1
        32: q^3+4q^2+3q+1
        33: 2q^3+4q^2+3q+1
        34: q^3+3q^2+3q+1
        35: 3q^2+3q+1
        36: q^3+4q^2+3q+1
        37: q^3+4q^2+3q+1
        38: q^3+4q^2+3q+1
        39: q^3+4q^2+3q+1
        40: 2q^3+4q^2+3q+1
        41: q^3+3q^2+3q+1
        42: 3q^2+3q+1
        43: q^3+4q^2+3q+1
        44: q^3+4q^2+3q+1
        45: q^3+4q^2+3q+1
        46: q^3+4q^2+3q+1
        47: 2q^3+4q^2+3q+1
        48: 2q^3+4q^2+3q+1
        49: q^3+4q^2+3q+1
        50: 3q^2+3q+1
        51: 3q^2+3q+1
        52: 2q^2+3q+1
        53: 2q^2+3q+1
        54: 2q^2+3q+1
        55: 2q^2+3q+1
        56: 3q^2+3q+1
        57: 3q^2+3q+1
        58: q^2+2q+1
        59: 2q+1
        60: 3q^2+3q+1
        61: 3q^2+3q+1
        62: q^3+4q^2+3q+1
        63: q^2+2q+1
        64: 2q^2+3q+1
        65: q^3+4q^2+3q+1
        66: q^2+2q+1
        67: 2q^2+3q+1
        68: q^3+4q^2+3q+1
        69: q^3+4q^2+3q+1
        70: q^3+3q^2+3q+1
        71: 3q^2+3q+1
        72: q^3+3q^2+3q+1
        73: 2q^2+3q+1
        74: 3q^2+3q+1
        75: 3q^2+3q+1
        76: q^3+4q^2+3q+1
        77: q^2+2q+1
        78: 3q^2+3q+1
        79: q^3+4q^2+3q+1
        80: q^3+4q^2+3q+1
        81: q^3+4q^2+3q+1
        82: q^3+4q^2+3q+1
        83: q^3+4q^2+3q+1
        84: 3q^2+3q+1
        85: q^3+3q^2+3q+1
        86: 2q^2+3q+1
        87: 3q^2+3q+1
        88: 3q^2+3q+1
        89: q^3+4q^2+3q+1
        90: q^2+2q+1
        91: 3q^2+3q+1
        92: q^3+4q^2+3q+1
        93: q^3+4q^2+3q+1
        94: q^3+4q^2+3q+1
        95: q^3+4q^2+3q+1
        96: q^3+4q^2+3q+1
        97: 2q^3+4q^2+3q+1
        98: q^3+3q^2+3q+1
        99: 3q^2+3q+1
       100: q^3+4q^2+3q+1
       101: q^3+4q^2+3q+1
       102: q^3+4q^2+3q+1
       103: q^3+4q^2+3q+1
       104: 3q^2+3q+1
       105: 2q^2+3q+1
       106: 2q^2+3q+1
       107: 2q^2+3q+1
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: 2q^2+3q+1
       111: q^2+2q+1
       112: 3q^2+3q+1
       113: 3q^2+3q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 3q^2+3q+1
       119: 2q^2+3q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q^2+3q+1
       123: 2q^2+3q+1
       124: 2q^2+3q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q^2+3q+1
       128: 2q^2+3q+1
       129: q^3+4q^2+3q+1
       130: q^2+2q+1
       131: q^2+3q+1
       132: q^3+3q^2+3q+1
       133: q^3+3q^2+3q+1
       134: 3q^2+3q+1
       135: 3q^2+3q+1
       136: 2q^2+3q+1
       137: 2q^2+3q+1
       138: 2q^2+3q+1
       139: 2q^2+3q+1
       140: 3q^2+3q+1
       141: 3q^2+3q+1
       142: q^2+2q+1
       143: 2q+1
       144: 3q^2+3q+1
       145: 3q^2+3q+1
       146: q^3+4q^2+3q+1
       147: q^2+2q+1
       148: 2q^2+3q+1
       149: q^3+4q^2+3q+1
       150: q^2+2q+1
       151: 2q^2+3q+1
       152: q^3+4q^2+3q+1
       153: q^3+4q^2+3q+1
       154: q^3+3q^2+3q+1
       155: 3q^2+3q+1
       156: 3q^2+3q+1
       157: 2q^2+3q+1
       158: 2q^2+3q+1
       159: 2q^2+3q+1
       160: 2q^2+3q+1
       161: 3q^2+3q+1
       162: 3q^2+3q+1
       163: q^2+2q+1
       164: 2q+1
       165: 3q^2+3q+1
       166: 3q^2+3q+1
       167: q^3+4q^2+3q+1
       168: q^2+2q+1
       169: 2q^2+3q+1
       170: q^3+4q^2+3q+1
       171: q^2+2q+1
       172: 2q^2+3q+1
       173: q^3+4q^2+3q+1
       174: q^3+4q^2+3q+1
       175: q^3+3q^2+3q+1
       176: 3q^2+3q+1
       177: q^3+3q^2+3q+1
       178: 2q^2+3q+1
       179: 3q^2+3q+1
       180: 3q^2+3q+1
       181: q^3+4q^2+3q+1
       182: q^2+2q+1
       183: 3q^2+3q+1
       184: q^3+4q^2+3q+1
       185: q^3+4q^2+3q+1
       186: q^3+4q^2+3q+1
       187: q^3+4q^2+3q+1
       188: q^3+4q^2+3q+1
       189: q^2+2q+1
       190: 2q^2+3q+1
       191: 2q^2+3q+1
       192: 2q^2+3q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: 2q^2+3q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: 3q^2+3q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 2q^2+3q+1
       207: 2q^2+3q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q^2+3q+1
       213: 2q^2+3q+1
       214: 2q^2+3q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: 2q^2+3q+1
       220: q^2+3q+1
       221: q^2+2q+1
       222: 2q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: q^3+3q^2+3q+1
       227: q^2+3q+1
       228: 3q^2+3q+1
       229: 2q^2+3q+1
       230: 2q^2+3q+1
       231: 2q^2+3q+1
       232: 2q^2+3q+1
       233: 2q^2+3q+1
       234: 2q^2+3q+1
       235: q^2+2q+1
       236: 3q^2+3q+1
       237: 3q^2+3q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 3q^2+3q+1
       243: 2q^2+3q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q^2+3q+1
       247: 2q^2+3q+1
       248: 2q^2+3q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: q^3+4q^2+3q+1
       254: q^2+2q+1
       255: q^2+3q+1
       256: q^3+3q^2+3q+1
       257: q^3+3q^2+3q+1
       258: 3q^2+3q+1
       259: 2q^2+3q+1
       260: 2q^2+3q+1
       261: 2q^2+3q+1
       262: 2q^2+3q+1
       263: 2q^2+3q+1
       264: 2q^2+3q+1
       265: q^2+2q+1
       266: 3q^2+3q+1
       267: 3q^2+3q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 3q^2+3q+1
       273: 2q^2+3q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q^2+3q+1
       277: 2q^2+3q+1
       278: 2q^2+3q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q^2+3q+1
       282: 2q^2+3q+1
       283: q^3+4q^2+3q+1
       284: q^2+2q+1
       285: q^2+3q+1
       286: q^3+3q^2+3q+1
       287: q^3+3q^2+3q+1
       288: 3q^2+3q+1
       289: 3q^2+3q+1
       290: 2q^2+3q+1
       291: 2q^2+3q+1
       292: 2q^2+3q+1
       293: 2q^2+3q+1
       294: 3q^2+3q+1
       295: 3q^2+3q+1
       296: q^2+2q+1
       297: 2q+1
       298: 3q^2+3q+1
       299: 3q^2+3q+1
       300: q^3+4q^2+3q+1
       301: q^2+2q+1
       302: 2q^2+3q+1
       303: q^3+4q^2+3q+1
       304: q^2+2q+1
       305: 2q^2+3q+1
       306: q^3+4q^2+3q+1
       307: q^3+4q^2+3q+1
       308: q^3+3q^2+3q+1
       309: q^2+2q+1
       310: q^2+2q+1
       311: 2q^2+3q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: q+1
       317: q^2+2q+1
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: 2q+1
       328: 2q^2+3q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: 2q+1
       336: 2q^2+3q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: 2q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: q^2+3q+1
       351: q^2+3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^2+2q+1
       357: 2q^2+3q+1
       358: 2q^2+3q+1
       359: 2q^2+3q+1
       360: q^2+2q+1
       361: q^2+2q+1
       362: 2q^2+3q+1
       363: q^2+2q+1
       364: q^2+2q+1
       365: 3q^2+3q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: 2q^2+3q+1
       374: 2q^2+3q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q^2+3q+1
       380: 2q^2+3q+1
       381: 2q^2+3q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: 2q^2+3q+1
       387: q^2+3q+1
       388: q^2+2q+1
       389: 2q+1
       390: q^2+3q+1
       391: q^2+3q+1
       392: q^3+3q^2+3q+1
       394: q^2+3q+1
       395: q^2+2q+1
       396: 2q^2+3q+1
       397: 2q^2+3q+1
       398: 2q^2+3q+1
       399: q^2+2q+1
       400: q^2+2q+1
       401: 2q^2+3q+1
       402: q^2+2q+1
       403: q^2+2q+1
       404: 3q^2+3q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: 2q^2+3q+1
       413: 2q^2+3q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: 2q^2+3q+1
       419: 2q^2+3q+1
       420: 2q^2+3q+1
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q^2+3q+1
       426: q^2+3q+1
       427: q^2+2q+1
       428: 2q+1
       429: q^2+3q+1
       430: q^2+3q+1
       431: q^3+3q^2+3q+1
       433: q^2+3q+1
       434: 3q^2+3q+1
       435: 2q^2+3q+1
       436: 2q^2+3q+1
       437: 2q^2+3q+1
       438: 2q^2+3q+1
       439: 2q^2+3q+1
       440: 2q^2+3q+1
       441: q^2+2q+1
       442: 3q^2+3q+1
       443: 3q^2+3q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 3q^2+3q+1
       449: 2q^2+3q+1
       450: q^2+2q+1
       451: 2q+1
       452: 2q^2+3q+1
       453: 2q^2+3q+1
       454: 2q^2+3q+1
       455: q^2+2q+1
       456: 2q+1
       457: 2q^2+3q+1
       458: 2q^2+3q+1
       459: q^3+4q^2+3q+1
       460: q^2+2q+1
       461: q^2+3q+1
       462: q^3+3q^2+3q+1
       463: q^3+3q^2+3q+1
       465: q^2+2q+1
       466: q+1
       467: q^2+2q+1
       468: q^2+2q+1
       469: q+1
       470: q+1
       471: q+1
       473: 2q+1
       474: q+1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       483: 2q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: 2q+1
       492: 2q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: 2q+1
       501: q^2+3q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: 2q+1
       509: q^2+3q+1
       510: q^2+3q+1
       515: q^2+3q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: 2q^2+3q+1
       519: q^2+2q+1
       520: q^2+2q+1
       521: q^2+2q+1
       522: q^2+2q+1
       523: q+1
       524: q^2+2q+1
       526: 2q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: q+1
       534: 2q+1
       535: 2q^2+3q+1
       536: 2q+1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: 2q+1
       543: 2q^2+3q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: 2q+1
       551: q^2+3q+1
       552: q^2+3q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: q^2+3q+1
       558: q^2+3q+1
       561: q^2+3q+1
       562: q^2+3q+1
       563: q^2+2q+1
       564: q^2+2q+1
       565: 2q^2+3q+1
       566: q^2+2q+1
       567: q^2+2q+1
       568: q^2+2q+1
       569: q^2+2q+1
       570: q+1
       571: q^2+2q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: q+1
       581: 2q+1
       582: 2q^2+3q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: 2q+1
       590: 2q^2+3q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: 2q+1
       598: q^2+3q+1
       599: q^2+3q+1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: q^2+3q+1
       605: q^2+3q+1
       608: q^2+3q+1
       609: q^2+3q+1
       610: q^2+2q+1
       611: 2q^2+3q+1
       612: 2q^2+3q+1
       613: 2q^2+3q+1
       614: q^2+2q+1
       615: q^2+2q+1
       616: 2q^2+3q+1
       617: q^2+2q+1
       618: q^2+2q+1
       619: 3q^2+3q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: 2q^2+3q+1
       628: 2q^2+3q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: 2q+1
       633: 2q^2+3q+1
       634: 2q^2+3q+1
       635: 2q^2+3q+1
       636: 2q+1
       637: 2q+1
       638: 2q+1
       639: 2q+1
       640: 2q^2+3q+1
       641: q^2+3q+1
       642: q^2+2q+1
       643: 2q+1
       644: q^2+3q+1
       645: q^2+3q+1
       646: q^3+3q^2+3q+1
       648: q^2+3q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       658: q+1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: 2q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       676: 2q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       686: 2q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: 2q+1
       695: q^2+3q+1
       702: q+1
       704: q^2+2q+1
       705: q+1
       706: q^2+2q+1
       707: q^2+2q+1
       708: q+1
       709: q+1
       710: q+1
       712: 2q+1
       713: q+1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       722: 2q+1
       723: 2q+1
       724: 2q+1
       725: 2q+1
       726: q+1
       727: q+1
       728: 2q+1
       729: q+1
       730: 2q+1
       731: 2q+1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: q+1
       739: 2q+1
       740: q^2+3q+1
       741: 2q+1
       742: 2q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: 2q+1
       748: q^2+3q+1
       749: q^2+3q+1
       754: q^2+3q+1
       756: q^2+2q+1
       757: q+1
       758: q^2+2q+1
       759: q^2+2q+1
       760: q+1
       761: q+1
       762: q+1
       764: 2q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       772: q+1
       774: 2q+1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: q+1
       782: 2q+1
       783: 2q+1
       784: 2q+1
       785: 2q+1
       786: 2q+1
       787: q+1
       788: q+1
       789: 2q+1
       790: q+1
       791: 2q+1
       792: q^2+3q+1
       793: 2q+1
       794: 2q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: 2q+1
       800: q^2+3q+1
       801: q^2+3q+1
       806: q^2+3q+1
       807: q^2+2q+1
       808: q^2+2q+1
       809: 2q^2+3q+1
       810: q^2+2q+1
       811: q^2+2q+1
       812: q^2+2q+1
       813: q^2+2q+1
       814: q+1
       815: q^2+2q+1
       817: 2q+1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: q+1
       825: 2q+1
       826: 2q^2+3q+1
       827: 2q+1
       828: 2q+1
       829: 2q+1
       830: 2q+1
       831: 2q+1
       832: 2q+1
       833: 2q+1
       834: 2q^2+3q+1
       835: 2q+1
       836: 2q+1
       837: 2q+1
       838: 2q+1
       839: 2q+1
       840: 2q+1
       841: 2q+1
       842: q^2+3q+1
       843: q^2+3q+1
       844: 2q+1
       845: 2q+1
       846: 2q+1
       847: 2q+1
       848: q^2+3q+1
       849: q^2+3q+1
       852: q^2+3q+1
       853: q^2+3q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: 2q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       897: q+1
       905: q+1
       907: q+1
       908: q+1
       909: q+1
       910: q+1
       911: q+1
       912: q+1
       915: q+1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       921: 1
       923: 2q+1
       924: q+1
       925: 2q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: 1
       931: q+1
       933: 2q+1
       934: q+1
       935: 2q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       943: 2q+1
       944: 2q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: q+1
       951: 2q+1
       952: q^2+3q+1
       959: q+1
       961: q+1
       962: q+1
       963: q+1
       964: q+1
       965: q+1
       966: q+1
       969: q+1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       977: 2q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: 1
       985: q+1
       987: 2q+1
       988: q+1
       989: 2q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: 1
       995: q+1
       997: 2q+1
       998: 2q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: q+1
      1005: 2q+1
      1006: q^2+3q+1
      1013: q+1
      1015: q^2+2q+1
      1016: q+1
      1017: q^2+2q+1
      1018: q^2+2q+1
      1019: q+1
      1020: q+1
      1021: q+1
      1023: 2q+1
      1024: q+1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: q+1
      1033: 2q+1
      1034: 2q+1
      1035: 2q+1
      1036: 2q+1
      1037: q+1
      1038: q+1
      1039: 2q+1
      1040: q+1
      1041: 2q+1
      1042: 2q+1
      1043: 2q+1
      1044: 2q+1
      1045: 2q+1
      1046: q+1
      1047: q+1
      1048: 2q+1
      1049: q+1
      1050: 2q+1
      1051: q^2+3q+1
      1052: 2q+1
      1053: 2q+1
      1054: 2q+1
      1055: 2q+1
      1056: 2q+1
      1057: 2q+1
      1058: 2q+1
      1059: q^2+3q+1
      1060: q^2+3q+1
      1065: q^2+3q+1
      1068: q+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1103: q+1
      1114: q+1
      1115: q+1
      1116: q+1
      1117: q+1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: q+1
      1130: 1
      1131: q+1
      1132: q+1
      1133: 1
      1134: 1
      1135: 1
      1138: q+1
      1139: 1
      1140: q+1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1146: 2q+1
      1147: q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1156: q+1
      1164: q+1
      1166: q+1
      1167: q+1
      1168: q+1
      1169: q+1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: q+1
      1182: 1
      1183: q+1
      1184: q+1
      1185: 1
      1186: 1
      1187: 1
      1190: q+1
      1191: 1
      1192: q+1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1198: 2q+1
      1199: q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1203: q+1
      1204: q+1
      1205: 1
      1206: q+1
      1208: q+1
      1216: q+1
      1218: q+1
      1219: q+1
      1220: q+1
      1221: q+1
      1222: q+1
      1223: q+1
      1226: q+1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1234: 2q+1
      1235: q+1
      1236: 2q+1
      1237: q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: 1
      1242: q+1
      1244: 2q+1
      1245: q+1
      1246: 2q+1
      1247: q+1
      1248: q+1
      1249: q+1
      1250: q+1
      1251: 1
      1252: q+1
      1254: 2q+1
      1255: 2q+1
      1256: 2q+1
      1257: 2q+1
      1258: q+1
      1259: q+1
      1260: 2q+1
      1261: q+1
      1262: 2q+1
      1263: q^2+3q+1
      1270: q+1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1312: q+1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: q+1
      1340: 1
      1341: q+1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1347: q+1
      1359: q+1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: q+1
      1387: 1
      1388: q+1
      1389: q+1
      1390: 1
      1391: 1
      1392: 1
      1394: q+1
      1405: q+1
      1406: q+1
      1407: q+1
      1408: q+1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: q+1
      1421: 1
      1422: q+1
      1423: q+1
      1424: 1
      1425: 1
      1426: 1
      1429: q+1
      1430: 1
      1431: q+1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1437: 2q+1
      1438: q+1
      1439: 2q+1
      1440: q+1
      1441: q+1
      1442: q+1
      1443: q+1
      1444: 1
      1445: q+1
      1447: q+1
      1455: q+1
      1463: 1
      1468: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1491: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1530: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1566: q+1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1593: q+1
      1594: 1
      1595: q+1
      1596: q+1
      1597: 1
      1598: 1
      1599: 1
      1601: q+1
      1622: 1
      1639: 1
      1644: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1669: 1
      1674: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1697: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1755: 1
      1776: 1
      1793: 1
      1798: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1860: 1

1861:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q^3+q^2+q+1
         6: q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^2+q+1
        11: q^3+q^2+q+1
        12: q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^3+q^2+q+1
        17: q^3+q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+q^2+q+1
        20: q+1
        21: q+1
        22: q^3+q^2+q+1
        23: q^3+q^2+q+1
        24: q^3+q^2+q+1
        25: q+1
        26: q^2+1
        27: q^2+q+1
        28: q^3+q^2+q+1
        29: q^2+q+1
        30: q^3+q^2+q+1
        31: q^2+q+1
        32: q^3+q^2+q+1
        33: q+1
        34: q^3+q^2+q+1
        35: q^3+q^2+q+1
        36: q^3+q^2+q+1
        37: q^2+q+1
        38: q^3+q^2+q+1
        39: q^3+q^2+q+1
        40: q+1
        41: q^3+q^2+q+1
        42: q^3+q^2+q+1
        43: q^3+q^2+q+1
        44: q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+q^2+q+1
        50: q+1
        51: q+1
        52: q+1
        53: q+1
        54: q^3+q^2+q+1
        55: q^3+q^2+q+1
        56: q^3+q^2+q+1
        57: q+1
        58: 1
        59: q^2+1
        60: q^2+q+1
        61: q^2+q+1
        62: q+1
        63: q^2+1
        64: q^2+q+1
        65: q+1
        66: q^2+1
        67: q^2+q+1
        68: q^3+q^2+q+1
        69: q^2+q+1
        70: q^3+q^2+q+1
        71: q+1
        72: q+1
        73: q^3+q^2+q+1
        74: q^3+q^2+q+1
        75: q^3+q^2+q+1
        76: q+1
        77: q^2+1
        78: q^2+q+1
        79: q^3+q^2+q+1
        80: q^2+q+1
        81: q^3+q^2+q+1
        82: q^2+q+1
        83: q^3+q^2+q+1
        84: q+1
        85: q+1
        86: q^3+q^2+q+1
        87: q^3+q^2+q+1
        88: q^3+q^2+q+1
        89: q+1
        90: q^2+1
        91: q^2+q+1
        92: q^3+q^2+q+1
        93: q^2+q+1
        94: q^3+q^2+q+1
        95: q^2+q+1
        96: q^3+q^2+q+1
        97: q+1
        98: q^3+q^2+q+1
        99: q^3+q^2+q+1
       100: q^3+q^2+q+1
       101: q^2+q+1
       102: q^3+q^2+q+1
       103: q^3+q^2+q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^3+q^2+q+1
       111: q^3+q^2+q+1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: q^2+1
       117: q^2+1
       118: q^2+q+1
       119: q+1
       120: 1
       121: q^2+1
       122: q^2+q+1
       123: q^2+q+1
       124: q+1
       125: 1
       126: q^2+1
       127: q^2+q+1
       128: q^2+q+1
       129: q+1
       130: q^2+1
       131: q^2+q+1
       132: q^3+q^2+q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q^3+q^2+q+1
       139: q^3+q^2+q+1
       140: q^3+q^2+q+1
       141: q+1
       142: 1
       143: q^2+1
       144: q^2+q+1
       145: q^2+q+1
       146: q+1
       147: q^2+1
       148: q^2+q+1
       149: q+1
       150: q^2+1
       151: q^2+q+1
       152: q^3+q^2+q+1
       153: q^2+q+1
       154: q^3+q^2+q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q^3+q^2+q+1
       160: q^3+q^2+q+1
       161: q^3+q^2+q+1
       162: q+1
       163: 1
       164: q^2+1
       165: q^2+q+1
       166: q^2+q+1
       167: q+1
       168: q^2+1
       169: q^2+q+1
       170: q+1
       171: q^2+1
       172: q^2+q+1
       173: q^3+q^2+q+1
       174: q^2+q+1
       175: q^3+q^2+q+1
       176: q+1
       177: q+1
       178: q^3+q^2+q+1
       179: q^3+q^2+q+1
       180: q^3+q^2+q+1
       181: q+1
       182: q^2+1
       183: q^2+q+1
       184: q^3+q^2+q+1
       185: q^2+q+1
       186: q^3+q^2+q+1
       187: q^2+q+1
       188: q^3+q^2+q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q^3+q^2+q+1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: q^2+1
       205: q^2+q+1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: q^2+1
       211: q^2+1
       212: q^2+q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: q^2+1
       218: q^2+1
       219: q^2+q+1
       220: q+1
       221: 1
       222: q^2+1
       223: q^2+q+1
       224: q^2+q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q^3+q^2+q+1
       235: q^3+q^2+q+1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: q^2+1
       241: q^2+1
       242: q^2+q+1
       243: q+1
       244: 1
       245: q^2+1
       246: q^2+q+1
       247: q^2+q+1
       248: q+1
       249: 1
       250: q^2+1
       251: q^2+q+1
       252: q^2+q+1
       253: q+1
       254: q^2+1
       255: q^2+q+1
       256: q^3+q^2+q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q^3+q^2+q+1
       265: q^3+q^2+q+1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: q^2+1
       271: q^2+1
       272: q^2+q+1
       273: q+1
       274: 1
       275: q^2+1
       276: q^2+q+1
       277: q^2+q+1
       278: q+1
       279: 1
       280: q^2+1
       281: q^2+q+1
       282: q^2+q+1
       283: q+1
       284: q^2+1
       285: q^2+q+1
       286: q^3+q^2+q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q^3+q^2+q+1
       293: q^3+q^2+q+1
       294: q^3+q^2+q+1
       295: q+1
       296: 1
       297: q^2+1
       298: q^2+q+1
       299: q^2+q+1
       300: q+1
       301: q^2+1
       302: q^2+q+1
       303: q+1
       304: q^2+1
       305: q^2+q+1
       306: q^3+q^2+q+1
       307: q^2+q+1
       308: q^3+q^2+q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q^2+1
       327: q+1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: q^2+1
       335: q^2+q+1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q^2+1
       343: q^2+q+1
       344: q+1
       345: q+1
       346: 1
       347: 1
       348: q^2+1
       349: q^2+1
       350: q^2+q+1
       351: q+1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q^3+q^2+q+1
       364: q+1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q^2+1
       372: q^2+q+1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: q^2+1
       378: q^2+1
       379: q^2+q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: q^2+1
       385: q^2+1
       386: q^2+q+1
       387: q+1
       388: 1
       389: q^2+1
       390: q^2+q+1
       391: q^2+q+1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q^3+q^2+q+1
       403: q+1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q^2+1
       411: q^2+q+1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: q^2+1
       417: q^2+1
       418: q^2+q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: q^2+1
       424: q^2+1
       425: q^2+q+1
       426: q+1
       427: 1
       428: q^2+1
       429: q^2+q+1
       430: q^2+q+1
       431: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q^3+q^2+q+1
       441: q^3+q^2+q+1
       442: q+1
       443: q+1
       444: 1
       445: 1
       446: q^2+1
       447: q^2+1
       448: q^2+q+1
       449: q+1
       450: 1
       451: q^2+1
       452: q^2+q+1
       453: q^2+q+1
       454: q+1
       455: 1
       456: q^2+1
       457: q^2+q+1
       458: q^2+q+1
       459: q+1
       460: q^2+1
       461: q^2+q+1
       462: q^3+q^2+q+1
       463: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q^2+1
       491: q+1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q^2+1
       500: q+1
       501: q+1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q^2+1
       508: q^2+q+1
       509: q+1
       510: q+1
       515: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       524: q+1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q^2+1
       534: q+1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: q^2+1
       542: q^2+q+1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: q^2+1
       550: q^2+q+1
       551: q+1
       552: q+1
       553: 1
       554: 1
       555: q^2+1
       556: q^2+1
       557: q^2+q+1
       558: q+1
       561: q+1
       562: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q^2+1
       581: q+1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: q^2+1
       589: q^2+q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: q^2+1
       597: q^2+q+1
       598: q+1
       599: q+1
       600: 1
       601: 1
       602: q^2+1
       603: q^2+1
       604: q^2+q+1
       605: q+1
       608: q+1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q^3+q^2+q+1
       618: q+1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: q^2+1
       626: q^2+q+1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: q^2+1
       632: q^2+1
       633: q^2+q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: q^2+1
       639: q^2+1
       640: q^2+q+1
       641: q+1
       642: 1
       643: q^2+1
       644: q^2+q+1
       645: q^2+q+1
       646: q+1
       648: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+1
       694: q+1
       695: q+1
       702: q+1
       705: q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: q+1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q^2+1
       730: q+1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q^2+1
       739: q+1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: q^2+1
       747: q^2+q+1
       748: q+1
       749: q+1
       754: q+1
       757: q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q^2+1
       782: q+1
       783: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q^2+1
       791: q+1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q^2+1
       799: q^2+q+1
       800: q+1
       801: q+1
       806: q+1
       808: q+1
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: q+1
       815: q+1
       817: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: q^2+1
       825: q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: q^2+1
       833: q^2+q+1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: q^2+1
       841: q^2+q+1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: q^2+1
       847: q^2+1
       848: q^2+q+1
       849: q+1
       852: q+1
       853: q+1
       857: q+1
       858: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: q+1
       905: q+1
       908: q+1
       909: q+1
       910: q+1
       911: q+1
       912: q+1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q^2+1
       951: q+1
       952: q+1
       959: q+1
       962: q+1
       963: q+1
       964: q+1
       965: q+1
       966: q+1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: q+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q^2+1
      1005: q+1
      1006: q+1
      1013: q+1
      1016: q+1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1021: q+1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: q^2+1
      1041: q+1
      1042: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: q^2+1
      1050: q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: q^2+1
      1058: q^2+q+1
      1059: q+1
      1060: q+1
      1065: q+1
      1069: q+1
      1074: 1
      1075: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1116: q+1
      1117: q+1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: q+1
      1164: q+1
      1168: q+1
      1169: q+1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: q+1
      1216: q+1
      1219: q+1
      1220: q+1
      1221: q+1
      1222: q+1
      1223: q+1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q^2+1
      1262: q+1
      1263: q+1
      1270: q+1
      1277: 1
      1282: 1
      1283: 1
      1289: 1
      1290: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1313: q+1
      1318: 1
      1319: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1360: q+1
      1365: 1
      1366: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1407: q+1
      1408: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q+1
      1455: q+1
      1464: 1
      1469: 1
      1474: 1
      1475: 1
      1492: 1
      1497: 1
      1498: 1
      1504: 1
      1505: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1531: 1
      1536: 1
      1537: 1
      1543: 1
      1544: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1567: q+1
      1572: 1
      1573: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1623: 1
      1640: 1
      1645: 1
      1650: 1
      1651: 1
      1670: 1
      1675: 1
      1680: 1
      1681: 1
      1698: 1
      1703: 1
      1704: 1
      1710: 1
      1711: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1756: 1
      1777: 1
      1794: 1
      1799: 1
      1804: 1
      1805: 1
      1861: 1

1862:    0: 2q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: 2q^3+4q^2+3q+1
         3: q^3+4q^2+3q+1
         4: 2q^3+4q^2+3q+1
         5: 2q^3+4q^2+3q+1
         6: q^3+3q^2+3q+1
         7: 2q^3+4q^2+3q+1
         8: q^3+4q^2+3q+1
         9: q^3+4q^2+3q+1
        10: 3q^2+3q+1
        11: q^3+4q^2+3q+1
        12: q^3+4q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: 2q^3+4q^2+3q+1
        15: q^3+4q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: 2q^3+4q^2+3q+1
        18: q^3+4q^2+3q+1
        19: 2q^3+4q^2+3q+1
        20: q^2+2q+1
        21: q^3+3q^2+3q+1
        22: q^3+4q^2+3q+1
        23: q^3+4q^2+3q+1
        24: q^3+4q^2+3q+1
        25: 2q^2+3q+1
        26: 3q^2+3q+1
        27: 3q^2+3q+1
        28: q^3+4q^2+3q+1
        29: 3q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 3q^2+3q+1
        32: q^3+4q^2+3q+1
        33: q^3+3q^2+3q+1
        34: 2q^3+4q^2+3q+1
        35: q^3+4q^2+3q+1
        36: q^3+4q^2+3q+1
        37: 3q^2+3q+1
        38: q^3+4q^2+3q+1
        39: q^3+4q^2+3q+1
        40: q^3+3q^2+3q+1
        41: 2q^3+4q^2+3q+1
        42: q^3+4q^2+3q+1
        43: q^3+4q^2+3q+1
        44: 3q^2+3q+1
        45: q^3+4q^2+3q+1
        46: q^3+4q^2+3q+1
        47: 2q^3+4q^2+3q+1
        48: 2q^3+4q^2+3q+1
        49: q^3+4q^2+3q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q^2+3q+1
        54: q^3+4q^2+3q+1
        55: q^3+4q^2+3q+1
        56: q^3+4q^2+3q+1
        57: 2q+1
        58: 2q^2+3q+1
        59: 3q^2+3q+1
        60: 3q^2+3q+1
        61: 3q^2+3q+1
        62: 2q^2+3q+1
        63: 3q^2+3q+1
        64: 2q^2+3q+1
        65: 2q^2+3q+1
        66: 3q^2+3q+1
        67: 2q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 3q^2+3q+1
        70: q^3+3q^2+3q+1
        71: q^2+2q+1
        72: q^3+3q^2+3q+1
        73: q^3+4q^2+3q+1
        74: q^3+4q^2+3q+1
        75: q^3+4q^2+3q+1
        76: 2q^2+3q+1
        77: 3q^2+3q+1
        78: 3q^2+3q+1
        79: q^3+4q^2+3q+1
        80: 3q^2+3q+1
        81: q^3+4q^2+3q+1
        82: 3q^2+3q+1
        83: q^3+4q^2+3q+1
        84: q^2+2q+1
        85: q^3+3q^2+3q+1
        86: q^3+4q^2+3q+1
        87: q^3+4q^2+3q+1
        88: q^3+4q^2+3q+1
        89: 2q^2+3q+1
        90: 3q^2+3q+1
        91: 3q^2+3q+1
        92: q^3+4q^2+3q+1
        93: 3q^2+3q+1
        94: q^3+4q^2+3q+1
        95: 3q^2+3q+1
        96: q^3+4q^2+3q+1
        97: q^3+3q^2+3q+1
        98: 2q^3+4q^2+3q+1
        99: q^3+4q^2+3q+1
       100: q^3+4q^2+3q+1
       101: 3q^2+3q+1
       102: q^3+4q^2+3q+1
       103: q^3+4q^2+3q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: 2q+1
       108: 2q^2+3q+1
       109: 2q^2+3q+1
       110: q^3+4q^2+3q+1
       111: q^3+3q^2+3q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q^2+3q+1
       116: 3q^2+3q+1
       117: 3q^2+3q+1
       118: 3q^2+3q+1
       119: 2q+1
       120: 2q^2+3q+1
       121: 2q^2+3q+1
       122: 2q^2+3q+1
       123: 2q^2+3q+1
       124: 2q+1
       125: 2q^2+3q+1
       126: 2q^2+3q+1
       127: 2q^2+3q+1
       128: 2q^2+3q+1
       129: 2q^2+3q+1
       130: 3q^2+3q+1
       131: q^2+3q+1
       132: q^3+3q^2+3q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q^2+3q+1
       138: q^3+4q^2+3q+1
       139: q^3+4q^2+3q+1
       140: q^3+4q^2+3q+1
       141: 2q+1
       142: 2q^2+3q+1
       143: 3q^2+3q+1
       144: 3q^2+3q+1
       145: 3q^2+3q+1
       146: 2q^2+3q+1
       147: 3q^2+3q+1
       148: 2q^2+3q+1
       149: 2q^2+3q+1
       150: 3q^2+3q+1
       151: 2q^2+3q+1
       152: q^3+4q^2+3q+1
       153: 3q^2+3q+1
       154: q^3+3q^2+3q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 2q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+4q^2+3q+1
       161: q^3+4q^2+3q+1
       162: 2q+1
       163: 2q^2+3q+1
       164: 3q^2+3q+1
       165: 3q^2+3q+1
       166: 3q^2+3q+1
       167: 2q^2+3q+1
       168: 3q^2+3q+1
       169: 2q^2+3q+1
       170: 2q^2+3q+1
       171: 3q^2+3q+1
       172: 2q^2+3q+1
       173: q^3+4q^2+3q+1
       174: 3q^2+3q+1
       175: q^3+3q^2+3q+1
       176: q^2+2q+1
       177: q^3+3q^2+3q+1
       178: q^3+4q^2+3q+1
       179: q^3+4q^2+3q+1
       180: q^3+4q^2+3q+1
       181: 2q^2+3q+1
       182: 3q^2+3q+1
       183: 3q^2+3q+1
       184: q^3+4q^2+3q+1
       185: 3q^2+3q+1
       186: q^3+4q^2+3q+1
       187: 3q^2+3q+1
       188: q^3+4q^2+3q+1
       190: q^2+2q+1
       191: 2q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q^2+3q+1
       196: q^3+3q^2+3q+1
       197: q^2+2q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q^2+3q+1
       203: 2q^2+3q+1
       204: 3q^2+3q+1
       205: q^2+3q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q^2+2q+1
       210: 2q^2+3q+1
       211: 2q^2+3q+1
       212: 2q^2+3q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: q^2+2q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: 2q^2+3q+1
       220: 2q+1
       221: 2q^2+3q+1
       222: q^2+3q+1
       223: q^2+3q+1
       224: q^2+3q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q^2+3q+1
       233: 2q^2+3q+1
       234: q^3+4q^2+3q+1
       235: q^3+3q^2+3q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q^2+3q+1
       240: 3q^2+3q+1
       241: 3q^2+3q+1
       242: 3q^2+3q+1
       243: 2q+1
       244: 2q^2+3q+1
       245: 2q^2+3q+1
       246: 2q^2+3q+1
       247: 2q^2+3q+1
       248: 2q+1
       249: 2q^2+3q+1
       250: 2q^2+3q+1
       251: 2q^2+3q+1
       252: 2q^2+3q+1
       253: 2q^2+3q+1
       254: 3q^2+3q+1
       255: q^2+3q+1
       256: q^3+3q^2+3q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q^2+3q+1
       263: 2q^2+3q+1
       264: q^3+4q^2+3q+1
       265: q^3+3q^2+3q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q^2+3q+1
       270: 3q^2+3q+1
       271: 3q^2+3q+1
       272: 3q^2+3q+1
       273: 2q+1
       274: 2q^2+3q+1
       275: 2q^2+3q+1
       276: 2q^2+3q+1
       277: 2q^2+3q+1
       278: 2q+1
       279: 2q^2+3q+1
       280: 2q^2+3q+1
       281: 2q^2+3q+1
       282: 2q^2+3q+1
       283: 2q^2+3q+1
       284: 3q^2+3q+1
       285: q^2+3q+1
       286: q^3+3q^2+3q+1
       287: q^2+2q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q^2+3q+1
       292: q^3+4q^2+3q+1
       293: q^3+4q^2+3q+1
       294: q^3+4q^2+3q+1
       295: 2q+1
       296: 2q^2+3q+1
       297: 3q^2+3q+1
       298: 3q^2+3q+1
       299: 3q^2+3q+1
       300: 2q^2+3q+1
       301: 3q^2+3q+1
       302: 2q^2+3q+1
       303: 2q^2+3q+1
       304: 3q^2+3q+1
       305: 2q^2+3q+1
       306: q^3+4q^2+3q+1
       307: 3q^2+3q+1
       308: q^3+3q^2+3q+1
       311: 2q+1
       312: 2q+1
       313: 2q+1
       314: 2q+1
       315: 2q+1
       316: 2q+1
       317: q^2+2q+1
       318: q^2+2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: 2q+1
       324: 2q+1
       325: 2q^2+3q+1
       326: q^2+3q+1
       327: 2q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: q+1
       332: q^2+2q+1
       333: q^2+2q+1
       334: 2q^2+3q+1
       335: q^2+3q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: q+1
       340: q^2+2q+1
       341: q^2+2q+1
       342: 2q^2+3q+1
       343: q^2+3q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: q+1
       348: q^2+3q+1
       349: q^2+3q+1
       350: q^2+3q+1
       351: q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       357: q^2+2q+1
       358: 2q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q^2+3q+1
       363: q^3+3q^2+3q+1
       364: q^2+2q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q^2+3q+1
       370: 2q^2+3q+1
       371: 3q^2+3q+1
       372: q^2+3q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+2q+1
       377: 2q^2+3q+1
       378: 2q^2+3q+1
       379: 2q^2+3q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: q^2+2q+1
       384: 2q^2+3q+1
       385: 2q^2+3q+1
       386: 2q^2+3q+1
       387: 2q+1
       388: 2q^2+3q+1
       389: q^2+3q+1
       390: q^2+3q+1
       391: q^2+3q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: 2q+1
       396: q^2+2q+1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q^2+3q+1
       402: q^3+3q^2+3q+1
       403: q^2+2q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q^2+3q+1
       409: 2q^2+3q+1
       410: 3q^2+3q+1
       411: q^2+3q+1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: q^2+2q+1
       416: 2q^2+3q+1
       417: 2q^2+3q+1
       418: 2q^2+3q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: q^2+2q+1
       423: 2q^2+3q+1
       424: 2q^2+3q+1
       425: 2q^2+3q+1
       426: 2q+1
       427: 2q^2+3q+1
       428: q^2+3q+1
       429: q^2+3q+1
       430: q^2+3q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: 2q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: 2q+1
       438: 2q^2+3q+1
       439: 2q^2+3q+1
       440: q^3+4q^2+3q+1
       441: q^3+3q^2+3q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q^2+3q+1
       446: 3q^2+3q+1
       447: 3q^2+3q+1
       448: 3q^2+3q+1
       449: 2q+1
       450: 2q^2+3q+1
       451: 2q^2+3q+1
       452: 2q^2+3q+1
       453: 2q^2+3q+1
       454: 2q+1
       455: 2q^2+3q+1
       456: 2q^2+3q+1
       457: 2q^2+3q+1
       458: 2q^2+3q+1
       459: 2q^2+3q+1
       460: 3q^2+3q+1
       461: q^2+3q+1
       462: q^3+3q^2+3q+1
       463: q^2+2q+1
       467: 2q+1
       468: 2q+1
       469: 2q+1
       470: 2q+1
       471: q+1
       472: q^2+2q+1
       475: 2q+1
       476: 2q+1
       477: 2q+1
       478: 2q+1
       479: 2q+1
       480: 2q+1
       481: q+1
       482: 2q+1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q^2+2q+1
       490: q^2+3q+1
       491: 2q+1
       493: 2q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q^2+2q+1
       499: q^2+3q+1
       500: 2q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 1
       505: q+1
       506: q+1
       507: q^2+3q+1
       508: q^2+3q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       518: 2q+1
       519: 2q+1
       520: 2q+1
       521: 2q+1
       522: 2q+1
       523: 2q+1
       524: q^2+2q+1
       525: q^2+2q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: 2q+1
       531: 2q+1
       532: 2q^2+3q+1
       533: q^2+3q+1
       534: 2q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: q+1
       539: q^2+2q+1
       540: q^2+2q+1
       541: 2q^2+3q+1
       542: q^2+3q+1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: q+1
       547: q^2+2q+1
       548: q^2+2q+1
       549: 2q^2+3q+1
       550: q^2+3q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: q+1
       555: q^2+3q+1
       556: q^2+3q+1
       557: q^2+3q+1
       558: q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q+1
       562: 2q+1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       568: 2q+1
       569: 2q+1
       570: 2q+1
       571: q^2+2q+1
       572: q^2+2q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: 2q+1
       578: 2q+1
       579: 2q^2+3q+1
       580: q^2+3q+1
       581: 2q+1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: q+1
       586: q^2+2q+1
       587: q^2+2q+1
       588: 2q^2+3q+1
       589: q^2+3q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: q+1
       594: q^2+2q+1
       595: q^2+2q+1
       596: 2q^2+3q+1
       597: q^2+3q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: q+1
       602: q^2+3q+1
       603: q^2+3q+1
       604: q^2+3q+1
       605: q+1
       606: q^2+2q+1
       607: 2q+1
       608: 2q+1
       609: 2q+1
       611: q^2+2q+1
       612: 2q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q^2+3q+1
       617: q^3+3q^2+3q+1
       618: q^2+2q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q^2+3q+1
       624: 2q^2+3q+1
       625: 3q^2+3q+1
       626: q^2+3q+1
       627: 2q+1
       628: 2q+1
       629: 2q+1
       630: q^2+2q+1
       631: 2q^2+3q+1
       632: 2q^2+3q+1
       633: 2q^2+3q+1
       634: 2q+1
       635: 2q+1
       636: 2q+1
       637: q^2+2q+1
       638: 2q^2+3q+1
       639: 2q^2+3q+1
       640: 2q^2+3q+1
       641: 2q+1
       642: 2q^2+3q+1
       643: q^2+3q+1
       644: q^2+3q+1
       645: q^2+3q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: 2q+1
       653: 2q+1
       654: q+1
       655: q+1
       656: q+1
       660: 2q+1
       661: 2q+1
       662: 2q+1
       663: 2q+1
       664: 1
       665: q+1
       668: q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: q+1
       674: q+1
       675: 2q+1
       678: q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: q+1
       684: q+1
       685: 2q+1
       687: 2q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q^2+3q+1
       694: 2q+1
       695: q+1
       696: q+1
       697: q+1
       698: 1
       699: q+1
       700: q+1
       701: 2q+1
       702: q+1
       706: 2q+1
       707: 2q+1
       708: 2q+1
       709: 2q+1
       710: q+1
       711: q^2+2q+1
       714: 2q+1
       715: 2q+1
       716: 2q+1
       717: 2q+1
       718: 2q+1
       719: 2q+1
       720: q+1
       721: 2q+1
       723: 2q+1
       724: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q^2+2q+1
       729: q^2+3q+1
       730: 2q+1
       732: 2q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q^2+2q+1
       738: q^2+3q+1
       739: 2q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 1
       744: q+1
       745: q+1
       746: q^2+3q+1
       747: q^2+3q+1
       748: q+1
       749: q+1
       750: q+1
       751: q+1
       752: 2q+1
       753: 2q+1
       754: 2q+1
       758: 2q+1
       759: 2q+1
       760: 2q+1
       761: 2q+1
       762: q+1
       763: q^2+2q+1
       766: 2q+1
       767: 2q+1
       768: 2q+1
       769: 2q+1
       770: 2q+1
       771: 2q+1
       772: q+1
       773: 2q+1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q^2+2q+1
       781: q^2+3q+1
       782: 2q+1
       784: 2q+1
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q^2+2q+1
       790: q^2+3q+1
       791: 2q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 1
       796: q+1
       797: q+1
       798: q^2+3q+1
       799: q^2+3q+1
       800: q+1
       801: q+1
       802: q+1
       803: q+1
       804: 2q+1
       805: 2q+1
       806: 2q+1
       809: 2q+1
       810: 2q+1
       811: 2q+1
       812: 2q+1
       813: 2q+1
       814: 2q+1
       815: q^2+2q+1
       816: q^2+2q+1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: 2q+1
       822: 2q+1
       823: 2q^2+3q+1
       824: q^2+3q+1
       825: 2q+1
       826: 2q+1
       827: 2q+1
       828: 2q+1
       829: q+1
       830: q^2+2q+1
       831: q^2+2q+1
       832: 2q^2+3q+1
       833: q^2+3q+1
       834: 2q+1
       835: 2q+1
       836: 2q+1
       837: q+1
       838: q^2+2q+1
       839: q^2+2q+1
       840: 2q^2+3q+1
       841: q^2+3q+1
       842: 2q+1
       843: 2q+1
       844: 2q+1
       845: q+1
       846: q^2+3q+1
       847: q^2+3q+1
       848: q^2+3q+1
       849: q+1
       850: q^2+2q+1
       851: 2q+1
       852: 2q+1
       853: 2q+1
       858: q+1
       859: q+1
       860: q+1
       865: 2q+1
       866: 1
       867: 1
       868: 1
       872: q+1
       873: q+1
       874: q+1
       875: q+1
       876: 1
       877: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       885: 1
       886: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: 2q+1
       898: q+1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: q+1
       905: q+1
       910: 2q+1
       911: q+1
       912: q+1
       913: q+1
       917: 2q+1
       918: 2q+1
       919: 2q+1
       920: 2q+1
       921: 1
       922: q+1
       925: q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: q+1
       931: q+1
       932: 2q+1
       935: q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: q+1
       941: q+1
       942: 2q+1
       944: 2q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q^2+3q+1
       951: 2q+1
       952: q+1
       953: q+1
       954: q+1
       955: 1
       956: q+1
       957: q+1
       958: 2q+1
       959: q+1
       964: 2q+1
       965: q+1
       966: q+1
       967: q+1
       971: 2q+1
       972: 2q+1
       973: 2q+1
       974: 2q+1
       975: 1
       976: q+1
       979: q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: q+1
       985: q+1
       986: 2q+1
       989: q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: q+1
       995: q+1
       996: 2q+1
       998: 2q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q^2+3q+1
      1005: 2q+1
      1006: q+1
      1007: q+1
      1008: q+1
      1009: 1
      1010: q+1
      1011: q+1
      1012: 2q+1
      1013: q+1
      1017: 2q+1
      1018: 2q+1
      1019: 2q+1
      1020: 2q+1
      1021: q+1
      1022: q^2+2q+1
      1025: 2q+1
      1026: 2q+1
      1027: 2q+1
      1028: 2q+1
      1029: 2q+1
      1030: 2q+1
      1031: q+1
      1032: 2q+1
      1034: 2q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q^2+2q+1
      1040: q^2+3q+1
      1041: 2q+1
      1043: 2q+1
      1044: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q^2+2q+1
      1049: q^2+3q+1
      1050: 2q+1
      1051: 2q+1
      1052: 2q+1
      1053: 2q+1
      1054: 1
      1055: q+1
      1056: q+1
      1057: q^2+3q+1
      1058: q^2+3q+1
      1059: q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: 2q+1
      1064: 2q+1
      1065: 2q+1
      1070: q+1
      1075: 1
      1076: 1
      1077: 1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: q+1
      1117: q+1
      1118: q+1
      1119: q+1
      1124: 2q+1
      1125: 1
      1126: 1
      1127: 1
      1131: q+1
      1132: q+1
      1133: q+1
      1134: q+1
      1135: 1
      1136: q+1
      1140: q+1
      1141: q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1155: 2q+1
      1157: q+1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: q+1
      1164: q+1
      1169: q+1
      1170: q+1
      1171: q+1
      1176: 2q+1
      1177: 1
      1178: 1
      1179: 1
      1183: q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: q+1
      1192: q+1
      1193: q+1
      1194: q+1
      1195: q+1
      1196: 1
      1197: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: q+1
      1207: 2q+1
      1209: q+1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: q+1
      1216: q+1
      1221: 2q+1
      1222: q+1
      1223: q+1
      1224: q+1
      1228: 2q+1
      1229: 2q+1
      1230: 2q+1
      1231: 2q+1
      1232: 1
      1233: q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: q+1
      1242: q+1
      1243: 2q+1
      1246: q+1
      1247: q+1
      1248: q+1
      1249: q+1
      1250: q+1
      1251: q+1
      1252: q+1
      1253: 2q+1
      1255: 2q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: q+1
      1261: q^2+3q+1
      1262: 2q+1
      1263: q+1
      1264: q+1
      1265: q+1
      1266: 1
      1267: q+1
      1268: q+1
      1269: 2q+1
      1270: q+1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1290: 1
      1291: 1
      1292: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1314: q+1
      1319: 1
      1320: 1
      1321: 1
      1326: q+1
      1327: 1
      1328: 1
      1329: 1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: q+1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1356: q+1
      1361: q+1
      1366: 1
      1367: 1
      1368: 1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1381: q+1
      1382: 1
      1383: 1
      1384: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: q+1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1403: q+1
      1408: q+1
      1409: q+1
      1410: q+1
      1415: 2q+1
      1416: 1
      1417: 1
      1418: 1
      1422: q+1
      1423: q+1
      1424: q+1
      1425: q+1
      1426: 1
      1427: q+1
      1431: q+1
      1432: q+1
      1433: q+1
      1434: q+1
      1435: 1
      1436: q+1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: q+1
      1446: 2q+1
      1448: q+1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: q+1
      1454: q+1
      1455: q+1
      1465: 1
      1470: 1
      1475: 1
      1476: 1
      1477: 1
      1482: 1
      1493: 1
      1498: 1
      1499: 1
      1500: 1
      1505: 1
      1506: 1
      1507: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1532: 1
      1537: 1
      1538: 1
      1539: 1
      1544: 1
      1545: 1
      1546: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1568: q+1
      1573: 1
      1574: 1
      1575: 1
      1580: q+1
      1581: 1
      1582: 1
      1583: 1
      1588: q+1
      1589: 1
      1590: 1
      1591: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1600: q+1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1610: q+1
      1624: 1
      1641: 1
      1646: 1
      1651: 1
      1652: 1
      1653: 1
      1658: 1
      1671: 1
      1676: 1
      1681: 1
      1682: 1
      1683: 1
      1688: 1
      1699: 1
      1704: 1
      1705: 1
      1706: 1
      1711: 1
      1712: 1
      1713: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1757: 1
      1778: 1
      1795: 1
      1800: 1
      1805: 1
      1806: 1
      1807: 1
      1812: 1
      1862: 1

1863:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: q+1
        53: q+1
        54: 1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: 1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: 1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: 1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: q+1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: q+1
       115: q+1
       116: 1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: 1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: q+1
       137: q+1
       138: 1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: 1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: q+1
       158: q+1
       159: 1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: 1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: 1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: 1
       201: q+1
       202: 1
       203: 1
       204: 1
       205: 1
       206: 1
       207: 1
       208: q+1
       209: q+1
       210: 1
       211: 1
       212: 1
       213: 1
       214: 1
       215: q+1
       216: q+1
       217: 1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: 1
       231: q+1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: q+1
       239: q+1
       240: 1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: q+1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: q+1
       269: q+1
       270: 1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: 1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: q+1
       291: q+1
       292: 1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: 1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: q+1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: q+1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: q+1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: q+1
       376: q+1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: q+1
       383: q+1
       384: 1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: q+1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: q+1
       415: q+1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: q+1
       422: q+1
       423: 1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: q+1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: q+1
       445: q+1
       446: 1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: q+1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: q+1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: q+1
       554: q+1
       555: 1
       556: 1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: q+1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: q+1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: q+1
       601: q+1
       602: 1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: q+1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: q+1
       630: q+1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: q+1
       637: q+1
       638: 1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       656: 1
       657: 1
       658: 1
       659: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       718: 1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: q+1
       751: q+1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: q+1
       803: q+1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: q+1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: q+1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: q+1
       845: q+1
       846: 1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: 1
       854: 1
       861: 1
       862: 1
       868: 1
       869: 1
       870: 1
       871: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       913: 1
       914: 1
       915: 1
       916: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       939: 1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       960: 1
       961: 1
       967: 1
       968: 1
       969: 1
       970: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: q+1
      1062: q+1
      1063: 1
      1064: 1
      1065: 1
      1071: 1
      1078: 1
      1079: 1
      1085: 1
      1086: 1
      1087: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1120: 1
      1121: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1172: 1
      1173: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1279: 1
      1286: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1315: 1
      1322: 1
      1323: 1
      1329: 1
      1330: 1
      1331: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1362: 1
      1369: 1
      1370: 1
      1376: 1
      1377: 1
      1378: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1411: 1
      1412: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1471: 1
      1478: 1
      1479: 1
      1485: 1
      1494: 1
      1501: 1
      1508: 1
      1509: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1523: 1
      1524: 1
      1533: 1
      1540: 1
      1547: 1
      1548: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1562: 1
      1563: 1
      1569: 1
      1576: 1
      1577: 1
      1583: 1
      1584: 1
      1585: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1625: 1
      1647: 1
      1654: 1
      1655: 1
      1661: 1
      1677: 1
      1684: 1
      1685: 1
      1691: 1
      1700: 1
      1707: 1
      1714: 1
      1715: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1729: 1
      1730: 1
      1758: 1
      1779: 1
      1801: 1
      1808: 1
      1809: 1
      1815: 1
      1863: 1

1864:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: 1
        24: q^2+q+1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: 1
        51: q^2+q+1
        52: q+1
        53: q+1
        54: 1
        55: q+1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: 1
        61: q^2+q+1
        62: q^2+q+1
        63: q+1
        64: q^2+q+1
        65: q^2+q+1
        66: q+1
        67: q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q+1
        73: q+1
        74: 1
        75: q^2+q+1
        76: q^2+q+1
        77: q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: q^2+q+1
        85: q+1
        86: q+1
        87: 1
        88: q^2+q+1
        89: q^2+q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q^2+q+1
        98: q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q^2+q+1
       103: q^2+q+1
       104: 1
       105: 1
       106: q+1
       107: q+1
       108: 1
       109: q+1
       110: 1
       111: 1
       112: 1
       113: q^2+q+1
       114: q+1
       115: q+1
       116: 1
       117: q+1
       118: 1
       119: q^2+q+1
       120: q+1
       121: q+1
       122: 1
       123: q^2+q+1
       124: q^2+q+1
       125: q+1
       126: q+1
       127: 1
       128: q^2+q+1
       129: q^2+q+1
       130: q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+q+1
       134: 1
       135: q^2+q+1
       136: q+1
       137: q+1
       138: 1
       139: q+1
       140: 1
       141: q^2+q+1
       142: q+1
       143: q+1
       144: 1
       145: q^2+q+1
       146: q^2+q+1
       147: q+1
       148: q^2+q+1
       149: q^2+q+1
       150: q+1
       151: q^2+q+1
       152: q^2+q+1
       153: q^2+q+1
       154: q^2+q+1
       155: 1
       156: q^2+q+1
       157: q+1
       158: q+1
       159: 1
       160: q+1
       161: 1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: 1
       166: q^2+q+1
       167: q^2+q+1
       168: q+1
       169: q^2+q+1
       170: q^2+q+1
       171: q+1
       172: q^2+q+1
       173: q^2+q+1
       174: q^2+q+1
       175: q^2+q+1
       176: q^2+q+1
       177: q+1
       178: q+1
       179: 1
       180: q^2+q+1
       181: q^2+q+1
       182: q+1
       183: q^2+q+1
       184: q^2+q+1
       185: q^2+q+1
       186: q^2+q+1
       187: q^2+q+1
       188: q^2+q+1
       189: 1
       190: 1
       191: 1
       192: q+1
       193: 1
       194: q+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q+1
       201: q+1
       202: 1
       203: q+1
       204: 1
       205: 1
       206: 1
       207: q^2+q+1
       208: q+1
       209: q+1
       210: 1
       211: q+1
       212: 1
       213: 1
       214: q^2+q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q^2+q+1
       221: q+1
       222: q+1
       223: 1
       224: q^2+q+1
       225: q^2+q+1
       226: q+1
       227: q^2+q+1
       228: 1
       229: 1
       230: q+1
       231: q+1
       232: 1
       233: q+1
       234: 1
       235: 1
       236: 1
       237: q^2+q+1
       238: q+1
       239: q+1
       240: 1
       241: q+1
       242: 1
       243: q^2+q+1
       244: q+1
       245: q+1
       246: 1
       247: q^2+q+1
       248: q^2+q+1
       249: q+1
       250: q+1
       251: 1
       252: q^2+q+1
       253: q^2+q+1
       254: q+1
       255: q^2+q+1
       256: q^2+q+1
       257: q^2+q+1
       258: 1
       259: 1
       260: q+1
       261: q+1
       262: 1
       263: q+1
       264: 1
       265: 1
       266: 1
       267: q^2+q+1
       268: q+1
       269: q+1
       270: 1
       271: q+1
       272: 1
       273: q^2+q+1
       274: q+1
       275: q+1
       276: 1
       277: q^2+q+1
       278: q^2+q+1
       279: q+1
       280: q+1
       281: 1
       282: q^2+q+1
       283: q^2+q+1
       284: q+1
       285: q^2+q+1
       286: q^2+q+1
       287: q^2+q+1
       288: 1
       289: q^2+q+1
       290: q+1
       291: q+1
       292: 1
       293: q+1
       294: 1
       295: q^2+q+1
       296: q+1
       297: q+1
       298: 1
       299: q^2+q+1
       300: q^2+q+1
       301: q+1
       302: q^2+q+1
       303: q^2+q+1
       304: q+1
       305: q^2+q+1
       306: q^2+q+1
       307: q^2+q+1
       308: q^2+q+1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       315: q+1
       316: 1
       317: 1
       319: 1
       320: 1
       321: 1
       322: q+1
       323: 1
       324: q+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: q+1
       331: q+1
       332: 1
       333: q+1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: q^2+q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q^2+q+1
       352: q+1
       353: q+1
       354: 1
       355: q^2+q+1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: 1
       361: q+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: 1
       370: q+1
       371: 1
       372: 1
       373: 1
       374: q^2+q+1
       375: q+1
       376: q+1
       377: 1
       378: q+1
       379: 1
       380: 1
       381: q^2+q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q^2+q+1
       388: q+1
       389: q+1
       390: 1
       391: q^2+q+1
       392: q^2+q+1
       393: q+1
       394: q^2+q+1
       395: 1
       396: 1
       397: 1
       398: q+1
       399: 1
       400: q+1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: q+1
       407: q+1
       408: 1
       409: q+1
       410: 1
       411: 1
       412: 1
       413: q^2+q+1
       414: q+1
       415: q+1
       416: 1
       417: q+1
       418: 1
       419: 1
       420: q^2+q+1
       421: q+1
       422: q+1
       423: 1
       424: q+1
       425: 1
       426: q^2+q+1
       427: q+1
       428: q+1
       429: 1
       430: q^2+q+1
       431: q^2+q+1
       432: q+1
       433: q^2+q+1
       434: 1
       435: 1
       436: q+1
       437: q+1
       438: 1
       439: q+1
       440: 1
       441: 1
       442: 1
       443: q^2+q+1
       444: q+1
       445: q+1
       446: 1
       447: q+1
       448: 1
       449: q^2+q+1
       450: q+1
       451: q+1
       452: 1
       453: q^2+q+1
       454: q^2+q+1
       455: q+1
       456: q+1
       457: 1
       458: q^2+q+1
       459: q^2+q+1
       460: q+1
       461: q^2+q+1
       462: q^2+q+1
       463: q^2+q+1
       465: 1
       466: 1
       467: 1
       470: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       479: q+1
       480: 1
       481: 1
       483: 1
       484: 1
       485: 1
       486: q+1
       487: 1
       488: q+1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q^2+q+1
       511: q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       522: q+1
       523: 1
       524: 1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: 1
       531: q+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: q+1
       538: q+1
       539: 1
       540: q+1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       552: q^2+q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q^2+q+1
       559: q+1
       560: q+1
       561: 1
       562: q^2+q+1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: q+1
       570: 1
       571: 1
       573: 1
       574: 1
       575: 1
       576: q+1
       577: 1
       578: q+1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: q+1
       585: q+1
       586: 1
       587: q+1
       588: 1
       589: 1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: q+1
       596: 1
       597: 1
       598: 1
       599: q^2+q+1
       600: q+1
       601: q+1
       602: 1
       603: q+1
       604: 1
       605: q^2+q+1
       606: q+1
       607: q+1
       608: 1
       609: q^2+q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: 1
       615: q+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: 1
       624: q+1
       625: 1
       626: 1
       627: 1
       628: q^2+q+1
       629: q+1
       630: q+1
       631: 1
       632: q+1
       633: 1
       634: 1
       635: q^2+q+1
       636: q+1
       637: q+1
       638: 1
       639: q+1
       640: 1
       641: q^2+q+1
       642: q+1
       643: q+1
       644: 1
       645: q^2+q+1
       646: q^2+q+1
       647: q+1
       648: q^2+q+1
       650: 1
       651: 1
       655: 1
       658: 1
       659: 1
       660: 1
       663: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: q+1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       682: q+1
       683: 1
       684: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       702: 1
       704: 1
       705: 1
       706: 1
       709: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       718: q+1
       719: 1
       720: 1
       722: 1
       723: 1
       724: 1
       725: q+1
       726: 1
       727: q+1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q^2+q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: q+1
       771: 1
       772: 1
       774: 1
       775: 1
       776: 1
       777: q+1
       778: 1
       779: q+1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: q+1
       796: 1
       797: q+1
       798: 1
       799: 1
       800: 1
       801: q^2+q+1
       802: q+1
       803: q+1
       804: 1
       805: q+1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: q+1
       814: 1
       815: 1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: 1
       822: q+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: q+1
       829: q+1
       830: 1
       831: q+1
       832: 1
       833: 1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: 1
       842: 1
       843: q^2+q+1
       844: q+1
       845: q+1
       846: 1
       847: q+1
       848: 1
       849: q^2+q+1
       850: q+1
       851: q+1
       852: 1
       853: q^2+q+1
       855: 1
       862: 1
       863: 1
       867: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       884: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       897: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       902: q+1
       903: 1
       904: 1
       905: 1
       907: 1
       908: 1
       912: 1
       915: 1
       916: 1
       917: 1
       920: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: q+1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: 1
       961: 1
       962: 1
       966: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: q+1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: 1
       991: 1
       993: q+1
       994: 1
       995: 1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: 1
      1002: q+1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1013: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: q+1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: 1
      1036: q+1
      1037: 1
      1038: q+1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: q+1
      1055: 1
      1056: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q^2+q+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: q+1
      1065: 1
      1072: 1
      1079: 1
      1080: 1
      1084: 1
      1087: 1
      1088: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1111: 1
      1114: 1
      1121: 1
      1122: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: q+1
      1153: 1
      1154: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1161: q+1
      1162: 1
      1163: 1
      1164: 1
      1166: 1
      1173: 1
      1174: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: q+1
      1205: 1
      1206: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1213: q+1
      1214: 1
      1215: 1
      1216: 1
      1218: 1
      1219: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: q+1
      1241: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1250: q+1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: 1
      1257: q+1
      1258: 1
      1259: q+1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1270: 1
      1280: 1
      1287: 1
      1294: 1
      1295: 1
      1299: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1316: 1
      1323: 1
      1324: 1
      1328: 1
      1331: 1
      1332: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: q+1
      1354: 1
      1355: 1
      1363: 1
      1370: 1
      1371: 1
      1375: 1
      1378: 1
      1379: 1
      1383: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1402: 1
      1405: 1
      1412: 1
      1413: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1431: 1
      1434: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: q+1
      1444: 1
      1445: 1
      1447: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1452: q+1
      1453: 1
      1454: 1
      1455: 1
      1472: 1
      1479: 1
      1480: 1
      1484: 1
      1495: 1
      1502: 1
      1509: 1
      1510: 1
      1514: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1534: 1
      1541: 1
      1548: 1
      1549: 1
      1553: 1
      1556: 1
      1557: 1
      1558: 1
      1561: 1
      1562: 1
      1570: 1
      1577: 1
      1578: 1
      1582: 1
      1585: 1
      1586: 1
      1590: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: q+1
      1608: 1
      1609: 1
      1626: 1
      1648: 1
      1655: 1
      1656: 1
      1660: 1
      1678: 1
      1685: 1
      1686: 1
      1690: 1
      1701: 1
      1708: 1
      1715: 1
      1716: 1
      1720: 1
      1723: 1
      1724: 1
      1725: 1
      1728: 1
      1729: 1
      1759: 1
      1780: 1
      1802: 1
      1809: 1
      1810: 1
      1814: 1
      1864: 1

1865:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: 1
        25: q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q^2+q+1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: 1
        62: q^2+q+1
        63: q+1
        64: q^2+q+1
        65: q^2+q+1
        66: q+1
        67: q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q+1
        73: q+1
        74: q^2+q+1
        75: 1
        76: q^2+q+1
        77: q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: q^2+q+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: 1
        89: q^2+q+1
        90: q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q^2+q+1
        98: q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q^2+q+1
       103: q^2+q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q^2+q+1
       113: 1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q^2+q+1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: 1
       124: q^2+q+1
       125: q+1
       126: q+1
       127: q^2+q+1
       128: 1
       129: q^2+q+1
       130: q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+q+1
       134: q^2+q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q^2+q+1
       142: q+1
       143: q+1
       144: q^2+q+1
       145: 1
       146: q^2+q+1
       147: q+1
       148: q^2+q+1
       149: q^2+q+1
       150: q+1
       151: q^2+q+1
       152: q^2+q+1
       153: q^2+q+1
       154: q^2+q+1
       155: q^2+q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q^2+q+1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: 1
       167: q^2+q+1
       168: q+1
       169: q^2+q+1
       170: q^2+q+1
       171: q+1
       172: q^2+q+1
       173: q^2+q+1
       174: q^2+q+1
       175: q^2+q+1
       176: q^2+q+1
       177: q+1
       178: q+1
       179: q^2+q+1
       180: 1
       181: q^2+q+1
       182: q+1
       183: q^2+q+1
       184: q^2+q+1
       185: q^2+q+1
       186: q^2+q+1
       187: q^2+q+1
       188: q^2+q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q^2+q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: q^2+q+1
       214: 1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: 1
       220: q^2+q+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: 1
       225: q^2+q+1
       226: q+1
       227: q^2+q+1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q^2+q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q^2+q+1
       244: q+1
       245: q+1
       246: q^2+q+1
       247: 1
       248: q^2+q+1
       249: q+1
       250: q+1
       251: q^2+q+1
       252: 1
       253: q^2+q+1
       254: q+1
       255: q^2+q+1
       256: q^2+q+1
       257: q^2+q+1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q^2+q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q^2+q+1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: 1
       278: q^2+q+1
       279: q+1
       280: q+1
       281: q^2+q+1
       282: 1
       283: q^2+q+1
       284: q+1
       285: q^2+q+1
       286: q^2+q+1
       287: q^2+q+1
       288: q^2+q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q^2+q+1
       296: q+1
       297: q+1
       298: q^2+q+1
       299: 1
       300: q^2+q+1
       301: q+1
       302: q^2+q+1
       303: q^2+q+1
       304: q+1
       305: q^2+q+1
       306: q^2+q+1
       307: q^2+q+1
       308: q^2+q+1
       309: 1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q^2+q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q^2+q+1
       352: q+1
       353: q+1
       354: q^2+q+1
       355: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q^2+q+1
       374: 1
       375: q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       380: q^2+q+1
       381: 1
       382: q+1
       383: q+1
       384: q+1
       385: 1
       386: 1
       387: q^2+q+1
       388: q+1
       389: q+1
       390: q^2+q+1
       391: 1
       392: q^2+q+1
       393: q+1
       394: q^2+q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q^2+q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       419: q^2+q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q^2+q+1
       427: q+1
       428: q+1
       429: q^2+q+1
       430: 1
       431: q^2+q+1
       432: q+1
       433: q^2+q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q^2+q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q^2+q+1
       450: q+1
       451: q+1
       452: q^2+q+1
       453: 1
       454: q^2+q+1
       455: q+1
       456: q+1
       457: q^2+q+1
       458: 1
       459: q^2+q+1
       460: q+1
       461: q^2+q+1
       462: q^2+q+1
       463: q^2+q+1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       473: 1
       474: 1
       475: 1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q^2+q+1
       510: 1
       511: q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: 1
       541: 1
       542: 1
       543: 1
       544: q+1
       545: 1
       546: q+1
       547: q+1
       548: 1
       549: 1
       550: 1
       551: q^2+q+1
       552: 1
       553: q+1
       554: q+1
       555: q+1
       556: 1
       557: 1
       558: q^2+q+1
       559: q+1
       560: q+1
       561: q^2+q+1
       562: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q^2+q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q^2+q+1
       606: q+1
       607: q+1
       608: q^2+q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q^2+q+1
       628: 1
       629: q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       634: q^2+q+1
       635: 1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: 1
       641: q^2+q+1
       642: q+1
       643: q+1
       644: q^2+q+1
       645: 1
       646: q^2+q+1
       647: q+1
       648: q^2+q+1
       650: 1
       652: 1
       654: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       666: 1
       667: 1
       668: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       702: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       712: 1
       713: 1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: q+1
       734: 1
       735: q+1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: q+1
       742: 1
       743: q+1
       744: q+1
       745: 1
       746: 1
       747: 1
       748: q^2+q+1
       749: 1
       750: q+1
       751: q+1
       752: q+1
       753: 1
       754: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       787: q+1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q^2+q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 1
       834: 1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       841: 1
       842: q^2+q+1
       843: 1
       844: q+1
       845: q+1
       846: q+1
       847: 1
       848: 1
       849: q^2+q+1
       850: q+1
       851: q+1
       852: q^2+q+1
       853: 1
       856: 1
       862: 1
       864: 1
       866: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: 1
       903: 1
       904: 1
       905: 1
       907: 1
       909: 1
       911: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       923: 1
       924: 1
       925: 1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       933: 1
       934: 1
       935: 1
       936: q+1
       938: 1
       939: 1
       940: 1
       941: 1
       943: 1
       944: 1
       945: q+1
       946: 1
       947: q+1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       959: 1
       961: 1
       963: 1
       965: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       987: 1
       988: 1
       989: 1
       990: q+1
       992: 1
       993: 1
       994: 1
       995: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: q+1
      1045: 1
      1046: q+1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: q+1
      1053: 1
      1054: q+1
      1055: q+1
      1056: 1
      1057: 1
      1058: 1
      1059: q^2+q+1
      1060: 1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: 1
      1065: 1
      1073: 1
      1079: 1
      1081: 1
      1083: 1
      1087: 1
      1089: 1
      1091: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1115: 1
      1121: 1
      1123: 1
      1125: 1
      1129: 1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1146: 1
      1147: 1
      1148: 1
      1149: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1167: 1
      1173: 1
      1175: 1
      1177: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1212: q+1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1218: 1
      1220: 1
      1222: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: 1
      1245: 1
      1246: 1
      1247: q+1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: 1
      1255: 1
      1256: q+1
      1257: 1
      1258: q+1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1270: 1
      1281: 1
      1288: 1
      1294: 1
      1296: 1
      1298: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1317: 1
      1323: 1
      1325: 1
      1327: 1
      1331: 1
      1333: 1
      1335: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1364: 1
      1370: 1
      1372: 1
      1374: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1394: 1
      1395: 1
      1396: 1
      1397: q+1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1406: 1
      1412: 1
      1414: 1
      1416: 1
      1420: 1
      1421: 1
      1423: 1
      1424: 1
      1426: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1437: 1
      1438: 1
      1439: 1
      1440: q+1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: 1
      1448: 1
      1449: q+1
      1450: 1
      1451: q+1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1473: 1
      1479: 1
      1481: 1
      1483: 1
      1496: 1
      1503: 1
      1509: 1
      1511: 1
      1513: 1
      1517: 1
      1518: 1
      1520: 1
      1521: 1
      1523: 1
      1535: 1
      1542: 1
      1548: 1
      1550: 1
      1552: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1571: 1
      1577: 1
      1579: 1
      1581: 1
      1585: 1
      1587: 1
      1589: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1601: 1
      1602: 1
      1603: 1
      1604: q+1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1627: 1
      1649: 1
      1655: 1
      1657: 1
      1659: 1
      1679: 1
      1685: 1
      1687: 1
      1689: 1
      1702: 1
      1709: 1
      1715: 1
      1717: 1
      1719: 1
      1723: 1
      1724: 1
      1726: 1
      1727: 1
      1729: 1
      1760: 1
      1781: 1
      1803: 1
      1809: 1
      1811: 1
      1813: 1
      1865: 1

1866:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q^3+q^2+q+1
         6: q+1
         7: q+1
         8: q+1
         9: q^3+q^2+q+1
        10: q+1
        11: q^3+q^2+q+1
        12: q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q+1
        15: q^3+q^2+q+1
        16: q^3+q^2+q+1
        17: q+1
        18: q^3+q^2+q+1
        19: q^3+q^2+q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q^3+q^2+q+1
        29: q+1
        30: q^3+q^2+q+1
        31: q+1
        32: q^3+q^2+q+1
        33: q+1
        34: q+1
        35: q+1
        36: q^3+q^2+q+1
        37: q+1
        38: q^3+q^2+q+1
        39: q^3+q^2+q+1
        40: q+1
        41: q+1
        42: q+1
        43: q^3+q^2+q+1
        44: q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q+1
        49: q^3+q^2+q+1
        50: q+1
        51: q+1
        52: q+1
        53: 1
        54: q+1
        55: q+1
        56: q+1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q^3+q^2+q+1
        69: q+1
        70: q^3+q^2+q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q^3+q^2+q+1
        80: q+1
        81: q^3+q^2+q+1
        82: q+1
        83: q^3+q^2+q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q^3+q^2+q+1
        93: q+1
        94: q^3+q^2+q+1
        95: q+1
        96: q^3+q^2+q+1
        97: q+1
        98: q+1
        99: q+1
       100: q^3+q^2+q+1
       101: q+1
       102: q^3+q^2+q+1
       103: q^3+q^2+q+1
       104: q+1
       105: q+1
       106: q+1
       107: 1
       108: 1
       109: 1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: 1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q^3+q^2+q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q^3+q^2+q+1
       153: q+1
       154: q^3+q^2+q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^3+q^2+q+1
       174: q+1
       175: q^3+q^2+q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q^3+q^2+q+1
       185: q+1
       186: q^3+q^2+q+1
       187: q+1
       188: q^3+q^2+q+1
       189: q+1
       190: q+1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q+1
       198: q+1
       199: q+1
       200: q+1
       201: 1
       202: 1
       203: 1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: 1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^3+q^2+q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: 1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^3+q^2+q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^3+q^2+q+1
       307: q+1
       308: q^3+q^2+q+1
       310: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       319: q+1
       320: q+1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q+1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       365: q+1
       366: q+1
       367: q+1
       368: 1
       369: 1
       370: 1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: 1
       384: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       404: q+1
       405: q+1
       406: q+1
       407: 1
       408: 1
       409: 1
       410: q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: 1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: 1
       446: q+1
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^3+q^2+q+1
       463: q+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       474: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       526: q+1
       527: q+1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q+1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: 1
       547: 1
       548: 1
       549: q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       573: q+1
       574: q+1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q+1
       582: q+1
       583: q+1
       584: q+1
       585: 1
       586: 1
       587: 1
       588: q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       619: q+1
       620: q+1
       621: q+1
       622: 1
       623: 1
       624: 1
       625: q+1
       626: q+1
       627: q+1
       628: q+1
       629: q+1
       630: 1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       637: 1
       638: q+1
       639: q+1
       640: q+1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       651: 1
       652: 1
       653: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       695: q+1
       696: q+1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: q+1
       702: q+1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       713: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       731: q+1
       732: q+1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q+1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: q+1
       750: q+1
       751: 1
       752: q+1
       753: q+1
       754: q+1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       765: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       774: q+1
       775: q+1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q+1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: q+1
       802: q+1
       803: 1
       804: q+1
       805: q+1
       806: q+1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       817: q+1
       818: q+1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: q+1
       826: q+1
       827: q+1
       828: q+1
       829: 1
       830: 1
       831: 1
       832: q+1
       833: q+1
       834: q+1
       835: q+1
       836: q+1
       837: 1
       838: 1
       839: 1
       840: q+1
       841: q+1
       842: q+1
       843: q+1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: q+1
       857: 1
       863: 1
       864: 1
       865: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       897: q+1
       898: q+1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: q+1
       908: 1
       909: 1
       910: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       924: q+1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       934: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       952: q+1
       953: q+1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: q+1
       959: q+1
       962: 1
       963: 1
       964: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       978: q+1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       988: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1006: q+1
      1007: q+1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: q+1
      1013: q+1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1024: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1033: q+1
      1034: q+1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: q+1
      1042: q+1
      1043: q+1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: q+1
      1051: q+1
      1052: q+1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: q+1
      1061: q+1
      1062: 1
      1063: q+1
      1064: q+1
      1065: q+1
      1074: 1
      1080: 1
      1081: 1
      1082: 1
      1088: 1
      1089: 1
      1090: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1104: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1116: 1
      1122: 1
      1123: 1
      1124: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1156: q+1
      1157: q+1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: q+1
      1168: 1
      1174: 1
      1175: 1
      1176: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1208: q+1
      1209: q+1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: q+1
      1219: 1
      1220: 1
      1221: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1235: q+1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1245: q+1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1254: q+1
      1255: q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1263: q+1
      1264: q+1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: q+1
      1270: q+1
      1282: 1
      1289: 1
      1295: 1
      1296: 1
      1297: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1318: 1
      1324: 1
      1325: 1
      1326: 1
      1332: 1
      1333: 1
      1334: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1348: q+1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1379: 1
      1380: 1
      1381: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1395: q+1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1407: 1
      1413: 1
      1414: 1
      1415: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1438: q+1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1447: q+1
      1448: q+1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q+1
      1474: 1
      1480: 1
      1481: 1
      1482: 1
      1497: 1
      1504: 1
      1510: 1
      1511: 1
      1512: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1536: 1
      1543: 1
      1549: 1
      1550: 1
      1551: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1586: 1
      1587: 1
      1588: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1602: q+1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1628: 1
      1650: 1
      1656: 1
      1657: 1
      1658: 1
      1680: 1
      1686: 1
      1687: 1
      1688: 1
      1703: 1
      1710: 1
      1716: 1
      1717: 1
      1718: 1
      1724: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1761: 1
      1782: 1
      1804: 1
      1810: 1
      1811: 1
      1812: 1
      1866: 1

1867:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q^3+q^2+q+1
         6: q^3+q^2+q+1
         7: q+1
         8: q^2+q+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q^3+q^2+q+1
        12: q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^3+q^2+q+1
        15: q^3+q^2+q+1
        16: q^3+q^2+q+1
        17: q^3+q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+q^2+q+1
        20: q^2+1
        21: q+1
        22: q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^3+q^2+q+1
        26: q+1
        27: q^2+q+1
        28: q^3+q^2+q+1
        29: q^3+q^2+q+1
        30: q^3+q^2+q+1
        31: q^3+q^2+q+1
        32: q^3+q^2+q+1
        33: q^3+q^2+q+1
        34: q+1
        35: q^2+q+1
        36: q^3+q^2+q+1
        37: q^3+q^2+q+1
        38: q^3+q^2+q+1
        39: q^3+q^2+q+1
        40: q^3+q^2+q+1
        41: q+1
        42: q^2+q+1
        43: q^3+q^2+q+1
        44: q^3+q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^3+q^2+q+1
        49: q^3+q^2+q+1
        50: q^2+1
        51: q^2+1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q^2+q+1
        57: q^2+1
        58: q+1
        59: q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^3+q^2+q+1
        63: q+1
        64: q^2+q+1
        65: q^3+q^2+q+1
        66: q+1
        67: q^2+q+1
        68: q^3+q^2+q+1
        69: q^3+q^2+q+1
        70: q^3+q^2+q+1
        71: q^2+1
        72: q+1
        73: q+1
        74: q^2+q+1
        75: q^2+q+1
        76: q^3+q^2+q+1
        77: q+1
        78: q^2+q+1
        79: q^3+q^2+q+1
        80: q^3+q^2+q+1
        81: q^3+q^2+q+1
        82: q^3+q^2+q+1
        83: q^3+q^2+q+1
        84: q^2+1
        85: q+1
        86: q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^3+q^2+q+1
        90: q+1
        91: q^2+q+1
        92: q^3+q^2+q+1
        93: q^3+q^2+q+1
        94: q^3+q^2+q+1
        95: q^3+q^2+q+1
        96: q^3+q^2+q+1
        97: q^3+q^2+q+1
        98: q+1
        99: q^2+q+1
       100: q^3+q^2+q+1
       101: q^3+q^2+q+1
       102: q^3+q^2+q+1
       103: q^3+q^2+q+1
       104: q^2+1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^2+1
       113: q^2+1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q^2+q+1
       119: q^2+1
       120: q+1
       121: q+1
       122: q^2+q+1
       123: q^2+q+1
       124: q^2+1
       125: q+1
       126: q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q^3+q^2+q+1
       130: q+1
       131: q^2+q+1
       132: q^3+q^2+q+1
       133: q^3+q^2+q+1
       134: q^2+1
       135: q^2+1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q^2+q+1
       141: q^2+1
       142: q+1
       143: q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^3+q^2+q+1
       147: q+1
       148: q^2+q+1
       149: q^3+q^2+q+1
       150: q+1
       151: q^2+q+1
       152: q^3+q^2+q+1
       153: q^3+q^2+q+1
       154: q^3+q^2+q+1
       155: q^2+1
       156: q^2+1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q^2+q+1
       162: q^2+1
       163: q+1
       164: q+1
       165: q^2+q+1
       166: q^2+q+1
       167: q^3+q^2+q+1
       168: q+1
       169: q^2+q+1
       170: q^3+q^2+q+1
       171: q+1
       172: q^2+q+1
       173: q^3+q^2+q+1
       174: q^3+q^2+q+1
       175: q^3+q^2+q+1
       176: q^2+1
       177: q+1
       178: q+1
       179: q^2+q+1
       180: q^2+q+1
       181: q^3+q^2+q+1
       182: q+1
       183: q^2+q+1
       184: q^3+q^2+q+1
       185: q^3+q^2+q+1
       186: q^3+q^2+q+1
       187: q^3+q^2+q+1
       188: q^3+q^2+q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: q^2+1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q^2+1
       207: q^2+1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q^2+q+1
       213: q^2+1
       214: q^2+1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q^2+q+1
       220: q^2+1
       221: q+1
       222: q+1
       223: q^2+q+1
       224: q^2+q+1
       225: q^3+q^2+q+1
       226: q+1
       227: q^2+q+1
       228: q^2+1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q^2+1
       237: q^2+1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q^2+q+1
       243: q^2+1
       244: q+1
       245: q+1
       246: q^2+q+1
       247: q^2+q+1
       248: q^2+1
       249: q+1
       250: q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q^3+q^2+q+1
       254: q+1
       255: q^2+q+1
       256: q^3+q^2+q+1
       257: q^3+q^2+q+1
       258: q^2+1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+1
       267: q^2+1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q^2+q+1
       273: q^2+1
       274: q+1
       275: q+1
       276: q^2+q+1
       277: q^2+q+1
       278: q^2+1
       279: q+1
       280: q+1
       281: q^2+q+1
       282: q^2+q+1
       283: q^3+q^2+q+1
       284: q+1
       285: q^2+q+1
       286: q^3+q^2+q+1
       287: q^3+q^2+q+1
       288: q^2+1
       289: q^2+1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: q^2+q+1
       295: q^2+1
       296: q+1
       297: q+1
       298: q^2+q+1
       299: q^2+q+1
       300: q^3+q^2+q+1
       301: q+1
       302: q^2+q+1
       303: q^3+q^2+q+1
       304: q+1
       305: q^2+q+1
       306: q^3+q^2+q+1
       307: q^3+q^2+q+1
       308: q^3+q^2+q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       327: q+1
       328: q^2+1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: q^2+1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: q^2+1
       345: q^2+1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: q^2+q+1
       351: q^2+1
       352: q+1
       353: q+1
       354: q^2+q+1
       355: q^2+q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: q^2+1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: q^2+1
       374: q^2+1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q^2+q+1
       380: q^2+1
       381: q^2+1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q^2+q+1
       387: q^2+1
       388: q+1
       389: q+1
       390: q^2+q+1
       391: q^2+q+1
       392: q^3+q^2+q+1
       393: q+1
       394: q^2+q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q^2+1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: q^2+1
       413: q^2+1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q^2+q+1
       419: q^2+1
       420: q^2+1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q^2+q+1
       426: q^2+1
       427: q+1
       428: q+1
       429: q^2+q+1
       430: q^2+q+1
       431: q^3+q^2+q+1
       432: q+1
       433: q^2+q+1
       434: q^2+1
       435: 1
       436: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q^2+1
       443: q^2+1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q^2+q+1
       449: q^2+1
       450: q+1
       451: q+1
       452: q^2+q+1
       453: q^2+q+1
       454: q^2+1
       455: q+1
       456: q+1
       457: q^2+q+1
       458: q^2+q+1
       459: q^3+q^2+q+1
       460: q+1
       461: q^2+q+1
       462: q^3+q^2+q+1
       463: q^3+q^2+q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: q^2+1
       502: 1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: q^2+1
       510: q^2+1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q^2+q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       534: q+1
       535: q^2+1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: q^2+1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: q^2+1
       552: q^2+1
       553: 1
       554: q+1
       555: q+1
       556: q+1
       557: q^2+q+1
       558: q^2+1
       559: q+1
       560: q+1
       561: q^2+q+1
       562: q^2+q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       581: q+1
       582: q^2+1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: q^2+1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: q^2+1
       599: q^2+1
       600: 1
       601: q+1
       602: q+1
       603: q+1
       604: q^2+q+1
       605: q^2+1
       606: q+1
       607: q+1
       608: q^2+q+1
       609: q^2+q+1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q^2+1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q^2+1
       628: q^2+1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q^2+q+1
       634: q^2+1
       635: q^2+1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q^2+q+1
       641: q^2+1
       642: q+1
       643: q+1
       644: q^2+q+1
       645: q^2+q+1
       646: q^3+q^2+q+1
       647: q+1
       648: q^2+q+1
       653: 1
       654: 1
       655: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: q^2+1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       730: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       739: q+1
       740: q^2+1
       741: 1
       742: 1
       743: 1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: q^2+1
       749: q^2+1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: q^2+q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       782: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       791: q+1
       792: q^2+1
       793: 1
       794: 1
       795: 1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       800: q^2+1
       801: q^2+1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: q^2+q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: q+1
       825: q+1
       826: q^2+1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       834: q^2+1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       842: q^2+1
       843: q^2+1
       844: 1
       845: q+1
       846: q+1
       847: q+1
       848: q^2+q+1
       849: q^2+1
       850: q+1
       851: q+1
       852: q^2+q+1
       853: q^2+q+1
       858: 1
       865: 1
       866: 1
       867: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: q+1
       905: q+1
       910: 1
       911: 1
       912: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       951: q+1
       952: q^2+1
       953: 1
       954: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: q+1
       964: 1
       965: 1
       966: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: q+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: q^2+1
      1007: 1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: q+1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: q+1
      1041: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: q+1
      1050: q+1
      1051: q^2+1
      1052: 1
      1053: 1
      1054: 1
      1055: q+1
      1056: q+1
      1057: q+1
      1058: q+1
      1059: q^2+1
      1060: q^2+1
      1061: 1
      1062: q+1
      1063: q+1
      1064: q+1
      1065: q^2+q+1
      1075: 1
      1082: 1
      1083: 1
      1084: 1
      1090: 1
      1091: 1
      1092: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: q+1
      1117: 1
      1124: 1
      1125: 1
      1126: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: q+1
      1164: q+1
      1169: 1
      1176: 1
      1177: 1
      1178: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: q+1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: q+1
      1216: q+1
      1221: 1
      1222: 1
      1223: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: q+1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: q+1
      1261: q+1
      1262: q+1
      1263: q^2+1
      1264: 1
      1265: 1
      1266: 1
      1267: q+1
      1268: q+1
      1269: q+1
      1270: q+1
      1283: 1
      1290: 1
      1297: 1
      1298: 1
      1299: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1319: 1
      1326: 1
      1327: 1
      1328: 1
      1334: 1
      1335: 1
      1336: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: q+1
      1366: 1
      1373: 1
      1374: 1
      1375: 1
      1381: 1
      1382: 1
      1383: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1402: q+1
      1408: 1
      1415: 1
      1416: 1
      1417: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: q+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: q+1
      1454: q+1
      1455: q+1
      1475: 1
      1482: 1
      1483: 1
      1484: 1
      1498: 1
      1505: 1
      1512: 1
      1513: 1
      1514: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1537: 1
      1544: 1
      1551: 1
      1552: 1
      1553: 1
      1558: 1
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      1562: 1
      1573: 1
      1580: 1
      1581: 1
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      1588: 1
      1589: 1
      1590: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1609: q+1
      1629: 1
      1651: 1
      1658: 1
      1659: 1
      1660: 1
      1681: 1
      1688: 1
      1689: 1
      1690: 1
      1704: 1
      1711: 1
      1718: 1
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      1720: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1729: 1
      1762: 1
      1783: 1
      1805: 1
      1812: 1
      1813: 1
      1814: 1
      1867: 1

1868:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
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        20: 1
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        22: 1
        23: 1
        24: 1
        25: 1
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        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
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        86: 1
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        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
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       102: 1
       103: 1
       105: 1
       107: 1
       108: 1
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       110: 1
       111: 1
       112: 1
       114: 1
       115: 1
       116: 1
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       118: 1
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       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
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       127: 1
       128: 1
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       165: 1
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       206: 1
       208: 1
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       212: 1
       213: 1
       215: 1
       216: 1
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       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
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       229: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       238: 1
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       240: 1
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       243: 1
       244: 1
       245: 1
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       250: 1
       251: 1
       252: 1
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       255: 1
       256: 1
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       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       268: 1
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       290: 1
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       297: 1
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       300: 1
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       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       312: 1
       314: 1
       316: 1
       317: 1
       318: 1
       321: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: 1
       329: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       337: 1
       339: 1
       340: 1
       341: 1
       342: 1
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       344: 1
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       397: 1
       399: 1
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       405: 1
       407: 1
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       469: 1
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       476: 1
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       485: 1
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       515: 1
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       530: 1
       531: 1
       532: 1
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       540: 1
       541: 1
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       556: 1
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       562: 1
       566: 1
       568: 1
       570: 1
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       572: 1
       575: 1
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       579: 1
       580: 1
       581: 1
       583: 1
       585: 1
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       609: 1
       612: 1
       614: 1
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       622: 1
       623: 1
       624: 1
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       627: 1
       629: 1
       630: 1
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       632: 1
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       636: 1
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       654: 1
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       662: 1
       664: 1
       665: 1
       669: 1
       671: 1
       673: 1
       674: 1
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       679: 1
       681: 1
       683: 1
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       685: 1
       688: 1
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       696: 1
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       699: 1
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       702: 1
       708: 1
       710: 1
       711: 1
       715: 1
       717: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
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       728: 1
       729: 1
       730: 1
       733: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       750: 1
       751: 1
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       753: 1
       754: 1
       760: 1
       762: 1
       763: 1
       767: 1
       769: 1
       771: 1
       772: 1
       773: 1
       776: 1
       778: 1
       779: 1
       780: 1
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       782: 1
       785: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       793: 1
       795: 1
       796: 1
       797: 1
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       799: 1
       800: 1
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       806: 1
       810: 1
       812: 1
       814: 1
       815: 1
       816: 1
       819: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       835: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       859: 1
       866: 1
       868: 1
       874: 1
       876: 1
       877: 1
       883: 1
       885: 1
       886: 1
       890: 1
       892: 1
       894: 1
       895: 1
       896: 1
       899: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       911: 1
       913: 1
       919: 1
       921: 1
       922: 1
       926: 1
       928: 1
       930: 1
       931: 1
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       936: 1
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      1815: 1
      1868: 1

1869:    0: 1
         1: 1
         2: 1
         3: 1
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       313: 1
       315: 1
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       338: 1
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       470: 1
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       477: 1
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       522: 1
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       525: 1
       529: 1
       530: 1
       531: 1
       532: 1
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       541: 1
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       562: 1
       567: 1
       569: 1
       570: 1
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       576: 1
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       580: 1
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       584: 1
       585: 1
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       592: 1
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       609: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       621: 1
       622: 1
       623: 1
       624: 1
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       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
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       635: 1
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       640: 1
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       642: 1
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       655: 1
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       664: 1
       665: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       680: 1
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       689: 1
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       709: 1
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       716: 1
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       734: 1
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       742: 1
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       746: 1
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       749: 1
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       786: 1
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       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
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       836: 1
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       838: 1
       839: 1
       840: 1
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       843: 1
       844: 1
       845: 1
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       847: 1
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       850: 1
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       860: 1
       867: 1
       868: 1
       875: 1
       876: 1
       877: 1
       884: 1
       885: 1
       886: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       912: 1
       913: 1
       920: 1
       921: 1
       922: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       937: 1
       939: 1
       940: 1
       941: 1
       942: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       966: 1
       967: 1
       974: 1
       975: 1
       976: 1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       991: 1
       993: 1
       994: 1
       995: 1
       996: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1020: 1
      1021: 1
      1022: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1046: 1
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      1048: 1
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      1050: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1077: 1
      1084: 1
      1085: 1
      1092: 1
      1093: 1
      1100: 1
      1101: 1
      1102: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1119: 1
      1126: 1
      1127: 1
      1134: 1
      1135: 1
      1136: 1
      1143: 1
      1144: 1
      1145: 1
      1150: 1
      1152: 1
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      1155: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1171: 1
      1178: 1
      1179: 1
      1186: 1
      1187: 1
      1188: 1
      1195: 1
      1196: 1
      1197: 1
      1202: 1
      1204: 1
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      1207: 1
      1211: 1
      1212: 1
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      1223: 1
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      1231: 1
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      1248: 1
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      1257: 1
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      1265: 1
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      1285: 1
      1292: 1
      1299: 1
      1300: 1
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      1321: 1
      1328: 1
      1329: 1
      1336: 1
      1337: 1
      1344: 1
      1345: 1
      1346: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1368: 1
      1375: 1
      1376: 1
      1383: 1
      1384: 1
      1391: 1
      1392: 1
      1393: 1
      1398: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1410: 1
      1417: 1
      1418: 1
      1425: 1
      1426: 1
      1427: 1
      1434: 1
      1435: 1
      1436: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1450: 1
      1451: 1
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      1455: 1
      1477: 1
      1484: 1
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      1500: 1
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      1522: 1
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      1539: 1
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      1553: 1
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      1575: 1
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      1590: 1
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      1600: 1
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      1660: 1
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      1690: 1
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      1706: 1
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      1728: 1
      1729: 1
      1730: 1
      1764: 1
      1785: 1
      1807: 1
      1814: 1
      1815: 1
      1869: 1

1870:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+q+1
       105: q^2+q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q+1
       112: q^2+q+1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q+1
       120: q^2+q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q^2+q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q^2+q+1
       191: q^2+q+1
       192: q^2+q+1
       193: q+1
       194: q+1
       195: q^2+q+1
       196: q+1
       197: q+1
       198: q^2+q+1
       199: q^2+q+1
       200: q^2+q+1
       201: q^2+q+1
       202: q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q^2+q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+q+1
       321: q^2+q+1
       322: q^2+q+1
       323: q+1
       324: q+1
       325: q^2+q+1
       326: q+1
       327: q+1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       666: q+1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       854: q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       859: q+1
       860: q+1
       861: q+1
       862: q+1
       863: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: 1
       903: q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1066: q+1
      1067: q+1
      1068: q+1
      1069: 1
      1070: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: q+1
      1272: 1
      1273: 1
      1274: q+1
      1275: q+1
      1276: q+1
      1277: 1
      1278: q+1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: 1
      1427: 1
      1428: 1
      1429: 1
      1432: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: q+1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1516: 1
      1517: 1
      1519: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1547: 1
      1555: 1
      1556: 1
      1559: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1584: 1
      1592: 1
      1593: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1654: 1
      1662: 1
      1663: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1684: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1714: 1
      1722: 1
      1723: 1
      1730: 1
      1731: 1
      1732: 1
      1733: 1
      1734: 1
      1735: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1743: 1
      1744: 1
      1750: 1
      1765: 1
      1768: 1
      1786: 1
      1787: 1
      1788: 1
      1808: 1
      1816: 1
      1817: 1
      1818: 1
      1819: 1
      1820: 1
      1849: 1
      1870: 1

1871:    0: 3q^4+9q^3+10q^2+5q+1
         1: 3q^4+9q^3+10q^2+5q+1
         2: q^4+7q^3+10q^2+5q+1
         3: 3q^4+9q^3+10q^2+5q+1
         4: q^4+7q^3+10q^2+5q+1
         5: q^4+7q^3+10q^2+5q+1
         6: q^4+7q^3+10q^2+5q+1
         7: q^4+7q^3+10q^2+5q+1
         8: q^4+7q^3+10q^2+5q+1
         9: 3q^4+9q^3+10q^2+5q+1
        10: q^4+7q^3+10q^2+5q+1
        11: q^4+7q^3+10q^2+5q+1
        12: q^4+7q^3+10q^2+5q+1
        13: q^4+7q^3+10q^2+5q+1
        14: 5q^3+10q^2+5q+1
        15: q^4+7q^3+10q^2+5q+1
        16: q^4+7q^3+10q^2+5q+1
        17: 5q^3+10q^2+5q+1
        18: q^4+7q^3+10q^2+5q+1
        19: 6q^3+10q^2+5q+1
        20: q^4+7q^3+10q^2+5q+1
        21: q^4+7q^3+10q^2+5q+1
        22: q^4+7q^3+10q^2+5q+1
        23: 3q^3+8q^2+5q+1
        24: 3q^3+8q^2+5q+1
        25: q^4+7q^3+10q^2+5q+1
        26: q^4+7q^3+10q^2+5q+1
        27: q^4+7q^3+10q^2+5q+1
        28: q^4+7q^3+10q^2+5q+1
        29: 5q^3+10q^2+5q+1
        30: q^4+7q^3+10q^2+5q+1
        31: 5q^3+10q^2+5q+1
        32: 6q^3+10q^2+5q+1
        33: 5q^3+10q^2+5q+1
        34: 5q^3+10q^2+5q+1
        35: 5q^3+10q^2+5q+1
        36: q^4+7q^3+10q^2+5q+1
        37: 3q^3+8q^2+5q+1
        38: 4q^3+8q^2+5q+1
        39: q^4+7q^3+10q^2+5q+1
        40: 5q^3+10q^2+5q+1
        41: 5q^3+10q^2+5q+1
        42: 5q^3+10q^2+5q+1
        43: q^4+7q^3+10q^2+5q+1
        44: 3q^3+8q^2+5q+1
        45: q^4+7q^3+10q^2+5q+1
        46: 4q^3+8q^2+5q+1
        47: 6q^3+10q^2+5q+1
        48: 4q^3+10q^2+5q+1
        49: 6q^3+10q^2+5q+1
        50: 3q^3+8q^2+5q+1
        51: 3q^3+8q^2+5q+1
        52: q^4+7q^3+10q^2+5q+1
        53: q^4+5q^3+8q^2+5q+1
        54: 3q^3+8q^2+5q+1
        55: 3q^3+8q^2+5q+1
        56: q^3+7q^2+5q+1
        57: q^4+7q^3+10q^2+5q+1
        58: q^4+7q^3+10q^2+5q+1
        59: q^4+7q^3+10q^2+5q+1
        60: 3q^3+8q^2+5q+1
        61: 3q^3+8q^2+5q+1
        62: 5q^3+10q^2+5q+1
        63: 5q^3+10q^2+5q+1
        64: 5q^3+10q^2+5q+1
        65: 5q^3+10q^2+5q+1
        66: 5q^3+10q^2+5q+1
        67: 5q^3+10q^2+5q+1
        68: 6q^3+10q^2+5q+1
        69: 4q^3+10q^2+5q+1
        70: 6q^3+10q^2+5q+1
        71: 5q^3+10q^2+5q+1
        72: 5q^3+10q^2+5q+1
        73: 5q^3+10q^2+5q+1
        74: q^3+6q^2+5q+1
        75: 3q^3+8q^2+5q+1
        76: 3q^3+8q^2+5q+1
        77: 3q^3+8q^2+5q+1
        78: 3q^3+8q^2+5q+1
        79: 4q^3+8q^2+5q+1
        80: q^3+6q^2+5q+1
        81: q^4+7q^3+10q^2+5q+1
        82: 3q^3+8q^2+5q+1
        83: 4q^3+8q^2+5q+1
        84: 5q^3+10q^2+5q+1
        85: 5q^3+10q^2+5q+1
        86: 5q^3+10q^2+5q+1
        87: 3q^3+8q^2+5q+1
        88: q^3+6q^2+5q+1
        89: 3q^3+8q^2+5q+1
        90: 3q^3+8q^2+5q+1
        91: 3q^3+8q^2+5q+1
        92: q^4+7q^3+10q^2+5q+1
        93: 3q^3+8q^2+5q+1
        94: 4q^3+8q^2+5q+1
        95: q^3+6q^2+5q+1
        96: 4q^3+8q^2+5q+1
        97: 4q^3+10q^2+5q+1
        98: 4q^3+10q^2+5q+1
        99: 4q^3+10q^2+5q+1
       100: 6q^3+10q^2+5q+1
       101: q^3+7q^2+5q+1
       102: 4q^3+8q^2+5q+1
       103: 4q^3+8q^2+5q+1
       104: q^3+7q^2+5q+1
       105: 3q^3+8q^2+5q+1
       106: 3q^3+8q^2+5q+1
       107: q^4+5q^3+8q^2+5q+1
       108: 2q^3+6q^2+5q+1
       109: 2q^3+6q^2+5q+1
       110: q^3+7q^2+5q+1
       111: q^3+7q^2+5q+1
       112: 3q^3+8q^2+5q+1
       113: 3q^3+8q^2+5q+1
       114: q^4+7q^3+10q^2+5q+1
       115: q^4+5q^3+8q^2+5q+1
       116: 3q^3+8q^2+5q+1
       117: 3q^3+8q^2+5q+1
       118: q^3+7q^2+5q+1
       119: 5q^3+10q^2+5q+1
       120: 5q^3+10q^2+5q+1
       121: 5q^3+10q^2+5q+1
       122: 3q^3+8q^2+5q+1
       123: q^3+6q^2+5q+1
       124: 5q^3+10q^2+5q+1
       125: 5q^3+10q^2+5q+1
       126: 5q^3+10q^2+5q+1
       127: q^3+6q^2+5q+1
       128: 3q^3+8q^2+5q+1
       129: 4q^3+10q^2+5q+1
       130: 4q^3+10q^2+5q+1
       131: 4q^3+10q^2+5q+1
       132: 6q^3+10q^2+5q+1
       133: q^3+7q^2+5q+1
       134: q^3+6q^2+5q+1
       135: 3q^3+8q^2+5q+1
       136: 5q^3+10q^2+5q+1
       137: 2q^3+6q^2+5q+1
       138: q^3+6q^2+5q+1
       139: 3q^3+8q^2+5q+1
       140: 5q^2+5q+1
       141: 3q^3+8q^2+5q+1
       142: 3q^3+8q^2+5q+1
       143: 3q^3+8q^2+5q+1
       144: 4q^2+5q+1
       145: 2q^3+6q^2+5q+1
       146: q^3+6q^2+5q+1
       147: q^3+6q^2+5q+1
       148: q^3+6q^2+5q+1
       149: 3q^3+8q^2+5q+1
       150: 3q^3+8q^2+5q+1
       151: 3q^3+8q^2+5q+1
       152: 4q^3+8q^2+5q+1
       153: q^3+6q^2+5q+1
       154: 4q^3+8q^2+5q+1
       155: 3q^3+8q^2+5q+1
       156: q^3+6q^2+5q+1
       157: 5q^3+10q^2+5q+1
       158: 2q^3+6q^2+5q+1
       159: 3q^3+8q^2+5q+1
       160: q^3+6q^2+5q+1
       161: 5q^2+5q+1
       162: 3q^3+8q^2+5q+1
       163: 3q^3+8q^2+5q+1
       164: 3q^3+8q^2+5q+1
       165: 2q^3+6q^2+5q+1
       166: 4q^2+5q+1
       167: 3q^3+8q^2+5q+1
       168: 3q^3+8q^2+5q+1
       169: 3q^3+8q^2+5q+1
       170: q^3+6q^2+5q+1
       171: q^3+6q^2+5q+1
       172: q^3+6q^2+5q+1
       173: 4q^3+8q^2+5q+1
       174: q^3+6q^2+5q+1
       175: 4q^3+8q^2+5q+1
       176: 4q^3+10q^2+5q+1
       177: 4q^3+10q^2+5q+1
       178: 4q^3+10q^2+5q+1
       179: q^3+6q^2+5q+1
       180: q^3+6q^2+5q+1
       181: q^3+7q^2+5q+1
       182: q^3+7q^2+5q+1
       183: q^3+7q^2+5q+1
       184: 4q^3+8q^2+5q+1
       185: 5q^2+5q+1
       186: 4q^3+8q^2+5q+1
       187: 5q^2+5q+1
       188: 3q^3+7q^2+5q+1
       189: q^3+7q^2+5q+1
       190: q^3+7q^2+5q+1
       191: 2q^3+6q^2+5q+1
       192: 2q^3+6q^2+5q+1
       193: 2q^3+6q^2+5q+1
       194: 2q^3+6q^2+5q+1
       195: q^3+5q^2+5q+1
       196: q^3+7q^2+5q+1
       197: 3q^2+4q+1
       198: q^3+7q^2+5q+1
       199: 3q^3+8q^2+5q+1
       200: 3q^3+8q^2+5q+1
       201: q^4+5q^3+8q^2+5q+1
       202: 2q^3+6q^2+5q+1
       203: 2q^3+6q^2+5q+1
       204: q^3+7q^2+5q+1
       205: q^3+7q^2+5q+1
       206: 3q^3+8q^2+5q+1
       207: q^3+6q^2+5q+1
       208: 5q^3+10q^2+5q+1
       209: 2q^3+6q^2+5q+1
       210: 3q^3+8q^2+5q+1
       211: q^3+6q^2+5q+1
       212: 5q^2+5q+1
       213: q^3+6q^2+5q+1
       214: 3q^3+8q^2+5q+1
       215: 5q^3+10q^2+5q+1
       216: 2q^3+6q^2+5q+1
       217: q^3+6q^2+5q+1
       218: 3q^3+8q^2+5q+1
       219: 5q^2+5q+1
       220: 4q^3+10q^2+5q+1
       221: 4q^3+10q^2+5q+1
       222: 4q^3+10q^2+5q+1
       223: q^3+6q^2+5q+1
       224: q^3+6q^2+5q+1
       225: q^3+7q^2+5q+1
       226: q^3+7q^2+5q+1
       227: q^3+7q^2+5q+1
       228: 5q^2+5q+1
       229: q^3+6q^2+5q+1
       230: 3q^3+8q^2+5q+1
       231: 2q^3+6q^2+5q+1
       232: 3q^2+5q+1
       233: q^3+4q^2+5q+1
       234: 5q^2+5q+1
       235: 5q^2+5q+1
       236: 4q^2+5q+1
       237: 2q^3+6q^2+5q+1
       238: 3q^3+8q^2+5q+1
       239: 2q^3+6q^2+5q+1
       240: 4q^2+5q+1
       241: 2q^3+6q^2+5q+1
       242: 3q^2+5q+1
       243: q^3+6q^2+5q+1
       244: q^3+6q^2+5q+1
       245: q^3+6q^2+5q+1
       246: 4q^2+5q+1
       247: 2q^2+3q+1
       248: 3q^3+8q^2+5q+1
       249: 3q^3+8q^2+5q+1
       250: 3q^3+8q^2+5q+1
       251: 4q^2+5q+1
       252: 2q^3+6q^2+5q+1
       253: q^3+6q^2+5q+1
       254: q^3+6q^2+5q+1
       255: q^3+6q^2+5q+1
       256: 4q^3+8q^2+5q+1
       257: 5q^2+5q+1
       258: 5q^2+5q+1
       259: 3q^3+8q^2+5q+1
       260: q^3+6q^2+5q+1
       261: 2q^3+6q^2+5q+1
       262: q^3+4q^2+5q+1
       263: 3q^2+5q+1
       264: 5q^2+5q+1
       265: 5q^2+5q+1
       266: 2q^3+6q^2+5q+1
       267: 4q^2+5q+1
       268: 3q^3+8q^2+5q+1
       269: 2q^3+6q^2+5q+1
       270: 2q^3+6q^2+5q+1
       271: 4q^2+5q+1
       272: 3q^2+5q+1
       273: 3q^3+8q^2+5q+1
       274: 3q^3+8q^2+5q+1
       275: 3q^3+8q^2+5q+1
       276: 2q^3+6q^2+5q+1
       277: 4q^2+5q+1
       278: q^3+6q^2+5q+1
       279: q^3+6q^2+5q+1
       280: q^3+6q^2+5q+1
       281: 2q^2+3q+1
       282: 4q^2+5q+1
       283: q^3+6q^2+5q+1
       284: q^3+6q^2+5q+1
       285: q^3+6q^2+5q+1
       286: 4q^3+8q^2+5q+1
       287: 5q^2+5q+1
       288: q^3+6q^2+5q+1
       289: q^3+6q^2+5q+1
       290: 4q^3+10q^2+5q+1
       291: q^3+5q^2+5q+1
       292: q^3+6q^2+5q+1
       293: q^3+6q^2+5q+1
       294: 4q^2+5q+1
       295: q^3+7q^2+5q+1
       296: q^3+7q^2+5q+1
       297: q^3+7q^2+5q+1
       298: 3q^2+5q+1
       299: 3q^2+5q+1
       300: 5q^2+5q+1
       301: 5q^2+5q+1
       302: 5q^2+5q+1
       303: 5q^2+5q+1
       304: 5q^2+5q+1
       305: 5q^2+5q+1
       306: 3q^3+7q^2+5q+1
       307: 4q^2+5q+1
       308: 3q^3+7q^2+5q+1
       309: 3q^2+4q+1
       310: q^3+7q^2+5q+1
       311: q^3+5q^2+5q+1
       312: 2q^3+6q^2+5q+1
       313: 2q^2+3q+1
       314: 2q^2+3q+1
       315: 2q^3+6q^2+5q+1
       316: q^3+5q^2+5q+1
       317: q^2+4q+1
       318: 3q^2+4q+1
       319: q^3+7q^2+5q+1
       320: q^3+7q^2+5q+1
       321: 2q^3+6q^2+5q+1
       322: 2q^3+6q^2+5q+1
       323: 2q^3+6q^2+5q+1
       324: 2q^3+6q^2+5q+1
       325: q^3+5q^2+5q+1
       326: q^3+7q^2+5q+1
       327: 3q^2+4q+1
       328: 5q^2+5q+1
       329: 3q^3+8q^2+5q+1
       330: q^3+6q^2+5q+1
       331: 2q^3+6q^2+5q+1
       332: q^3+4q^2+5q+1
       333: 3q^2+5q+1
       334: 5q^2+5q+1
       335: 5q^2+5q+1
       336: 5q^2+5q+1
       337: q^3+6q^2+5q+1
       338: 3q^3+8q^2+5q+1
       339: 2q^3+6q^2+5q+1
       340: 3q^2+5q+1
       341: q^3+4q^2+5q+1
       342: 5q^2+5q+1
       343: 5q^2+5q+1
       344: q^3+6q^2+5q+1
       345: q^3+6q^2+5q+1
       346: 4q^3+10q^2+5q+1
       347: q^3+5q^2+5q+1
       348: q^3+6q^2+5q+1
       349: q^3+6q^2+5q+1
       350: 4q^2+5q+1
       351: q^3+7q^2+5q+1
       352: q^3+7q^2+5q+1
       353: q^3+7q^2+5q+1
       354: 3q^2+5q+1
       355: 3q^2+5q+1
       356: 5q^2+5q+1
       357: 5q^2+5q+1
       358: 3q^2+5q+1
       359: q^3+4q^2+5q+1
       360: 3q^2+5q+1
       361: q^3+4q^2+5q+1
       362: 2q^2+5q+1
       363: 5q^2+5q+1
       364: q^2+4q+1
       365: 3q^2+5q+1
       366: 4q^2+5q+1
       367: 2q^3+6q^2+5q+1
       368: 2q^3+6q^2+5q+1
       369: 3q^2+5q+1
       370: q^3+4q^2+5q+1
       371: 3q^2+5q+1
       372: 3q^2+5q+1
       373: 4q^2+5q+1
       374: 2q^2+3q+1
       375: q^3+6q^2+5q+1
       376: 2q^2+3q+1
       377: 4q^2+5q+1
       378: 2q^2+3q+1
       379: q^2+3q+1
       380: 4q^2+5q+1
       381: 2q^3+6q^2+5q+1
       382: 3q^3+8q^2+5q+1
       383: 2q^3+6q^2+5q+1
       384: 4q^2+5q+1
       385: 2q^3+6q^2+5q+1
       386: 3q^2+5q+1
       387: q^3+6q^2+5q+1
       388: q^3+6q^2+5q+1
       389: q^3+6q^2+5q+1
       390: 4q^2+5q+1
       391: 2q^2+3q+1
       392: 5q^2+5q+1
       393: 5q^2+5q+1
       394: 5q^2+5q+1
       395: 5q^2+5q+1
       396: 5q^2+5q+1
       397: q^3+4q^2+5q+1
       398: 3q^2+5q+1
       399: q^3+4q^2+5q+1
       400: 3q^2+5q+1
       401: 2q^2+5q+1
       402: 5q^2+5q+1
       403: q^2+4q+1
       404: 3q^2+5q+1
       405: 2q^3+6q^2+5q+1
       406: 4q^2+5q+1
       407: 2q^3+6q^2+5q+1
       408: q^3+4q^2+5q+1
       409: 3q^2+5q+1
       410: 3q^2+5q+1
       411: 3q^2+5q+1
       412: 2q^3+6q^2+5q+1
       413: 4q^2+5q+1
       414: 3q^3+8q^2+5q+1
       415: 2q^3+6q^2+5q+1
       416: 2q^3+6q^2+5q+1
       417: 4q^2+5q+1
       418: 3q^2+5q+1
       419: 2q^2+3q+1
       420: 4q^2+5q+1
       421: q^3+6q^2+5q+1
       422: 2q^2+3q+1
       423: 2q^2+3q+1
       424: 4q^2+5q+1
       425: q^2+3q+1
       426: q^3+6q^2+5q+1
       427: q^3+6q^2+5q+1
       428: q^3+6q^2+5q+1
       429: 2q^2+3q+1
       430: 4q^2+5q+1
       431: 5q^2+5q+1
       432: 5q^2+5q+1
       433: 5q^2+5q+1
       434: 4q^2+5q+1
       435: q^3+6q^2+5q+1
       436: q^3+6q^2+5q+1
       437: q^3+5q^2+5q+1
       438: 2q^2+5q+1
       439: 2q^2+5q+1
       440: 4q^2+5q+1
       441: 4q^2+5q+1
       442: 3q^2+5q+1
       443: 3q^2+5q+1
       444: q^3+7q^2+5q+1
       445: q^3+5q^2+5q+1
       446: 3q^2+5q+1
       447: 3q^2+5q+1
       448: q^2+5q+1
       449: 5q^2+5q+1
       450: 5q^2+5q+1
       451: 5q^2+5q+1
       452: 3q^2+5q+1
       453: q^2+3q+1
       454: 5q^2+5q+1
       455: 5q^2+5q+1
       456: 5q^2+5q+1
       457: q^2+3q+1
       458: 3q^2+5q+1
       459: 4q^2+5q+1
       460: 4q^2+5q+1
       461: 4q^2+5q+1
       462: 3q^3+7q^2+5q+1
       463: 4q^2+5q+1
       464: 3q^2+4q+1
       465: q^2+4q+1
       466: q^3+5q^2+5q+1
       467: 2q^2+3q+1
       468: 2q^2+3q+1
       469: 2q^2+3q+1
       470: 2q^2+3q+1
       471: q^2+4q+1
       472: q^2+4q+1
       473: 3q^2+4q+1
       474: q^3+7q^2+5q+1
       475: q^3+5q^2+5q+1
       476: 2q^3+6q^2+5q+1
       477: 2q^2+3q+1
       478: 2q^2+3q+1
       479: 2q^3+6q^2+5q+1
       480: q^3+5q^2+5q+1
       481: q^2+4q+1
       482: 3q^2+4q+1
       483: 5q^2+5q+1
       484: 5q^2+5q+1
       485: q^3+4q^2+5q+1
       486: 3q^2+5q+1
       487: q^3+4q^2+5q+1
       488: 3q^2+5q+1
       489: 2q^2+5q+1
       490: 5q^2+5q+1
       491: q^2+4q+1
       492: 5q^2+5q+1
       493: 5q^2+5q+1
       494: 3q^2+5q+1
       495: q^3+4q^2+5q+1
       496: 3q^2+5q+1
       497: q^3+4q^2+5q+1
       498: 2q^2+5q+1
       499: 5q^2+5q+1
       500: q^2+4q+1
       501: 4q^2+5q+1
       502: q^3+6q^2+5q+1
       503: q^3+6q^2+5q+1
       504: q^3+5q^2+5q+1
       505: 2q^2+5q+1
       506: 2q^2+5q+1
       507: 4q^2+5q+1
       508: 4q^2+5q+1
       509: 3q^2+5q+1
       510: 3q^2+5q+1
       511: q^3+7q^2+5q+1
       512: q^3+5q^2+5q+1
       513: 3q^2+5q+1
       514: 3q^2+5q+1
       515: q^2+5q+1
       516: q^2+4q+1
       517: 5q^2+5q+1
       518: 2q^2+5q+1
       519: 3q^2+5q+1
       520: 2q+1
       521: q^2+3q+1
       522: q^3+4q^2+5q+1
       523: 2q^2+5q+1
       524: 4q+1
       525: q^2+4q+1
       526: 3q^2+5q+1
       527: 3q^2+5q+1
       528: 3q^2+5q+1
       529: q^3+4q^2+5q+1
       530: 3q^2+5q+1
       531: q^3+4q^2+5q+1
       532: 2q^2+5q+1
       533: 3q^2+5q+1
       534: q^2+4q+1
       535: q^2+3q+1
       536: 4q^2+5q+1
       537: 2q^2+3q+1
       538: 2q^2+3q+1
       539: q^2+3q+1
       540: 2q+1
       541: q^2+3q+1
       542: q^2+3q+1
       543: 3q^2+5q+1
       544: 4q^2+5q+1
       545: 2q^3+6q^2+5q+1
       546: 2q^3+6q^2+5q+1
       547: 3q^2+5q+1
       548: q^3+4q^2+5q+1
       549: 3q^2+5q+1
       550: 3q^2+5q+1
       551: 4q^2+5q+1
       552: 2q^2+3q+1
       553: q^3+6q^2+5q+1
       554: 2q^2+3q+1
       555: 4q^2+5q+1
       556: 2q^2+3q+1
       557: q^2+3q+1
       558: 5q^2+5q+1
       559: 5q^2+5q+1
       560: 5q^2+5q+1
       561: 3q^2+5q+1
       562: q^2+3q+1
       563: q^2+4q+1
       564: 5q^2+5q+1
       565: 2q^2+5q+1
       566: q^3+4q^2+5q+1
       567: q^2+3q+1
       568: 2q+1
       569: 3q^2+5q+1
       570: 2q^2+5q+1
       571: 4q+1
       572: q^2+4q+1
       573: 3q^2+5q+1
       574: 3q^2+5q+1
       575: q^3+4q^2+5q+1
       576: 3q^2+5q+1
       577: q^3+4q^2+5q+1
       578: 3q^2+5q+1
       579: 2q^2+5q+1
       580: 3q^2+5q+1
       581: q^2+4q+1
       582: 3q^2+5q+1
       583: 2q^3+6q^2+5q+1
       584: 4q^2+5q+1
       585: 2q^3+6q^2+5q+1
       586: q^3+4q^2+5q+1
       587: 3q^2+5q+1
       588: 3q^2+5q+1
       589: 3q^2+5q+1
       590: q^2+3q+1
       591: 2q^2+3q+1
       592: 4q^2+5q+1
       593: 2q^2+3q+1
       594: 2q+1
       595: q^2+3q+1
       596: q^2+3q+1
       597: q^2+3q+1
       598: 2q^2+3q+1
       599: 4q^2+5q+1
       600: q^3+6q^2+5q+1
       601: 2q^2+3q+1
       602: 2q^2+3q+1
       603: 4q^2+5q+1
       604: q^2+3q+1
       605: 5q^2+5q+1
       606: 5q^2+5q+1
       607: 5q^2+5q+1
       608: q^2+3q+1
       609: 3q^2+5q+1
       610: 4q^2+5q+1
       611: 4q^2+5q+1
       612: 2q^2+5q+1
       613: 2q^2+5q+1
       614: 2q^2+5q+1
       615: 2q^2+5q+1
       616: q^2+5q+1
       617: 4q^2+5q+1
       618: 4q+1
       619: q^2+5q+1
       620: 3q^2+5q+1
       621: 3q^2+5q+1
       622: q^3+5q^2+5q+1
       623: 2q^2+5q+1
       624: 2q^2+5q+1
       625: q^2+5q+1
       626: q^2+5q+1
       627: 3q^2+5q+1
       628: q^2+3q+1
       629: 5q^2+5q+1
       630: 2q^2+3q+1
       631: 3q^2+5q+1
       632: q^2+3q+1
       633: 3q+1
       634: q^2+3q+1
       635: 3q^2+5q+1
       636: 5q^2+5q+1
       637: 2q^2+3q+1
       638: q^2+3q+1
       639: 3q^2+5q+1
       640: 3q+1
       641: 4q^2+5q+1
       642: 4q^2+5q+1
       643: 4q^2+5q+1
       644: q^2+3q+1
       645: q^2+3q+1
       646: 4q^2+5q+1
       647: 4q^2+5q+1
       648: 4q^2+5q+1
       649: q^2+4q+1
       650: q^2+4q+1
       651: 2q^2+3q+1
       652: 2q^2+3q+1
       653: q^2+2q+1
       654: 2q+1
       655: 2q+1
       656: q^2+4q+1
       657: 3q^2+4q+1
       658: q^2+4q+1
       659: q^3+5q^2+5q+1
       660: 2q^2+3q+1
       661: 2q^2+3q+1
       662: 2q^2+3q+1
       663: 2q^2+3q+1
       664: q^2+4q+1
       665: q^2+4q+1
       666: q^2+4q+1
       667: 5q^2+5q+1
       668: 2q^2+5q+1
       669: q^3+4q^2+5q+1
       670: q^2+3q+1
       671: 2q+1
       672: 3q^2+5q+1
       673: 2q^2+5q+1
       674: 4q+1
       675: q^2+4q+1
       676: q^2+4q+1
       677: 5q^2+5q+1
       678: 2q^2+5q+1
       679: 3q^2+5q+1
       680: 2q+1
       681: q^2+3q+1
       682: q^3+4q^2+5q+1
       683: 2q^2+5q+1
       684: 4q+1
       685: q^2+4q+1
       686: 4q^2+5q+1
       687: 4q^2+5q+1
       688: 2q^2+5q+1
       689: 2q^2+5q+1
       690: 2q^2+5q+1
       691: 2q^2+5q+1
       692: q^2+5q+1
       693: 4q^2+5q+1
       694: 4q+1
       695: q^2+5q+1
       696: 3q^2+5q+1
       697: 3q^2+5q+1
       698: q^3+5q^2+5q+1
       699: 2q^2+5q+1
       700: 2q^2+5q+1
       701: q^2+5q+1
       702: q^2+5q+1
       703: q^2+4q+1
       704: 4q+1
       705: 2q^2+5q+1
       706: 2q+1
       707: q^2+3q+1
       708: q^2+3q+1
       709: 2q+1
       710: 4q+1
       711: 4q+1
       712: q^2+4q+1
       713: 3q^2+5q+1
       714: 2q^2+5q+1
       715: 3q^2+5q+1
       716: 2q+1
       717: q^2+3q+1
       718: q^3+4q^2+5q+1
       719: 2q^2+5q+1
       720: 2q+1
       721: q^2+4q+1
       722: q^2+3q+1
       723: q^2+3q+1
       724: q^2+3q+1
       725: 2q+1
       726: q^2+3q+1
       727: 2q+1
       728: 2q+1
       729: q^2+3q+1
       730: 2q+1
       731: 3q^2+5q+1
       732: 3q^2+5q+1
       733: 3q^2+5q+1
       734: q^3+4q^2+5q+1
       735: 3q^2+5q+1
       736: q^3+4q^2+5q+1
       737: 2q^2+5q+1
       738: 3q^2+5q+1
       739: q^2+4q+1
       740: q^2+3q+1
       741: 4q^2+5q+1
       742: 2q^2+3q+1
       743: 2q^2+3q+1
       744: q^2+3q+1
       745: 2q+1
       746: q^2+3q+1
       747: q^2+3q+1
       748: 3q^2+5q+1
       749: q^2+3q+1
       750: 5q^2+5q+1
       751: 2q^2+3q+1
       752: 3q^2+5q+1
       753: q^2+3q+1
       754: 3q+1
       755: q^2+4q+1
       756: 4q+1
       757: 2q^2+5q+1
       758: q^2+3q+1
       759: 2q+1
       760: 2q+1
       761: q^2+3q+1
       762: 4q+1
       763: 4q+1
       764: q^2+4q+1
       765: 3q^2+5q+1
       766: 2q^2+5q+1
       767: q^3+4q^2+5q+1
       768: q^2+3q+1
       769: 2q+1
       770: 3q^2+5q+1
       771: 2q^2+5q+1
       772: 2q+1
       773: q^2+4q+1
       774: 3q^2+5q+1
       775: 3q^2+5q+1
       776: q^3+4q^2+5q+1
       777: 3q^2+5q+1
       778: q^3+4q^2+5q+1
       779: 3q^2+5q+1
       780: 2q^2+5q+1
       781: 3q^2+5q+1
       782: q^2+4q+1
       783: q^2+3q+1
       784: q^2+3q+1
       785: 2q+1
       786: q^2+3q+1
       787: 2q+1
       788: q^2+3q+1
       789: 2q+1
       790: q^2+3q+1
       791: 2q+1
       792: q^2+3q+1
       793: 2q^2+3q+1
       794: 4q^2+5q+1
       795: 2q^2+3q+1
       796: 2q+1
       797: q^2+3q+1
       798: q^2+3q+1
       799: q^2+3q+1
       800: q^2+3q+1
       801: 3q^2+5q+1
       802: 5q^2+5q+1
       803: 2q^2+3q+1
       804: q^2+3q+1
       805: 3q^2+5q+1
       806: 3q+1
       807: 4q+1
       808: 4q^2+5q+1
       809: q^2+5q+1
       810: 2q^2+5q+1
       811: 2q+1
       812: 2q+1
       813: 2q^2+5q+1
       814: q^2+5q+1
       815: 4q+1
       816: 4q+1
       817: q^2+5q+1
       818: q^2+5q+1
       819: 2q^2+5q+1
       820: 2q^2+5q+1
       821: 2q^2+5q+1
       822: 2q^2+5q+1
       823: q^2+5q+1
       824: q^2+5q+1
       825: 4q+1
       826: 3q+1
       827: 3q^2+5q+1
       828: q^2+3q+1
       829: 2q^2+3q+1
       830: q^2+3q+1
       831: 2q+1
       832: 3q+1
       833: 3q+1
       834: 3q+1
       835: q^2+3q+1
       836: 3q^2+5q+1
       837: 2q^2+3q+1
       838: 2q+1
       839: q^2+3q+1
       840: 3q+1
       841: 3q+1
       842: q^2+3q+1
       843: q^2+3q+1
       844: 4q^2+5q+1
       845: q^2+2q+1
       846: q^2+3q+1
       847: q^2+3q+1
       848: 2q+1
       849: 4q^2+5q+1
       850: 4q^2+5q+1
       851: 4q^2+5q+1
       852: q^2+3q+1
       853: q^2+3q+1
       854: q^2+4q+1
       855: 2q+1
       856: 2q+1
       857: q^2+2q+1
       858: q+1
       859: 2q+1
       860: 2q+1
       861: q^2+4q+1
       862: q^2+4q+1
       863: 2q^2+3q+1
       864: 2q^2+3q+1
       865: q^2+2q+1
       866: 2q+1
       867: 2q+1
       868: q^2+4q+1
       869: q^2+4q+1
       870: 4q+1
       871: 2q^2+5q+1
       872: q^2+3q+1
       873: 2q+1
       874: 2q+1
       875: q^2+3q+1
       876: 4q+1
       877: 4q+1
       878: q^2+4q+1
       879: 4q+1
       880: 2q^2+5q+1
       881: 2q+1
       882: q^2+3q+1
       883: q^2+3q+1
       884: 2q+1
       885: 4q+1
       886: 4q+1
       887: 4q+1
       888: 4q^2+5q+1
       889: q^2+5q+1
       890: 2q^2+5q+1
       891: 2q+1
       892: 2q+1
       893: 2q^2+5q+1
       894: q^2+5q+1
       895: 4q+1
       896: 4q+1
       897: q^2+5q+1
       898: q^2+5q+1
       899: 2q^2+5q+1
       900: 2q^2+5q+1
       901: 2q^2+5q+1
       902: 2q^2+5q+1
       903: q^2+5q+1
       904: q^2+5q+1
       905: 4q+1
       906: 4q+1
       907: 4q+1
       908: 2q+1
       909: q^2+3q+1
       910: q+1
       911: 2q+1
       912: q+1
       913: 4q+1
       914: q^2+4q+1
       915: 2q+1
       916: 2q^2+5q+1
       917: 2q+1
       918: q^2+3q+1
       919: q^2+3q+1
       920: 2q+1
       921: 2q+1
       922: 2q+1
       923: 2q+1
       924: q^2+3q+1
       925: 2q+1
       926: q^2+3q+1
       927: q+1
       929: 2q+1
       930: 2q+1
       931: q+1
       932: 2q+1
       933: q^2+4q+1
       934: 3q^2+5q+1
       935: 2q^2+5q+1
       936: 3q^2+5q+1
       937: 2q+1
       938: q^2+3q+1
       939: q^3+4q^2+5q+1
       940: 2q^2+5q+1
       941: 2q+1
       942: q^2+4q+1
       943: q^2+3q+1
       944: q^2+3q+1
       945: q^2+3q+1
       946: 2q+1
       947: q^2+3q+1
       948: 2q+1
       949: 2q+1
       950: q^2+3q+1
       951: 2q+1
       952: 3q+1
       953: 3q^2+5q+1
       954: q^2+3q+1
       955: 2q^2+3q+1
       956: q^2+3q+1
       957: 2q+1
       958: 3q+1
       959: 3q+1
       960: 4q+1
       961: 4q+1
       962: q^2+3q+1
       963: 2q+1
       964: q+1
       965: q+1
       966: 2q+1
       967: 4q+1
       968: q^2+4q+1
       969: 2q+1
       970: 2q^2+5q+1
       971: q^2+3q+1
       972: 2q+1
       973: 2q+1
       974: q^2+3q+1
       975: 2q+1
       976: 2q+1
       977: q^2+4q+1
       978: 3q^2+5q+1
       979: 2q^2+5q+1
       980: q^3+4q^2+5q+1
       981: q^2+3q+1
       982: 2q+1
       983: 3q^2+5q+1
       984: 2q^2+5q+1
       985: 2q+1
       986: q^2+4q+1
       987: 2q+1
       988: q^2+3q+1
       989: 2q+1
       990: 2q+1
       992: q+1
       993: q^2+3q+1
       994: 2q+1
       995: q+1
       996: 2q+1
       997: q^2+3q+1
       998: q^2+3q+1
       999: 2q+1
      1000: q^2+3q+1
      1001: 2q+1
      1002: q^2+3q+1
      1003: 2q+1
      1004: q^2+3q+1
      1005: 2q+1
      1006: 3q+1
      1007: q^2+3q+1
      1008: 3q^2+5q+1
      1009: 2q^2+3q+1
      1010: 2q+1
      1011: q^2+3q+1
      1012: 3q+1
      1013: 3q+1
      1014: 4q+1
      1015: 4q+1
      1016: q^2+5q+1
      1017: 2q+1
      1018: 2q+1
      1019: 2q+1
      1020: 2q+1
      1021: 4q+1
      1022: 4q+1
      1023: 4q+1
      1024: q^2+5q+1
      1025: q^2+5q+1
      1026: 2q^2+5q+1
      1027: 2q+1
      1028: 2q+1
      1029: 2q^2+5q+1
      1030: q^2+5q+1
      1031: q+1
      1032: 4q+1
      1033: 3q+1
      1034: 3q+1
      1035: q^2+3q+1
      1036: 2q+1
      1037: q^2+3q+1
      1038: 2q+1
      1039: 2q+1
      1040: 3q+1
      1041: 2q+1
      1042: 3q+1
      1043: 3q+1
      1044: 2q+1
      1045: q^2+3q+1
      1046: 2q+1
      1047: q^2+3q+1
      1048: 2q+1
      1049: 3q+1
      1050: 2q+1
      1051: 2q+1
      1052: q^2+3q+1
      1053: q^2+3q+1
      1054: q^2+2q+1
      1055: q+1
      1056: q+1
      1057: 2q+1
      1058: 2q+1
      1059: q^2+3q+1
      1060: q^2+3q+1
      1061: 4q^2+5q+1
      1062: q^2+2q+1
      1063: q^2+3q+1
      1064: q^2+3q+1
      1065: 2q+1
      1066: 2q+1
      1067: 2q+1
      1068: q+1
      1069: q+1
      1070: q+1
      1071: q^2+4q+1
      1072: 2q+1
      1073: 2q+1
      1074: q^2+2q+1
      1075: q+1
      1076: 2q+1
      1077: 2q+1
      1078: 4q+1
      1079: 4q+1
      1080: q^2+3q+1
      1081: 2q+1
      1082: q+1
      1083: q+1
      1084: 2q+1
      1085: 4q+1
      1086: 4q+1
      1087: 4q+1
      1088: 2q+1
      1089: q^2+3q+1
      1090: q+1
      1091: 2q+1
      1092: q+1
      1093: 4q+1
      1094: 4q+1
      1095: 4q+1
      1096: q^2+5q+1
      1097: 2q+1
      1098: 2q+1
      1099: 2q+1
      1100: 2q+1
      1101: 4q+1
      1102: 4q+1
      1103: 4q+1
      1104: q^2+5q+1
      1105: q^2+5q+1
      1106: 2q^2+5q+1
      1107: 2q+1
      1108: 2q+1
      1109: 2q^2+5q+1
      1110: q^2+5q+1
      1111: q+1
      1112: 4q+1
      1113: 4q+1
      1114: q+1
      1115: 2q+1
      1116: q+1
      1117: 1
      1118: 2q+1
      1119: q+1
      1120: 2q+1
      1121: 2q+1
      1122: 2q+1
      1123: q^2+3q+1
      1124: q+1
      1125: q+1
      1126: 1
      1127: 2q+1
      1128: 2q+1
      1129: q+1
      1130: 2q+1
      1131: q+1
      1134: q+1
      1135: q+1
      1136: q+1
      1137: q^2+4q+1
      1138: 2q+1
      1139: 2q^2+5q+1
      1140: 2q+1
      1141: q^2+3q+1
      1142: q^2+3q+1
      1143: 2q+1
      1144: 2q+1
      1145: 2q+1
      1146: 2q+1
      1147: q^2+3q+1
      1148: 2q+1
      1149: q^2+3q+1
      1150: q+1
      1152: 2q+1
      1153: 2q+1
      1154: q+1
      1155: 2q+1
      1156: 3q+1
      1157: 3q+1
      1158: q^2+3q+1
      1159: 2q+1
      1160: q^2+3q+1
      1161: 2q+1
      1162: 2q+1
      1163: 3q+1
      1164: 2q+1
      1165: 4q+1
      1166: 2q+1
      1167: q+1
      1168: q+1
      1169: 1
      1170: q+1
      1171: 2q+1
      1172: 2q+1
      1173: 2q+1
      1174: q^2+3q+1
      1175: 2q+1
      1176: q+1
      1177: 1
      1178: q+1
      1179: 2q+1
      1180: q^2+4q+1
      1181: 2q+1
      1182: 2q^2+5q+1
      1183: q^2+3q+1
      1184: 2q+1
      1185: 2q+1
      1186: q^2+3q+1
      1187: 2q+1
      1188: 2q+1
      1189: 2q+1
      1190: q+1
      1191: 2q+1
      1193: q+1
      1194: q+1
      1196: q+1
      1197: q+1
      1198: 2q+1
      1199: q^2+3q+1
      1200: 2q+1
      1201: 2q+1
      1203: q+1
      1204: q^2+3q+1
      1205: 2q+1
      1206: q+1
      1207: 2q+1
      1208: 3q+1
      1209: 3q+1
      1210: 2q+1
      1211: q^2+3q+1
      1212: 2q+1
      1213: q^2+3q+1
      1214: 2q+1
      1215: 3q+1
      1216: 2q+1
      1217: 4q+1
      1218: 4q+1
      1219: 2q+1
      1220: 2q+1
      1221: q+1
      1222: q+1
      1223: q+1
      1224: 4q+1
      1225: 4q+1
      1226: q+1
      1227: q^2+5q+1
      1228: 2q+1
      1229: 2q+1
      1230: 2q+1
      1231: 2q+1
      1232: q+1
      1233: q+1
      1234: 2q+1
      1235: 3q+1
      1236: 2q+1
      1237: q^2+3q+1
      1238: q+1
      1240: 2q+1
      1241: 2q+1
      1242: 1
      1243: 2q+1
      1244: 2q+1
      1245: 3q+1
      1246: 2q+1
      1247: 2q+1
      1249: q+1
      1250: q^2+3q+1
      1251: 2q+1
      1252: 1
      1253: 2q+1
      1254: 2q+1
      1255: 2q+1
      1256: q+1
      1257: q+1
      1258: q+1
      1259: q+1
      1260: q+1
      1261: 2q+1
      1262: q+1
      1263: 2q+1
      1264: q^2+3q+1
      1265: q^2+3q+1
      1266: q^2+2q+1
      1267: q+1
      1268: q+1
      1269: 2q+1
      1270: 2q+1
      1271: q+1
      1272: q+1
      1273: q+1
      1274: 2q+1
      1275: 2q+1
      1276: q+1
      1277: q+1
      1278: q+1
      1279: 4q+1
      1280: 2q+1
      1281: q+1
      1282: q+1
      1283: 1
      1284: q+1
      1285: 2q+1
      1286: 4q+1
      1287: q+1
      1288: 2q+1
      1289: q+1
      1290: 1
      1291: 2q+1
      1292: q+1
      1293: 4q+1
      1294: 4q+1
      1295: 2q+1
      1296: 2q+1
      1297: q+1
      1298: q+1
      1299: q+1
      1300: 4q+1
      1301: 4q+1
      1302: q+1
      1303: q^2+5q+1
      1304: 2q+1
      1305: 2q+1
      1306: 2q+1
      1307: 2q+1
      1308: q+1
      1309: q+1
      1310: q+1
      1311: 2q+1
      1312: 1
      1313: 1
      1314: 1
      1315: 2q+1
      1316: 1
      1317: q+1
      1318: q+1
      1319: 1
      1320: q+1
      1321: 1
      1322: q+1
      1323: q+1
      1324: q+1
      1328: 1
      1329: q+1
      1330: 2q+1
      1331: 2q+1
      1332: 2q+1
      1333: q^2+3q+1
      1334: q+1
      1335: q+1
      1336: 1
      1337: 2q+1
      1338: 2q+1
      1339: q+1
      1340: 2q+1
      1341: q+1
      1344: q+1
      1345: q+1
      1346: q+1
      1347: 2q+1
      1348: 3q+1
      1349: 2q+1
      1350: q^2+3q+1
      1351: q+1
      1353: 2q+1
      1354: 2q+1
      1355: 1
      1356: 2q+1
      1357: 2q+1
      1358: q+1
      1359: 1
      1360: 1
      1361: 1
      1362: 2q+1
      1363: q+1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: q+1
      1369: 2q+1
      1370: 2q+1
      1371: q^2+3q+1
      1372: 2q+1
      1373: q+1
      1374: 1
      1375: q+1
      1376: 2q+1
      1377: q+1
      1378: q+1
      1380: q+1
      1382: 1
      1384: q+1
      1385: 2q+1
      1386: q+1
      1387: 2q+1
      1389: q+1
      1390: q+1
      1392: q+1
      1393: q+1
      1394: 2q+1
      1395: 3q+1
      1396: 2q+1
      1397: 2q+1
      1399: q+1
      1400: q^2+3q+1
      1401: 2q+1
      1402: 1
      1403: 2q+1
      1404: 4q+1
      1405: q+1
      1406: q+1
      1407: q+1
      1408: 1
      1409: q+1
      1410: q+1
      1411: q+1
      1412: q+1
      1413: 2q+1
      1414: 2q+1
      1415: q+1
      1416: 1
      1417: 1
      1418: q+1
      1419: 2q+1
      1420: 1
      1421: 2q+1
      1422: q+1
      1425: q+1
      1426: 1
      1427: 1
      1428: 2q+1
      1429: 1
      1430: 2q+1
      1432: q+1
      1433: q+1
      1435: 1
      1436: 1
      1437: q+1
      1438: 2q+1
      1439: q+1
      1440: q+1
      1443: q+1
      1444: q+1
      1445: 1
      1446: q+1
      1447: 2q+1
      1448: 2q+1
      1449: q+1
      1450: q+1
      1451: q+1
      1452: q+1
      1453: q+1
      1454: 2q+1
      1455: q+1
      1456: q+1
      1458: q+1
      1459: q+1
      1460: q+1
      1461: 2q+1
      1462: q+1
      1463: 1
      1464: 1
      1465: 1
      1466: q+1
      1467: 2q+1
      1468: 1
      1469: 1
      1470: 1
      1471: 4q+1
      1472: q+1
      1473: q+1
      1474: q+1
      1475: 1
      1476: q+1
      1477: q+1
      1478: q+1
      1479: q+1
      1480: 2q+1
      1481: 2q+1
      1482: q+1
      1483: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: q+1
      1491: 1
      1492: 1
      1493: 1
      1494: q+1
      1495: 1
      1500: 1
      1501: 2q+1
      1502: 1
      1503: q+1
      1504: q+1
      1505: 1
      1506: q+1
      1507: 1
      1508: q+1
      1509: q+1
      1510: q+1
      1514: 1
      1515: q+1
      1516: 2q+1
      1517: 1
      1518: 2q+1
      1519: q+1
      1522: q+1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: q+1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 2q+1
      1534: q+1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: q+1
      1540: q+1
      1542: 1
      1545: 1
      1547: q+1
      1548: q+1
      1550: q+1
      1552: 1
      1554: q+1
      1555: 2q+1
      1556: 1
      1557: 2q+1
      1559: q+1
      1560: q+1
      1562: 1
      1563: 1
      1564: q+1
      1565: q+1
      1566: 1
      1567: 1
      1568: 1
      1569: q+1
      1570: 1
      1571: 1
      1572: q+1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: q+1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1587: q+1
      1589: 1
      1591: 1
      1592: q+1
      1593: 1
      1594: q+1
      1599: 1
      1600: 1
      1601: q+1
      1602: 2q+1
      1603: q+1
      1604: q+1
      1607: q+1
      1608: q+1
      1609: 1
      1610: q+1
      1612: q+1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: q+1
      1621: q+1
      1622: 1
      1623: 1
      1624: 1
      1625: q+1
      1626: 1
      1627: 1
      1628: q+1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1642: 1
      1643: q+1
      1644: 1
      1645: 1
      1646: 1
      1647: q+1
      1648: 1
      1653: 1
      1654: 1
      1655: 1
      1656: q+1
      1660: 1
      1661: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: q+1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1677: q+1
      1679: 1
      1682: 1
      1684: 1
      1685: 1
      1687: q+1
      1689: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1706: 1
      1707: 1
      1709: 1
      1712: 1
      1714: 1
      1715: 1
      1721: 1
      1722: q+1
      1723: 1
      1724: q+1
      1729: 1
      1730: 1
      1732: 1
      1734: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1742: 1
      1743: 1
      1745: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1758: 1
      1759: 1
      1764: 1
      1766: 1
      1768: 1
      1769: 1
      1770: 1
      1775: 1
      1779: 1
      1781: 1
      1784: 1
      1786: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1797: 1
      1801: 1
      1808: 1
      1809: 1
      1815: 1
      1818: 1
      1820: 1
      1821: 1
      1822: 1
      1826: 1
      1831: 1
      1837: 1
      1845: 1
      1850: 1
      1863: 1
      1871: 1

1872:    0: 2q^4+3q^3+4q^2+q+1
         1: q^3+4q^2+q+1
         2: 2q^4+3q^3+4q^2+q+1
         3: 2q^4+3q^3+4q^2+q+1
         4: q^4+2q^3+4q^2+q+1
         5: q^4+2q^3+4q^2+q+1
         6: q^3+4q^2+q+1
         7: q^3+4q^2+q+1
         8: 2q^4+3q^3+4q^2+q+1
         9: q^3+4q^2+q+1
        10: 2q^4+3q^3+4q^2+q+1
        11: q^4+2q^3+4q^2+q+1
        12: q^4+2q^3+4q^2+q+1
        13: 4q^2+q+1
        14: q^4+2q^3+4q^2+q+1
        15: q^4+2q^3+4q^2+q+1
        16: 4q^2+q+1
        17: q^4+2q^3+4q^2+q+1
        18: q^4+2q^3+4q^2+q+1
        19: 2q^3+4q^2+q+1
        20: q^3+4q^2+q+1
        21: q^3+4q^2+q+1
        22: q^3+4q^2+q+1
        23: q^4+2q^3+4q^2+q+1
        24: q^4+2q^3+4q^2+q+1
        25: q^3+4q^2+q+1
        26: q^3+4q^2+q+1
        27: 2q^4+3q^3+4q^2+q+1
        28: 4q^2+q+1
        29: q^4+2q^3+4q^2+q+1
        30: 4q^2+q+1
        31: q^4+2q^3+4q^2+q+1
        32: 2q^3+4q^2+q+1
        33: 4q^2+q+1
        34: 4q^2+q+1
        35: q^4+2q^3+4q^2+q+1
        36: 4q^2+q+1
        37: q^4+2q^3+4q^2+q+1
        38: q^3+3q^2+q+1
        39: q^4+2q^3+4q^2+q+1
        40: 4q^2+q+1
        41: 4q^2+q+1
        42: q^4+2q^3+4q^2+q+1
        43: 4q^2+q+1
        44: q^4+2q^3+4q^2+q+1
        45: q^4+2q^3+4q^2+q+1
        46: q^3+3q^2+q+1
        47: 4q^2+q+1
        48: 2q^3+4q^2+q+1
        49: 2q^3+4q^2+q+1
        50: 2q^2+q+1
        51: 2q^2+q+1
        52: q^3+4q^2+q+1
        53: q^3+4q^2+q+1
        54: 4q^2+q+1
        55: 4q^2+q+1
        56: 2q^3+4q^2+q+1
        57: q^3+4q^2+q+1
        58: q^3+4q^2+q+1
        59: q^3+4q^2+q+1
        60: q^4+2q^3+4q^2+q+1
        61: q^4+2q^3+4q^2+q+1
        62: 4q^2+q+1
        63: 4q^2+q+1
        64: q^4+2q^3+4q^2+q+1
        65: 4q^2+q+1
        66: 4q^2+q+1
        67: q^4+2q^3+4q^2+q+1
        68: 4q^2+q+1
        69: 2q^3+4q^2+q+1
        70: 2q^3+4q^2+q+1
        71: 4q^2+q+1
        72: 4q^2+q+1
        73: 4q^2+q+1
        74: q^3+3q^2+q+1
        75: q^4+2q^3+4q^2+q+1
        76: 4q^2+q+1
        77: 2q^2+q+1
        78: q^4+2q^3+4q^2+q+1
        79: 3q^2+q+1
        80: q^3+3q^2+q+1
        81: 4q^2+q+1
        82: q^4+2q^3+4q^2+q+1
        83: q^3+3q^2+q+1
        84: 4q^2+q+1
        85: 4q^2+q+1
        86: 4q^2+q+1
        87: q^4+2q^3+4q^2+q+1
        88: q^3+3q^2+q+1
        89: 4q^2+q+1
        90: 2q^2+q+1
        91: q^4+2q^3+4q^2+q+1
        92: 4q^2+q+1
        93: q^4+2q^3+4q^2+q+1
        94: 3q^2+q+1
        95: q^3+3q^2+q+1
        96: q^3+3q^2+q+1
        97: 4q^2+q+1
        98: 4q^2+q+1
        99: 2q^3+4q^2+q+1
       100: 4q^2+q+1
       101: 2q^3+4q^2+q+1
       102: q^3+3q^2+q+1
       103: q^3+3q^2+q+1
       104: q^2+q+1
       105: 2q^2+q+1
       106: 2q^2+q+1
       107: q^3+4q^2+q+1
       108: 4q^2+q+1
       109: 4q^2+q+1
       110: 4q^2+q+1
       111: 2q^3+4q^2+q+1
       112: 2q^2+q+1
       113: 2q^2+q+1
       114: q^3+4q^2+q+1
       115: q^3+4q^2+q+1
       116: 4q^2+q+1
       117: 4q^2+q+1
       118: 2q^3+4q^2+q+1
       119: 4q^2+q+1
       120: 4q^2+q+1
       121: 4q^2+q+1
       122: q^4+2q^3+4q^2+q+1
       123: q^3+3q^2+q+1
       124: 4q^2+q+1
       125: 4q^2+q+1
       126: 4q^2+q+1
       127: q^3+3q^2+q+1
       128: q^4+2q^3+4q^2+q+1
       129: 4q^2+q+1
       130: 4q^2+q+1
       131: 2q^3+4q^2+q+1
       132: 4q^2+q+1
       133: 2q^3+4q^2+q+1
       134: q^2+q+1
       135: 2q^2+q+1
       136: 4q^2+q+1
       137: 4q^2+q+1
       138: 3q^2+q+1
       139: 4q^2+q+1
       140: q^3+3q^2+q+1
       141: 4q^2+q+1
       142: 2q^2+q+1
       143: 2q^2+q+1
       144: q^3+3q^2+q+1
       145: q^4+2q^3+4q^2+q+1
       146: 3q^2+q+1
       147: q^2+q+1
       148: q^3+3q^2+q+1
       149: 4q^2+q+1
       150: 2q^2+q+1
       151: q^4+2q^3+4q^2+q+1
       152: 3q^2+q+1
       153: q^3+3q^2+q+1
       154: q^3+3q^2+q+1
       155: 2q^2+q+1
       156: q^2+q+1
       157: 4q^2+q+1
       158: 4q^2+q+1
       159: 4q^2+q+1
       160: 3q^2+q+1
       161: q^3+3q^2+q+1
       162: 4q^2+q+1
       163: 2q^2+q+1
       164: 2q^2+q+1
       165: q^4+2q^3+4q^2+q+1
       166: q^3+3q^2+q+1
       167: 4q^2+q+1
       168: 2q^2+q+1
       169: q^4+2q^3+4q^2+q+1
       170: 3q^2+q+1
       171: q^2+q+1
       172: q^3+3q^2+q+1
       173: 3q^2+q+1
       174: q^3+3q^2+q+1
       175: q^3+3q^2+q+1
       176: 4q^2+q+1
       177: 4q^2+q+1
       178: 4q^2+q+1
       179: q^3+3q^2+q+1
       180: q^3+3q^2+q+1
       181: 4q^2+q+1
       182: q^2+q+1
       183: 2q^3+4q^2+q+1
       184: 3q^2+q+1
       185: q^3+3q^2+q+1
       186: 3q^2+q+1
       187: q^3+3q^2+q+1
       188: 3q^2+q+1
       189: q^2+q+1
       190: q^2+q+1
       191: 2q^2+q+1
       192: 2q^2+q+1
       193: 4q^2+q+1
       194: 4q^2+q+1
       195: 4q^2+q+1
       196: 4q^2+q+1
       197: 2q^3+4q^2+q+1
       198: q^2+q+1
       199: 2q^2+q+1
       200: 2q^2+q+1
       201: q^3+4q^2+q+1
       202: 4q^2+q+1
       203: 4q^2+q+1
       204: 4q^2+q+1
       205: 2q^3+4q^2+q+1
       206: 2q^2+q+1
       207: q^2+q+1
       208: 4q^2+q+1
       209: 4q^2+q+1
       210: 4q^2+q+1
       211: 3q^2+q+1
       212: q^3+3q^2+q+1
       213: q^2+q+1
       214: 2q^2+q+1
       215: 4q^2+q+1
       216: 4q^2+q+1
       217: 3q^2+q+1
       218: 4q^2+q+1
       219: q^3+3q^2+q+1
       220: 4q^2+q+1
       221: 4q^2+q+1
       222: 4q^2+q+1
       223: q^3+3q^2+q+1
       224: q^3+3q^2+q+1
       225: 4q^2+q+1
       226: q^2+q+1
       227: 2q^3+4q^2+q+1
       228: q+1
       229: q^2+q+1
       230: 2q^2+q+1
       231: 4q^2+q+1
       232: 3q^2+q+1
       233: 4q^2+q+1
       234: 3q^2+q+1
       235: q^3+3q^2+q+1
       236: q^2+q+1
       237: 2q^2+q+1
       238: 2q^2+q+1
       239: 2q^2+q+1
       240: q^2+q+1
       241: 2q^2+q+1
       242: q^3+3q^2+q+1
       243: 3q^2+q+1
       244: q^2+q+1
       245: q^2+q+1
       246: q^3+3q^2+q+1
       247: 2q^2+1
       248: 4q^2+q+1
       249: 2q^2+q+1
       250: 2q^2+q+1
       251: q^3+3q^2+q+1
       252: q^4+2q^3+4q^2+q+1
       253: 3q^2+q+1
       254: q^2+q+1
       255: q^3+3q^2+q+1
       256: 3q^2+q+1
       257: q^3+3q^2+q+1
       258: q+1
       259: 2q^2+q+1
       260: q^2+q+1
       261: 4q^2+q+1
       262: 4q^2+q+1
       263: 3q^2+q+1
       264: 3q^2+q+1
       265: q^3+3q^2+q+1
       266: 2q^2+q+1
       267: q^2+q+1
       268: 2q^2+q+1
       269: 2q^2+q+1
       270: 2q^2+q+1
       271: q^2+q+1
       272: q^3+3q^2+q+1
       273: 4q^2+q+1
       274: 2q^2+q+1
       275: 2q^2+q+1
       276: q^4+2q^3+4q^2+q+1
       277: q^3+3q^2+q+1
       278: 3q^2+q+1
       279: q^2+q+1
       280: q^2+q+1
       281: 2q^2+1
       282: q^3+3q^2+q+1
       283: 3q^2+q+1
       284: q^2+q+1
       285: q^3+3q^2+q+1
       286: 3q^2+q+1
       287: q^3+3q^2+q+1
       288: q^2+q+1
       289: q^2+q+1
       290: 4q^2+q+1
       291: 4q^2+q+1
       292: 3q^2+q+1
       293: 3q^2+q+1
       294: 3q^2+q+1
       295: 4q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q^3+3q^2+q+1
       299: q^3+3q^2+q+1
       300: 3q^2+q+1
       301: q+1
       302: q^3+3q^2+q+1
       303: 3q^2+q+1
       304: q+1
       305: q^3+3q^2+q+1
       306: 3q^2+q+1
       307: 3q^2+q+1
       308: 3q^2+q+1
       309: q^2+q+1
       310: q^2+q+1
       311: q^2+q+1
       312: 2q^2+q+1
       313: q^2+q+1
       314: q^2+q+1
       315: 2q^2+q+1
       316: 4q^2+q+1
       317: 4q^2+q+1
       318: q^2+q+1
       319: q^2+q+1
       320: q^2+q+1
       321: 2q^2+q+1
       322: 2q^2+q+1
       323: 4q^2+q+1
       324: 4q^2+q+1
       325: 4q^2+q+1
       326: 4q^2+q+1
       327: 2q^3+4q^2+q+1
       328: q+1
       329: 2q^2+q+1
       330: q^2+q+1
       331: 4q^2+q+1
       332: 4q^2+q+1
       333: 3q^2+q+1
       334: 3q^2+q+1
       335: q^3+3q^2+q+1
       336: q+1
       337: q^2+q+1
       338: 2q^2+q+1
       339: 4q^2+q+1
       340: 3q^2+q+1
       341: 4q^2+q+1
       342: 3q^2+q+1
       343: q^3+3q^2+q+1
       344: q^2+q+1
       345: q^2+q+1
       346: 4q^2+q+1
       347: 4q^2+q+1
       348: 3q^2+q+1
       349: 3q^2+q+1
       350: 3q^2+q+1
       351: 4q^2+q+1
       352: q^2+q+1
       353: q^2+q+1
       354: q^3+3q^2+q+1
       355: q^3+3q^2+q+1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: 2q^2+q+1
       360: 3q^2+q+1
       361: 4q^2+q+1
       362: 3q^2+q+1
       363: 3q^2+q+1
       364: q^3+3q^2+q+1
       365: q+1
       366: q+1
       367: q^2+q+1
       368: 2q^2+q+1
       369: q^2+q+1
       370: 2q^2+q+1
       371: q^2+q+1
       372: q^3+3q^2+q+1
       373: q^2+q+1
       374: q^2+1
       375: q^2+q+1
       376: q^2+q+1
       377: q^2+q+1
       378: q^2+1
       379: 2q^2+1
       380: q^2+q+1
       381: 2q^2+q+1
       382: 2q^2+q+1
       383: 2q^2+q+1
       384: q^2+q+1
       385: 2q^2+q+1
       386: q^3+3q^2+q+1
       387: 3q^2+q+1
       388: q^2+q+1
       389: q^2+q+1
       390: q^3+3q^2+q+1
       391: 2q^2+1
       392: 3q^2+q+1
       393: q+1
       394: q^3+3q^2+q+1
       395: q+1
       396: q+1
       397: 2q^2+q+1
       398: q^2+q+1
       399: 4q^2+q+1
       400: 3q^2+q+1
       401: 3q^2+q+1
       402: 3q^2+q+1
       403: q^3+3q^2+q+1
       404: q+1
       405: q^2+q+1
       406: q+1
       407: 2q^2+q+1
       408: 2q^2+q+1
       409: q^2+q+1
       410: q^2+q+1
       411: q^3+3q^2+q+1
       412: 2q^2+q+1
       413: q^2+q+1
       414: 2q^2+q+1
       415: 2q^2+q+1
       416: 2q^2+q+1
       417: q^2+q+1
       418: q^3+3q^2+q+1
       419: q^2+1
       420: q^2+q+1
       421: q^2+q+1
       422: q^2+q+1
       423: q^2+1
       424: q^2+q+1
       425: 2q^2+1
       426: 3q^2+q+1
       427: q^2+q+1
       428: q^2+q+1
       429: 2q^2+1
       430: q^3+3q^2+q+1
       431: 3q^2+q+1
       432: q+1
       433: q^3+3q^2+q+1
       434: q+1
       435: q^2+q+1
       436: q^2+q+1
       437: 4q^2+q+1
       438: 3q^2+q+1
       439: 3q^2+q+1
       440: 3q^2+q+1
       441: 3q^2+q+1
       442: q^2+q+1
       443: q^2+q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q+1
       447: q+1
       448: 3q^2+q+1
       449: 3q^2+q+1
       450: q+1
       451: q+1
       452: q^3+3q^2+q+1
       453: 2q^2+1
       454: 3q^2+q+1
       455: q+1
       456: q+1
       457: 2q^2+1
       458: q^3+3q^2+q+1
       459: 3q^2+q+1
       460: q+1
       461: 3q^2+q+1
       462: 3q^2+q+1
       463: 3q^2+q+1
       465: q^2+q+1
       466: q^2+q+1
       467: q+1
       468: q+1
       469: q^2+q+1
       470: q^2+q+1
       471: 4q^2+q+1
       472: q^2+q+1
       473: q^2+q+1
       474: q^2+q+1
       475: q^2+q+1
       476: 2q^2+q+1
       477: q^2+q+1
       478: q^2+q+1
       479: 2q^2+q+1
       480: 4q^2+q+1
       481: 4q^2+q+1
       482: q^2+q+1
       483: q+1
       484: q+1
       485: 2q^2+q+1
       486: q^2+q+1
       487: 4q^2+q+1
       488: 3q^2+q+1
       489: 3q^2+q+1
       490: 3q^2+q+1
       491: q^3+3q^2+q+1
       492: q+1
       493: q+1
       494: q^2+q+1
       495: 2q^2+q+1
       496: 3q^2+q+1
       497: 4q^2+q+1
       498: 3q^2+q+1
       499: 3q^2+q+1
       500: q^3+3q^2+q+1
       501: q+1
       502: q^2+q+1
       503: q^2+q+1
       504: 4q^2+q+1
       505: 3q^2+q+1
       506: 3q^2+q+1
       507: 3q^2+q+1
       508: 3q^2+q+1
       509: q^2+q+1
       510: q^2+q+1
       511: q^2+q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       515: 3q^2+q+1
       516: q+1
       517: q+1
       518: q+1
       519: q^2+q+1
       520: q^2+1
       521: q^2+q+1
       522: 2q^2+q+1
       523: 3q^2+q+1
       524: 3q^2+q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q^2+q+1
       530: q^2+q+1
       531: 2q^2+q+1
       532: q^2+q+1
       533: q^2+q+1
       534: q^3+3q^2+q+1
       535: 1
       536: q+1
       537: 1
       538: q^2+q+1
       539: q^2+q+1
       540: q^2+1
       541: q^2+1
       542: 2q^2+1
       543: q+1
       544: q+1
       545: q^2+q+1
       546: 2q^2+q+1
       547: q^2+q+1
       548: 2q^2+q+1
       549: q^2+q+1
       550: q^3+3q^2+q+1
       551: q^2+q+1
       552: q^2+1
       553: q^2+q+1
       554: q^2+q+1
       555: q^2+q+1
       556: q^2+1
       557: 2q^2+1
       558: 3q^2+q+1
       559: q+1
       560: q+1
       561: q^3+3q^2+q+1
       562: 2q^2+1
       563: q+1
       564: q+1
       565: q+1
       566: 2q^2+q+1
       567: q^2+q+1
       568: q^2+1
       569: q^2+q+1
       570: 3q^2+q+1
       571: 3q^2+q+1
       572: q+1
       573: q+1
       574: q+1
       575: q^2+q+1
       576: q+1
       577: 2q^2+q+1
       578: q^2+q+1
       579: q^2+q+1
       580: q^2+q+1
       581: q^3+3q^2+q+1
       582: q+1
       583: q^2+q+1
       584: q+1
       585: 2q^2+q+1
       586: 2q^2+q+1
       587: q^2+q+1
       588: q^2+q+1
       589: q^3+3q^2+q+1
       590: 1
       591: 1
       592: q+1
       593: q^2+q+1
       594: q^2+1
       595: q^2+q+1
       596: q^2+1
       597: 2q^2+1
       598: q^2+1
       599: q^2+q+1
       600: q^2+q+1
       601: q^2+q+1
       602: q^2+1
       603: q^2+q+1
       604: 2q^2+1
       605: 3q^2+q+1
       606: q+1
       607: q+1
       608: 2q^2+1
       609: q^3+3q^2+q+1
       610: q+1
       611: q+1
       612: q^2+q+1
       613: q^2+q+1
       614: 3q^2+q+1
       615: 3q^2+q+1
       616: 3q^2+q+1
       617: 3q^2+q+1
       618: 3q^2+q+1
       619: q+1
       620: q+1
       621: q+1
       622: q^2+q+1
       623: q+1
       624: q+1
       625: q+1
       626: 3q^2+q+1
       627: q^2+q+1
       628: q^2+1
       629: q+1
       630: q+1
       631: q+1
       632: 1
       633: 2q^2+1
       634: q^2+1
       635: q^2+q+1
       636: q+1
       637: q+1
       638: 1
       639: q+1
       640: 2q^2+1
       641: 3q^2+q+1
       642: q+1
       643: q+1
       644: 2q^2+1
       645: 2q^2+1
       646: 3q^2+q+1
       647: q+1
       648: 3q^2+q+1
       650: q^2+q+1
       651: q+1
       652: q+1
       653: q+1
       654: q^2+q+1
       655: q^2+q+1
       656: q^2+q+1
       658: q^2+q+1
       659: q^2+q+1
       660: q+1
       661: q+1
       662: q^2+q+1
       663: q^2+q+1
       664: 4q^2+q+1
       665: q^2+q+1
       666: q+1
       667: q+1
       668: q+1
       669: 2q^2+q+1
       670: q^2+q+1
       671: q^2+1
       672: q^2+q+1
       673: 3q^2+q+1
       674: 3q^2+q+1
       675: q+1
       676: q+1
       677: q+1
       678: q+1
       679: q^2+q+1
       680: q^2+1
       681: q^2+q+1
       682: 2q^2+q+1
       683: 3q^2+q+1
       684: 3q^2+q+1
       685: q+1
       686: q+1
       687: q+1
       688: q^2+q+1
       689: q^2+q+1
       690: 3q^2+q+1
       691: 3q^2+q+1
       692: 3q^2+q+1
       693: 3q^2+q+1
       694: 3q^2+q+1
       695: q+1
       696: q+1
       697: q+1
       698: q^2+q+1
       699: q+1
       700: q+1
       701: q+1
       702: 3q^2+q+1
       704: q+1
       705: q+1
       706: 1
       707: q+1
       708: q^2+q+1
       709: q^2+1
       710: 3q^2+q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       716: 1
       717: q+1
       718: q^2+q+1
       719: q^2+q+1
       720: q^2+q+1
       721: q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q^2+q+1
       727: q^2+1
       728: q^2+1
       729: q^2+1
       730: 2q^2+1
       731: q+1
       732: q+1
       733: q+1
       734: q^2+q+1
       735: q^2+q+1
       736: 2q^2+q+1
       737: q^2+q+1
       738: q^2+q+1
       739: q^3+3q^2+q+1
       740: 1
       741: q+1
       742: 1
       743: q^2+q+1
       744: q^2+q+1
       745: q^2+1
       746: q^2+1
       747: 2q^2+1
       748: q^2+q+1
       749: q^2+1
       750: q+1
       751: q+1
       752: q+1
       753: 1
       754: 2q^2+1
       756: q+1
       757: q+1
       758: q+1
       759: 1
       760: q^2+1
       761: q^2+q+1
       762: 3q^2+q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q^2+q+1
       768: q+1
       769: 1
       770: q+1
       771: q^2+q+1
       772: q^2+q+1
       773: q+1
       774: q+1
       775: q+1
       776: q^2+q+1
       777: q+1
       778: 2q^2+q+1
       779: q^2+q+1
       780: q^2+q+1
       781: q^2+q+1
       782: q^3+3q^2+q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q^2+1
       788: q^2+q+1
       789: q^2+1
       790: q^2+1
       791: 2q^2+1
       792: 1
       793: 1
       794: q+1
       795: q^2+q+1
       796: q^2+1
       797: q^2+q+1
       798: q^2+1
       799: 2q^2+1
       800: q^2+1
       801: q^2+q+1
       802: q+1
       803: q+1
       804: 1
       805: q+1
       806: 2q^2+1
       807: q+1
       808: q+1
       809: q+1
       810: q^2+q+1
       811: q^2+1
       812: q^2+1
       813: q^2+q+1
       814: 3q^2+q+1
       815: 3q^2+q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: 3q^2+q+1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 2q^2+1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: 2q^2+1
       842: q^2+1
       843: q^2+1
       844: q+1
       845: q+1
       846: 1
       847: 1
       848: q^2+1
       849: 3q^2+q+1
       850: q+1
       851: q+1
       852: 2q^2+1
       853: 2q^2+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       859: q+1
       860: q+1
       862: q^2+q+1
       863: q+1
       864: q+1
       865: q+1
       866: q^2+q+1
       867: q^2+q+1
       868: q^2+q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: q^2+1
       875: q^2+q+1
       876: 3q^2+q+1
       877: q+1
       879: q+1
       880: q+1
       881: 1
       882: q+1
       883: q^2+q+1
       884: q^2+1
       885: 3q^2+q+1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: q^2+q+1
       891: q^2+1
       892: q^2+1
       893: q^2+q+1
       894: 3q^2+q+1
       895: 3q^2+q+1
       896: q+1
       897: q+1
       898: q+1
       899: q+1
       900: q+1
       901: q+1
       902: q+1
       903: q+1
       904: q+1
       905: 3q^2+q+1
       907: q+1
       908: 1
       909: q+1
       910: 1
       911: q^2+q+1
       912: q^2+1
       913: q+1
       915: q+1
       916: q+1
       917: 1
       918: q+1
       919: q+1
       920: 1
       921: q^2+q+1
       922: q+1
       923: 1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: q^2+1
       931: q^2+1
       932: 1
       933: q+1
       934: q+1
       935: q+1
       936: q+1
       937: 1
       938: q+1
       939: q^2+q+1
       940: q^2+q+1
       941: q^2+q+1
       942: q+1
       943: 1
       944: 1
       945: q+1
       946: 1
       947: q^2+q+1
       948: q^2+1
       949: q^2+1
       950: q^2+1
       951: 2q^2+1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       959: 2q^2+1
       961: q+1
       962: q+1
       963: 1
       964: 1
       965: q^2+1
       966: q^2+q+1
       967: q+1
       969: q+1
       970: q+1
       971: q+1
       972: 1
       973: 1
       974: q+1
       975: q^2+q+1
       976: q+1
       977: q+1
       978: q+1
       979: q+1
       980: q^2+q+1
       981: q+1
       982: 1
       983: q+1
       984: q^2+q+1
       985: q^2+q+1
       986: q+1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: q^2+1
       995: q^2+1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: q^2+1
      1002: q^2+q+1
      1003: q^2+1
      1004: q^2+1
      1005: 2q^2+1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1013: 2q^2+1
      1015: q+1
      1016: q+1
      1017: 1
      1018: 1
      1019: q^2+1
      1020: q^2+1
      1021: 3q^2+q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 1
      1028: 1
      1029: q+1
      1030: q+1
      1031: q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 2q^2+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: 2q^2+1
      1051: 1
      1052: 1
      1053: 1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: q^2+1
      1059: q^2+1
      1060: q^2+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: 1
      1065: q^2+1
      1068: q+1
      1069: q+1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1079: q+1
      1080: q+1
      1081: 1
      1082: 1
      1083: q^2+1
      1084: q^2+q+1
      1085: q+1
      1087: q+1
      1088: 1
      1089: q+1
      1090: 1
      1091: q^2+q+1
      1092: q^2+1
      1093: q+1
      1095: q+1
      1096: q+1
      1097: 1
      1098: 1
      1099: q^2+1
      1100: q^2+1
      1101: 3q^2+q+1
      1102: q+1
      1103: q+1
      1104: q+1
      1105: q+1
      1106: q+1
      1107: 1
      1108: 1
      1109: q+1
      1110: q+1
      1111: q+1
      1112: q+1
      1114: 1
      1115: q+1
      1116: 1
      1117: 1
      1118: q+1
      1119: 1
      1121: q+1
      1122: 1
      1123: q+1
      1124: 1
      1125: q+1
      1126: 1
      1127: q+1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: q^2+1
      1136: 1
      1138: q+1
      1139: q+1
      1140: 1
      1141: q+1
      1142: q+1
      1143: 1
      1144: q^2+q+1
      1145: q+1
      1146: 1
      1147: 1
      1148: 1
      1149: q+1
      1150: 1
      1152: 1
      1153: q^2+1
      1154: q^2+1
      1155: 1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: 1
      1162: 1
      1163: 1
      1164: 2q^2+1
      1166: q+1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: q+1
      1173: q+1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: q+1
      1179: q+1
      1181: q+1
      1182: q+1
      1183: q+1
      1184: 1
      1185: 1
      1186: q+1
      1187: q^2+q+1
      1188: q+1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: q^2+1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: q+1
      1205: q^2+1
      1206: q^2+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1213: q+1
      1214: 1
      1215: 1
      1216: 2q^2+1
      1218: q+1
      1219: 1
      1220: 1
      1221: 1
      1222: q^2+1
      1223: q^2+1
      1224: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q^2+1
      1263: 1
      1264: 1
      1265: 1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: q^2+1
      1272: q+1
      1273: q+1
      1276: q+1
      1277: q+1
      1278: q+1
      1280: q+1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: q+1
      1287: 1
      1288: q+1
      1289: 1
      1290: 1
      1291: q+1
      1292: 1
      1294: q+1
      1295: 1
      1296: 1
      1297: 1
      1298: q^2+1
      1299: q^2+1
      1300: q+1
      1302: q+1
      1303: q+1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: q+1
      1309: q+1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: q+1
      1318: 1
      1319: 1
      1320: q+1
      1321: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1331: q+1
      1332: 1
      1333: q+1
      1334: 1
      1335: q+1
      1336: 1
      1337: q+1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: q^2+1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q+1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: q+1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: q+1
      1370: q+1
      1371: q+1
      1372: 1
      1373: 1
      1374: 1
      1375: q+1
      1376: q+1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: q^2+1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1412: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: q+1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q^2+1
      1457: q+1
      1459: q+1
      1460: q+1
      1463: 1
      1464: 1
      1465: 1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1479: q+1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: q+1
      1487: 1
      1488: 1
      1491: 1
      1492: 1
      1493: 1
      1495: 1
      1500: 1
      1502: 1
      1503: q+1
      1504: 1
      1505: 1
      1506: q+1
      1507: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1531: 1
      1532: 1
      1534: q+1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: q+1
      1542: 1
      1545: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1593: 1
      1594: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1613: q+1
      1615: 1
      1616: 1
      1618: 1
      1619: 1
      1622: 1
      1623: 1
      1624: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1633: 1
      1635: 1
      1636: 1
      1644: 1
      1645: 1
      1646: 1
      1648: 1
      1653: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1663: 1
      1665: 1
      1666: 1
      1669: 1
      1670: 1
      1671: 1
      1679: 1
      1682: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1693: 1
      1694: 1
      1697: 1
      1698: 1
      1699: 1
      1701: 1
      1706: 1
      1709: 1
      1712: 1
      1715: 1
      1721: 1
      1723: 1
      1724: 1
      1729: 1
      1730: 1
      1733: 1
      1735: 1
      1737: 1
      1738: 1
      1741: 1
      1742: 1
      1743: 1
      1746: 1
      1751: 1
      1752: 1
      1759: 1
      1764: 1
      1767: 1
      1769: 1
      1770: 1
      1781: 1
      1784: 1
      1787: 1
      1789: 1
      1790: 1
      1809: 1
      1815: 1
      1819: 1
      1821: 1
      1822: 1
      1827: 1
      1838: 1
      1851: 1
      1872: 1

1873:    0: q^4+q^3+3q^2+2q+1
         1: q^4+q^3+3q^2+2q+1
         2: q^4+q^3+3q^2+2q+1
         3: q^4+3q^2+2q+1
         4: q^4+q^3+3q^2+2q+1
         5: q^4+q^3+3q^2+2q+1
         6: q^4+q^3+3q^2+2q+1
         7: q^4+q^3+3q^2+2q+1
         8: q^4+3q^2+2q+1
         9: q^4+3q^2+2q+1
        10: q^4+3q^2+2q+1
        11: q^4+3q^2+2q+1
        12: 2q^2+2q+1
        13: q^4+q^3+3q^2+2q+1
        14: q^4+q^3+3q^2+2q+1
        15: q^4+3q^2+2q+1
        16: q^4+q^3+3q^2+2q+1
        17: q^4+q^3+3q^2+2q+1
        18: 2q^2+2q+1
        19: q^4+q^3+3q^2+2q+1
        20: q^4+3q^2+2q+1
        21: q^4+q^3+3q^2+2q+1
        22: q^4+3q^2+2q+1
        23: q^4+3q^2+2q+1
        24: 2q^2+2q+1
        25: q^4+3q^2+2q+1
        26: q^4+3q^2+2q+1
        27: q^4+3q^2+2q+1
        28: q^4+3q^2+2q+1
        29: q^4+3q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q^4+q^3+3q^2+2q+1
        34: q^4+q^3+3q^2+2q+1
        35: q^4+3q^2+2q+1
        36: q^4+3q^2+2q+1
        37: q^4+3q^2+2q+1
        38: q^4+3q^2+2q+1
        39: 2q^2+2q+1
        40: q^4+q^3+3q^2+2q+1
        41: q^4+q^3+3q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: q^4+q^3+3q^2+2q+1
        48: q^4+q^3+3q^2+2q+1
        49: 2q^2+2q+1
        50: q^4+3q^2+2q+1
        51: 2q^2+2q+1
        52: q^4+3q^2+2q+1
        53: q^4+3q^2+2q+1
        54: q^4+3q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: q^4+3q^2+2q+1
        58: q^4+3q^2+2q+1
        59: q^4+3q^2+2q+1
        60: q^4+3q^2+2q+1
        61: 2q^2+2q+1
        62: q^4+3q^2+2q+1
        63: q^4+3q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q^4+3q^2+2q+1
        72: q^4+q^3+3q^2+2q+1
        73: q^4+3q^2+2q+1
        74: q^4+3q^2+2q+1
        75: 2q^2+2q+1
        76: q^4+3q^2+2q+1
        77: q^4+3q^2+2q+1
        78: q^4+3q^2+2q+1
        79: q^4+3q^2+2q+1
        80: q^4+3q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^2+2q+1
        85: q^4+q^3+3q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^4+q^3+3q^2+2q+1
        98: q^4+q^3+3q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       104: 2q^2+2q+1
       105: q^4+3q^2+2q+1
       106: 2q^2+2q+1
       107: q^4+3q^2+2q+1
       108: q^4+3q^2+2q+1
       109: 2q^2+2q+1
       110: 2q^2+2q+1
       111: q^2+2q+1
       112: q^4+3q^2+2q+1
       113: 2q^2+2q+1
       114: q^4+3q^2+2q+1
       115: q^4+3q^2+2q+1
       116: q^4+3q^2+2q+1
       117: 2q^2+2q+1
       118: 2q^2+2q+1
       119: q^2+2q+1
       120: q^4+3q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q+1
       124: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: 2q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q^4+3q^2+2q+1
       135: 2q^2+2q+1
       136: q^4+3q^2+2q+1
       137: q^4+3q^2+2q+1
       138: q^4+3q^2+2q+1
       139: 2q^2+2q+1
       140: 2q^2+2q+1
       141: q^4+3q^2+2q+1
       142: q^4+3q^2+2q+1
       143: q^4+3q^2+2q+1
       144: q^4+3q^2+2q+1
       145: 2q^2+2q+1
       146: q^4+3q^2+2q+1
       147: q^4+3q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+2q+1
       153: 2q^2+2q+1
       154: q^2+2q+1
       155: 2q^2+2q+1
       156: q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: q^2+2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: q^4+q^3+3q^2+2q+1
       178: 2q^2+2q+1
       179: 2q^2+2q+1
       180: q^2+2q+1
       181: 2q^2+2q+1
       182: 2q^2+2q+1
       183: 2q^2+2q+1
       184: 2q^2+2q+1
       185: 2q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: 2q^2+2q+1
       191: q^4+3q^2+2q+1
       192: 2q^2+2q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: 2q^2+2q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: 2q^2+2q+1
       199: q^4+3q^2+2q+1
       200: 2q^2+2q+1
       201: q^4+3q^2+2q+1
       202: q^4+3q^2+2q+1
       203: 2q^2+2q+1
       204: 2q^2+2q+1
       205: 2q+1
       206: q^2+2q+1
       207: q+1
       208: q^2+2q+1
       209: q^2+2q+1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: q^2+2q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: q^2+2q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: q^4+3q^2+2q+1
       230: 2q^2+2q+1
       231: q^4+3q^2+2q+1
       232: q^4+3q^2+2q+1
       233: 2q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: q^4+3q^2+2q+1
       237: 2q^2+2q+1
       238: q^4+3q^2+2q+1
       239: q^4+3q^2+2q+1
       240: q^4+3q^2+2q+1
       241: 2q^2+2q+1
       242: 2q^2+2q+1
       243: q^2+2q+1
       244: q^4+3q^2+2q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q+1
       248: q^2+2q+1
       249: 2q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: 2q^2+2q+1
       260: q^2+2q+1
       261: 2q^2+2q+1
       262: 2q^2+2q+1
       263: q^2+2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q^2+2q+1
       267: q^2+2q+1
       268: 2q^2+2q+1
       269: 2q^2+2q+1
       270: 2q^2+2q+1
       271: q^2+2q+1
       272: q^2+2q+1
       273: q^2+2q+1
       274: 2q^2+2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: q+1
       279: q^2+2q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q^2+2q+1
       289: q^2+2q+1
       290: 2q^2+2q+1
       291: 2q^2+2q+1
       292: 2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q^2+2q+1
       296: 2q^2+2q+1
       297: 2q^2+2q+1
       298: 2q^2+2q+1
       299: q^2+2q+1
       300: 2q^2+2q+1
       301: 2q^2+2q+1
       302: q^2+2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q^2+2q+1
       310: q^2+2q+1
       311: 2q^2+2q+1
       312: q^2+2q+1
       313: q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: 2q+1
       317: q^2+2q+1
       318: q^2+2q+1
       319: 2q+1
       320: 2q^2+2q+1
       321: q^4+3q^2+2q+1
       322: 2q^2+2q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: 2q^2+2q+1
       326: 2q+1
       327: 2q+1
       328: q+1
       329: q^2+2q+1
       330: q+1
       331: q^2+2q+1
       332: q^2+2q+1
       333: q+1
       334: q+1
       335: q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: q^2+2q+1
       339: q^2+2q+1
       340: q^2+2q+1
       341: q^2+2q+1
       342: q^2+2q+1
       343: 2q+1
       344: 2q+1
       345: q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: q+1
       350: q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: q+1
       356: q^2+2q+1
       357: 2q^2+2q+1
       358: q^4+3q^2+2q+1
       359: 2q^2+2q+1
       360: q^2+2q+1
       361: q^2+2q+1
       362: 2q^2+2q+1
       363: q^2+2q+1
       364: q^2+2q+1
       365: 2q^2+2q+1
       366: q^4+3q^2+2q+1
       367: 2q^2+2q+1
       368: q^4+3q^2+2q+1
       369: q^4+3q^2+2q+1
       370: 2q^2+2q+1
       371: 2q^2+2q+1
       372: 2q+1
       373: q^2+2q+1
       374: q+1
       375: q^2+2q+1
       376: q^2+2q+1
       377: q^2+2q+1
       378: q+1
       379: q+1
       380: q^2+2q+1
       381: q^2+2q+1
       382: q^2+2q+1
       383: q^2+2q+1
       384: q^2+2q+1
       385: q^2+2q+1
       386: q^2+2q+1
       387: 2q+1
       388: 2q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: 2q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q^2+2q+1
       398: q^2+2q+1
       399: q^2+2q+1
       400: q+1
       401: q^2+2q+1
       402: q^2+2q+1
       403: q^2+2q+1
       404: q^2+2q+1
       405: 2q^2+2q+1
       406: q^2+2q+1
       407: 2q^2+2q+1
       408: 2q^2+2q+1
       409: q^2+2q+1
       410: q^2+2q+1
       411: q+1
       412: q^2+2q+1
       413: q+1
       414: q^2+2q+1
       415: q^2+2q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: 1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q+1
       434: q^2+2q+1
       435: 2q^2+2q+1
       436: q^2+2q+1
       437: 2q^2+2q+1
       438: 2q^2+2q+1
       439: q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q^2+2q+1
       443: q^2+2q+1
       444: 2q^2+2q+1
       445: 2q^2+2q+1
       446: 2q^2+2q+1
       447: q^2+2q+1
       448: q^2+2q+1
       449: q^2+2q+1
       450: 2q^2+2q+1
       451: q^2+2q+1
       452: q^2+2q+1
       453: q+1
       454: q+1
       455: q^2+2q+1
       456: q+1
       457: q+1
       458: q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q^2+2q+1
       465: q^2+2q+1
       466: 2q+1
       467: q+1
       468: q^2+2q+1
       469: 2q+1
       470: q+1
       471: 2q+1
       472: q^2+2q+1
       473: 2q+1
       474: 2q+1
       475: 2q^2+2q+1
       476: q^2+2q+1
       477: q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: 2q+1
       481: 2q+1
       482: 2q+1
       483: q+1
       484: q+1
       485: q^2+2q+1
       486: q+1
       487: q^2+2q+1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: q^2+2q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: q+1
       502: 2q+1
       503: q+1
       504: 2q+1
       505: 2q+1
       506: q+1
       507: q+1
       508: q+1
       509: 2q+1
       510: q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: q+1
       515: q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: 2q^2+2q+1
       519: q^2+2q+1
       520: q+1
       521: q^2+2q+1
       522: q^2+2q+1
       523: 2q+1
       524: q^2+2q+1
       525: q^2+2q+1
       526: 2q+1
       527: 2q^2+2q+1
       528: q^4+3q^2+2q+1
       529: 2q^2+2q+1
       530: q^2+2q+1
       531: q^2+2q+1
       532: 2q^2+2q+1
       533: 2q+1
       534: 2q+1
       535: q+1
       536: q^2+2q+1
       537: q+1
       538: q^2+2q+1
       539: q^2+2q+1
       540: q+1
       541: q+1
       542: q+1
       543: q^2+2q+1
       544: q^2+2q+1
       545: q^2+2q+1
       546: q^2+2q+1
       547: q^2+2q+1
       548: q^2+2q+1
       549: q^2+2q+1
       550: 2q+1
       551: 2q+1
       552: q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: q+1
       557: q+1
       558: 2q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q+1
       562: q+1
       563: q^2+2q+1
       564: q^2+2q+1
       565: q^2+2q+1
       566: q^2+2q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: q^2+2q+1
       572: q^2+2q+1
       573: q+1
       574: q^2+2q+1
       575: 2q^2+2q+1
       576: q^2+2q+1
       577: q^2+2q+1
       578: q+1
       579: q^2+2q+1
       580: q+1
       581: q+1
       582: q+1
       583: q^2+2q+1
       584: q+1
       585: q^2+2q+1
       586: q^2+2q+1
       587: q+1
       588: q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q^2+2q+1
       607: q+1
       608: q+1
       609: 1
       610: q^2+2q+1
       611: q^2+2q+1
       612: 2q^2+2q+1
       613: q^2+2q+1
       614: q^2+2q+1
       615: q+1
       616: q^2+2q+1
       617: q^2+2q+1
       618: q^2+2q+1
       619: q^2+2q+1
       620: 2q^2+2q+1
       621: q^2+2q+1
       622: 2q^2+2q+1
       623: 2q^2+2q+1
       624: q^2+2q+1
       625: q^2+2q+1
       626: q+1
       627: q^2+2q+1
       628: q+1
       629: q^2+2q+1
       630: q^2+2q+1
       631: q^2+2q+1
       632: q+1
       633: q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: q+1
       645: 1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q^2+2q+1
       650: 2q+1
       651: q+1
       652: 2q+1
       653: q+1
       654: 2q+1
       655: q+1
       656: 2q+1
       657: 2q+1
       658: 2q+1
       659: 2q+1
       660: q+1
       661: q^2+2q+1
       662: 2q+1
       663: q+1
       664: 2q+1
       665: 2q+1
       666: q+1
       667: q+1
       668: q+1
       669: q^2+2q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       676: 2q+1
       677: 2q+1
       678: q^2+2q+1
       679: q+1
       681: q^2+2q+1
       682: q^2+2q+1
       683: q+1
       684: 2q+1
       685: 2q+1
       686: q+1
       687: q+1
       688: 2q+1
       689: q+1
       690: q+1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: 2q+1
       697: q+1
       698: 2q+1
       699: 2q+1
       700: q+1
       701: q+1
       702: 1
       703: q^2+2q+1
       704: q^2+2q+1
       705: 2q+1
       706: q+1
       707: q^2+2q+1
       708: 2q+1
       709: q+1
       710: 2q+1
       711: q^2+2q+1
       712: 2q+1
       713: 2q+1
       714: 2q^2+2q+1
       715: q^2+2q+1
       716: q+1
       717: q^2+2q+1
       718: q^2+2q+1
       719: 2q+1
       720: 2q+1
       721: 2q+1
       722: q+1
       723: q+1
       724: q^2+2q+1
       725: q+1
       726: q^2+2q+1
       727: 1
       728: q+1
       729: q+1
       730: q+1
       731: 2q+1
       732: q^2+2q+1
       733: q^2+2q+1
       734: q^2+2q+1
       735: q+1
       736: q^2+2q+1
       737: q^2+2q+1
       738: 2q+1
       739: 2q+1
       740: q+1
       741: 2q+1
       742: q+1
       743: 2q+1
       744: 2q+1
       745: q+1
       746: q+1
       747: q+1
       748: 2q+1
       749: q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: q+1
       754: q+1
       755: q^2+2q+1
       756: q^2+2q+1
       757: q+1
       758: q+1
       759: q+1
       760: q+1
       761: 1
       762: q+1
       763: q^2+2q+1
       764: q+1
       765: q+1
       766: q^2+2q+1
       767: q^2+2q+1
       768: q+1
       769: q+1
       770: q+1
       771: q+1
       772: q+1
       773: q+1
       774: 1
       775: q+1
       776: q^2+2q+1
       777: q+1
       778: q^2+2q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: q+1
       784: q+1
       785: q+1
       786: q+1
       788: q+1
       789: q+1
       790: q+1
       791: q+1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: q^2+2q+1
       808: q^2+2q+1
       809: q^2+2q+1
       810: q^2+2q+1
       811: q+1
       812: q+1
       813: q+1
       814: q+1
       815: q^2+2q+1
       816: q^2+2q+1
       817: q+1
       818: q^2+2q+1
       819: 2q^2+2q+1
       820: q^2+2q+1
       821: q^2+2q+1
       822: q+1
       823: q^2+2q+1
       824: q+1
       825: q+1
       826: q+1
       827: q^2+2q+1
       828: q+1
       829: q^2+2q+1
       830: q^2+2q+1
       831: q+1
       832: q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       842: q+1
       843: 1
       844: q+1
       845: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       853: 1
       854: 2q+1
       855: q+1
       856: 2q+1
       857: q+1
       858: q+1
       859: 2q+1
       860: q+1
       861: 2q+1
       862: 2q+1
       863: q+1
       864: 2q+1
       865: q+1
       866: 2q+1
       867: q+1
       868: 2q+1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: 2q+1
       879: 2q+1
       880: q+1
       882: q^2+2q+1
       883: q+1
       885: q+1
       886: 2q+1
       887: q+1
       888: q+1
       889: q+1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: 2q+1
       900: q+1
       901: q+1
       902: 1
       903: q+1
       904: 1
       905: 1
       906: q^2+2q+1
       907: 2q+1
       908: q+1
       909: 2q+1
       910: q+1
       911: 2q+1
       912: q+1
       913: 2q+1
       914: 2q+1
       915: 2q+1
       916: 2q+1
       917: q+1
       918: q^2+2q+1
       919: 2q+1
       920: q+1
       921: 2q+1
       922: 2q+1
       923: q+1
       924: q+1
       925: q+1
       926: q^2+2q+1
       927: q+1
       928: 1
       929: 1
       930: 1
       931: q+1
       932: q+1
       933: 2q+1
       934: 2q+1
       935: q^2+2q+1
       936: q+1
       938: q^2+2q+1
       939: q^2+2q+1
       940: q+1
       941: 2q+1
       942: 2q+1
       943: q+1
       944: q+1
       945: 2q+1
       946: q+1
       947: q+1
       948: 1
       949: q+1
       950: q+1
       951: q+1
       952: q+1
       953: 2q+1
       954: q+1
       955: 2q+1
       956: 2q+1
       957: q+1
       958: q+1
       959: 1
       960: q^2+2q+1
       961: q+1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       967: q+1
       968: q+1
       969: q+1
       970: q+1
       971: q+1
       972: q+1
       973: q+1
       974: 1
       975: q+1
       976: q+1
       977: 1
       978: 1
       979: q+1
       980: q^2+2q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: q+1
       988: q+1
       989: q+1
       992: q+1
       993: q+1
       995: q+1
       996: q+1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1014: q^2+2q+1
      1015: q^2+2q+1
      1016: q+1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: 1
      1021: q+1
      1022: q^2+2q+1
      1023: q+1
      1024: q+1
      1025: q^2+2q+1
      1026: q^2+2q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: q+1
      1031: q+1
      1032: q+1
      1033: 1
      1034: q+1
      1035: q^2+2q+1
      1036: q+1
      1037: q^2+2q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: q+1
      1043: q+1
      1044: q+1
      1045: q+1
      1047: q+1
      1048: q+1
      1049: q+1
      1050: q+1
      1051: 1
      1052: q+1
      1053: 1
      1054: q+1
      1055: q+1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: 1
      1065: 1
      1066: q+1
      1067: 2q+1
      1068: q+1
      1069: 1
      1070: q+1
      1071: 2q+1
      1072: q+1
      1073: 2q+1
      1074: q+1
      1075: q+1
      1076: 2q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 2q+1
      1087: q+1
      1089: q+1
      1091: q+1
      1093: q+1
      1094: q+1
      1095: q+1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 2q+1
      1114: q+1
      1115: 2q+1
      1116: q+1
      1117: q+1
      1118: 2q+1
      1119: q+1
      1120: 2q+1
      1121: 2q+1
      1122: q+1
      1123: 2q+1
      1124: q+1
      1125: 2q+1
      1126: q+1
      1127: 2q+1
      1128: q+1
      1129: q+1
      1130: 1
      1131: q+1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: q+1
      1137: 2q+1
      1138: 2q+1
      1139: q+1
      1141: q^2+2q+1
      1142: q+1
      1144: q+1
      1145: 2q+1
      1146: q+1
      1147: q+1
      1148: q+1
      1149: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1155: q+1
      1156: 1
      1157: q+1
      1158: 2q+1
      1159: q+1
      1160: q+1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1165: q+1
      1166: 1
      1167: q+1
      1168: 1
      1169: 1
      1170: q+1
      1171: 1
      1172: q+1
      1173: q+1
      1174: 1
      1175: q+1
      1176: 1
      1177: q+1
      1178: 1
      1179: q+1
      1180: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: q+1
      1190: q+1
      1193: q+1
      1197: q+1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q^2+2q+1
      1218: q+1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1224: q+1
      1225: q+1
      1226: q+1
      1227: q+1
      1228: q+1
      1229: q+1
      1230: q+1
      1231: 1
      1232: q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: q+1
      1237: q^2+2q+1
      1238: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: q+1
      1245: q+1
      1246: q+1
      1249: q+1
      1250: q+1
      1252: q+1
      1253: q+1
      1254: 1
      1255: 1
      1256: q+1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1270: 1
      1271: q+1
      1272: 1
      1273: 1
      1274: q+1
      1275: 2q+1
      1276: q+1
      1277: 1
      1278: q+1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: q+1
      1291: q+1
      1293: q+1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1310: q+1
      1311: 2q+1
      1312: q+1
      1313: 1
      1314: q+1
      1315: 2q+1
      1316: q+1
      1317: 2q+1
      1318: q+1
      1319: q+1
      1320: 2q+1
      1321: q+1
      1322: q+1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: 2q+1
      1331: q+1
      1333: q+1
      1335: q+1
      1337: q+1
      1338: q+1
      1339: q+1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: q+1
      1347: 1
      1348: 1
      1349: q+1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1358: q+1
      1359: 1
      1360: 1
      1361: 1
      1362: q+1
      1363: 1
      1364: q+1
      1365: 1
      1366: 1
      1367: q+1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: q+1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1404: q+1
      1405: 1
      1406: q+1
      1407: 1
      1408: 1
      1409: q+1
      1410: 1
      1411: q+1
      1412: q+1
      1413: 1
      1414: q+1
      1415: 1
      1416: q+1
      1417: 1
      1418: q+1
      1419: 1
      1420: 1
      1421: 1
      1422: q+1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1428: q+1
      1429: q+1
      1432: q+1
      1436: q+1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: q+1
      1450: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: q+1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1467: q+1
      1471: 1
      1473: 1
      1476: 1
      1478: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1489: q+1
      1490: 2q+1
      1491: q+1
      1492: 1
      1493: q+1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: q+1
      1503: q+1
      1506: q+1
      1508: q+1
      1509: 1
      1511: 1
      1513: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1520: 1
      1521: 1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: q+1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1547: 1
      1555: 1
      1556: 1
      1559: 1
      1563: 1
      1564: 1
      1565: q+1
      1566: 1
      1567: 1
      1568: 1
      1569: q+1
      1570: 1
      1571: q+1
      1572: 1
      1573: 1
      1574: q+1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1584: q+1
      1592: 1
      1593: 1
      1596: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1606: 1
      1607: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1614: 1
      1615: 1
      1616: 1
      1621: 1
      1625: 1
      1627: 1
      1630: 1
      1632: 1
      1633: 1
      1634: q+1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1643: q+1
      1647: 1
      1649: 1
      1652: 1
      1654: 1
      1655: 1
      1657: 1
      1659: 1
      1661: 1
      1662: 1
      1663: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1684: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: q+1
      1697: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1714: 1
      1722: 1
      1723: 1
      1726: 1
      1730: 1
      1731: 1
      1732: 1
      1733: 1
      1740: 1
      1744: 1
      1745: 1
      1746: 1
      1747: 1
      1748: 1
      1749: 1
      1754: 1
      1758: 1
      1760: 1
      1763: 1
      1765: 1
      1768: 1
      1786: 1
      1787: 1
      1788: 1
      1791: 1
      1792: 1
      1793: 1
      1795: 1
      1808: 1
      1816: 1
      1823: 1
      1824: 1
      1825: 1
      1832: 1
      1849: 1
      1852: 1
      1873: 1

1874:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: 1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: 1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: 1
        17: 1
        18: 1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: 1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: 1
        29: 1
        30: q^2+1
        31: q^2+1
        32: 1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: 1
        55: q^2+1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: 1
        61: q^2+1
        62: 1
        63: 1
        64: 1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: 1
        69: 1
        70: 1
        71: q^2+1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: q^2+1
       107: q^2+1
       108: 1
       109: q^2+1
       110: 1
       111: 1
       112: 1
       113: q^2+1
       114: q^2+1
       115: q^2+1
       116: 1
       117: q^2+1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: q^2+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: q^2+1
       136: q^2+1
       137: q^2+1
       138: 1
       139: q^2+1
       140: 1
       141: q^2+1
       142: q^2+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: 1
       192: q^2+1
       193: 1
       194: q^2+1
       195: 1
       196: 1
       197: 1
       198: 1
       199: 1
       200: q^2+1
       201: q^2+1
       202: 1
       203: q^2+1
       204: 1
       205: 1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: 1
       213: 1
       214: q^2+1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: q^2+1
       231: q^2+1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       236: 1
       237: q^2+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: 1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: q^2+1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: q^2+1
       323: 1
       324: q^2+1
       325: 1
       326: 1
       327: 1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q^2+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: q^2+1
       360: 1
       361: q^2+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: q^2+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       420: 1
       421: 1
       422: 1
       424: 1
       426: 1
       427: 1
       428: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: q^2+1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: q^2+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       592: 1
       593: 1
       595: 1
       599: 1
       600: 1
       601: 1
       603: 1
       605: 1
       606: 1
       607: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       635: 1
       636: 1
       637: 1
       639: 1
       641: 1
       642: 1
       643: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: q^2+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       786: 1
       788: 1
       794: 1
       795: 1
       797: 1
       801: 1
       802: 1
       803: 1
       805: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       836: 1
       837: 1
       839: 1
       843: 1
       844: 1
       845: 1
       847: 1
       849: 1
       850: 1
       851: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: q^2+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       993: 1
      1000: 1
      1002: 1
      1008: 1
      1009: 1
      1011: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1045: 1
      1047: 1
      1053: 1
      1054: 1
      1056: 1
      1060: 1
      1061: 1
      1062: 1
      1064: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1204: 1
      1211: 1
      1213: 1
      1217: 1
      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1250: 1
      1257: 1
      1259: 1
      1265: 1
      1266: 1
      1268: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1400: 1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1443: 1
      1450: 1
      1452: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1607: 1
      1611: 1
      1612: 1
      1613: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1625: 1
      1626: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1667: 1
      1695: 1
      1700: 1
      1701: 1
      1706: 1
      1731: 1
      1734: 1
      1735: 1
      1739: 1
      1744: 1
      1745: 1
      1746: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1758: 1
      1759: 1
      1764: 1
      1791: 1
      1817: 1
      1823: 1
      1826: 1
      1827: 1
      1831: 1
      1874: 1

1875:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
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        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: 1
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        91: 1
        92: q+1
        93: 1
        94: q+1
        95: 1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
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       102: q+1
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       104: q+1
       105: q+1
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       107: q+1
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       114: q+1
       115: q+1
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       122: q+1
       123: q+1
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       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
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       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: 1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
       170: 1
       171: 1
       172: 1
       173: q+1
       174: 1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: 1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: 1
       262: 1
       263: 1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: 1
       273: 1
       274: 1
       275: 1
       276: 1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: 1
       332: 1
       333: 1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: 1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q+1
       403: 1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: 1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       524: 1
       525: 1
       526: q+1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: 1
       711: 1
       712: 1
       713: q+1
       714: q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: q+1
       720: 1
       721: 1
       722: q+1
       723: q+1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: 1
       731: q+1
       732: q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: 1
       740: q+1
       741: q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: q+1
       909: q+1
       910: q+1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: q+1
       917: q+1
       918: q+1
       919: q+1
       920: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: q+1
       935: q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: 1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       986: 1
       987: 1
       988: 1
       996: 1
       997: 1
       998: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: q+1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: q+1
      1123: q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: q+1
      1140: q+1
      1141: q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1180: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1189: 1
      1198: 1
      1199: 1
      1207: 1
      1208: 1
      1209: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1243: 1
      1244: 1
      1245: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1365: 1
      1371: 1
      1372: 1
      1373: 1
      1385: 1
      1394: 1
      1395: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1428: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1525: 1
      1526: 1
      1527: 1
      1536: 1
      1555: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1572: 1
      1578: 1
      1579: 1
      1580: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1628: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1656: 1
      1657: 1
      1658: 1
      1662: 1
      1692: 1
      1693: 1
      1694: 1
      1703: 1
      1722: 1
      1732: 1
      1734: 1
      1736: 1
      1737: 1
      1738: 1
      1745: 1
      1747: 1
      1748: 1
      1749: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1754: 1
      1755: 1
      1756: 1
      1757: 1
      1761: 1
      1786: 1
      1818: 1
      1824: 1
      1826: 1
      1828: 1
      1829: 1
      1830: 1
      1875: 1

1876:    0: q^3+2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: 2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: 2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: 2q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^3+2q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: 2q^2+2q+1
        37: q^3+2q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: 2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^2+2q+1
        58: 2q^2+2q+1
        59: 2q^2+2q+1
        60: q^3+2q^2+2q+1
        61: q^3+2q^2+2q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: q^3+2q^2+2q+1
        68: 2q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: 2q^2+2q+1
        73: 2q^2+2q+1
        74: q^3+2q^2+2q+1
        75: q^3+2q^2+2q+1
        76: 2q^2+2q+1
        77: 2q^2+2q+1
        78: q^3+2q^2+2q+1
        79: 2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: 2q^2+2q+1
        82: q^3+2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 2q+1
        85: 2q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: 2q^2+2q+1
       109: 2q^2+2q+1
       110: 2q^2+2q+1
       111: q^2+2q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: 2q^2+2q+1
       116: 2q^2+2q+1
       117: 2q^2+2q+1
       118: q^3+2q^2+2q+1
       119: 2q+1
       120: 2q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q^2+2q+1
       126: 2q^2+2q+1
       127: q^3+2q^2+2q+1
       128: q^3+2q^2+2q+1
       129: 2q^2+2q+1
       130: 2q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
       140: q^3+2q^2+2q+1
       141: q^2+2q+1
       142: 2q^2+2q+1
       143: 2q^2+2q+1
       144: q^3+2q^2+2q+1
       145: q^3+2q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: q^3+2q^2+2q+1
       152: 2q^2+2q+1
       153: q^3+2q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: q+1
       164: q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^2+2q+1
       168: q+1
       169: q^2+2q+1
       170: q^2+2q+1
       171: q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: 2q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: q^2+2q+1
       182: q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: 2q+1
       194: q^2+2q+1
       195: 2q^2+2q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: 2q^2+2q+1
       203: 2q^2+2q+1
       204: 2q^2+2q+1
       205: q^2+2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q^2+2q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q^2+2q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: 2q^2+2q+1
       217: 2q^2+2q+1
       218: 2q^2+2q+1
       219: q^3+2q^2+2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: 2q^2+2q+1
       233: 2q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: q^2+2q+1
       237: q^2+2q+1
       238: q^2+2q+1
       239: 2q^2+2q+1
       240: 2q^2+2q+1
       241: 2q^2+2q+1
       242: q^3+2q^2+2q+1
       243: 2q+1
       244: 2q^2+2q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: 2q^2+2q+1
       250: 2q^2+2q+1
       251: q^3+2q^2+2q+1
       252: q^3+2q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: q^2+2q+1
       263: q^2+2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q^2+2q+1
       273: 2q+1
       274: q+1
       275: q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q+1
       279: q+1
       280: 1
       281: q+1
       282: q+1
       283: q^2+2q+1
       284: q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: q^2+2q+1
       299: q^2+2q+1
       300: q^2+2q+1
       301: q+1
       302: q^2+2q+1
       303: q^2+2q+1
       304: q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q^2+2q+1
       312: 2q+1
       313: 2q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: 2q+1
       317: q^2+2q+1
       318: q+1
       319: q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: 2q+1
       324: q^2+2q+1
       325: 2q^2+2q+1
       326: q^2+2q+1
       327: q^2+2q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: q^2+2q+1
       333: q^2+2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: q^2+2q+1
       339: q^2+2q+1
       340: 2q^2+2q+1
       341: 2q^2+2q+1
       342: 2q^2+2q+1
       343: q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: q^2+2q+1
       360: 2q+1
       361: q^2+2q+1
       362: 2q^2+2q+1
       363: q^2+2q+1
       364: q^2+2q+1
       365: q^2+2q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: 2q^2+2q+1
       370: 2q^2+2q+1
       371: 2q^2+2q+1
       372: q^2+2q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: q^2+2q+1
       377: q^2+2q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: q^2+2q+1
       381: q^2+2q+1
       382: q^2+2q+1
       383: 2q^2+2q+1
       384: 2q^2+2q+1
       385: 2q^2+2q+1
       386: q^3+2q^2+2q+1
       387: 2q+1
       388: 2q^2+2q+1
       389: q^2+2q+1
       390: q^2+2q+1
       391: q^2+2q+1
       392: q^2+2q+1
       393: q+1
       394: q^2+2q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: q+1
       401: q^2+2q+1
       402: q^2+2q+1
       403: q^2+2q+1
       404: 2q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: 2q+1
       413: 2q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q^2+2q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q+1
       427: q+1
       428: 1
       429: q+1
       430: q+1
       431: q^2+2q+1
       432: q+1
       433: q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: q^2+2q+1
       439: q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q^2+2q+1
       449: 2q+1
       450: q+1
       451: q+1
       452: q^2+2q+1
       453: q^2+2q+1
       454: q+1
       455: q+1
       456: 1
       457: q+1
       458: q+1
       459: q^2+2q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: q+1
       467: 2q+1
       468: q^2+2q+1
       469: 2q+1
       470: 2q+1
       471: 2q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+2q+1
       476: 2q+1
       477: 2q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: 2q+1
       481: q^2+2q+1
       482: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: 2q+1
       488: q+1
       489: q^2+2q+1
       490: q^2+2q+1
       491: q^2+2q+1
       492: q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: q^2+2q+1
       496: 2q+1
       497: q^2+2q+1
       498: 2q^2+2q+1
       499: q^2+2q+1
       500: q^2+2q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: q^2+2q+1
       506: q^2+2q+1
       507: q^2+2q+1
       508: q^2+2q+1
       509: 2q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q^2+2q+1
       516: q+1
       517: q+1
       518: q^2+2q+1
       519: 2q+1
       520: 2q+1
       521: q^2+2q+1
       522: q^2+2q+1
       523: 2q+1
       524: q^2+2q+1
       525: q+1
       526: q+1
       527: q^2+2q+1
       528: q^2+2q+1
       529: q^2+2q+1
       530: 2q+1
       531: q^2+2q+1
       532: 2q^2+2q+1
       533: q^2+2q+1
       534: q^2+2q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: 2q+1
       539: q^2+2q+1
       540: q^2+2q+1
       541: q^2+2q+1
       542: q^2+2q+1
       543: q^2+2q+1
       544: q^2+2q+1
       545: q^2+2q+1
       546: q^2+2q+1
       547: 2q^2+2q+1
       548: 2q^2+2q+1
       549: 2q^2+2q+1
       550: q^2+2q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: q^2+2q+1
       555: q^2+2q+1
       556: q^2+2q+1
       557: q^2+2q+1
       558: 2q+1
       559: q+1
       560: q+1
       561: q^2+2q+1
       562: q^2+2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       568: q+1
       569: q+1
       570: q+1
       571: q^2+2q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: q+1
       582: 2q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q+1
       598: q+1
       599: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q+1
       605: q+1
       606: q+1
       607: 1
       608: q+1
       609: q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: 2q+1
       615: q+1
       616: q^2+2q+1
       617: q^2+2q+1
       618: q^2+2q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: 2q+1
       628: 2q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q^2+2q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q+1
       650: q+1
       651: q+1
       652: q+1
       653: 2q+1
       654: 2q+1
       655: 2q+1
       656: q+1
       658: q+1
       659: q+1
       660: 2q+1
       661: q^2+2q+1
       662: 2q+1
       663: 2q+1
       664: 2q+1
       665: q+1
       666: q+1
       667: q+1
       668: 2q+1
       669: 2q+1
       670: 2q+1
       671: q+1
       672: q+1
       673: q+1
       674: q^2+2q+1
       675: q+1
       676: q+1
       677: q+1
       678: q^2+2q+1
       679: 2q+1
       680: 2q+1
       681: q^2+2q+1
       682: q^2+2q+1
       683: 2q+1
       684: q^2+2q+1
       685: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: 2q+1
       691: q+1
       692: q^2+2q+1
       693: q^2+2q+1
       694: q^2+2q+1
       695: 2q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       704: q+1
       705: q+1
       706: 2q+1
       707: q^2+2q+1
       708: 2q+1
       709: 2q+1
       710: 2q+1
       711: q+1
       712: q+1
       713: q+1
       714: q^2+2q+1
       715: 2q+1
       716: 2q+1
       717: q^2+2q+1
       718: q^2+2q+1
       719: 2q+1
       720: q^2+2q+1
       721: q+1
       722: q+1
       723: 2q+1
       724: 2q+1
       725: 2q+1
       726: 2q+1
       727: q+1
       728: q^2+2q+1
       729: q^2+2q+1
       730: q^2+2q+1
       731: q+1
       732: q^2+2q+1
       733: q^2+2q+1
       734: q^2+2q+1
       735: 2q+1
       736: q^2+2q+1
       737: 2q^2+2q+1
       738: q^2+2q+1
       739: q^2+2q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 2q+1
       744: q^2+2q+1
       745: q^2+2q+1
       746: q^2+2q+1
       747: q^2+2q+1
       748: 2q+1
       749: 2q+1
       750: q+1
       751: q+1
       752: q+1
       753: q+1
       754: q^2+2q+1
       756: q+1
       757: 1
       758: 2q+1
       759: q+1
       760: q+1
       761: q+1
       762: q+1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: q+1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: q+1
       800: q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: 2q+1
       811: 2q+1
       812: q+1
       813: q+1
       814: q+1
       815: q^2+2q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: 1
       823: q+1
       824: 1
       825: q+1
       826: 2q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       855: q+1
       856: q+1
       857: q+1
       858: 2q+1
       859: q+1
       860: q+1
       862: q+1
       863: q+1
       864: q+1
       865: 2q+1
       866: 2q+1
       867: 2q+1
       868: q+1
       870: q+1
       871: 1
       872: 2q+1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       879: q+1
       880: q+1
       881: 2q+1
       882: q^2+2q+1
       883: 2q+1
       884: 2q+1
       885: 2q+1
       886: q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: 2q+1
       891: 2q+1
       892: q+1
       893: q+1
       894: q+1
       895: q^2+2q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: q+1
       902: 1
       903: q+1
       904: 1
       905: q+1
       907: q+1
       908: q+1
       909: q+1
       910: 2q+1
       911: 2q+1
       912: 2q+1
       913: q+1
       915: q+1
       916: q+1
       917: 2q+1
       918: q^2+2q+1
       919: 2q+1
       920: 2q+1
       921: 2q+1
       922: q+1
       923: q+1
       924: q+1
       925: 2q+1
       926: 2q+1
       927: 2q+1
       928: q+1
       929: q+1
       930: q+1
       931: q^2+2q+1
       932: q+1
       933: q+1
       934: q+1
       935: q^2+2q+1
       936: 2q+1
       937: 2q+1
       938: q^2+2q+1
       939: q^2+2q+1
       940: 2q+1
       941: q^2+2q+1
       942: q+1
       943: q+1
       944: 2q+1
       945: 2q+1
       946: 2q+1
       947: 2q+1
       948: q+1
       949: q^2+2q+1
       950: q^2+2q+1
       951: q^2+2q+1
       952: 2q+1
       953: q+1
       954: q+1
       955: q+1
       956: q+1
       957: q+1
       958: q+1
       959: q+1
       961: 1
       962: 1
       963: 1
       964: q+1
       965: q+1
       966: q+1
       967: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: q+1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q+1
      1015: q+1
      1016: 1
      1017: 2q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: q+1
      1027: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q+1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1068: q+1
      1069: 1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: q+1
      1083: q+1
      1084: q+1
      1085: 1
      1087: q+1
      1088: q+1
      1089: q+1
      1090: 2q+1
      1091: 2q+1
      1092: 2q+1
      1093: q+1
      1095: q+1
      1096: 1
      1097: 2q+1
      1098: q+1
      1099: q+1
      1100: q+1
      1101: q+1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: q+1
      1107: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: q+1
      1115: q+1
      1116: q+1
      1117: 2q+1
      1118: q+1
      1119: q+1
      1121: q+1
      1122: q+1
      1123: q+1
      1124: 2q+1
      1125: 2q+1
      1126: 2q+1
      1127: q+1
      1129: q+1
      1130: 1
      1131: 2q+1
      1132: q+1
      1133: q+1
      1134: q+1
      1135: q+1
      1136: q+1
      1138: q+1
      1139: q+1
      1140: 2q+1
      1141: q^2+2q+1
      1142: 2q+1
      1143: 2q+1
      1144: 2q+1
      1145: q+1
      1146: q+1
      1147: q+1
      1148: 2q+1
      1149: 2q+1
      1150: 2q+1
      1151: q+1
      1152: q+1
      1153: q+1
      1154: q^2+2q+1
      1155: q+1
      1156: 1
      1157: q+1
      1158: q+1
      1159: q+1
      1160: q+1
      1161: 1
      1162: q+1
      1163: 1
      1164: q+1
      1166: 1
      1167: 1
      1168: 1
      1169: q+1
      1170: 1
      1171: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: q+1
      1222: q+1
      1223: q+1
      1224: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q+1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q+1
      1272: 1
      1273: 1
      1276: q+1
      1277: 1
      1278: q+1
      1280: 1
      1281: 1
      1282: 1
      1283: q+1
      1284: 1
      1285: 1
      1287: q+1
      1288: q+1
      1289: q+1
      1290: 2q+1
      1291: q+1
      1292: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: q+1
      1298: q+1
      1299: q+1
      1300: 1
      1302: 1
      1303: 1
      1304: q+1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1312: q+1
      1313: 1
      1314: q+1
      1316: q+1
      1317: q+1
      1318: q+1
      1319: 2q+1
      1320: q+1
      1321: q+1
      1323: 1
      1324: 1
      1325: 1
      1326: q+1
      1327: q+1
      1328: q+1
      1329: 1
      1331: q+1
      1332: q+1
      1333: q+1
      1334: 2q+1
      1335: 2q+1
      1336: 2q+1
      1337: q+1
      1339: q+1
      1340: 1
      1341: 2q+1
      1342: q+1
      1343: q+1
      1344: q+1
      1345: q+1
      1346: q+1
      1347: 1
      1348: 1
      1349: q+1
      1350: q+1
      1351: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1405: 1
      1406: 1
      1407: 1
      1408: q+1
      1409: 1
      1410: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1420: 1
      1421: 1
      1422: q+1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1429: 1
      1432: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q+1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1468: q+1
      1469: 1
      1470: q+1
      1472: 1
      1473: 1
      1474: 1
      1475: q+1
      1476: 1
      1477: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: q+1
      1492: 1
      1493: q+1
      1495: 1
      1496: 1
      1497: 1
      1498: q+1
      1499: 1
      1500: 1
      1502: q+1
      1503: q+1
      1504: q+1
      1505: 2q+1
      1506: q+1
      1507: q+1
      1509: 1
      1510: 1
      1511: 1
      1512: q+1
      1513: q+1
      1514: q+1
      1515: 1
      1517: 1
      1518: 1
      1519: q+1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1532: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1556: 1
      1559: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1593: 1
      1596: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1606: 1
      1607: 1
      1609: 1
      1610: 1
      1613: 1
      1615: 1
      1616: 1
      1618: 1
      1619: 1
      1622: 1
      1623: 1
      1624: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1633: 1
      1635: 1
      1636: 1
      1639: 1
      1640: 1
      1641: 1
      1644: q+1
      1645: 1
      1646: q+1
      1648: 1
      1649: 1
      1650: 1
      1651: q+1
      1652: 1
      1653: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1663: 1
      1669: 1
      1671: 1
      1693: 1
      1694: 1
      1697: 1
      1699: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1723: 1
      1726: 1
      1730: 1
      1733: 1
      1735: 1
      1737: 1
      1738: 1
      1741: 1
      1743: 1
      1746: 1
      1748: 1
      1749: 1
      1751: 1
      1752: 1
      1755: 1
      1756: 1
      1757: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1787: 1
      1793: 1
      1795: 1
      1819: 1
      1825: 1
      1827: 1
      1829: 1
      1830: 1
      1833: 1
      1835: 1
      1876: 1

1877:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: 2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: 2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 2q^2+2q+1
        77: 2q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q+1
        85: 2q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: 2q+1
       120: 2q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: 2q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: 2q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: 2q^2+2q+1
       148: 2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+2q+1
       153: 2q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: 2q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: q+1
       194: q^2+q+1
       195: q^2+2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q^2+2q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: q^2+2q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q+1
       236: q^2+2q+1
       237: q^2+2q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: q^2+2q+1
       241: q^2+2q+1
       242: q^2+2q+1
       243: 2q+1
       244: 2q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q^2+2q+1
       249: 2q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: q+1
       279: q^2+2q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: 2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q^2+2q+1
       312: q+1
       313: q+1
       314: q^2+q+1
       315: q^2+q+1
       316: 1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: q+1
       324: q^2+q+1
       325: q^2+2q+1
       326: q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: q^2+2q+1
       339: q^2+2q+1
       340: q^2+2q+1
       341: q^2+2q+1
       342: q^2+2q+1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: q^2+2q+1
       360: q+1
       361: q^2+q+1
       362: q^2+2q+1
       363: q+1
       364: q+1
       365: q^2+2q+1
       366: q^2+2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: q^2+2q+1
       371: q^2+2q+1
       372: q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q^2+2q+1
       381: q^2+2q+1
       382: q^2+2q+1
       383: q^2+2q+1
       384: q^2+2q+1
       385: q^2+2q+1
       386: q^2+2q+1
       387: 2q+1
       388: 2q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: 2q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q^2+2q+1
       428: q+1
       429: q+1
       430: q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: q^2+2q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: q+1
       455: q^2+2q+1
       456: q+1
       457: q+1
       458: q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: 1
       467: q+1
       468: q^2+q+1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+2q+1
       476: q+1
       477: q+1
       478: q^2+q+1
       479: q^2+q+1
       480: 1
       481: q+1
       482: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: q^2+2q+1
       496: q+1
       497: q^2+q+1
       498: q^2+2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: 2q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: q^2+2q+1
       519: q+1
       520: q+1
       521: q^2+q+1
       522: q^2+q+1
       523: 1
       524: q+1
       525: q+1
       526: q+1
       527: q^2+2q+1
       528: q^2+2q+1
       529: q^2+2q+1
       530: q+1
       531: q^2+q+1
       532: q^2+2q+1
       533: q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       543: q^2+2q+1
       544: q^2+2q+1
       545: q^2+2q+1
       546: q^2+2q+1
       547: q^2+2q+1
       548: q^2+2q+1
       549: q^2+2q+1
       550: q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 2q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q+1
       562: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: 1
       581: 1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: 1
       598: q+1
       599: q+1
       600: q+1
       601: q+1
       602: q+1
       603: q+1
       604: q+1
       605: q+1
       606: q^2+2q+1
       607: q+1
       608: q+1
       609: q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: 2q+1
       628: 2q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: q+1
       658: q+1
       659: 1
       660: q+1
       661: q^2+q+1
       662: 1
       663: 1
       664: 1
       665: q+1
       666: q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: q^2+2q+1
       679: q+1
       680: q+1
       681: q^2+q+1
       682: q^2+q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       696: 2q+1
       697: 2q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: 2q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       707: q^2+q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: q+1
       713: q+1
       714: q^2+2q+1
       715: q+1
       716: q+1
       717: q^2+q+1
       718: q^2+q+1
       719: 1
       720: q+1
       721: q+1
       722: q+1
       723: 2q+1
       724: 2q+1
       725: 2q+1
       726: q+1
       727: q+1
       728: 2q+1
       729: q+1
       730: q+1
       731: q+1
       732: q^2+2q+1
       733: q^2+2q+1
       734: q^2+2q+1
       735: q+1
       736: q^2+q+1
       737: q^2+2q+1
       738: q+1
       739: q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: 2q+1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: 2q+1
       754: 2q+1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: 1
       782: 1
       783: 1
       784: q+1
       785: q+1
       786: q+1
       788: q+1
       789: q+1
       790: 1
       791: 1
       792: q+1
       793: q+1
       794: q+1
       795: q+1
       796: q+1
       797: q+1
       798: q+1
       799: 1
       800: q+1
       801: q+1
       802: q+1
       803: q+1
       804: q+1
       805: q+1
       806: q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: 2q+1
       827: 2q+1
       828: 2q+1
       829: 2q+1
       830: 2q+1
       831: 2q+1
       832: 2q+1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: q+1
       843: q+1
       844: q+1
       845: q+1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       853: q+1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       881: q+1
       882: q^2+q+1
       883: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: 2q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: q+1
       915: q+1
       916: 1
       917: q+1
       918: q^2+q+1
       919: 1
       920: 1
       921: 1
       922: q+1
       923: q+1
       924: q+1
       925: 2q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: 1
       931: q+1
       932: q+1
       933: q+1
       934: q+1
       935: q^2+2q+1
       936: q+1
       937: q+1
       938: q^2+q+1
       939: q^2+q+1
       940: 1
       941: q+1
       942: q+1
       943: q+1
       944: 2q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: q+1
       951: q+1
       952: 2q+1
       953: 2q+1
       954: 2q+1
       955: 2q+1
       956: 2q+1
       957: 2q+1
       958: 2q+1
       959: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 2q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: q+1
       992: q+1
       993: q+1
       995: 1
       996: 1
       997: 1
       998: q+1
       999: q+1
      1000: q+1
      1002: q+1
      1003: q+1
      1004: 1
      1005: 1
      1006: q+1
      1007: q+1
      1008: q+1
      1009: q+1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 2q+1
      1035: 2q+1
      1036: 2q+1
      1037: q+1
      1038: q+1
      1039: 2q+1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: q+1
      1052: q+1
      1053: q+1
      1054: q+1
      1055: q+1
      1056: q+1
      1057: q+1
      1058: 1
      1059: q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: q+1
      1065: q+1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: 2q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: q+1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: q+1
      1129: q+1
      1130: 1
      1131: q+1
      1132: q+1
      1133: 1
      1134: 1
      1135: 1
      1136: q+1
      1137: q+1
      1138: q+1
      1139: 1
      1140: q+1
      1141: q^2+q+1
      1142: 1
      1143: 1
      1144: 1
      1145: q+1
      1146: q+1
      1147: q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1155: q+1
      1156: 1
      1157: 2q+1
      1158: 2q+1
      1159: 2q+1
      1160: q+1
      1161: q+1
      1162: 2q+1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: q+1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: q+1
      1197: 1
      1198: 1
      1199: 1
      1200: q+1
      1203: q+1
      1204: q+1
      1206: 1
      1207: 1
      1208: 1
      1209: q+1
      1210: q+1
      1211: q+1
      1213: q+1
      1214: q+1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 2q+1
      1237: q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1249: q+1
      1250: q+1
      1252: 1
      1253: 1
      1254: 1
      1255: q+1
      1256: q+1
      1257: q+1
      1259: q+1
      1260: q+1
      1261: 1
      1262: 1
      1263: q+1
      1264: q+1
      1265: q+1
      1266: q+1
      1267: q+1
      1268: q+1
      1269: q+1
      1270: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: q+1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: q+1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: q+1
      1339: q+1
      1340: 1
      1341: q+1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1346: q+1
      1347: 1
      1348: 1
      1349: 2q+1
      1350: q+1
      1351: q+1
      1352: q+1
      1353: q+1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: q+1
      1393: 1
      1394: 1
      1395: 1
      1396: q+1
      1399: q+1
      1400: q+1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1422: q+1
      1423: q+1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1432: q+1
      1436: 1
      1437: 1
      1438: 1
      1439: q+1
      1442: q+1
      1443: q+1
      1445: 1
      1446: 1
      1447: 1
      1448: q+1
      1449: q+1
      1450: q+1
      1452: q+1
      1453: q+1
      1454: 1
      1455: 1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: q+1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: q+1
      1520: q+1
      1521: 1
      1522: 1
      1523: 1
      1524: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1547: 1
      1555: 1
      1556: 1
      1559: q+1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1584: 1
      1592: 1
      1593: 1
      1596: q+1
      1600: 1
      1601: 1
      1602: 1
      1603: q+1
      1606: q+1
      1607: q+1
      1609: 1
      1610: 1
      1614: 1
      1617: 1
      1620: 1
      1621: 1
      1622: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1634: 1
      1637: 1
      1638: 1
      1639: 1
      1641: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1684: 1
      1692: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1714: 1
      1722: 1
      1723: 1
      1726: q+1
      1730: 1
      1736: 1
      1739: 1
      1740: 1
      1741: 1
      1743: 1
      1747: 1
      1750: 1
      1753: 1
      1754: 1
      1755: 1
      1757: 1
      1758: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1768: 1
      1788: 1
      1791: 1
      1792: 1
      1793: 1
      1795: 1
      1808: 1
      1820: 1
      1828: 1
      1831: 1
      1832: 1
      1833: 1
      1835: 1
      1852: 1
      1877: 1

1878:    0: 2q^2+q+1
         1: 2q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: 2q^2+q+1
         5: 2q^2+q+1
         6: 2q^2+q+1
         7: q^2+q+1
         8: 2q^2+q+1
         9: 2q^2+q+1
        10: 2q^2+q+1
        11: 2q^2+q+1
        12: 2q^2+q+1
        13: 2q^2+q+1
        14: 2q^2+q+1
        15: 2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: 2q^2+q+1
        19: 2q^2+q+1
        20: 2q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: 2q^2+q+1
        24: q^2+q+1
        25: 2q^2+q+1
        26: q^2+q+1
        27: 2q^2+q+1
        28: 2q^2+q+1
        29: 2q^2+q+1
        30: 2q^2+q+1
        31: 2q^2+q+1
        32: 2q^2+q+1
        33: 2q^2+q+1
        34: q^2+q+1
        35: 2q^2+q+1
        36: 2q^2+q+1
        37: 2q^2+q+1
        38: 2q^2+q+1
        39: 2q^2+q+1
        40: 2q^2+q+1
        41: q^2+q+1
        42: 2q^2+q+1
        43: 2q^2+q+1
        44: 2q^2+q+1
        45: 2q^2+q+1
        46: q^2+q+1
        47: 2q^2+q+1
        48: 2q^2+q+1
        49: 2q^2+q+1
        50: 2q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q^2+q+1
        57: 2q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: 2q^2+q+1
        61: q^2+q+1
        62: 2q^2+q+1
        63: q^2+q+1
        64: 2q^2+q+1
        65: 2q^2+q+1
        66: q^2+q+1
        67: 2q^2+q+1
        68: 2q^2+q+1
        69: 2q^2+q+1
        70: 2q^2+q+1
        71: 2q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: 2q^2+q+1
        75: q^2+q+1
        76: 2q^2+q+1
        77: q^2+q+1
        78: 2q^2+q+1
        79: 2q^2+q+1
        80: 2q^2+q+1
        81: 2q^2+q+1
        82: 2q^2+q+1
        83: 2q^2+q+1
        84: 2q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: 2q^2+q+1
        88: q+1
        89: 2q^2+q+1
        90: q^2+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: 2q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: 2q^2+q+1
        98: q^2+q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: 2q^2+q+1
       102: 2q^2+q+1
       103: q^2+q+1
       104: q^2+q+1
       105: q^2+q+1
       106: q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q+1
       110: q+1
       111: q^2+q+1
       112: 2q^2+q+1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q^2+q+1
       117: q+1
       118: q^2+q+1
       119: 2q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: 2q^2+q+1
       123: q+1
       124: 2q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: 2q^2+q+1
       128: q^2+q+1
       129: 2q^2+q+1
       130: q^2+q+1
       131: 2q^2+q+1
       132: 2q^2+q+1
       133: 2q^2+q+1
       134: 2q^2+q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q+1
       140: q^2+q+1
       141: 2q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: 2q^2+q+1
       145: q^2+q+1
       146: 2q^2+q+1
       147: q^2+q+1
       148: 2q^2+q+1
       149: 2q^2+q+1
       150: q^2+q+1
       151: 2q^2+q+1
       152: 2q^2+q+1
       153: 2q^2+q+1
       154: 2q^2+q+1
       155: 2q^2+q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: 2q^2+q+1
       163: q^2+1
       164: q^2+1
       165: 2q^2+q+1
       166: q+1
       167: 2q^2+q+1
       168: q^2+1
       169: 2q^2+q+1
       170: q^2+q+1
       171: 1
       172: q^2+q+1
       173: q^2+q+1
       174: q^2+q+1
       175: q^2+q+1
       176: 2q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: 2q^2+q+1
       180: q+1
       181: 2q^2+q+1
       182: q^2+1
       183: 2q^2+q+1
       184: 2q^2+q+1
       185: 2q^2+q+1
       186: q^2+q+1
       187: q^2+q+1
       188: q^2+q+1
       189: q^2+q+1
       190: q+1
       191: q^2+q+1
       192: q+1
       193: q^2+q+1
       194: q+1
       195: q+1
       196: q+1
       197: q^2+q+1
       198: q^2+q+1
       199: q^2+q+1
       200: q+1
       201: q^2+q+1
       202: q^2+q+1
       203: q+1
       204: q+1
       205: q^2+q+1
       206: 2q^2+q+1
       207: q+1
       208: q^2+q+1
       209: q^2+q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: 2q^2+q+1
       214: q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: q^2+q+1
       218: q+1
       219: q^2+q+1
       220: 2q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: 2q^2+q+1
       224: q+1
       225: 2q^2+q+1
       226: q^2+1
       227: 2q^2+q+1
       228: q^2+q+1
       229: q^2+q+1
       230: q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q+1
       234: q+1
       235: q^2+q+1
       236: 2q^2+q+1
       237: q^2+q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q^2+q+1
       241: q+1
       242: q^2+q+1
       243: 2q^2+q+1
       244: q^2+q+1
       245: q^2+q+1
       246: 2q^2+q+1
       247: q+1
       248: 2q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: 2q^2+q+1
       252: q^2+q+1
       253: 2q^2+q+1
       254: q^2+q+1
       255: 2q^2+q+1
       256: 2q^2+q+1
       257: 2q^2+q+1
       258: q+1
       259: q^2+q+1
       260: q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: 2q^2+q+1
       267: q+1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: q+1
       273: 2q^2+q+1
       274: q^2+1
       275: q^2+1
       276: 2q^2+q+1
       277: q+1
       278: q^2+q+1
       279: 1
       280: 1
       281: q^2+q+1
       282: q+1
       283: q^2+q+1
       284: 1
       285: q^2+q+1
       286: q^2+q+1
       287: q^2+q+1
       288: 2q^2+q+1
       289: q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q^2+q+1
       293: q+1
       294: q+1
       295: 2q^2+q+1
       296: q^2+1
       297: q^2+1
       298: 2q^2+q+1
       299: q+1
       300: 2q^2+q+1
       301: q^2+1
       302: 2q^2+q+1
       303: q^2+q+1
       304: 1
       305: q^2+q+1
       306: q^2+q+1
       307: q^2+q+1
       308: q^2+q+1
       309: q^2+q+1
       310: q+1
       311: q+1
       312: q^2+q+1
       313: 1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       319: q^2+q+1
       320: q+1
       321: q^2+q+1
       322: q+1
       323: q^2+q+1
       324: q+1
       325: q+1
       326: q+1
       327: q^2+q+1
       328: q+1
       329: q^2+q+1
       330: q+1
       331: q^2+q+1
       332: q^2+q+1
       333: q+1
       334: q+1
       335: q+1
       336: q^2+q+1
       337: q^2+q+1
       338: q+1
       339: q^2+q+1
       340: q^2+q+1
       341: q+1
       342: q+1
       343: q^2+q+1
       344: 2q^2+q+1
       345: q+1
       346: q^2+q+1
       347: q^2+q+1
       348: q^2+q+1
       349: q+1
       350: q+1
       351: 2q^2+q+1
       352: q^2+1
       353: q^2+1
       354: 2q^2+q+1
       355: q+1
       356: q^2+q+1
       357: q+1
       358: q^2+q+1
       359: q+1
       360: q^2+q+1
       361: q+1
       362: q+1
       363: q+1
       364: q^2+q+1
       365: q^2+q+1
       366: q^2+q+1
       367: q+1
       368: q^2+q+1
       369: q^2+q+1
       370: q+1
       371: q+1
       372: q^2+q+1
       373: 2q^2+q+1
       374: q+1
       375: q^2+q+1
       376: q^2+q+1
       377: q^2+q+1
       378: q+1
       379: q+1
       380: 2q^2+q+1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+q+1
       384: q^2+q+1
       385: q+1
       386: q^2+q+1
       387: 2q^2+q+1
       388: q^2+q+1
       389: q^2+q+1
       390: 2q^2+q+1
       391: q+1
       392: 2q^2+q+1
       393: q^2+1
       394: 2q^2+q+1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q+1
       399: q^2+q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q^2+1
       406: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: q+1
       412: 2q^2+q+1
       413: q+1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: q+1
       419: q^2+q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q^2+q+1
       427: 1
       428: 1
       429: q^2+q+1
       430: q+1
       431: q^2+q+1
       432: 1
       433: q^2+q+1
       434: q+1
       435: q^2+q+1
       436: q+1
       437: q^2+q+1
       438: q^2+q+1
       439: q+1
       440: q+1
       441: q+1
       442: 2q^2+q+1
       443: q+1
       444: q^2+1
       445: q^2+1
       446: q^2+1
       447: 1
       448: q+1
       449: 2q^2+q+1
       450: q^2+1
       451: q^2+1
       452: 2q^2+q+1
       453: q+1
       454: q^2+q+1
       455: 1
       456: 1
       457: q^2+q+1
       458: q+1
       459: q^2+q+1
       460: 1
       461: q^2+q+1
       462: q^2+q+1
       463: q^2+q+1
       465: q+1
       466: q+1
       467: 1
       468: q+1
       469: q+1
       470: 1
       471: q+1
       473: q^2+q+1
       474: q+1
       475: q+1
       476: q^2+q+1
       477: 1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       483: q+1
       484: q+1
       485: q^2+q+1
       486: q+1
       487: q^2+q+1
       488: q+1
       489: q+1
       490: q+1
       491: q+1
       492: q^2+q+1
       493: q+1
       494: q^2+q+1
       495: q+1
       496: q^2+q+1
       497: q+1
       498: q+1
       499: q+1
       500: q^2+q+1
       501: q+1
       502: q^2+q+1
       503: q+1
       504: q^2+q+1
       505: q^2+q+1
       506: q+1
       507: q+1
       508: q+1
       509: 2q^2+q+1
       510: q+1
       511: q^2+1
       512: q^2+1
       513: q^2+1
       514: 1
       515: q+1
       516: q^2+q+1
       517: q+1
       518: q+1
       519: q^2+q+1
       520: 1
       521: q+1
       522: q+1
       523: q+1
       524: q+1
       526: q^2+q+1
       527: q+1
       528: q^2+q+1
       529: q+1
       530: q^2+q+1
       531: q+1
       532: q+1
       533: q+1
       534: q^2+q+1
       535: q+1
       536: q^2+q+1
       537: q+1
       538: q^2+q+1
       539: q^2+q+1
       540: q+1
       541: q+1
       542: q+1
       543: q^2+q+1
       544: q^2+q+1
       545: q+1
       546: q^2+q+1
       547: q^2+q+1
       548: q+1
       549: q+1
       550: q^2+q+1
       551: 2q^2+q+1
       552: q+1
       553: q^2+q+1
       554: q^2+q+1
       555: q^2+q+1
       556: q+1
       557: q+1
       558: 2q^2+q+1
       559: q^2+1
       560: q^2+1
       561: 2q^2+q+1
       562: q+1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: 1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       573: q+1
       574: 1
       575: q^2+1
       576: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: q+1
       582: q+1
       583: q^2+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q+1
       598: q^2+q+1
       599: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q+1
       605: q^2+q+1
       606: 1
       607: 1
       608: q^2+q+1
       609: q+1
       610: q+1
       611: q+1
       612: q^2+q+1
       613: q+1
       614: q^2+q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q^2+1
       621: 1
       622: q^2+1
       623: q^2+1
       624: 1
       625: 1
       626: q+1
       627: 2q^2+q+1
       628: q+1
       629: q^2+1
       630: q^2+1
       631: q^2+1
       632: 1
       633: q+1
       634: q^2+q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q^2+q+1
       642: 1
       643: 1
       644: q^2+q+1
       645: q+1
       646: q^2+q+1
       647: 1
       648: q^2+q+1
       650: q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       658: q+1
       659: q+1
       660: 1
       661: q+1
       662: q+1
       663: 1
       664: q+1
       666: q+1
       667: q+1
       668: q+1
       669: q^2+q+1
       670: 1
       671: q+1
       672: q+1
       673: q+1
       674: q+1
       676: q^2+q+1
       677: q+1
       678: q+1
       679: q^2+q+1
       680: 1
       681: q+1
       682: q+1
       683: q+1
       684: q+1
       686: q+1
       687: q+1
       688: q^2+q+1
       689: q+1
       690: q^2+q+1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q^2+1
       697: 1
       698: q^2+1
       699: q^2+1
       700: 1
       701: 1
       702: q+1
       704: q+1
       705: q+1
       706: 1
       707: q+1
       708: q+1
       709: 1
       710: q+1
       712: q^2+q+1
       713: q+1
       714: q+1
       715: q^2+q+1
       716: 1
       717: q+1
       718: q+1
       719: q+1
       720: q+1
       722: q+1
       723: q+1
       724: q^2+q+1
       725: q+1
       726: q^2+q+1
       727: q+1
       728: q+1
       729: q+1
       730: q+1
       731: q^2+q+1
       732: q+1
       733: q^2+q+1
       734: q+1
       735: q^2+q+1
       736: q+1
       737: q+1
       738: q+1
       739: q^2+q+1
       740: q+1
       741: q^2+q+1
       742: q+1
       743: q^2+q+1
       744: q^2+q+1
       745: q+1
       746: q+1
       747: q+1
       748: 2q^2+q+1
       749: q+1
       750: q^2+1
       751: q^2+1
       752: q^2+1
       753: 1
       754: q+1
       756: q+1
       757: q+1
       758: 1
       759: q+1
       760: q+1
       761: 1
       762: q+1
       764: q+1
       765: 1
       766: 1
       767: q^2+1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: q+1
       783: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: q+1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: q+1
       800: q^2+q+1
       801: q+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q+1
       807: q+1
       808: q+1
       809: q+1
       810: q^2+q+1
       811: 1
       812: q+1
       813: q+1
       814: q+1
       815: q+1
       817: q+1
       818: 1
       819: q^2+1
       820: 1
       821: q^2+1
       822: 1
       823: 1
       824: 1
       825: q+1
       826: q+1
       827: q^2+1
       828: 1
       829: q^2+1
       830: q^2+1
       831: 1
       832: 1
       833: q+1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: q^2+q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q^2+q+1
       850: 1
       851: 1
       852: q^2+q+1
       853: q+1
       855: 1
       856: q+1
       857: 1
       858: 1
       862: q+1
       863: 1
       864: q+1
       865: 1
       866: q+1
       867: 1
       870: q+1
       871: q+1
       872: 1
       873: q+1
       874: q+1
       875: 1
       876: q+1
       879: q+1
       880: q+1
       881: 1
       882: q+1
       883: q+1
       884: 1
       885: q+1
       887: q+1
       888: q+1
       889: q+1
       890: q^2+q+1
       891: 1
       892: q+1
       893: q+1
       894: q+1
       895: q+1
       897: q+1
       898: 1
       899: q^2+1
       900: 1
       901: q^2+1
       902: 1
       903: 1
       904: 1
       905: q+1
       907: q+1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       915: q+1
       916: q+1
       917: 1
       918: q+1
       919: q+1
       920: 1
       921: q+1
       923: q+1
       924: q+1
       925: q+1
       926: q^2+q+1
       927: 1
       928: q+1
       929: q+1
       930: q+1
       931: q+1
       933: q^2+q+1
       934: q+1
       935: q+1
       936: q^2+q+1
       937: 1
       938: q+1
       939: q+1
       940: q+1
       941: q+1
       943: q+1
       944: q+1
       945: q^2+q+1
       946: q+1
       947: q^2+q+1
       948: q+1
       949: q+1
       950: q+1
       951: q+1
       952: q+1
       953: q^2+1
       954: 1
       955: q^2+1
       956: q^2+1
       957: 1
       958: 1
       959: q+1
       961: q+1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: q+1
       978: 1
       979: 1
       980: q^2+1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       987: q+1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: q+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: q+1
      1006: q+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q+1
      1015: q+1
      1016: q+1
      1017: 1
      1018: q+1
      1019: q+1
      1020: 1
      1021: q+1
      1023: q+1
      1024: 1
      1025: 1
      1026: q^2+1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: q+1
      1034: 1
      1035: q^2+1
      1036: 1
      1037: q^2+1
      1038: 1
      1039: 1
      1040: 1
      1041: q+1
      1042: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q+1
      1059: q^2+q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1068: 1
      1069: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1079: q+1
      1080: 1
      1081: q+1
      1082: 1
      1083: q+1
      1084: 1
      1087: q+1
      1088: 1
      1089: q+1
      1090: 1
      1091: q+1
      1092: 1
      1095: q+1
      1096: q+1
      1097: 1
      1098: q+1
      1099: q+1
      1100: 1
      1101: q+1
      1103: q+1
      1104: 1
      1105: 1
      1106: q^2+1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1114: 1
      1115: q+1
      1116: 1
      1117: 1
      1121: q+1
      1122: 1
      1123: q+1
      1124: 1
      1125: q+1
      1126: 1
      1129: q+1
      1130: q+1
      1131: 1
      1132: q+1
      1133: q+1
      1134: 1
      1135: q+1
      1138: q+1
      1139: q+1
      1140: 1
      1141: q+1
      1142: q+1
      1143: 1
      1144: q+1
      1146: q+1
      1147: q+1
      1148: q+1
      1149: q^2+q+1
      1150: 1
      1151: q+1
      1152: q+1
      1153: q+1
      1154: q+1
      1156: q+1
      1157: 1
      1158: q^2+1
      1159: 1
      1160: q^2+1
      1161: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 1
      1167: q+1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1198: q+1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: q+1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: q+1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: q+1
      1235: 1
      1236: 1
      1237: q^2+1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: q+1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q+1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q+1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1281: q+1
      1282: 1
      1283: 1
      1287: 1
      1288: q+1
      1289: 1
      1290: 1
      1294: q+1
      1295: 1
      1296: q+1
      1297: 1
      1298: q+1
      1299: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1312: 1
      1313: 1
      1316: 1
      1317: q+1
      1318: 1
      1319: 1
      1323: q+1
      1324: 1
      1325: q+1
      1326: 1
      1327: q+1
      1328: 1
      1331: q+1
      1332: 1
      1333: q+1
      1334: 1
      1335: q+1
      1336: 1
      1339: q+1
      1340: q+1
      1341: 1
      1342: q+1
      1343: q+1
      1344: 1
      1345: q+1
      1347: q+1
      1348: 1
      1349: 1
      1350: q^2+1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1359: 1
      1360: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1380: 1
      1382: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1394: q+1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1405: 1
      1406: q+1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1437: q+1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q+1
      1459: 1
      1463: 1
      1464: 1
      1468: 1
      1469: 1
      1472: 1
      1473: q+1
      1474: 1
      1475: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1496: q+1
      1497: 1
      1498: 1
      1502: 1
      1503: q+1
      1504: 1
      1505: 1
      1509: q+1
      1510: 1
      1511: q+1
      1512: 1
      1513: q+1
      1514: 1
      1517: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1526: 1
      1530: 1
      1531: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1542: 1
      1548: 1
      1550: 1
      1552: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1566: 1
      1567: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1585: 1
      1587: 1
      1589: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1601: q+1
      1602: 1
      1603: 1
      1604: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1615: 1
      1618: 1
      1622: 1
      1623: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1635: 1
      1639: 1
      1640: 1
      1644: 1
      1645: 1
      1648: 1
      1649: q+1
      1650: 1
      1651: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1665: 1
      1669: 1
      1670: 1
      1679: 1
      1685: 1
      1687: 1
      1689: 1
      1693: 1
      1697: 1
      1698: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1709: 1
      1715: 1
      1717: 1
      1719: 1
      1723: 1
      1724: 1
      1726: 1
      1727: 1
      1729: 1
      1737: 1
      1741: 1
      1742: 1
      1748: 1
      1751: 1
      1755: 1
      1756: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1769: 1
      1781: 1
      1789: 1
      1793: 1
      1794: 1
      1803: 1
      1809: 1
      1811: 1
      1813: 1
      1821: 1
      1829: 1
      1833: 1
      1834: 1
      1853: 1
      1865: 1
      1878: 1

1879:    0: 2q^2+q+1
         1: 2q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: 2q^2+q+1
         5: 2q^2+q+1
         6: q^2+q+1
         7: 2q^2+q+1
         8: 2q^2+q+1
         9: 2q^2+q+1
        10: 2q^2+q+1
        11: 2q^2+q+1
        12: 2q^2+q+1
        13: 2q^2+q+1
        14: 2q^2+q+1
        15: 2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: 2q^2+q+1
        19: 2q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 2q^2+q+1
        23: 2q^2+q+1
        24: 2q^2+q+1
        25: q^2+q+1
        26: 2q^2+q+1
        27: 2q^2+q+1
        28: 2q^2+q+1
        29: 2q^2+q+1
        30: 2q^2+q+1
        31: 2q^2+q+1
        32: 2q^2+q+1
        33: q^2+q+1
        34: 2q^2+q+1
        35: 2q^2+q+1
        36: 2q^2+q+1
        37: 2q^2+q+1
        38: 2q^2+q+1
        39: 2q^2+q+1
        40: q^2+q+1
        41: 2q^2+q+1
        42: 2q^2+q+1
        43: 2q^2+q+1
        44: q^2+q+1
        45: 2q^2+q+1
        46: q^2+q+1
        47: 2q^2+q+1
        48: 2q^2+q+1
        49: 2q^2+q+1
        50: q^2+q+1
        51: q^2+1
        52: q^2+q+1
        53: q^2+q+1
        54: 2q^2+q+1
        55: 2q^2+q+1
        56: 2q^2+q+1
        57: q^2+q+1
        58: q^2+q+1
        59: 2q^2+q+1
        60: 2q^2+q+1
        61: 2q^2+q+1
        62: q^2+q+1
        63: 2q^2+q+1
        64: 2q^2+q+1
        65: q^2+q+1
        66: 2q^2+q+1
        67: 2q^2+q+1
        68: 2q^2+q+1
        69: 2q^2+q+1
        70: 2q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: 2q^2+q+1
        74: 2q^2+q+1
        75: 2q^2+q+1
        76: q^2+q+1
        77: 2q^2+q+1
        78: 2q^2+q+1
        79: 2q^2+q+1
        80: 2q^2+q+1
        81: 2q^2+q+1
        82: 2q^2+q+1
        83: 2q^2+q+1
        84: q^2+q+1
        85: q^2+q+1
        86: 2q^2+q+1
        87: 2q^2+q+1
        88: q^2+q+1
        89: q+1
        90: q^2+q+1
        91: q^2+q+1
        92: 2q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q+1
        96: q^2+q+1
        97: q^2+q+1
        98: 2q^2+q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: q^2+q+1
       102: 2q^2+q+1
       103: q^2+q+1
       104: q^2+1
       105: q^2+q+1
       106: q^2+1
       107: q^2+q+1
       108: q^2+q+1
       109: q^2+q+1
       110: 2q^2+q+1
       111: 2q^2+q+1
       112: q^2+q+1
       113: q^2+1
       114: q^2+q+1
       115: q^2+q+1
       116: 2q^2+q+1
       117: 2q^2+q+1
       118: 2q^2+q+1
       119: q^2+q+1
       120: q^2+q+1
       121: 2q^2+q+1
       122: 2q^2+q+1
       123: q^2+q+1
       124: q^2+q+1
       125: q^2+q+1
       126: 2q^2+q+1
       127: 2q^2+q+1
       128: 2q^2+q+1
       129: q^2+q+1
       130: 2q^2+q+1
       131: 2q^2+q+1
       132: 2q^2+q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+1
       136: q^2+q+1
       137: q^2+q+1
       138: 2q^2+q+1
       139: 2q^2+q+1
       140: 2q^2+q+1
       141: q^2+q+1
       142: q^2+q+1
       143: 2q^2+q+1
       144: 2q^2+q+1
       145: 2q^2+q+1
       146: q^2+q+1
       147: 2q^2+q+1
       148: 2q^2+q+1
       149: q^2+q+1
       150: 2q^2+q+1
       151: 2q^2+q+1
       152: 2q^2+q+1
       153: 2q^2+q+1
       154: 2q^2+q+1
       155: q^2+q+1
       156: 1
       157: q^2+q+1
       158: q+1
       159: 2q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q+1
       163: q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q^2+q+1
       174: q+1
       175: q^2+q+1
       176: q^2+q+1
       177: q^2+q+1
       178: 2q^2+q+1
       179: 2q^2+q+1
       180: q^2+q+1
       181: q+1
       182: q^2+q+1
       183: q^2+q+1
       184: 2q^2+q+1
       185: q^2+q+1
       186: q^2+q+1
       187: q+1
       188: q^2+q+1
       189: q^2+1
       190: q^2+1
       191: q^2+q+1
       192: q^2+1
       193: q^2+q+1
       194: q^2+q+1
       195: q^2+q+1
       196: 2q^2+q+1
       197: q^2+q+1
       198: q^2+1
       199: q^2+q+1
       200: q^2+1
       201: q^2+q+1
       202: q^2+q+1
       203: q^2+q+1
       204: 2q^2+q+1
       205: 2q^2+q+1
       206: q^2+q+1
       207: 1
       208: q^2+q+1
       209: q+1
       210: 2q^2+q+1
       211: q^2+q+1
       212: q^2+q+1
       213: q^2+q+1
       214: q^2+1
       215: q^2+q+1
       216: q^2+q+1
       217: 2q^2+q+1
       218: 2q^2+q+1
       219: 2q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 2q^2+q+1
       223: 2q^2+q+1
       224: q^2+q+1
       225: q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+1
       229: q^2+q+1
       230: q^2+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: 2q^2+q+1
       235: 2q^2+q+1
       236: q^2+q+1
       237: q^2+1
       238: q^2+q+1
       239: q^2+q+1
       240: 2q^2+q+1
       241: 2q^2+q+1
       242: 2q^2+q+1
       243: q^2+q+1
       244: q^2+q+1
       245: 2q^2+q+1
       246: 2q^2+q+1
       247: q^2+q+1
       248: q^2+q+1
       249: q^2+q+1
       250: 2q^2+q+1
       251: 2q^2+q+1
       252: 2q^2+q+1
       253: q^2+q+1
       254: 2q^2+q+1
       255: 2q^2+q+1
       256: 2q^2+q+1
       257: q^2+q+1
       258: 1
       259: q^2+q+1
       260: 1
       261: q+1
       262: q+1
       263: q+1
       264: q^2+q+1
       265: q^2+q+1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q^2+q+1
       287: q+1
       288: q^2+q+1
       289: 1
       290: q^2+q+1
       291: q+1
       292: 2q^2+q+1
       293: q^2+q+1
       294: q^2+q+1
       295: q+1
       296: q+1
       297: q^2+q+1
       298: q^2+q+1
       299: q+1
       300: q+1
       301: q^2+q+1
       302: q^2+q+1
       303: q+1
       304: q+1
       305: q+1
       306: q^2+q+1
       307: q+1
       308: q^2+q+1
       310: q^2+1
       311: q^2+1
       312: q^2+q+1
       313: 1
       314: q^2+q+1
       315: q^2+1
       316: q^2+q+1
       317: q+1
       318: q^2+q+1
       319: q^2+1
       320: q^2+1
       321: q^2+q+1
       322: q^2+1
       323: q^2+q+1
       324: q^2+q+1
       325: q^2+q+1
       326: 2q^2+q+1
       327: q^2+q+1
       328: 1
       329: q^2+q+1
       330: 1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+q+1
       335: q^2+q+1
       336: q^2+1
       337: q^2+q+1
       338: q^2+1
       339: q^2+q+1
       340: q^2+q+1
       341: q^2+q+1
       342: 2q^2+q+1
       343: 2q^2+q+1
       344: q^2+q+1
       345: 1
       346: q^2+q+1
       347: q+1
       348: 2q^2+q+1
       349: q^2+q+1
       350: q^2+q+1
       351: q+1
       352: q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q+1
       356: q^2+1
       357: q^2+1
       358: q^2+q+1
       359: q^2+1
       360: q^2+q+1
       361: q^2+q+1
       362: q^2+q+1
       363: 2q^2+q+1
       364: q^2+q+1
       365: q^2+1
       366: q^2+q+1
       367: q^2+1
       368: q^2+q+1
       369: q^2+q+1
       370: q^2+q+1
       371: 2q^2+q+1
       372: 2q^2+q+1
       373: q^2+q+1
       374: 1
       375: q^2+q+1
       376: q+1
       377: 2q^2+q+1
       378: q^2+q+1
       379: q^2+q+1
       380: q^2+q+1
       381: q^2+1
       382: q^2+q+1
       383: q^2+q+1
       384: 2q^2+q+1
       385: 2q^2+q+1
       386: 2q^2+q+1
       387: q^2+q+1
       388: q^2+q+1
       389: 2q^2+q+1
       390: 2q^2+q+1
       391: q^2+q+1
       392: q+1
       393: q^2+q+1
       394: q^2+q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: q+1
       401: q+1
       402: q^2+q+1
       403: q+1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: q+1
       420: 1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: q^2+q+1
       436: 1
       437: q+1
       438: q+1
       439: q+1
       440: q^2+q+1
       441: q^2+q+1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q^2+q+1
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: q^2+q+1
       452: q^2+q+1
       453: q+1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+q+1
       463: q+1
       466: q^2+1
       467: 1
       468: q^2+1
       469: q^2+q+1
       470: 1
       471: q+1
       472: q+1
       474: q^2+1
       475: q^2+1
       476: q^2+q+1
       477: 1
       478: q^2+q+1
       479: q^2+1
       480: q^2+q+1
       481: q+1
       482: q^2+q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: q+1
       489: q+1
       490: q^2+q+1
       491: q+1
       492: q^2+1
       493: q^2+1
       494: q^2+q+1
       495: q^2+1
       496: q^2+q+1
       497: q^2+q+1
       498: q^2+q+1
       499: 2q^2+q+1
       500: q^2+q+1
       501: 1
       502: q^2+q+1
       503: 1
       504: q+1
       505: q+1
       506: q+1
       507: q^2+q+1
       508: q^2+q+1
       509: q+1
       510: 1
       511: q+1
       512: q+1
       513: q^2+q+1
       514: q+1
       515: q+1
       517: q^2+1
       518: q^2+1
       519: q^2+q+1
       520: 1
       521: q^2+q+1
       522: q^2+1
       523: q^2+q+1
       524: q+1
       525: q^2+q+1
       526: q^2+1
       527: q^2+1
       528: q^2+q+1
       529: q^2+1
       530: q^2+q+1
       531: q^2+q+1
       532: q^2+q+1
       533: 2q^2+q+1
       534: q^2+q+1
       535: 1
       536: q^2+q+1
       537: 1
       538: q+1
       539: q+1
       540: q+1
       541: q^2+q+1
       542: q^2+q+1
       543: q^2+1
       544: q^2+q+1
       545: q^2+1
       546: q^2+q+1
       547: q^2+q+1
       548: q^2+q+1
       549: 2q^2+q+1
       550: 2q^2+q+1
       551: q^2+q+1
       552: 1
       553: q^2+q+1
       554: q+1
       555: 2q^2+q+1
       556: q^2+q+1
       557: q^2+q+1
       558: q+1
       559: q+1
       560: q^2+q+1
       561: q^2+q+1
       562: q+1
       564: 1
       565: 1
       566: q+1
       567: 1
       568: q+1
       569: 1
       570: q+1
       571: q+1
       572: q+1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: 1
       591: q+1
       592: 1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: 1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: q+1
       616: q+1
       617: q^2+q+1
       618: q+1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q+1
       628: 1
       629: q+1
       630: q+1
       631: q^2+q+1
       632: q+1
       633: q+1
       634: q+1
       635: 1
       636: q+1
       637: 1
       638: q+1
       639: q+1
       640: q+1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       651: 1
       652: q^2+1
       653: 1
       654: q+1
       655: 1
       656: q+1
       659: q^2+1
       660: 1
       661: q^2+1
       662: q^2+q+1
       663: 1
       664: q+1
       665: q+1
       667: 1
       668: 1
       669: q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: q+1
       675: q+1
       677: q^2+1
       678: q^2+1
       679: q^2+q+1
       680: 1
       681: q^2+q+1
       682: q^2+1
       683: q^2+q+1
       684: q+1
       685: q^2+q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: q+1
       692: q+1
       693: q^2+q+1
       694: q+1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       705: q^2+1
       706: 1
       707: q^2+1
       708: q^2+q+1
       709: 1
       710: q+1
       711: q+1
       713: q^2+1
       714: q^2+1
       715: q^2+q+1
       716: 1
       717: q^2+q+1
       718: q^2+1
       719: q^2+q+1
       720: q+1
       721: q^2+q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: q+1
       728: q+1
       729: q^2+q+1
       730: q+1
       731: q^2+1
       732: q^2+1
       733: q^2+q+1
       734: q^2+1
       735: q^2+q+1
       736: q^2+q+1
       737: q^2+q+1
       738: 2q^2+q+1
       739: q^2+q+1
       740: 1
       741: q^2+q+1
       742: 1
       743: q+1
       744: q+1
       745: q+1
       746: q^2+q+1
       747: q^2+q+1
       748: q+1
       749: 1
       750: q+1
       751: q+1
       752: q^2+q+1
       753: q+1
       754: q+1
       757: 1
       758: 1
       759: 1
       760: q+1
       761: 1
       762: q+1
       763: q+1
       765: 1
       766: 1
       767: q+1
       768: 1
       769: q+1
       770: 1
       771: q+1
       772: 1
       773: q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: q+1
       792: 1
       793: q+1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: 1
       802: q+1
       803: 1
       804: q+1
       805: q+1
       806: q+1
       808: 1
       809: 1
       810: q+1
       811: 1
       812: q+1
       813: 1
       814: q+1
       815: q+1
       816: q+1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       834: 1
       835: q+1
       836: 1
       837: 1
       838: 1
       839: 1
       840: q+1
       841: q+1
       842: q+1
       843: 1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: q+1
       857: 1
       858: 1
       859: q+1
       860: 1
       863: 1
       864: q^2+1
       865: 1
       866: q+1
       867: 1
       868: q+1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: q+1
       877: q+1
       880: q^2+1
       881: 1
       882: q^2+1
       883: q^2+q+1
       884: 1
       885: q+1
       886: q+1
       888: 1
       889: 1
       890: q+1
       891: 1
       892: q+1
       893: 1
       894: q+1
       895: q+1
       896: q+1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: q+1
       903: q+1
       904: q+1
       905: q+1
       908: 1
       909: q^2+1
       910: 1
       911: q+1
       912: 1
       913: q+1
       916: q^2+1
       917: 1
       918: q^2+1
       919: q^2+q+1
       920: 1
       921: q+1
       922: q+1
       924: 1
       925: 1
       926: q+1
       927: 1
       928: q+1
       929: 1
       930: q+1
       931: q+1
       932: q+1
       934: q^2+1
       935: q^2+1
       936: q^2+q+1
       937: 1
       938: q^2+q+1
       939: q^2+1
       940: q^2+q+1
       941: q+1
       942: q^2+q+1
       943: 1
       944: 1
       945: q+1
       946: 1
       947: q+1
       948: q+1
       949: q+1
       950: q^2+q+1
       951: q+1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: q+1
       958: q+1
       959: q+1
       962: 1
       963: 1
       964: 1
       965: q+1
       966: 1
       967: q+1
       970: 1
       971: 1
       972: 1
       973: q+1
       974: 1
       975: 1
       976: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       985: 1
       986: q+1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: q+1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: q+1
      1006: 1
      1007: q+1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: q+1
      1013: q+1
      1016: 1
      1017: 1
      1018: 1
      1019: q+1
      1020: 1
      1021: q+1
      1022: q+1
      1024: 1
      1025: 1
      1026: q+1
      1027: 1
      1028: q+1
      1029: 1
      1030: q+1
      1031: 1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: q+1
      1050: q+1
      1051: 1
      1052: q+1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: 1
      1061: q+1
      1062: 1
      1063: q+1
      1064: q+1
      1065: q+1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: q+1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1083: q+1
      1084: 1
      1085: q+1
      1088: 1
      1089: q^2+1
      1090: 1
      1091: q+1
      1092: 1
      1093: q+1
      1096: 1
      1097: 1
      1098: 1
      1099: q+1
      1100: 1
      1101: q+1
      1102: q+1
      1104: 1
      1105: 1
      1106: q+1
      1107: 1
      1108: q+1
      1109: 1
      1110: q+1
      1111: 1
      1112: q+1
      1116: 1
      1117: 1
      1118: q+1
      1119: 1
      1122: 1
      1123: q^2+1
      1124: 1
      1125: q+1
      1126: 1
      1127: q+1
      1130: 1
      1131: 1
      1132: 1
      1133: q+1
      1134: 1
      1135: q+1
      1136: q+1
      1139: q^2+1
      1140: 1
      1141: q^2+1
      1142: q^2+q+1
      1143: 1
      1144: q+1
      1145: q+1
      1147: 1
      1148: 1
      1149: q+1
      1150: 1
      1151: q+1
      1152: 1
      1153: q+1
      1154: q+1
      1155: q+1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: q+1
      1162: q+1
      1163: q+1
      1164: q+1
      1168: 1
      1169: 1
      1170: q+1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1187: 1
      1188: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: q+1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: q+1
      1216: q+1
      1219: 1
      1220: 1
      1221: 1
      1222: q+1
      1223: 1
      1224: q+1
      1227: 1
      1228: 1
      1229: 1
      1230: q+1
      1231: 1
      1232: 1
      1233: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1239: q+1
      1240: 1
      1241: q+1
      1242: 1
      1243: q+1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: q+1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: q+1
      1263: 1
      1264: q+1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: q+1
      1270: q+1
      1273: 1
      1277: 1
      1278: 1
      1282: 1
      1283: 1
      1284: q+1
      1285: 1
      1289: 1
      1290: 1
      1291: q+1
      1292: 1
      1295: 1
      1296: 1
      1297: 1
      1298: q+1
      1299: 1
      1300: q+1
      1303: 1
      1304: 1
      1305: 1
      1306: q+1
      1307: 1
      1308: 1
      1309: 1
      1313: 1
      1314: 1
      1318: 1
      1319: 1
      1320: q+1
      1321: 1
      1324: 1
      1325: 1
      1326: 1
      1327: q+1
      1328: 1
      1329: q+1
      1332: 1
      1333: q^2+1
      1334: 1
      1335: q+1
      1336: 1
      1337: q+1
      1340: 1
      1341: 1
      1342: 1
      1343: q+1
      1344: 1
      1345: q+1
      1346: q+1
      1348: 1
      1349: 1
      1350: q+1
      1351: 1
      1352: q+1
      1353: 1
      1354: q+1
      1355: 1
      1356: q+1
      1360: 1
      1361: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1380: 1
      1382: 1
      1384: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: q+1
      1407: 1
      1408: 1
      1409: q+1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1421: 1
      1422: 1
      1423: 1
      1424: q+1
      1425: 1
      1426: 1
      1427: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: q+1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q+1
      1455: q+1
      1460: 1
      1464: 1
      1465: 1
      1469: 1
      1470: 1
      1474: 1
      1475: 1
      1476: q+1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1488: 1
      1492: 1
      1493: 1
      1497: 1
      1498: 1
      1499: q+1
      1500: 1
      1504: 1
      1505: 1
      1506: q+1
      1507: 1
      1510: 1
      1511: 1
      1512: 1
      1513: q+1
      1514: 1
      1515: q+1
      1518: 1
      1519: 1
      1520: 1
      1521: q+1
      1522: 1
      1523: 1
      1524: 1
      1527: 1
      1531: 1
      1532: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1545: 1
      1550: 1
      1552: 1
      1554: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1567: 1
      1568: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1587: 1
      1589: 1
      1591: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1600: 1
      1602: 1
      1603: 1
      1604: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1610: q+1
      1616: 1
      1619: 1
      1623: 1
      1624: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1636: 1
      1640: 1
      1641: 1
      1645: 1
      1646: 1
      1650: 1
      1651: 1
      1652: q+1
      1653: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1666: 1
      1670: 1
      1671: 1
      1682: 1
      1687: 1
      1689: 1
      1691: 1
      1694: 1
      1698: 1
      1699: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1712: 1
      1717: 1
      1719: 1
      1721: 1
      1724: 1
      1726: 1
      1727: 1
      1729: 1
      1730: 1
      1738: 1
      1742: 1
      1743: 1
      1749: 1
      1752: 1
      1756: 1
      1757: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1770: 1
      1784: 1
      1790: 1
      1794: 1
      1795: 1
      1806: 1
      1811: 1
      1813: 1
      1815: 1
      1822: 1
      1830: 1
      1834: 1
      1835: 1
      1854: 1
      1868: 1
      1879: 1

1880:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: 1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: 1
        13: 1
        14: 1
        15: 1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: 1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: 1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: 1
        48: 1
        49: 1
        50: q^2+1
        51: 1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: 1
        56: 1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: 1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: q^2+1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: q^2+1
       106: 1
       107: q^2+1
       108: q^2+1
       109: 1
       110: 1
       111: 1
       112: q^2+1
       113: 1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: 1
       118: 1
       119: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: q^2+1
       156: 1
       157: q^2+1
       158: q^2+1
       159: q^2+1
       160: 1
       161: 1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: 1
       177: 1
       178: 1
       179: 1
       180: 1
       181: 1
       182: 1
       183: 1
       184: 1
       185: 1
       186: 1
       187: 1
       188: 1
       189: 1
       190: 1
       191: q^2+1
       192: 1
       193: q^2+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q^2+1
       200: 1
       201: q^2+1
       202: q^2+1
       203: 1
       204: 1
       205: 1
       206: q^2+1
       207: 1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: 1
       220: 1
       221: 1
       222: 1
       223: 1
       224: 1
       225: 1
       226: 1
       227: 1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: 1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: 1
       259: q^2+1
       260: 1
       261: q^2+1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       267: 1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: 1
       273: q^2+1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: 1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: 1
       310: 1
       311: 1
       312: q^2+1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q^2+1
       322: 1
       323: q^2+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q^2+1
       330: 1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: 1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: 1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       375: 1
       376: 1
       377: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       392: 1
       393: 1
       394: 1
       395: 1
       396: 1
       397: q^2+1
       398: 1
       399: q^2+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q^2+1
       406: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: 1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       464: 1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: q^2+1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q^2+1
       486: 1
       487: q^2+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       536: 1
       538: 1
       539: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       553: 1
       554: 1
       555: 1
       558: 1
       559: 1
       560: 1
       561: 1
       563: 1
       564: 1
       565: 1
       566: q^2+1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q^2+1
       576: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q^2+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       629: 1
       630: 1
       631: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: q^2+1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       724: 1
       726: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       741: 1
       743: 1
       744: 1
       748: 1
       750: 1
       751: 1
       752: 1
       755: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q^2+1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       827: 1
       829: 1
       830: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       844: 1
       845: 1
       846: 1
       849: 1
       850: 1
       851: 1
       852: 1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       926: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       945: 1
       947: 1
       953: 1
       955: 1
       956: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q^2+1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1035: 1
      1037: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1052: 1
      1054: 1
      1055: 1
      1059: 1
      1061: 1
      1062: 1
      1063: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1149: 1
      1158: 1
      1160: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1237: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1256: 1
      1258: 1
      1264: 1
      1266: 1
      1267: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1350: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1428: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1440: 1
      1449: 1
      1451: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1478: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1490: 1
      1501: 1
      1503: 1
      1506: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1584: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1604: 1
      1611: 1
      1612: 1
      1613: 1
      1614: 1
      1615: 1
      1616: 1
      1621: 1
      1625: 1
      1627: 1
      1630: 1
      1643: 1
      1662: 1
      1663: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1684: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1696: 1
      1707: 1
      1709: 1
      1712: 1
      1731: 1
      1732: 1
      1733: 1
      1740: 1
      1765: 1
      1766: 1
      1767: 1
      1768: 1
      1769: 1
      1770: 1
      1775: 1
      1779: 1
      1781: 1
      1784: 1
      1797: 1
      1816: 1
      1836: 1
      1837: 1
      1838: 1
      1845: 1
      1880: 1

1881:    0: q^4+q^3+3q^2+2q+1
         1: q^4+q^3+3q^2+2q+1
         2: q^4+q^3+3q^2+2q+1
         3: q^4+3q^2+2q+1
         4: q^4+q^3+3q^2+2q+1
         5: q^4+q^3+3q^2+2q+1
         6: q^4+q^3+3q^2+2q+1
         7: q^4+q^3+3q^2+2q+1
         8: q^4+3q^2+2q+1
         9: q^4+3q^2+2q+1
        10: q^4+3q^2+2q+1
        11: 2q^2+2q+1
        12: q^4+3q^2+2q+1
        13: q^4+q^3+3q^2+2q+1
        14: q^4+q^3+3q^2+2q+1
        15: 2q^2+2q+1
        16: q^4+q^3+3q^2+2q+1
        17: q^4+q^3+3q^2+2q+1
        18: q^4+3q^2+2q+1
        19: q^4+q^3+3q^2+2q+1
        20: q^4+3q^2+2q+1
        21: q^4+q^3+3q^2+2q+1
        22: q^4+3q^2+2q+1
        23: 2q^2+2q+1
        24: q^4+3q^2+2q+1
        25: q^4+3q^2+2q+1
        26: q^4+3q^2+2q+1
        27: q^4+3q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: q^4+3q^2+2q+1
        31: q^4+3q^2+2q+1
        32: 2q^2+2q+1
        33: q^4+q^3+3q^2+2q+1
        34: q^4+q^3+3q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: q^4+q^3+3q^2+2q+1
        41: q^4+q^3+3q^2+2q+1
        42: q^4+3q^2+2q+1
        43: q^4+3q^2+2q+1
        44: q^4+3q^2+2q+1
        45: 2q^2+2q+1
        46: q^4+3q^2+2q+1
        47: q^4+q^3+3q^2+2q+1
        48: q^4+q^3+3q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^4+3q^2+2q+1
        52: q^4+3q^2+2q+1
        53: q^4+3q^2+2q+1
        54: 2q^2+2q+1
        55: q^4+3q^2+2q+1
        56: 2q^2+2q+1
        57: q^4+3q^2+2q+1
        58: q^4+3q^2+2q+1
        59: q^4+3q^2+2q+1
        60: 2q^2+2q+1
        61: q^4+3q^2+2q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: q^2+2q+1
        65: q^4+3q^2+2q+1
        66: q^4+3q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: q^4+q^3+3q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        75: 2q^2+2q+1
        76: 2q^2+2q+1
        77: 2q^2+2q+1
        78: 2q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: q^2+2q+1
        84: q^4+3q^2+2q+1
        85: q^4+q^3+3q^2+2q+1
        86: q^4+3q^2+2q+1
        87: 2q^2+2q+1
        88: q^4+3q^2+2q+1
        89: q^4+3q^2+2q+1
        90: q^4+3q^2+2q+1
        91: q^4+3q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: q^4+3q^2+2q+1
        95: q^4+3q^2+2q+1
        96: 2q^2+2q+1
        97: q^4+q^3+3q^2+2q+1
        98: q^4+q^3+3q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       104: 2q^2+2q+1
       105: 2q^2+2q+1
       106: q^4+3q^2+2q+1
       107: q^4+3q^2+2q+1
       108: 2q^2+2q+1
       109: q^4+3q^2+2q+1
       110: 2q^2+2q+1
       111: q^2+2q+1
       112: 2q^2+2q+1
       113: q^4+3q^2+2q+1
       114: q^4+3q^2+2q+1
       115: q^4+3q^2+2q+1
       116: 2q^2+2q+1
       117: q^4+3q^2+2q+1
       118: 2q^2+2q+1
       119: q^2+2q+1
       120: 2q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: q^4+3q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: 2q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q^2+2q+1
       142: 2q^2+2q+1
       143: 2q^2+2q+1
       144: q^2+2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q^2+2q+1
       156: q^4+3q^2+2q+1
       157: q^4+3q^2+2q+1
       158: q^4+3q^2+2q+1
       159: 2q^2+2q+1
       160: q^4+3q^2+2q+1
       161: 2q^2+2q+1
       162: q^4+3q^2+2q+1
       163: q^4+3q^2+2q+1
       164: q^4+3q^2+2q+1
       165: 2q^2+2q+1
       166: q^4+3q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: q^2+2q+1
       170: q^4+3q^2+2q+1
       171: q^4+3q^2+2q+1
       172: q^2+2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: q^4+q^3+3q^2+2q+1
       178: 2q^2+2q+1
       179: q^2+2q+1
       180: 2q^2+2q+1
       181: 2q^2+2q+1
       182: 2q^2+2q+1
       183: 2q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: 2q^2+2q+1
       187: 2q^2+2q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: 2q^2+2q+1
       191: 2q^2+2q+1
       192: q^4+3q^2+2q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: 2q^2+2q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: 2q^2+2q+1
       199: 2q^2+2q+1
       200: q^4+3q^2+2q+1
       201: q^4+3q^2+2q+1
       202: 2q^2+2q+1
       203: q^4+3q^2+2q+1
       204: 2q^2+2q+1
       205: 2q+1
       206: q^2+2q+1
       207: q^2+2q+1
       208: q^2+2q+1
       209: q^2+2q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: q^2+2q+1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: 2q^2+2q+1
       232: q^2+2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q^2+2q+1
       237: 2q^2+2q+1
       238: 2q^2+2q+1
       239: 2q^2+2q+1
       240: q^2+2q+1
       241: 2q^2+2q+1
       242: q^2+2q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       247: q+1
       248: q^2+2q+1
       249: 2q^2+2q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q^2+2q+1
       259: 2q^2+2q+1
       260: q^4+3q^2+2q+1
       261: q^4+3q^2+2q+1
       262: 2q^2+2q+1
       263: q^4+3q^2+2q+1
       264: 2q^2+2q+1
       265: q^2+2q+1
       266: 2q^2+2q+1
       267: q^4+3q^2+2q+1
       268: q^4+3q^2+2q+1
       269: q^4+3q^2+2q+1
       270: 2q^2+2q+1
       271: q^4+3q^2+2q+1
       272: 2q^2+2q+1
       273: q^2+2q+1
       274: 2q^2+2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q^2+2q+1
       279: q^4+3q^2+2q+1
       280: q^2+2q+1
       281: q+1
       282: q^2+2q+1
       283: 2q^2+2q+1
       284: 2q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q^2+2q+1
       289: 2q^2+2q+1
       290: 2q^2+2q+1
       291: 2q^2+2q+1
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q^2+2q+1
       295: 2q^2+2q+1
       296: 2q^2+2q+1
       297: 2q^2+2q+1
       298: q^2+2q+1
       299: 2q^2+2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q+1
       303: 2q^2+2q+1
       304: 2q^2+2q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q^2+2q+1
       310: q^2+2q+1
       311: 2q^2+2q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: q+1
       315: q^2+2q+1
       316: 2q+1
       317: q^2+2q+1
       318: q^2+2q+1
       319: 2q+1
       320: 2q^2+2q+1
       321: 2q^2+2q+1
       322: q^4+3q^2+2q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: 2q^2+2q+1
       326: 2q+1
       327: 2q+1
       328: q^2+2q+1
       329: q^2+2q+1
       330: q^2+2q+1
       331: q^2+2q+1
       332: q^2+2q+1
       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: q^2+2q+1
       339: q^2+2q+1
       340: q+1
       341: q^2+2q+1
       342: q+1
       343: q+1
       344: q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: q+1
       355: 2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q^2+2q+1
       360: q+1
       361: q^2+2q+1
       362: q^2+2q+1
       363: q^2+2q+1
       364: q^2+2q+1
       365: q^2+2q+1
       366: q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: q^2+2q+1
       370: 2q^2+2q+1
       371: q^2+2q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q+1
       381: q^2+2q+1
       382: q^2+2q+1
       383: q^2+2q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: 1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q+1
       395: q^2+2q+1
       396: 2q^2+2q+1
       397: 2q^2+2q+1
       398: q^4+3q^2+2q+1
       399: q^2+2q+1
       400: q^2+2q+1
       401: 2q^2+2q+1
       402: q^2+2q+1
       403: q^2+2q+1
       404: 2q^2+2q+1
       405: 2q^2+2q+1
       406: q^4+3q^2+2q+1
       407: q^4+3q^2+2q+1
       408: 2q^2+2q+1
       409: q^4+3q^2+2q+1
       410: 2q^2+2q+1
       411: 2q+1
       412: q^2+2q+1
       413: q^2+2q+1
       414: q^2+2q+1
       415: q^2+2q+1
       416: q^2+2q+1
       417: q^2+2q+1
       418: q^2+2q+1
       419: q+1
       420: q^2+2q+1
       421: q^2+2q+1
       422: q^2+2q+1
       423: q+1
       424: q^2+2q+1
       425: q+1
       426: 2q+1
       427: 2q^2+2q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: 2q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: 2q^2+2q+1
       437: 2q^2+2q+1
       438: q^2+2q+1
       439: 2q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q^2+2q+1
       443: 2q^2+2q+1
       444: 2q^2+2q+1
       445: 2q^2+2q+1
       446: q^2+2q+1
       447: 2q^2+2q+1
       448: q^2+2q+1
       449: q+1
       450: q^2+2q+1
       451: q+1
       452: q+1
       453: q+1
       454: q^2+2q+1
       455: 2q^2+2q+1
       456: q^2+2q+1
       457: q+1
       458: q^2+2q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q^2+2q+1
       465: q^2+2q+1
       466: 2q+1
       467: q^2+2q+1
       468: q+1
       469: q+1
       470: 2q+1
       471: 2q+1
       472: q^2+2q+1
       473: 2q+1
       474: 2q+1
       475: 2q^2+2q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: q+1
       479: q^2+2q+1
       480: 2q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+2q+1
       485: q^2+2q+1
       486: q^2+2q+1
       487: q^2+2q+1
       488: q+1
       489: q^2+2q+1
       490: 2q+1
       491: 2q+1
       492: q+1
       493: q+1
       494: q+1
       495: q^2+2q+1
       496: 1
       497: q^2+2q+1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: 2q+1
       504: 2q+1
       505: q+1
       506: 2q+1
       507: q+1
       508: q+1
       509: q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: q+1
       514: 2q+1
       515: q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: q^2+2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q^2+2q+1
       523: q+1
       524: q^2+2q+1
       525: q^2+2q+1
       526: q+1
       527: q^2+2q+1
       528: q^2+2q+1
       529: 2q^2+2q+1
       530: q+1
       531: q^2+2q+1
       532: q^2+2q+1
       533: q+1
       534: q+1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: q+1
       544: q+1
       545: q^2+2q+1
       546: q^2+2q+1
       547: q+1
       548: q^2+2q+1
       549: q+1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q^2+2q+1
       560: q+1
       561: 1
       562: q+1
       563: q^2+2q+1
       564: q^2+2q+1
       565: 2q^2+2q+1
       566: q^2+2q+1
       567: q^2+2q+1
       568: q+1
       569: q^2+2q+1
       570: 2q+1
       571: q^2+2q+1
       572: q^2+2q+1
       573: 2q+1
       574: 2q^2+2q+1
       575: 2q^2+2q+1
       576: q^4+3q^2+2q+1
       577: q^2+2q+1
       578: q^2+2q+1
       579: 2q^2+2q+1
       580: 2q+1
       581: 2q+1
       582: q^2+2q+1
       583: q^2+2q+1
       584: q^2+2q+1
       585: q^2+2q+1
       586: q^2+2q+1
       587: q^2+2q+1
       588: q^2+2q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: q^2+2q+1
       593: q^2+2q+1
       594: q+1
       595: q^2+2q+1
       596: q+1
       597: q+1
       598: q+1
       599: 2q+1
       600: 2q+1
       601: 2q+1
       602: q+1
       603: 2q+1
       604: q+1
       605: 2q+1
       606: q^2+2q+1
       607: 2q+1
       608: q+1
       609: 2q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: q^2+2q+1
       613: 2q^2+2q+1
       614: q+1
       615: q^2+2q+1
       616: q^2+2q+1
       617: q^2+2q+1
       618: q^2+2q+1
       619: q^2+2q+1
       620: q^2+2q+1
       621: 2q^2+2q+1
       622: 2q^2+2q+1
       623: q^2+2q+1
       624: 2q^2+2q+1
       625: q^2+2q+1
       626: q+1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: q+1
       635: q^2+2q+1
       636: q^2+2q+1
       637: q^2+2q+1
       638: q+1
       639: q^2+2q+1
       640: q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: 1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q^2+2q+1
       650: 2q+1
       651: 2q+1
       652: q+1
       653: q+1
       654: q+1
       655: 2q+1
       656: 2q+1
       657: 2q+1
       658: 2q+1
       659: 2q+1
       660: q^2+2q+1
       661: q+1
       662: q+1
       663: 2q+1
       664: 2q+1
       665: 2q+1
       666: 2q+1
       667: 2q+1
       668: q^2+2q+1
       669: q^2+2q+1
       670: q^2+2q+1
       672: q+1
       673: q+1
       674: 2q+1
       675: 2q+1
       676: q+1
       677: q+1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q^2+2q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: 2q+1
       690: 1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q+1
       697: 2q+1
       698: 2q+1
       699: q+1
       700: 2q+1
       701: q+1
       702: 1
       703: q^2+2q+1
       704: q^2+2q+1
       705: q+1
       706: q+1
       707: q+1
       708: 1
       709: q+1
       710: q+1
       711: q^2+2q+1
       712: q+1
       713: q+1
       714: q^2+2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q^2+2q+1
       719: q+1
       720: q+1
       721: q+1
       722: q+1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       728: q+1
       729: q+1
       730: q+1
       731: 1
       732: q+1
       733: q+1
       734: q^2+2q+1
       735: 1
       736: q^2+2q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 1
       755: q^2+2q+1
       756: q^2+2q+1
       757: 2q+1
       758: q^2+2q+1
       759: q+1
       760: q+1
       761: 2q+1
       762: 2q+1
       763: q^2+2q+1
       764: 2q+1
       765: 2q+1
       766: 2q^2+2q+1
       767: q^2+2q+1
       768: q^2+2q+1
       769: q+1
       770: q^2+2q+1
       771: 2q+1
       772: 2q+1
       773: 2q+1
       774: 2q+1
       775: q^2+2q+1
       776: q^2+2q+1
       777: q^2+2q+1
       778: q^2+2q+1
       779: q+1
       780: q^2+2q+1
       781: 2q+1
       782: 2q+1
       783: q+1
       784: q+1
       785: q+1
       786: q^2+2q+1
       787: 1
       788: q^2+2q+1
       789: q+1
       790: q+1
       791: q+1
       792: q+1
       793: q+1
       794: 2q+1
       795: 2q+1
       796: q+1
       797: 2q+1
       798: q+1
       799: q+1
       800: q+1
       801: 2q+1
       802: 2q+1
       803: 2q+1
       804: q+1
       805: 2q+1
       806: q+1
       807: q^2+2q+1
       808: q^2+2q+1
       809: q^2+2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q^2+2q+1
       814: q+1
       815: q^2+2q+1
       816: q^2+2q+1
       817: q+1
       818: q^2+2q+1
       819: q^2+2q+1
       820: 2q^2+2q+1
       821: q+1
       822: q^2+2q+1
       823: q^2+2q+1
       824: q+1
       825: q+1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       834: q+1
       835: q+1
       836: q^2+2q+1
       837: q^2+2q+1
       838: q+1
       839: q^2+2q+1
       840: q+1
       841: 1
       842: 1
       843: q+1
       844: q+1
       845: q+1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: 1
       853: q+1
       854: 2q+1
       855: 2q+1
       856: q+1
       857: q+1
       858: q+1
       859: q+1
       860: 2q+1
       861: 2q+1
       862: 2q+1
       863: 2q+1
       864: q+1
       865: q+1
       866: q+1
       867: 2q+1
       868: 2q+1
       869: 2q+1
       870: 2q+1
       871: q+1
       872: q^2+2q+1
       875: q+1
       876: q+1
       877: 2q+1
       878: q+1
       879: q+1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: 2q+1
       901: 1
       902: q+1
       903: q+1
       904: 1
       905: 1
       906: q^2+2q+1
       907: q+1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       913: q+1
       914: q+1
       915: q+1
       916: q+1
       917: q+1
       918: q+1
       919: 1
       920: q+1
       921: q+1
       922: q+1
       923: q+1
       924: q+1
       925: q+1
       926: q+1
       927: q+1
       931: q+1
       932: q+1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q^2+2q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: 1
       960: q^2+2q+1
       961: 2q+1
       962: 2q+1
       963: q+1
       964: q+1
       965: q+1
       966: 2q+1
       967: 2q+1
       968: 2q+1
       969: 2q+1
       970: 2q+1
       971: q^2+2q+1
       972: q+1
       973: q+1
       974: 2q+1
       975: 2q+1
       976: 2q+1
       977: 2q+1
       978: 2q+1
       979: q^2+2q+1
       980: q^2+2q+1
       981: q^2+2q+1
       983: q+1
       984: q+1
       985: 2q+1
       986: 2q+1
       987: q+1
       988: q+1
       989: q+1
       990: 1
       991: 1
       992: q+1
       993: q^2+2q+1
       994: 1
       995: q+1
       996: q+1
       997: q+1
       998: q+1
       999: q+1
      1000: 2q+1
      1001: 1
      1002: q+1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: q+1
      1007: q+1
      1008: 2q+1
      1009: 2q+1
      1010: q+1
      1011: 2q+1
      1012: q+1
      1013: 1
      1014: q^2+2q+1
      1015: q^2+2q+1
      1016: q+1
      1017: q+1
      1018: q+1
      1019: 1
      1020: q+1
      1021: q+1
      1022: q^2+2q+1
      1023: q+1
      1024: q+1
      1025: q^2+2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q^2+2q+1
      1030: q+1
      1031: q+1
      1032: q+1
      1033: q+1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1039: q+1
      1040: q+1
      1041: q+1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q^2+2q+1
      1046: 1
      1047: q^2+2q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: q+1
      1055: 1
      1056: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: q+1
      1065: 1
      1066: 2q+1
      1067: q+1
      1068: q+1
      1069: 1
      1070: q+1
      1071: 2q+1
      1072: 2q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: 2q+1
      1078: 2q+1
      1079: q+1
      1080: q+1
      1084: q+1
      1085: q+1
      1086: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1113: q+1
      1114: q+1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: q+1
      1120: q+1
      1121: q+1
      1122: q+1
      1123: 1
      1124: 1
      1125: 1
      1126: q+1
      1127: q+1
      1128: q+1
      1129: q+1
      1131: q+1
      1136: q+1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 2q+1
      1166: 2q+1
      1167: q+1
      1168: q+1
      1169: q+1
      1170: q+1
      1171: 2q+1
      1172: 2q+1
      1173: 2q+1
      1174: 2q+1
      1175: q+1
      1176: q+1
      1177: q+1
      1178: 2q+1
      1179: 2q+1
      1180: 2q+1
      1181: 2q+1
      1182: q+1
      1183: q^2+2q+1
      1186: q+1
      1187: q+1
      1188: 2q+1
      1189: q+1
      1190: q+1
      1191: 1
      1192: 1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1197: q+1
      1198: q+1
      1199: q+1
      1200: q+1
      1201: 1
      1202: 1
      1204: q+1
      1205: 1
      1206: q+1
      1207: q+1
      1208: 1
      1209: q+1
      1210: q+1
      1211: 2q+1
      1212: 1
      1213: q+1
      1214: q+1
      1215: 1
      1216: 1
      1217: q^2+2q+1
      1218: q+1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1224: q+1
      1225: q+1
      1226: q+1
      1227: q+1
      1228: q+1
      1229: q+1
      1230: 1
      1231: q+1
      1232: q+1
      1233: q+1
      1234: q+1
      1235: q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1242: q+1
      1243: q+1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1249: q+1
      1250: q^2+2q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: q+1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1270: 1
      1271: q+1
      1272: 1
      1273: 1
      1274: 2q+1
      1275: q+1
      1276: q+1
      1277: 1
      1278: q+1
      1279: q+1
      1280: q+1
      1285: q+1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1310: q+1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: q+1
      1316: q+1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: q+1
      1322: q+1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1357: 2q+1
      1358: q+1
      1359: q+1
      1360: 1
      1361: q+1
      1362: 2q+1
      1363: 2q+1
      1364: q+1
      1365: q+1
      1366: q+1
      1367: q+1
      1368: 2q+1
      1369: 2q+1
      1370: q+1
      1371: q+1
      1375: q+1
      1376: q+1
      1377: q+1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: q+1
      1386: q+1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: q+1
      1394: 1
      1395: 1
      1396: q+1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1404: q+1
      1405: q+1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: q+1
      1411: q+1
      1412: q+1
      1413: q+1
      1414: 1
      1415: 1
      1416: 1
      1417: q+1
      1418: q+1
      1419: q+1
      1420: q+1
      1422: q+1
      1427: q+1
      1428: 1
      1429: 1
      1430: 1
      1431: 1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: q+1
      1459: 1
      1460: 1
      1461: q+1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: q+1
      1490: 1
      1491: 1
      1493: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1516: 1
      1517: 1
      1519: 1
      1524: 1
      1525: q+1
      1526: 1
      1527: 1
      1528: 2q+1
      1529: q+1
      1530: q+1
      1531: 1
      1532: q+1
      1533: q+1
      1534: q+1
      1539: q+1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: q+1
      1548: 1
      1549: 1
      1553: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1558: 1
      1561: 1
      1562: 1
      1563: 1
      1564: q+1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: q+1
      1570: q+1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: q+1
      1576: q+1
      1584: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1595: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1625: 1
      1626: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1654: 1
      1662: 1
      1663: 1
      1664: q+1
      1665: 1
      1666: 1
      1667: q+1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1683: 1
      1684: 1
      1685: 1
      1686: 1
      1690: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: q+1
      1696: 1
      1697: 1
      1699: 1
      1707: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1722: 1
      1723: 1
      1725: 1
      1730: 1
      1731: 1
      1734: 1
      1735: 1
      1739: 1
      1744: 1
      1750: 1
      1765: 1
      1766: 1
      1767: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1779: 1
      1780: 1
      1785: 1
      1786: 1
      1787: 1
      1788: 1
      1796: 1
      1797: 1
      1798: 1
      1800: 1
      1808: 1
      1817: 1
      1836: 1
      1839: 1
      1840: 1
      1844: 1
      1849: 1
      1855: 1
      1881: 1

1882:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
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        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: 1
        38: q+1
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        42: q+1
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        44: q+1
        45: q+1
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        47: q+1
        48: q+1
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        64: q+1
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        67: q+1
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        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: 1
        77: 1
        78: 1
        79: q+1
        80: 1
        81: q+1
        82: 1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: 1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q+1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: 1
       134: q+1
       135: q+1
       136: q+1
       137: 1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: q+1
       153: 1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: 1
       182: 1
       183: 1
       184: q+1
       185: 1
       186: q+1
       187: 1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: 1
       198: q+1
       199: q+1
       200: q+1
       201: q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q+1
       214: q+1
       215: q+1
       216: 1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: 1
       226: 1
       227: 1
       228: q+1
       229: q+1
       230: q+1
       231: 1
       232: 1
       233: 1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: 1
       249: 1
       250: 1
       251: 1
       252: 1
       253: 1
       254: 1
       255: 1
       256: q+1
       257: 1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: 1
       288: q+1
       289: q+1
       290: q+1
       291: 1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: 1
       297: 1
       298: 1
       299: 1
       300: 1
       301: 1
       302: 1
       303: 1
       304: 1
       305: 1
       306: q+1
       307: 1
       308: q+1
       309: 1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: 1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: 1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: 1
       340: 1
       341: 1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: 1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: 1
       353: 1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q+1
       364: 1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: 1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: q+1
       420: q+1
       421: q+1
       422: 1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: 1
       432: 1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: 1
       438: 1
       439: 1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: q+1
       463: 1
       464: 1
       465: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: 1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: 1
       483: q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: q+1
       493: q+1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: 1
       516: 1
       517: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: 1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: 1
       572: 1
       573: q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: 1
       594: 1
       595: 1
       596: q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: 1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q+1
       618: 1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: 1
       658: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: 1
       677: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       721: 1
       722: 1
       723: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       752: 1
       753: 1
       754: 1
       755: 1
       756: 1
       757: q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: 1
       763: 1
       764: 1
       765: q+1
       766: q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: q+1
       772: 1
       773: 1
       774: q+1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: q+1
       784: q+1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: q+1
       872: q+1
       873: q+1
       874: q+1
       875: q+1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       923: 1
       924: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       942: 1
       943: 1
       944: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       958: 1
       959: 1
       960: 1
       961: 1
       962: q+1
       963: q+1
       964: q+1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: q+1
       971: q+1
       972: q+1
       973: q+1
       974: q+1
       975: 1
       976: 1
       977: 1
       978: q+1
       979: q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: q+1
       985: 1
       986: 1
       987: 1
       988: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1032: 1
      1033: 1
      1034: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1128: 1
      1137: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1146: 1
      1147: 1
      1155: 1
      1156: 1
      1157: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: q+1
      1183: q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1234: 1
      1235: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1253: 1
      1254: 1
      1255: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1318: 1
      1332: 1
      1333: 1
      1334: 1
      1338: 1
      1347: 1
      1348: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1419: 1
      1428: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1437: 1
      1438: 1
      1446: 1
      1447: 1
      1448: 1
      1454: 1
      1455: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1486: 1
      1487: 1
      1488: 1
      1504: 1
      1516: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1572: 1
      1586: 1
      1587: 1
      1588: 1
      1592: 1
      1601: 1
      1602: 1
      1610: 1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1628: 1
      1632: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1686: 1
      1687: 1
      1688: 1
      1692: 1
      1693: 1
      1694: 1
      1710: 1
      1722: 1
      1732: 1
      1734: 1
      1736: 1
      1737: 1
      1738: 1
      1766: 1
      1768: 1
      1769: 1
      1770: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1775: 1
      1776: 1
      1777: 1
      1778: 1
      1782: 1
      1786: 1
      1818: 1
      1837: 1
      1839: 1
      1841: 1
      1842: 1
      1843: 1
      1882: 1

1883:    0: q^3+2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: 2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: 2q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^3+2q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: 2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: 2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: q^2+2q+1
        58: 2q^2+2q+1
        59: 2q^2+2q+1
        60: q^3+2q^2+2q+1
        61: q^3+2q^2+2q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: q^3+2q^2+2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^2+2q+1
        71: 2q+1
        72: 2q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q^2+2q+1
        77: q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^3+2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^3+2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: 2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: q^3+2q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: 2q^2+2q+1
       109: 2q^2+2q+1
       110: 2q^2+2q+1
       111: q^2+2q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: 2q^2+2q+1
       116: 2q^2+2q+1
       117: 2q^2+2q+1
       118: q^3+2q^2+2q+1
       119: q^2+2q+1
       120: 2q^2+2q+1
       121: 2q^2+2q+1
       122: q^3+2q^2+2q+1
       123: q^3+2q^2+2q+1
       124: 2q+1
       125: 2q^2+2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: 2q^2+2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       142: q+1
       143: q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^2+2q+1
       147: q+1
       148: q+1
       149: q^2+2q+1
       150: q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: 2q^2+2q+1
       161: q^3+2q^2+2q+1
       162: q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^3+2q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: q^3+2q^2+2q+1
       170: 2q^2+2q+1
       171: 2q^2+2q+1
       172: q^2+2q+1
       173: 2q^2+2q+1
       174: q^3+2q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: 2q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: q^2+2q+1
       182: q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: q^2+2q+1
       194: 2q+1
       195: 2q^2+2q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: 2q^2+2q+1
       203: 2q^2+2q+1
       204: 2q^2+2q+1
       205: q^2+2q+1
       206: q^2+2q+1
       207: q^2+2q+1
       208: q^2+2q+1
       209: 2q^2+2q+1
       210: 2q^2+2q+1
       211: 2q^2+2q+1
       212: q^3+2q^2+2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: q^2+2q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q+1
       227: q^2+2q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: q^2+2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q^2+2q+1
       243: q+1
       244: q+1
       245: 1
       246: q+1
       247: q+1
       248: 2q+1
       249: q+1
       250: q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: 2q^2+2q+1
       263: 2q^2+2q+1
       264: 2q^2+2q+1
       265: q^2+2q+1
       266: q^2+2q+1
       267: q^2+2q+1
       268: q^2+2q+1
       269: 2q^2+2q+1
       270: 2q^2+2q+1
       271: 2q^2+2q+1
       272: q^3+2q^2+2q+1
       273: q^2+2q+1
       274: 2q^2+2q+1
       275: 2q^2+2q+1
       276: q^3+2q^2+2q+1
       277: q^3+2q^2+2q+1
       278: 2q+1
       279: 2q^2+2q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: 2q^2+2q+1
       284: 2q^2+2q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: q+1
       297: q+1
       298: q^2+2q+1
       299: q^2+2q+1
       300: q^2+2q+1
       301: q+1
       302: q+1
       303: q^2+2q+1
       304: q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q^2+2q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: 2q+1
       315: 2q+1
       316: 2q+1
       317: q^2+2q+1
       318: q+1
       319: q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: q^2+2q+1
       324: 2q+1
       325: 2q^2+2q+1
       326: q^2+2q+1
       327: q^2+2q+1
       328: q^2+2q+1
       329: q^2+2q+1
       330: q^2+2q+1
       331: q^2+2q+1
       332: 2q^2+2q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: q^2+2q+1
       341: q^2+2q+1
       342: q^2+2q+1
       343: q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: 2q+1
       362: q^2+2q+1
       363: q^2+2q+1
       364: q^2+2q+1
       365: 2q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: 2q+1
       381: 2q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q^2+2q+1
       387: q+1
       388: q+1
       389: 1
       390: q+1
       391: q+1
       392: q^2+2q+1
       393: q+1
       394: q+1
       395: q+1
       396: q^2+2q+1
       397: q^2+2q+1
       398: q^2+2q+1
       399: q^2+2q+1
       400: 2q+1
       401: 2q^2+2q+1
       402: q^2+2q+1
       403: q^2+2q+1
       404: q^2+2q+1
       405: q^2+2q+1
       406: q^2+2q+1
       407: q^2+2q+1
       408: 2q^2+2q+1
       409: 2q^2+2q+1
       410: 2q^2+2q+1
       411: q^2+2q+1
       412: q^2+2q+1
       413: q^2+2q+1
       414: q^2+2q+1
       415: 2q^2+2q+1
       416: 2q^2+2q+1
       417: 2q^2+2q+1
       418: q^3+2q^2+2q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: q^2+2q+1
       423: q^2+2q+1
       424: q^2+2q+1
       425: q^2+2q+1
       426: 2q+1
       427: 2q^2+2q+1
       428: q^2+2q+1
       429: q^2+2q+1
       430: q^2+2q+1
       431: q^2+2q+1
       432: q+1
       433: q^2+2q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: q^2+2q+1
       439: q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q^2+2q+1
       449: q+1
       450: q+1
       451: 1
       452: q+1
       453: q+1
       454: 2q+1
       455: q+1
       456: q+1
       457: q^2+2q+1
       458: q^2+2q+1
       459: q^2+2q+1
       460: q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: q+1
       467: q^2+2q+1
       468: 2q+1
       469: 2q+1
       470: 2q+1
       471: 2q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+2q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: 2q+1
       479: 2q+1
       480: 2q+1
       481: q^2+2q+1
       482: q+1
       483: q+1
       484: q^2+2q+1
       485: q^2+2q+1
       486: q^2+2q+1
       487: q^2+2q+1
       488: 2q+1
       489: 2q^2+2q+1
       490: q^2+2q+1
       491: q^2+2q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: 2q+1
       498: q^2+2q+1
       499: q^2+2q+1
       500: q^2+2q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: q^2+2q+1
       506: q^2+2q+1
       507: q^2+2q+1
       508: q^2+2q+1
       509: 2q+1
       510: 2q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q^2+2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: 2q+1
       522: 2q+1
       523: q+1
       524: q^2+2q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: q+1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q+1
       543: 2q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: q+1
       552: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q+1
       558: q+1
       559: q+1
       560: 1
       561: q+1
       562: q+1
       563: q+1
       564: q+1
       565: q^2+2q+1
       566: q^2+2q+1
       567: q^2+2q+1
       568: 2q+1
       569: 2q+1
       570: 2q+1
       571: q^2+2q+1
       572: q+1
       573: q+1
       574: q^2+2q+1
       575: q^2+2q+1
       576: q^2+2q+1
       577: q^2+2q+1
       578: 2q+1
       579: 2q^2+2q+1
       580: q^2+2q+1
       581: q^2+2q+1
       582: q^2+2q+1
       583: q^2+2q+1
       584: q^2+2q+1
       585: q^2+2q+1
       586: 2q^2+2q+1
       587: 2q^2+2q+1
       588: 2q^2+2q+1
       589: q^2+2q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: q^2+2q+1
       595: q^2+2q+1
       596: q^2+2q+1
       597: q^2+2q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: q^2+2q+1
       602: q^2+2q+1
       603: q^2+2q+1
       604: q^2+2q+1
       605: 2q+1
       606: q+1
       607: q+1
       608: q^2+2q+1
       609: q^2+2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: 2q+1
       616: q^2+2q+1
       617: q^2+2q+1
       618: q^2+2q+1
       619: 2q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: 2q+1
       635: 2q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q^2+2q+1
       641: q+1
       642: q+1
       643: 1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q+1
       650: q+1
       651: q+1
       652: q+1
       653: 2q+1
       654: 2q+1
       655: 2q+1
       656: q+1
       658: q+1
       659: q+1
       660: q^2+2q+1
       661: 2q+1
       662: 2q+1
       663: 2q+1
       664: 2q+1
       665: q+1
       666: q+1
       667: q+1
       668: q^2+2q+1
       669: q^2+2q+1
       670: q^2+2q+1
       671: 2q+1
       672: 2q+1
       673: 2q+1
       674: q^2+2q+1
       675: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: 2q+1
       682: 2q+1
       683: q+1
       684: q^2+2q+1
       685: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: 2q+1
       692: q^2+2q+1
       693: q^2+2q+1
       694: q^2+2q+1
       695: 2q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       704: q+1
       705: 1
       706: q+1
       707: 2q+1
       708: q+1
       709: q+1
       710: q+1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: q+1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: q+1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: q+1
       748: q+1
       749: q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       756: q+1
       757: q+1
       758: q^2+2q+1
       759: 2q+1
       760: 2q+1
       761: 2q+1
       762: 2q+1
       763: q+1
       764: q+1
       765: q+1
       766: q^2+2q+1
       767: q^2+2q+1
       768: q^2+2q+1
       769: 2q+1
       770: 2q+1
       771: 2q+1
       772: q^2+2q+1
       773: q+1
       774: q+1
       775: q^2+2q+1
       776: q^2+2q+1
       777: q^2+2q+1
       778: q^2+2q+1
       779: 2q+1
       780: 2q^2+2q+1
       781: q^2+2q+1
       782: q^2+2q+1
       783: q+1
       784: 2q+1
       785: 2q+1
       786: 2q+1
       787: q+1
       788: 2q+1
       789: q^2+2q+1
       790: q^2+2q+1
       791: q^2+2q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 2q+1
       796: q^2+2q+1
       797: q^2+2q+1
       798: q^2+2q+1
       799: q^2+2q+1
       800: 2q+1
       801: 2q+1
       802: q+1
       803: q+1
       804: q+1
       805: q+1
       806: q^2+2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: 2q+1
       813: 2q+1
       814: q+1
       815: q^2+2q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: q+1
       823: q+1
       824: 1
       825: q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       834: 2q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       850: q+1
       851: 1
       852: q+1
       853: q+1
       855: q+1
       856: q+1
       857: q+1
       858: 2q+1
       859: q+1
       860: q+1
       862: q+1
       863: q+1
       864: q+1
       865: 2q+1
       866: 2q+1
       867: 2q+1
       868: q+1
       870: q+1
       871: q+1
       872: q^2+2q+1
       873: 2q+1
       874: 2q+1
       875: 2q+1
       876: 2q+1
       877: q+1
       879: q+1
       880: 1
       881: q+1
       882: 2q+1
       883: q+1
       884: q+1
       885: q+1
       886: q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: 2q+1
       893: 2q+1
       894: q+1
       895: q^2+2q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: q+1
       903: q+1
       904: 1
       905: q+1
       907: 1
       908: 1
       909: 1
       910: q+1
       911: q+1
       912: q+1
       913: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: q+1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q+1
       961: q+1
       962: q+1
       963: q+1
       964: 2q+1
       965: 2q+1
       966: 2q+1
       967: q+1
       969: q+1
       970: q+1
       971: q^2+2q+1
       972: 2q+1
       973: 2q+1
       974: 2q+1
       975: 2q+1
       976: q+1
       977: q+1
       978: q+1
       979: q^2+2q+1
       980: q^2+2q+1
       981: q^2+2q+1
       982: 2q+1
       983: 2q+1
       984: 2q+1
       985: q^2+2q+1
       986: q+1
       987: q+1
       988: q+1
       989: 2q+1
       990: q+1
       991: q+1
       992: 2q+1
       993: 2q+1
       994: q+1
       995: q^2+2q+1
       996: q+1
       997: q+1
       998: 2q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: 2q+1
      1003: q^2+2q+1
      1004: q^2+2q+1
      1005: q^2+2q+1
      1006: 2q+1
      1007: q+1
      1008: q+1
      1009: q+1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: 2q+1
      1019: q+1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: q+1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q+1
      1059: q+1
      1060: q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1068: q+1
      1069: 1
      1070: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: 2q+1
      1076: q+1
      1077: q+1
      1079: q+1
      1080: q+1
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: 2q+1
      1085: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: q+1
      1091: q+1
      1092: q+1
      1093: 1
      1095: q+1
      1096: 1
      1097: q+1
      1098: 2q+1
      1099: q+1
      1100: q+1
      1101: q+1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1108: q+1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: q+1
      1118: 1
      1119: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1129: 1
      1131: 1
      1136: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: q+1
      1167: q+1
      1168: q+1
      1169: 2q+1
      1170: q+1
      1171: q+1
      1173: q+1
      1174: q+1
      1175: q+1
      1176: 2q+1
      1177: 2q+1
      1178: 2q+1
      1179: q+1
      1181: q+1
      1182: q+1
      1183: q^2+2q+1
      1184: 2q+1
      1185: 2q+1
      1186: 2q+1
      1187: 2q+1
      1188: q+1
      1190: q+1
      1191: 1
      1192: q+1
      1193: 2q+1
      1194: q+1
      1195: q+1
      1196: q+1
      1197: q+1
      1198: q+1
      1199: q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1203: 2q+1
      1204: 2q+1
      1205: q+1
      1206: q^2+2q+1
      1207: q+1
      1208: 1
      1209: q+1
      1210: q+1
      1211: q+1
      1212: 1
      1213: q+1
      1214: q+1
      1215: 1
      1216: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: q+1
      1222: q+1
      1223: q+1
      1224: 1
      1226: 1
      1227: 1
      1228: 1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1249: q+1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: q+1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q+1
      1272: 1
      1273: 1
      1276: q+1
      1277: 1
      1278: q+1
      1280: q+1
      1281: q+1
      1282: q+1
      1283: 2q+1
      1284: q+1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: q+1
      1291: 1
      1292: 1
      1294: 1
      1295: 1
      1296: 1
      1297: q+1
      1298: q+1
      1299: q+1
      1300: 1
      1302: 1
      1303: 1
      1304: 1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1359: q+1
      1360: 1
      1361: q+1
      1363: q+1
      1364: q+1
      1365: q+1
      1366: 2q+1
      1367: q+1
      1368: q+1
      1370: q+1
      1371: q+1
      1372: q+1
      1373: 2q+1
      1374: 2q+1
      1375: 2q+1
      1376: q+1
      1378: 1
      1379: 1
      1380: 1
      1381: q+1
      1382: q+1
      1383: q+1
      1384: 1
      1386: q+1
      1387: 1
      1388: q+1
      1389: 2q+1
      1390: q+1
      1391: q+1
      1392: q+1
      1393: q+1
      1394: 1
      1395: 1
      1396: q+1
      1397: 1
      1398: 1
      1399: q+1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1405: 1
      1406: 1
      1407: 1
      1408: q+1
      1409: 1
      1410: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1420: 1
      1422: 1
      1427: 1
      1429: 1
      1430: 1
      1431: 1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1453: 1
      1454: 1
      1455: q+1
      1457: 1
      1459: 1
      1460: 1
      1463: q+1
      1464: 1
      1465: q+1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1473: 1
      1474: 1
      1475: q+1
      1476: 1
      1477: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1493: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1517: 1
      1519: 1
      1524: 1
      1526: 1
      1527: 1
      1530: q+1
      1531: 1
      1532: q+1
      1534: q+1
      1535: q+1
      1536: q+1
      1537: 2q+1
      1538: q+1
      1539: q+1
      1541: 1
      1542: 1
      1543: 1
      1544: q+1
      1545: 1
      1546: 1
      1548: 1
      1549: 1
      1550: 1
      1551: q+1
      1552: q+1
      1553: q+1
      1554: 1
      1556: 1
      1557: 1
      1558: 1
      1559: q+1
      1560: 1
      1561: 1
      1562: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1593: 1
      1595: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1609: 1
      1610: 1
      1613: 1
      1615: 1
      1616: 1
      1618: 1
      1619: 1
      1622: 1
      1623: 1
      1624: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1633: 1
      1644: 1
      1646: 1
      1663: 1
      1665: 1
      1666: 1
      1669: q+1
      1670: 1
      1671: q+1
      1674: 1
      1675: 1
      1676: 1
      1678: 1
      1679: 1
      1680: 1
      1681: q+1
      1682: 1
      1683: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1693: 1
      1694: 1
      1697: 1
      1699: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1723: 1
      1725: 1
      1730: 1
      1733: 1
      1735: 1
      1737: 1
      1738: 1
      1741: 1
      1743: 1
      1767: 1
      1769: 1
      1770: 1
      1772: 1
      1773: 1
      1776: 1
      1777: 1
      1778: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1787: 1
      1798: 1
      1800: 1
      1819: 1
      1838: 1
      1840: 1
      1842: 1
      1843: 1
      1846: 1
      1848: 1
      1883: 1

1884:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: q^2+2q+1
        21: 2q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: 2q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: 2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: 2q+1
        72: 2q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: 2q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       120: 2q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 2q+1
       125: 2q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: 2q^2+2q+1
       130: 2q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: 2q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: q^2+2q+1
       170: 2q^2+2q+1
       171: 2q^2+2q+1
       172: 2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: 2q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: q^2+2q+1
       193: q^2+q+1
       194: q+1
       195: q^2+2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: q^2+2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: q^2+2q+1
       204: q^2+2q+1
       205: q+1
       206: q^2+2q+1
       207: q^2+2q+1
       208: q^2+2q+1
       209: q^2+2q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: q+1
       244: q^2+2q+1
       245: q+1
       246: q+1
       247: q+1
       248: 2q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: q^2+2q+1
       263: q^2+2q+1
       264: q^2+2q+1
       265: q+1
       266: q^2+2q+1
       267: q^2+2q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q^2+2q+1
       271: q^2+2q+1
       272: q^2+2q+1
       273: q^2+2q+1
       274: 2q^2+2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 2q+1
       279: 2q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q^2+2q+1
       284: 2q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q^2+2q+1
       312: q^2+q+1
       313: q^2+q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+2q+1
       321: q^2+2q+1
       322: q^2+2q+1
       323: q^2+q+1
       324: q+1
       325: q^2+2q+1
       326: q+1
       327: q+1
       328: q^2+2q+1
       329: q^2+2q+1
       330: q^2+2q+1
       331: q^2+2q+1
       332: q^2+2q+1
       333: q^2+2q+1
       334: q^2+2q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: q+1
       388: q^2+2q+1
       389: q+1
       390: q+1
       391: q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q+1
       395: q+1
       396: q^2+2q+1
       397: q^2+2q+1
       398: q^2+2q+1
       399: q^2+q+1
       400: q+1
       401: q^2+2q+1
       402: q+1
       403: q+1
       404: q^2+2q+1
       405: q^2+2q+1
       406: q^2+2q+1
       407: q^2+2q+1
       408: q^2+2q+1
       409: q^2+2q+1
       410: q^2+2q+1
       411: q+1
       412: q^2+2q+1
       413: q^2+2q+1
       414: q^2+2q+1
       415: q^2+2q+1
       416: q^2+2q+1
       417: q^2+2q+1
       418: q^2+2q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: 2q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: 2q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: q+1
       450: q^2+2q+1
       451: q+1
       452: q+1
       453: q+1
       454: 2q+1
       455: q^2+2q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: 1
       467: q^2+q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+2q+1
       476: q^2+q+1
       477: q^2+q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       482: q+1
       483: q+1
       484: q^2+2q+1
       485: q^2+2q+1
       486: q^2+2q+1
       487: q^2+q+1
       488: q+1
       489: q^2+2q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: 2q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: 1
       534: 1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: 1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: 1
       551: q+1
       552: q+1
       553: q+1
       554: q+1
       555: q+1
       556: q+1
       557: q+1
       558: q+1
       559: q^2+2q+1
       560: q+1
       561: q+1
       562: q+1
       563: q+1
       564: q+1
       565: q^2+2q+1
       566: q^2+q+1
       567: q^2+q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: q+1
       574: q^2+2q+1
       575: q^2+2q+1
       576: q^2+2q+1
       577: q^2+q+1
       578: q+1
       579: q^2+2q+1
       580: q+1
       581: q+1
       582: q^2+2q+1
       583: q^2+2q+1
       584: q^2+2q+1
       585: q^2+2q+1
       586: q^2+2q+1
       587: q^2+2q+1
       588: q^2+2q+1
       589: q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 2q+1
       606: q^2+2q+1
       607: 2q+1
       608: 2q+1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 2q+1
       635: 2q+1
       636: 2q+1
       637: 2q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: q+1
       642: q^2+2q+1
       643: q+1
       644: q+1
       645: q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q+1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: q+1
       658: q+1
       659: 1
       660: q^2+q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       665: q+1
       666: q+1
       667: q+1
       668: q^2+2q+1
       669: q^2+q+1
       670: q^2+q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       696: 2q+1
       697: 2q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: 2q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       728: q+1
       729: 1
       730: 1
       731: 1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: 1
       739: 1
       740: q+1
       741: q+1
       742: q+1
       743: q+1
       744: q+1
       745: q+1
       746: q+1
       747: 1
       748: q+1
       749: q+1
       750: q+1
       751: q+1
       752: q+1
       753: q+1
       754: q+1
       755: q+1
       756: q+1
       757: 1
       758: q^2+q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: q+1
       765: q+1
       766: q^2+2q+1
       767: q^2+q+1
       768: q^2+q+1
       769: q+1
       770: q+1
       771: 1
       772: q+1
       773: q+1
       774: q+1
       775: q^2+2q+1
       776: q^2+2q+1
       777: q^2+2q+1
       778: q^2+q+1
       779: q+1
       780: q^2+2q+1
       781: q+1
       782: q+1
       783: q+1
       784: 2q+1
       785: 2q+1
       786: 2q+1
       787: q+1
       788: q+1
       789: 2q+1
       790: q+1
       791: q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: q+1
       800: 2q+1
       801: 2q+1
       802: 2q+1
       803: 2q+1
       804: 2q+1
       805: 2q+1
       806: 2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 2q+1
       835: 2q+1
       836: 2q+1
       837: 2q+1
       838: 2q+1
       839: 2q+1
       840: 2q+1
       841: 1
       842: q+1
       843: q+1
       844: q+1
       845: q+1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       850: q^2+2q+1
       851: q+1
       852: q+1
       853: q+1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q^2+q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: 2q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: q+1
       926: q+1
       927: q+1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 2q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: q+1
       945: q+1
       946: q+1
       947: q+1
       949: q+1
       950: 1
       951: 1
       952: q+1
       953: q+1
       954: q+1
       955: q+1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: q+1
       969: q+1
       970: 1
       971: q^2+q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       976: q+1
       977: q+1
       978: q+1
       979: q^2+2q+1
       980: q^2+q+1
       981: q^2+q+1
       982: q+1
       983: q+1
       984: 1
       985: q+1
       986: q+1
       987: q+1
       988: q+1
       989: 2q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: 1
       995: q+1
       996: q+1
       997: q+1
       998: 2q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1006: 2q+1
      1007: 2q+1
      1008: 2q+1
      1009: 2q+1
      1010: 2q+1
      1011: 2q+1
      1012: 2q+1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: 2q+1
      1044: 2q+1
      1045: 2q+1
      1046: q+1
      1047: q+1
      1048: 2q+1
      1049: 1
      1050: 1
      1051: q+1
      1052: q+1
      1053: q+1
      1054: q+1
      1055: q+1
      1056: q+1
      1057: q+1
      1058: 1
      1059: q+1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: q+1
      1065: q+1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: 2q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: q+1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: q+1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: q+1
      1149: q+1
      1150: q+1
      1154: 1
      1155: 1
      1156: 1
      1157: q+1
      1158: q+1
      1159: q+1
      1160: q+1
      1162: q+1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: q+1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: q+1
      1181: q+1
      1182: 1
      1183: q^2+q+1
      1184: q+1
      1185: 1
      1186: 1
      1187: 1
      1188: q+1
      1189: q+1
      1190: q+1
      1191: 1
      1192: q+1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1197: q+1
      1198: q+1
      1199: q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1203: q+1
      1204: q+1
      1205: 1
      1206: q+1
      1207: q+1
      1208: 1
      1209: 2q+1
      1210: 2q+1
      1211: 2q+1
      1212: q+1
      1213: q+1
      1214: 2q+1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 2q+1
      1247: q+1
      1248: q+1
      1249: q+1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: q+1
      1256: q+1
      1257: q+1
      1258: q+1
      1260: q+1
      1261: 1
      1262: 1
      1263: q+1
      1264: q+1
      1265: q+1
      1266: q+1
      1267: q+1
      1268: q+1
      1269: q+1
      1270: 1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: q+1
      1346: 1
      1347: 1
      1348: 1
      1349: q+1
      1350: q+1
      1351: q+1
      1355: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: q+1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: q+1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: q+1
      1386: q+1
      1387: 1
      1388: q+1
      1389: q+1
      1390: 1
      1391: 1
      1392: 1
      1393: q+1
      1394: 1
      1395: 1
      1396: 2q+1
      1397: q+1
      1398: q+1
      1399: q+1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: q+1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1431: q+1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: q+1
      1440: q+1
      1441: q+1
      1445: 1
      1446: 1
      1447: 1
      1448: q+1
      1449: q+1
      1450: q+1
      1451: q+1
      1453: q+1
      1454: 1
      1455: 1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1516: 1
      1517: 1
      1519: q+1
      1524: 1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: q+1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1558: q+1
      1559: q+1
      1560: 1
      1561: 1
      1562: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1584: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1595: q+1
      1600: 1
      1601: 1
      1602: 1
      1603: q+1
      1604: q+1
      1605: q+1
      1609: 1
      1610: 1
      1614: 1
      1617: 1
      1620: 1
      1621: 1
      1622: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1634: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1654: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1672: 1
      1673: 1
      1674: 1
      1676: 1
      1677: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1684: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1692: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1707: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1722: 1
      1723: 1
      1725: q+1
      1730: 1
      1736: 1
      1739: 1
      1740: 1
      1741: 1
      1743: 1
      1750: 1
      1768: 1
      1771: 1
      1774: 1
      1775: 1
      1776: 1
      1778: 1
      1779: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1788: 1
      1796: 1
      1797: 1
      1798: 1
      1800: 1
      1808: 1
      1820: 1
      1841: 1
      1844: 1
      1845: 1
      1846: 1
      1848: 1
      1855: 1
      1884: 1

1885:    0: 2q^2+q+1
         1: 2q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: 2q^2+q+1
         5: 2q^2+q+1
         6: 2q^2+q+1
         7: q^2+q+1
         8: 2q^2+q+1
         9: 2q^2+q+1
        10: 2q^2+q+1
        11: 2q^2+q+1
        12: 2q^2+q+1
        13: 2q^2+q+1
        14: 2q^2+q+1
        15: 2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: 2q^2+q+1
        19: 2q^2+q+1
        20: 2q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: 2q^2+q+1
        25: 2q^2+q+1
        26: q^2+q+1
        27: 2q^2+q+1
        28: 2q^2+q+1
        29: 2q^2+q+1
        30: 2q^2+q+1
        31: 2q^2+q+1
        32: 2q^2+q+1
        33: 2q^2+q+1
        34: q^2+q+1
        35: 2q^2+q+1
        36: 2q^2+q+1
        37: 2q^2+q+1
        38: q^2+q+1
        39: 2q^2+q+1
        40: 2q^2+q+1
        41: q^2+q+1
        42: 2q^2+q+1
        43: 2q^2+q+1
        44: 2q^2+q+1
        45: 2q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: 2q^2+q+1
        49: 2q^2+q+1
        50: q^2+q+1
        51: 2q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q^2+q+1
        56: q^2+q+1
        57: 2q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: 2q^2+q+1
        62: 2q^2+q+1
        63: q^2+q+1
        64: 2q^2+q+1
        65: 2q^2+q+1
        66: q^2+q+1
        67: 2q^2+q+1
        68: 2q^2+q+1
        69: 2q^2+q+1
        70: 2q^2+q+1
        71: 2q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q+1
        75: 2q^2+q+1
        76: 2q^2+q+1
        77: q^2+1
        78: 2q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: 2q^2+q+1
        82: 2q^2+q+1
        83: q^2+q+1
        84: 2q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: 2q^2+q+1
        89: 2q^2+q+1
        90: q^2+q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: 2q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: 2q^2+q+1
        97: 2q^2+q+1
        98: q^2+q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: 2q^2+q+1
       102: q^2+q+1
       103: 2q^2+q+1
       104: q^2+q+1
       105: q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q+1
       109: q^2+q+1
       110: q+1
       111: q^2+q+1
       112: q^2+q+1
       113: 2q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q^2+q+1
       118: q^2+q+1
       119: 2q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: 2q^2+q+1
       124: 2q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q+1
       128: 2q^2+q+1
       129: 2q^2+q+1
       130: q^2+q+1
       131: 2q^2+q+1
       132: 2q^2+q+1
       133: 2q^2+q+1
       134: q+1
       135: 2q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: 2q^2+q+1
       142: q^2+1
       143: q^2+1
       144: q+1
       145: 2q^2+q+1
       146: q^2+q+1
       147: 1
       148: q^2+q+1
       149: 2q^2+q+1
       150: q^2+1
       151: 2q^2+q+1
       152: q^2+q+1
       153: q^2+q+1
       154: q^2+q+1
       155: q^2+q+1
       156: 2q^2+q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q+1
       160: q^2+q+1
       161: q^2+q+1
       162: 2q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: 2q^2+q+1
       167: 2q^2+q+1
       168: q^2+q+1
       169: 2q^2+q+1
       170: 2q^2+q+1
       171: q^2+q+1
       172: 2q^2+q+1
       173: 2q^2+q+1
       174: 2q^2+q+1
       175: 2q^2+q+1
       176: 2q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q+1
       180: 2q^2+q+1
       181: 2q^2+q+1
       182: q^2+1
       183: 2q^2+q+1
       184: q^2+q+1
       185: q^2+q+1
       186: 2q^2+q+1
       187: 2q^2+q+1
       188: q^2+q+1
       189: q^2+q+1
       190: q+1
       191: q+1
       192: q^2+q+1
       193: q+1
       194: q^2+q+1
       195: q+1
       196: q+1
       197: q^2+q+1
       198: q^2+q+1
       199: q+1
       200: q^2+q+1
       201: q^2+q+1
       202: q+1
       203: q^2+q+1
       204: q+1
       205: q^2+q+1
       206: q^2+q+1
       207: 2q^2+q+1
       208: q^2+q+1
       209: q^2+q+1
       210: q+1
       211: q^2+q+1
       212: q^2+q+1
       213: q+1
       214: 2q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: 2q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q+1
       224: 2q^2+q+1
       225: 2q^2+q+1
       226: q^2+1
       227: 2q^2+q+1
       228: q+1
       229: q+1
       230: q^2+q+1
       231: q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q+1
       235: q+1
       236: q+1
       237: 2q^2+q+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: q+1
       243: q^2+q+1
       244: 1
       245: 1
       246: q+1
       247: q^2+q+1
       248: 2q^2+q+1
       249: q^2+1
       250: q^2+1
       251: q+1
       252: 2q^2+q+1
       253: q^2+q+1
       254: 1
       255: q^2+q+1
       256: q^2+q+1
       257: q^2+q+1
       258: q^2+q+1
       259: q+1
       260: q^2+q+1
       261: q^2+q+1
       262: q+1
       263: q^2+q+1
       264: q+1
       265: q^2+q+1
       266: q^2+q+1
       267: 2q^2+q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q+1
       271: q^2+q+1
       272: q^2+q+1
       273: 2q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: 2q^2+q+1
       278: 2q^2+q+1
       279: q^2+q+1
       280: q^2+q+1
       281: q+1
       282: 2q^2+q+1
       283: 2q^2+q+1
       284: q^2+q+1
       285: 2q^2+q+1
       286: 2q^2+q+1
       287: 2q^2+q+1
       288: q+1
       289: 2q^2+q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q+1
       293: q^2+q+1
       294: q+1
       295: 2q^2+q+1
       296: q^2+1
       297: q^2+1
       298: q+1
       299: 2q^2+q+1
       300: q^2+q+1
       301: 1
       302: q^2+q+1
       303: 2q^2+q+1
       304: q^2+1
       305: 2q^2+q+1
       306: q^2+q+1
       307: q^2+q+1
       308: q^2+q+1
       309: q^2+q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: q^2+q+1
       316: q+1
       317: q+1
       319: q^2+q+1
       320: q+1
       321: q+1
       322: q^2+q+1
       323: q+1
       324: q^2+q+1
       325: q+1
       326: q+1
       327: q^2+q+1
       328: q^2+q+1
       329: q+1
       330: q^2+q+1
       331: q^2+q+1
       332: q+1
       333: q^2+q+1
       334: q+1
       335: q^2+q+1
       336: q+1
       337: q+1
       338: q^2+q+1
       339: q^2+q+1
       340: q+1
       341: q^2+q+1
       342: q+1
       343: q+1
       344: q+1
       345: 2q^2+q+1
       346: q^2+q+1
       347: q^2+q+1
       348: q+1
       349: q^2+q+1
       350: q+1
       351: 2q^2+q+1
       352: q^2+1
       353: q^2+1
       354: q+1
       355: 2q^2+q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: q+1
       373: q+1
       374: q^2+q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: q+1
       381: 2q^2+q+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: q+1
       387: q^2+q+1
       388: 1
       389: 1
       390: q+1
       391: q^2+q+1
       392: q^2+q+1
       393: 1
       394: q^2+q+1
       395: q^2+q+1
       396: q+1
       397: q+1
       398: q^2+q+1
       399: q+1
       400: q^2+q+1
       401: q+1
       402: q+1
       403: q^2+q+1
       404: q^2+q+1
       405: q+1
       406: q^2+q+1
       407: q^2+q+1
       408: q+1
       409: q^2+q+1
       410: q+1
       411: q^2+q+1
       412: q^2+q+1
       413: 2q^2+q+1
       414: q^2+q+1
       415: q^2+q+1
       416: q+1
       417: q^2+q+1
       418: q^2+q+1
       419: q+1
       420: 2q^2+q+1
       421: q^2+q+1
       422: q^2+q+1
       423: q+1
       424: q^2+q+1
       425: q+1
       426: 2q^2+q+1
       427: q^2+q+1
       428: q^2+q+1
       429: q+1
       430: 2q^2+q+1
       431: 2q^2+q+1
       432: q^2+1
       433: 2q^2+q+1
       434: q+1
       435: q+1
       436: q^2+q+1
       437: q^2+q+1
       438: q+1
       439: q^2+q+1
       440: q+1
       441: q+1
       442: q+1
       443: 2q^2+q+1
       444: q^2+1
       445: q^2+1
       446: 1
       447: q^2+1
       448: q+1
       449: q^2+q+1
       450: 1
       451: 1
       452: q+1
       453: q^2+q+1
       454: 2q^2+q+1
       455: q^2+1
       456: q^2+1
       457: q+1
       458: 2q^2+q+1
       459: q^2+q+1
       460: 1
       461: q^2+q+1
       462: q^2+q+1
       463: q^2+q+1
       465: q+1
       466: q+1
       467: q+1
       468: 1
       469: 1
       470: q+1
       471: q+1
       473: q^2+q+1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: q^2+q+1
       480: q+1
       481: q+1
       483: q^2+q+1
       484: q+1
       485: q+1
       486: q^2+q+1
       487: q+1
       488: q^2+q+1
       489: q+1
       490: q+1
       491: q^2+q+1
       492: q+1
       493: q+1
       494: q+1
       495: q^2+q+1
       496: q+1
       497: q^2+q+1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q^2+q+1
       504: q^2+q+1
       505: q+1
       506: q^2+q+1
       507: q+1
       508: q+1
       509: q+1
       510: 2q^2+q+1
       511: q^2+1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: q^2+q+1
       523: q+1
       524: q+1
       526: q+1
       527: 1
       528: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: q+1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q+1
       543: q+1
       544: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: q+1
       551: q+1
       552: q^2+q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q+1
       558: q^2+q+1
       559: 1
       560: 1
       561: q+1
       562: q^2+q+1
       563: q^2+q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: q^2+q+1
       570: q+1
       571: q+1
       573: q^2+q+1
       574: q+1
       575: q+1
       576: q^2+q+1
       577: q+1
       578: q^2+q+1
       579: q+1
       580: q+1
       581: q^2+q+1
       582: q^2+q+1
       583: q+1
       584: q^2+q+1
       585: q^2+q+1
       586: q+1
       587: q^2+q+1
       588: q+1
       589: q^2+q+1
       590: q+1
       591: q+1
       592: q^2+q+1
       593: q^2+q+1
       594: q+1
       595: q^2+q+1
       596: q+1
       597: q+1
       598: q+1
       599: 2q^2+q+1
       600: q^2+q+1
       601: q^2+q+1
       602: q+1
       603: q^2+q+1
       604: q+1
       605: 2q^2+q+1
       606: q^2+1
       607: q^2+1
       608: q+1
       609: 2q^2+q+1
       610: q+1
       611: q+1
       612: q+1
       613: q^2+q+1
       614: q+1
       615: q^2+q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: 1
       621: q^2+1
       622: q^2+1
       623: 1
       624: q^2+1
       625: 1
       626: q+1
       627: q+1
       628: q^2+q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: q+1
       635: 2q^2+q+1
       636: q^2+1
       637: q^2+1
       638: 1
       639: q^2+1
       640: q+1
       641: q^2+q+1
       642: 1
       643: 1
       644: q+1
       645: q^2+q+1
       646: q^2+q+1
       647: 1
       648: q^2+q+1
       650: q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       658: q+1
       659: q+1
       660: q+1
       661: 1
       662: 1
       663: q+1
       664: q+1
       666: q^2+q+1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: q^2+q+1
       673: q+1
       674: q+1
       676: q+1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       681: 1
       682: q^2+q+1
       683: q+1
       684: q+1
       686: q+1
       687: q+1
       688: q+1
       689: q^2+q+1
       690: q+1
       691: q^2+q+1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: 1
       697: q^2+1
       698: q^2+1
       699: 1
       700: q^2+1
       701: 1
       702: q+1
       704: q+1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: q+1
       710: q+1
       712: q+1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: q^2+1
       719: 1
       720: 1
       722: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: q+1
       731: q+1
       732: 1
       733: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: q+1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: q+1
       748: q+1
       749: q^2+q+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q+1
       756: q+1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: q+1
       762: q+1
       764: q^2+q+1
       765: q+1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: q^2+q+1
       771: q+1
       772: q+1
       774: q^2+q+1
       775: q+1
       776: q+1
       777: q^2+q+1
       778: q+1
       779: q^2+q+1
       780: q+1
       781: q+1
       782: q^2+q+1
       783: q+1
       784: q+1
       785: q+1
       786: q^2+q+1
       787: q+1
       788: q^2+q+1
       789: q+1
       790: q+1
       791: q+1
       792: q+1
       793: q+1
       794: q^2+q+1
       795: q^2+q+1
       796: q+1
       797: q^2+q+1
       798: q+1
       799: q+1
       800: q+1
       801: 2q^2+q+1
       802: q^2+1
       803: q^2+1
       804: 1
       805: q^2+1
       806: q+1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: q^2+q+1
       814: q+1
       815: q+1
       817: q+1
       818: 1
       819: 1
       820: q^2+1
       821: 1
       822: q^2+1
       823: 1
       824: 1
       825: q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       834: q+1
       835: 1
       836: q^2+1
       837: q^2+1
       838: 1
       839: q^2+1
       840: 1
       841: q+1
       842: q+1
       843: q^2+q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q^2+q+1
       850: 1
       851: 1
       852: q+1
       853: q^2+q+1
       855: q+1
       856: 1
       857: 1
       858: 1
       862: q+1
       863: q+1
       864: 1
       865: 1
       866: 1
       867: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: q+1
       876: q+1
       879: q+1
       880: q+1
       881: q+1
       882: 1
       883: 1
       884: q+1
       885: q+1
       887: q+1
       888: q+1
       889: q+1
       890: q+1
       891: q+1
       892: 1
       893: q^2+q+1
       894: q+1
       895: q+1
       897: q+1
       898: 1
       899: 1
       900: q^2+1
       901: 1
       902: q^2+1
       903: 1
       904: 1
       905: q+1
       907: q+1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: q+1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: q^2+1
       940: 1
       941: 1
       943: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: q+1
       952: q+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q+1
       961: q+1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       969: q+1
       970: q+1
       971: q+1
       972: 1
       973: 1
       974: q+1
       975: q+1
       977: q^2+q+1
       978: q+1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: q^2+q+1
       984: q+1
       985: q+1
       987: q+1
       988: q+1
       989: q+1
       990: q+1
       991: q+1
       992: 1
       993: q^2+q+1
       994: q+1
       995: q+1
       997: q+1
       998: q+1
       999: q+1
      1000: q^2+q+1
      1001: q+1
      1002: q^2+q+1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: q+1
      1007: 1
      1008: q^2+1
      1009: q^2+1
      1010: 1
      1011: q^2+1
      1012: 1
      1013: q+1
      1015: q+1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: q+1
      1021: q+1
      1023: q+1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: q^2+1
      1030: 1
      1031: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q+1
      1042: q+1
      1043: 1
      1044: 1
      1045: q^2+1
      1046: 1
      1047: q^2+1
      1048: 1
      1049: 1
      1050: q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q+1
      1059: q+1
      1060: q^2+q+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q+1
      1068: 1
      1069: 1
      1072: q+1
      1073: 1
      1074: 1
      1075: 1
      1079: q+1
      1080: q+1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1087: q+1
      1088: q+1
      1089: 1
      1090: 1
      1091: 1
      1092: q+1
      1095: q+1
      1096: q+1
      1097: q+1
      1098: 1
      1099: 1
      1100: q+1
      1101: q+1
      1103: q+1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: q^2+1
      1110: 1
      1111: 1
      1114: q+1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1146: q+1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1156: q+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: q+1
      1167: 1
      1168: 1
      1169: 1
      1173: q+1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: q+1
      1181: q+1
      1182: q+1
      1183: q+1
      1184: 1
      1185: 1
      1186: q+1
      1187: q+1
      1190: q+1
      1191: q+1
      1192: q+1
      1193: 1
      1194: 1
      1195: q+1
      1196: q+1
      1198: q+1
      1199: q+1
      1200: q+1
      1201: q+1
      1202: q+1
      1203: 1
      1204: q^2+q+1
      1205: q+1
      1206: q+1
      1208: q+1
      1209: 1
      1210: 1
      1211: q^2+1
      1212: 1
      1213: q^2+1
      1214: 1
      1215: 1
      1216: q+1
      1218: q+1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: q+1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1244: q+1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: q^2+1
      1251: 1
      1252: 1
      1254: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q+1
      1263: q+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q+1
      1272: 1
      1276: 1
      1277: 1
      1280: q+1
      1281: 1
      1282: 1
      1283: 1
      1287: q+1
      1288: 1
      1289: 1
      1290: 1
      1294: q+1
      1295: q+1
      1296: 1
      1297: 1
      1298: 1
      1299: q+1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1312: 1
      1313: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1347: q+1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1359: 1
      1360: 1
      1363: q+1
      1364: 1
      1365: 1
      1366: 1
      1370: q+1
      1371: q+1
      1372: 1
      1373: 1
      1374: 1
      1375: q+1
      1378: q+1
      1379: q+1
      1380: 1
      1381: 1
      1382: 1
      1383: q+1
      1386: q+1
      1387: q+1
      1388: q+1
      1389: 1
      1390: 1
      1391: q+1
      1392: q+1
      1394: q+1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: q^2+1
      1401: 1
      1402: 1
      1405: q+1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1437: q+1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q+1
      1459: 1
      1463: 1
      1464: 1
      1468: 1
      1469: 1
      1472: q+1
      1473: 1
      1474: 1
      1475: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1514: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1526: 1
      1530: 1
      1531: 1
      1534: q+1
      1535: 1
      1536: 1
      1537: 1
      1541: q+1
      1542: 1
      1543: 1
      1544: 1
      1548: q+1
      1549: q+1
      1550: 1
      1551: 1
      1552: 1
      1553: q+1
      1556: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1566: 1
      1567: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1582: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1601: q+1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: 1
      1608: 1
      1609: 1
      1615: 1
      1618: 1
      1622: 1
      1623: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1635: 1
      1644: 1
      1645: 1
      1648: 1
      1655: 1
      1656: 1
      1660: 1
      1665: 1
      1669: 1
      1670: 1
      1674: 1
      1675: 1
      1678: q+1
      1679: 1
      1680: 1
      1681: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1693: 1
      1697: 1
      1698: 1
      1701: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1715: 1
      1716: 1
      1720: 1
      1723: 1
      1724: 1
      1725: 1
      1728: 1
      1729: 1
      1737: 1
      1741: 1
      1742: 1
      1751: 1
      1759: 1
      1769: 1
      1772: 1
      1776: 1
      1777: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1789: 1
      1798: 1
      1799: 1
      1802: 1
      1809: 1
      1810: 1
      1814: 1
      1821: 1
      1842: 1
      1846: 1
      1847: 1
      1856: 1
      1864: 1
      1885: 1

1886:    0: 2q^2+q+1
         1: 2q^2+q+1
         2: 2q^2+q+1
         3: 2q^2+q+1
         4: 2q^2+q+1
         5: 2q^2+q+1
         6: q^2+q+1
         7: 2q^2+q+1
         8: 2q^2+q+1
         9: 2q^2+q+1
        10: 2q^2+q+1
        11: 2q^2+q+1
        12: 2q^2+q+1
        13: 2q^2+q+1
        14: 2q^2+q+1
        15: 2q^2+q+1
        16: 2q^2+q+1
        17: 2q^2+q+1
        18: 2q^2+q+1
        19: 2q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: 2q^2+q+1
        23: 2q^2+q+1
        24: 2q^2+q+1
        25: q^2+q+1
        26: 2q^2+q+1
        27: 2q^2+q+1
        28: 2q^2+q+1
        29: 2q^2+q+1
        30: 2q^2+q+1
        31: 2q^2+q+1
        32: 2q^2+q+1
        33: q^2+q+1
        34: 2q^2+q+1
        35: 2q^2+q+1
        36: 2q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: 2q^2+q+1
        40: q^2+q+1
        41: 2q^2+q+1
        42: 2q^2+q+1
        43: 2q^2+q+1
        44: 2q^2+q+1
        45: 2q^2+q+1
        46: 2q^2+q+1
        47: 2q^2+q+1
        48: 2q^2+q+1
        49: 2q^2+q+1
        50: q^2+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: 2q^2+q+1
        55: 2q^2+q+1
        56: 2q^2+q+1
        57: q^2+q+1
        58: q^2+q+1
        59: 2q^2+q+1
        60: 2q^2+q+1
        61: 2q^2+q+1
        62: q^2+q+1
        63: 2q^2+q+1
        64: 2q^2+q+1
        65: q^2+q+1
        66: 2q^2+q+1
        67: 2q^2+q+1
        68: 2q^2+q+1
        69: 2q^2+q+1
        70: 2q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: 2q^2+q+1
        74: q^2+q+1
        75: 2q^2+q+1
        76: q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q+1
        81: 2q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: q^2+q+1
        85: q^2+q+1
        86: 2q^2+q+1
        87: 2q^2+q+1
        88: 2q^2+q+1
        89: q^2+q+1
        90: 2q^2+q+1
        91: 2q^2+q+1
        92: 2q^2+q+1
        93: 2q^2+q+1
        94: 2q^2+q+1
        95: 2q^2+q+1
        96: 2q^2+q+1
        97: q^2+q+1
        98: 2q^2+q+1
        99: 2q^2+q+1
       100: 2q^2+q+1
       101: q^2+q+1
       102: q^2+q+1
       103: 2q^2+q+1
       104: q^2+1
       105: q^2+1
       106: q^2+q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q^2+q+1
       110: 2q^2+q+1
       111: 2q^2+q+1
       112: q^2+1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: 2q^2+q+1
       117: 2q^2+q+1
       118: 2q^2+q+1
       119: q^2+q+1
       120: q^2+q+1
       121: 2q^2+q+1
       122: 2q^2+q+1
       123: 2q^2+q+1
       124: q^2+q+1
       125: q^2+q+1
       126: 2q^2+q+1
       127: q^2+q+1
       128: 2q^2+q+1
       129: q^2+q+1
       130: 2q^2+q+1
       131: 2q^2+q+1
       132: 2q^2+q+1
       133: q^2+q+1
       134: 1
       135: q^2+q+1
       136: q^2+q+1
       137: q+1
       138: q^2+q+1
       139: 2q^2+q+1
       140: q^2+q+1
       141: q+1
       142: q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q^2+q+1
       153: q+1
       154: q^2+q+1
       155: q^2+1
       156: q^2+q+1
       157: q^2+q+1
       158: q^2+q+1
       159: 2q^2+q+1
       160: 2q^2+q+1
       161: 2q^2+q+1
       162: q^2+q+1
       163: q^2+q+1
       164: 2q^2+q+1
       165: 2q^2+q+1
       166: 2q^2+q+1
       167: q^2+q+1
       168: 2q^2+q+1
       169: 2q^2+q+1
       170: q^2+q+1
       171: 2q^2+q+1
       172: 2q^2+q+1
       173: 2q^2+q+1
       174: 2q^2+q+1
       175: 2q^2+q+1
       176: q^2+q+1
       177: q^2+q+1
       178: 2q^2+q+1
       179: q^2+q+1
       180: 2q^2+q+1
       181: q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q^2+q+1
       185: q+1
       186: 2q^2+q+1
       187: q^2+q+1
       188: q^2+q+1
       189: q^2+1
       190: q^2+1
       191: q^2+1
       192: q^2+q+1
       193: q^2+q+1
       194: q^2+q+1
       195: q^2+q+1
       196: 2q^2+q+1
       197: q^2+q+1
       198: q^2+1
       199: q^2+1
       200: q^2+q+1
       201: q^2+q+1
       202: q^2+q+1
       203: q^2+q+1
       204: 2q^2+q+1
       205: 2q^2+q+1
       206: q^2+1
       207: q^2+q+1
       208: q^2+q+1
       209: q^2+q+1
       210: 2q^2+q+1
       211: 2q^2+q+1
       212: 2q^2+q+1
       213: 1
       214: q^2+q+1
       215: q^2+q+1
       216: q+1
       217: q^2+q+1
       218: 2q^2+q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: 2q^2+q+1
       223: q^2+q+1
       224: 2q^2+q+1
       225: q+1
       226: q^2+q+1
       227: q^2+q+1
       228: 1
       229: 1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: q+1
       234: q^2+q+1
       235: q^2+q+1
       236: 1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q+1
       249: q+1
       250: q^2+q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q^2+q+1
       257: q+1
       258: q^2+1
       259: q^2+1
       260: q^2+q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q^2+q+1
       264: 2q^2+q+1
       265: 2q^2+q+1
       266: q^2+1
       267: q^2+q+1
       268: q^2+q+1
       269: q^2+q+1
       270: 2q^2+q+1
       271: 2q^2+q+1
       272: 2q^2+q+1
       273: q^2+q+1
       274: q^2+q+1
       275: 2q^2+q+1
       276: 2q^2+q+1
       277: 2q^2+q+1
       278: q^2+q+1
       279: q^2+q+1
       280: 2q^2+q+1
       281: q^2+q+1
       282: 2q^2+q+1
       283: q^2+q+1
       284: 2q^2+q+1
       285: 2q^2+q+1
       286: 2q^2+q+1
       287: q^2+q+1
       288: 1
       289: q^2+q+1
       290: q^2+q+1
       291: q+1
       292: q^2+q+1
       293: 2q^2+q+1
       294: q^2+q+1
       295: q+1
       296: q+1
       297: q^2+q+1
       298: q+1
       299: q^2+q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q^2+q+1
       305: q^2+q+1
       306: q^2+q+1
       307: q+1
       308: q^2+q+1
       310: q^2+1
       311: q^2+1
       312: q^2+1
       313: q^2+q+1
       314: 1
       315: q^2+q+1
       316: q^2+q+1
       317: q+1
       318: q^2+q+1
       319: q^2+1
       320: q^2+1
       321: q^2+1
       322: q^2+q+1
       323: q^2+q+1
       324: q^2+q+1
       325: q^2+q+1
       326: 2q^2+q+1
       327: q^2+q+1
       328: q^2+1
       329: q^2+1
       330: q^2+q+1
       331: q^2+q+1
       332: q^2+q+1
       333: q^2+q+1
       334: 2q^2+q+1
       335: 2q^2+q+1
       336: 1
       337: 1
       338: q^2+q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+q+1
       343: q^2+q+1
       344: 1
       345: q^2+q+1
       346: q^2+q+1
       347: q+1
       348: q^2+q+1
       349: 2q^2+q+1
       350: q^2+q+1
       351: q+1
       352: q+1
       353: q^2+q+1
       354: q+1
       355: q^2+q+1
       356: 1
       357: 1
       358: 1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q^2+q+1
       364: q+1
       365: 1
       366: 1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: 1
       374: q+1
       375: q+1
       376: 1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q^2+1
       396: q^2+1
       397: q^2+1
       398: q^2+q+1
       399: q^2+q+1
       400: q^2+q+1
       401: q^2+q+1
       402: 2q^2+q+1
       403: q^2+q+1
       404: q^2+1
       405: q^2+1
       406: q^2+q+1
       407: q^2+q+1
       408: q^2+q+1
       409: q^2+q+1
       410: 2q^2+q+1
       411: 2q^2+q+1
       412: q^2+1
       413: q^2+q+1
       414: q^2+q+1
       415: q^2+q+1
       416: 2q^2+q+1
       417: 2q^2+q+1
       418: 2q^2+q+1
       419: 1
       420: q^2+q+1
       421: q^2+q+1
       422: q+1
       423: q^2+q+1
       424: 2q^2+q+1
       425: q^2+q+1
       426: q^2+q+1
       427: q^2+q+1
       428: 2q^2+q+1
       429: q^2+q+1
       430: 2q^2+q+1
       431: q+1
       432: q^2+q+1
       433: q^2+q+1
       434: 1
       435: 1
       436: q^2+q+1
       437: q+1
       438: q+1
       439: q+1
       440: q^2+q+1
       441: q^2+q+1
       442: 1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q^2+q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: q+1
       455: q+1
       456: q^2+q+1
       457: q+1
       458: q^2+q+1
       459: q+1
       460: q+1
       461: q+1
       462: q^2+q+1
       463: q+1
       466: q^2+1
       467: q^2+1
       468: 1
       469: 1
       470: q^2+q+1
       471: q+1
       472: q+1
       474: q^2+1
       475: q^2+1
       476: q^2+1
       477: q^2+q+1
       478: 1
       479: q^2+q+1
       480: q^2+q+1
       481: q+1
       482: q^2+q+1
       483: q^2+1
       484: q^2+1
       485: q^2+1
       486: q^2+q+1
       487: q^2+q+1
       488: q^2+q+1
       489: q^2+q+1
       490: 2q^2+q+1
       491: q^2+q+1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q^2+q+1
       500: q+1
       501: 1
       502: 1
       503: q^2+q+1
       504: q+1
       505: q+1
       506: q+1
       507: q^2+q+1
       508: q^2+q+1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q^2+q+1
       515: q+1
       517: 1
       518: 1
       519: 1
       520: q+1
       521: 1
       522: q+1
       523: q+1
       524: q+1
       525: q+1
       526: 1
       527: 1
       528: 1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: 1
       537: q+1
       538: 1
       539: 1
       540: 1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: 1
       552: q+1
       553: q+1
       554: 1
       555: q+1
       556: q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       564: q^2+1
       565: q^2+1
       566: q^2+1
       567: q^2+q+1
       568: 1
       569: q^2+q+1
       570: q^2+q+1
       571: q+1
       572: q^2+q+1
       573: q^2+1
       574: q^2+1
       575: q^2+1
       576: q^2+q+1
       577: q^2+q+1
       578: q^2+q+1
       579: q^2+q+1
       580: 2q^2+q+1
       581: q^2+q+1
       582: q^2+1
       583: q^2+1
       584: q^2+q+1
       585: q^2+q+1
       586: q^2+q+1
       587: q^2+q+1
       588: 2q^2+q+1
       589: 2q^2+q+1
       590: 1
       591: 1
       592: q^2+q+1
       593: q+1
       594: q+1
       595: q+1
       596: q^2+q+1
       597: q^2+q+1
       598: 1
       599: q^2+q+1
       600: q^2+q+1
       601: q+1
       602: q^2+q+1
       603: 2q^2+q+1
       604: q^2+q+1
       605: q+1
       606: q+1
       607: q^2+q+1
       608: q+1
       609: q^2+q+1
       610: 1
       611: 1
       612: 1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q^2+q+1
       618: q+1
       619: 1
       620: 1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: 1
       628: q+1
       629: q+1
       630: 1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q^2+q+1
       640: q+1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       651: q^2+1
       652: 1
       653: 1
       654: 1
       655: q+1
       656: q+1
       659: q^2+1
       660: q^2+1
       661: 1
       662: 1
       663: q^2+q+1
       664: q+1
       665: q+1
       667: q^2+1
       668: q^2+1
       669: q^2+1
       670: q^2+q+1
       671: 1
       672: q^2+q+1
       673: q^2+q+1
       674: q+1
       675: q^2+q+1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q^2+q+1
       694: q+1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       705: 1
       706: 1
       707: 1
       708: 1
       709: q+1
       710: q+1
       711: q+1
       713: 1
       714: 1
       715: 1
       716: q+1
       717: 1
       718: q+1
       719: q+1
       720: 1
       721: q+1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q+1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: q+1
       740: 1
       741: 1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: q+1
       750: q+1
       751: 1
       752: q+1
       753: q+1
       754: q+1
       757: q^2+1
       758: q^2+1
       759: 1
       760: 1
       761: q^2+q+1
       762: q+1
       763: q+1
       765: q^2+1
       766: q^2+1
       767: q^2+1
       768: q^2+q+1
       769: 1
       770: q^2+q+1
       771: q^2+q+1
       772: q+1
       773: q^2+q+1
       774: q^2+1
       775: q^2+1
       776: q^2+1
       777: q^2+q+1
       778: q^2+q+1
       779: q^2+q+1
       780: q^2+q+1
       781: 2q^2+q+1
       782: q^2+q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: q^2+q+1
       791: q+1
       792: 1
       793: 1
       794: q^2+q+1
       795: q+1
       796: q+1
       797: q+1
       798: q^2+q+1
       799: q^2+q+1
       800: 1
       801: q+1
       802: q+1
       803: q+1
       804: q+1
       805: q^2+q+1
       806: q+1
       808: 1
       809: 1
       810: 1
       811: q+1
       812: 1
       813: q+1
       814: q+1
       815: q+1
       816: q+1
       817: 1
       818: 1
       819: 1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: 1
       828: q+1
       829: 1
       830: 1
       831: 1
       832: q+1
       833: q+1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       842: 1
       843: q+1
       844: q+1
       845: 1
       846: q+1
       847: q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: q+1
       857: 1
       858: 1
       859: 1
       860: q+1
       863: q^2+1
       864: 1
       865: 1
       866: 1
       867: q+1
       868: q+1
       871: q^2+1
       872: q^2+1
       873: 1
       874: 1
       875: q^2+q+1
       876: q+1
       877: q+1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: q+1
       886: q+1
       888: 1
       889: 1
       890: 1
       891: q+1
       892: 1
       893: q+1
       894: q+1
       895: q+1
       896: q+1
       897: 1
       898: 1
       899: 1
       900: q+1
       901: q+1
       902: q+1
       903: q+1
       904: q+1
       905: q+1
       908: 1
       909: 1
       910: 1
       911: 1
       912: q+1
       913: q+1
       916: 1
       917: 1
       918: 1
       919: 1
       920: q+1
       921: 1
       922: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: q+1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: q+1
       952: 1
       953: 1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: q+1
       959: q+1
       962: q^2+1
       963: 1
       964: 1
       965: 1
       966: q+1
       967: q+1
       970: q^2+1
       971: q^2+1
       972: 1
       973: 1
       974: q^2+q+1
       975: q+1
       976: q+1
       978: q^2+1
       979: q^2+1
       980: q^2+1
       981: q^2+q+1
       982: 1
       983: q^2+q+1
       984: q^2+q+1
       985: q+1
       986: q^2+q+1
       988: 1
       989: 1
       990: 1
       991: q+1
       992: 1
       993: q+1
       994: q+1
       995: q+1
       996: q+1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: q+1
      1002: q+1
      1003: q+1
      1004: q^2+q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: q+1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: q+1
      1021: q+1
      1022: q+1
      1024: 1
      1025: 1
      1026: 1
      1027: q+1
      1028: 1
      1029: q+1
      1030: q+1
      1031: 1
      1032: q+1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: q+1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: q+1
      1050: q+1
      1051: 1
      1052: 1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: 1
      1060: q+1
      1061: q+1
      1062: 1
      1063: q+1
      1064: q+1
      1065: q+1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: q+1
      1080: q^2+1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: q+1
      1093: q+1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: q+1
      1101: q+1
      1102: q+1
      1104: 1
      1105: 1
      1106: 1
      1107: q+1
      1108: 1
      1109: q+1
      1110: q+1
      1111: 1
      1112: q+1
      1116: 1
      1117: 1
      1118: 1
      1119: q+1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1144: 1
      1145: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: q+1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: q+1
      1164: q+1
      1168: 1
      1169: 1
      1170: 1
      1171: q+1
      1174: q^2+1
      1175: 1
      1176: 1
      1177: 1
      1178: q+1
      1179: q+1
      1182: q^2+1
      1183: q^2+1
      1184: 1
      1185: 1
      1186: q^2+q+1
      1187: q+1
      1188: q+1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: q+1
      1196: q+1
      1197: q+1
      1199: 1
      1200: 1
      1201: 1
      1202: q+1
      1203: 1
      1204: q+1
      1205: q+1
      1206: q+1
      1207: q+1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: q+1
      1213: q+1
      1214: q+1
      1215: q+1
      1216: q+1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1224: q+1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: q+1
      1232: 1
      1233: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: q+1
      1245: 1
      1246: 1
      1247: 1
      1248: q+1
      1249: 1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: q+1
      1263: 1
      1264: 1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: q+1
      1270: q+1
      1273: 1
      1277: 1
      1278: 1
      1282: 1
      1283: 1
      1284: 1
      1285: q+1
      1289: 1
      1290: 1
      1291: 1
      1292: q+1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: q+1
      1300: q+1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: q+1
      1308: 1
      1309: 1
      1313: 1
      1314: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1324: 1
      1328: 1
      1329: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1356: q+1
      1360: 1
      1361: 1
      1365: 1
      1366: 1
      1367: 1
      1368: q+1
      1371: q^2+1
      1372: 1
      1373: 1
      1374: 1
      1375: q+1
      1376: q+1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: q+1
      1384: q+1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: q+1
      1392: q+1
      1393: q+1
      1395: 1
      1396: 1
      1397: 1
      1398: q+1
      1399: 1
      1400: q+1
      1401: q+1
      1402: 1
      1403: q+1
      1407: 1
      1408: 1
      1409: 1
      1410: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: q+1
      1435: 1
      1436: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1446: q+1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q+1
      1455: q+1
      1460: 1
      1464: 1
      1465: 1
      1469: 1
      1470: 1
      1474: 1
      1475: 1
      1476: 1
      1477: q+1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1488: 1
      1492: 1
      1493: 1
      1500: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1510: 1
      1514: 1
      1515: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1527: 1
      1531: 1
      1532: 1
      1536: 1
      1537: 1
      1538: 1
      1539: q+1
      1543: 1
      1544: 1
      1545: 1
      1546: q+1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: q+1
      1554: q+1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: q+1
      1562: 1
      1563: 1
      1567: 1
      1568: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1578: 1
      1582: 1
      1583: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1600: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: 1
      1608: 1
      1609: 1
      1610: q+1
      1616: 1
      1619: 1
      1623: 1
      1624: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1636: 1
      1645: 1
      1646: 1
      1653: 1
      1656: 1
      1660: 1
      1661: 1
      1666: 1
      1670: 1
      1671: 1
      1675: 1
      1676: 1
      1680: 1
      1681: 1
      1682: 1
      1683: q+1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1694: 1
      1698: 1
      1699: 1
      1706: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1716: 1
      1720: 1
      1721: 1
      1724: 1
      1725: 1
      1728: 1
      1729: 1
      1730: 1
      1738: 1
      1742: 1
      1743: 1
      1752: 1
      1764: 1
      1770: 1
      1773: 1
      1777: 1
      1778: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1790: 1
      1799: 1
      1800: 1
      1807: 1
      1810: 1
      1814: 1
      1815: 1
      1822: 1
      1843: 1
      1847: 1
      1848: 1
      1857: 1
      1869: 1
      1886: 1

1887:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
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        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q+1
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        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q+1
        51: q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
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        63: q+1
        64: q+1
        65: q+1
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        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q+1
        75: q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q+1
        88: q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q^2+q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: 1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q+1
       160: q+1
       161: q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q+1
       180: q+1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q+1
       201: q^2+q+1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: 1
       214: q+1
       215: q+1
       216: q+1
       217: 1
       218: q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: q^2+q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: 1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q^2+q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q+1
       293: q+1
       294: q+1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: 1
       314: 1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: 1
       338: q+1
       339: q+1
       340: 1
       341: q+1
       342: 1
       343: 1
       344: 1
       345: 1
       346: q+1
       347: q+1
       348: 1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: 1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q^2+q+1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: q+1
       374: 1
       375: q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       380: 1
       381: q+1
       382: q+1
       383: q+1
       384: 1
       385: q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q^2+q+1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       419: 1
       420: q+1
       421: q+1
       422: q+1
       423: 1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q^2+q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q+1
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: 1
       478: 1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: 1
       495: q+1
       496: 1
       497: q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: 1
       504: q+1
       505: 1
       506: 1
       507: 1
       508: 1
       509: 1
       510: 1
       511: q+1
       512: q+1
       513: 1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: 1
       521: 1
       522: q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q+1
       546: q+1
       547: 1
       548: q+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: q+1
       554: q+1
       555: 1
       556: 1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: 1
       568: 1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: q+1
       596: 1
       597: 1
       598: 1
       599: 1
       600: q+1
       601: q+1
       602: 1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q^2+q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q+1
       628: 1
       629: q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       634: 1
       635: q+1
       636: q+1
       637: q+1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: 1
       661: 1
       662: 1
       663: 1
       664: q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q+1
       670: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       681: 1
       682: q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: 1
       698: q+1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: q+1
       706: 1
       707: 1
       708: 1
       709: 1
       710: q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       716: 1
       717: 1
       718: q+1
       719: q+1
       720: q+1
       721: q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q+1
       735: 1
       736: q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: q+1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: q+1
       751: q+1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q+1
       768: 1
       769: 1
       770: q+1
       771: q+1
       772: q+1
       773: q+1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: q+1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: q+1
       803: q+1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: 1
       812: 1
       813: q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: 1
       842: 1
       843: 1
       844: q+1
       845: q+1
       846: 1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: 1
       854: q+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: q+1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       875: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: q+1
       914: q+1
       915: q+1
       916: q+1
       917: 1
       918: 1
       919: 1
       920: 1
       921: q+1
       922: q+1
       923: 1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       938: 1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: q+1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: q+1
       968: q+1
       969: q+1
       970: q+1
       971: 1
       972: 1
       973: 1
       974: 1
       975: q+1
       976: q+1
       977: 1
       978: 1
       979: 1
       980: q+1
       981: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: q+1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 1
      1028: 1
      1029: q+1
      1030: q+1
      1031: q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: q+1
      1062: q+1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: q+1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: q+1
      1121: q+1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: q+1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: q+1
      1173: q+1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: q+1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: q+1
      1225: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: q+1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: q+1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1404: q+1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: q+1
      1412: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: q+1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1467: 1
      1471: 1
      1478: 1
      1479: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1503: 1
      1506: 1
      1508: 1
      1509: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1562: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: q+1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1625: 1
      1632: 1
      1633: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1643: 1
      1647: 1
      1654: 1
      1655: 1
      1661: 1
      1662: 1
      1663: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1673: 1
      1677: 1
      1684: 1
      1685: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1706: 1
      1707: 1
      1709: 1
      1712: 1
      1714: 1
      1715: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1729: 1
      1730: 1
      1731: 1
      1744: 1
      1745: 1
      1746: 1
      1758: 1
      1765: 1
      1766: 1
      1767: 1
      1779: 1
      1786: 1
      1787: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1797: 1
      1801: 1
      1808: 1
      1809: 1
      1815: 1
      1823: 1
      1836: 1
      1849: 1
      1850: 1
      1851: 1
      1863: 1
      1887: 1

1888:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: 2q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: 2q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: 2q^2+2q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: 2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: q^2+2q+1
        52: 2q^2+2q+1
        53: q^2+2q+1
        54: 2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: 2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: 2q^2+2q+1
        74: 2q^2+2q+1
        75: q^2+2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: 2q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: 2q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: 2q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: 2q^2+2q+1
       106: q^2+2q+1
       107: q^2+2q+1
       108: q^2+2q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: q^2+2q+1
       113: 2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: 2q+1
       118: 2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q+1
       124: 2q+1
       125: 2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: 2q^2+2q+1
       135: q^2+2q+1
       136: 2q^2+2q+1
       137: q^2+2q+1
       138: 2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: 2q^2+2q+1
       156: q^2+2q+1
       157: 2q^2+2q+1
       158: q^2+2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q+1
       171: 2q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: 2q^2+2q+1
       178: 2q^2+2q+1
       179: 2q^2+2q+1
       180: q^2+2q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: 2q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: q^2+2q+1
       192: 2q+1
       193: q^2+2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: q^2+2q+1
       200: 2q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: q^2+2q+1
       207: q+1
       208: q^2+2q+1
       209: q^2+q+1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: 2q^2+2q+1
       230: q^2+2q+1
       231: q^2+2q+1
       232: q^2+2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q^2+2q+1
       237: 2q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: q^2+2q+1
       241: 2q+1
       242: 2q+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q^2+2q+1
       259: 2q^2+2q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: q^2+2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: q^2+2q+1
       267: 2q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q^2+2q+1
       271: 2q+1
       272: 2q+1
       273: q^2+2q+1
       274: q^2+2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q+1
       278: 2q+1
       279: 2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: 2q^2+2q+1
       289: q^2+2q+1
       290: 2q^2+2q+1
       291: q^2+2q+1
       292: 2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q^2+2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       309: q+1
       310: q^2+2q+1
       311: 2q+1
       312: q^2+2q+1
       313: q+1
       314: 2q+1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: q^2+2q+1
       322: 2q+1
       323: q^2+2q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       328: q+1
       329: q^2+2q+1
       330: q+1
       331: q^2+q+1
       332: q^2+q+1
       333: q+1
       334: q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: q+1
       346: 2q+1
       347: 1
       348: 2q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: q^2+2q+1
       357: q^2+2q+1
       358: q^2+2q+1
       359: 2q+1
       360: q^2+2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: q^2+2q+1
       367: 2q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: q^2+2q+1
       374: q+1
       375: q^2+2q+1
       376: q^2+q+1
       377: q^2+2q+1
       378: q+1
       379: q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: 2q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: q^2+2q+1
       398: 2q+1
       399: q^2+2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: q^2+2q+1
       406: 2q+1
       407: q^2+2q+1
       408: q^2+2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: q^2+2q+1
       413: q+1
       414: q^2+2q+1
       415: q^2+q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       429: 2q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q^2+2q+1
       435: 2q^2+2q+1
       436: q^2+2q+1
       437: q^2+2q+1
       438: q^2+2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q^2+2q+1
       443: 2q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: q^2+2q+1
       447: 2q+1
       448: 2q+1
       449: q^2+2q+1
       450: q^2+2q+1
       451: q^2+2q+1
       452: q^2+2q+1
       453: q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: q+1
       466: 2q+1
       467: q+1
       468: 2q+1
       469: 2q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: 2q+1
       475: 2q+1
       476: q^2+2q+1
       477: q+1
       478: 2q+1
       479: 2q+1
       480: 2q+1
       481: 1
       482: q+1
       483: q+1
       484: q+1
       485: q^2+q+1
       486: q+1
       487: q^2+q+1
       488: q+1
       489: q+1
       490: q+1
       491: 1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: q+1
       502: 2q+1
       503: q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: q+1
       510: 1
       511: q+1
       512: 1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: q^2+2q+1
       520: q+1
       521: 2q+1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: q^2+2q+1
       529: 2q+1
       530: q^2+2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: q+1
       536: q^2+2q+1
       537: q+1
       538: q^2+q+1
       539: q^2+q+1
       540: q+1
       541: q+1
       542: q+1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: q+1
       553: 2q+1
       554: 1
       555: 2q+1
       556: q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: q^2+2q+1
       567: q+1
       568: 2q+1
       569: 2q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: q^2+2q+1
       576: 2q+1
       577: q^2+2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: q+1
       583: q^2+2q+1
       584: q+1
       585: q^2+q+1
       586: q^2+q+1
       587: q+1
       588: q+1
       589: q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: q+1
       594: q+1
       595: q+1
       596: 2q+1
       597: 2q+1
       598: 2q+1
       599: q+1
       600: 2q+1
       601: 1
       602: 2q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q^2+2q+1
       611: q^2+2q+1
       612: q^2+2q+1
       613: 2q+1
       614: q^2+2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: q^2+2q+1
       621: 2q+1
       622: q^2+2q+1
       623: q^2+2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: q^2+2q+1
       628: q+1
       629: q^2+2q+1
       630: q^2+q+1
       631: q^2+2q+1
       632: q+1
       633: q+1
       634: 2q+1
       635: 2q+1
       636: 2q+1
       637: q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: q+1
       652: 2q+1
       653: q+1
       654: q+1
       655: 1
       656: q+1
       657: q+1
       658: 1
       659: 2q+1
       660: q+1
       661: 2q+1
       662: 2q+1
       663: q+1
       664: 1
       665: 1
       666: 1
       667: q+1
       668: q+1
       669: q^2+q+1
       670: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: 1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: 2q+1
       706: q+1
       707: 2q+1
       708: 2q+1
       709: q+1
       710: q+1
       711: q+1
       712: q+1
       713: 2q+1
       714: 2q+1
       715: q^2+2q+1
       716: q+1
       717: 2q+1
       718: 2q+1
       719: 2q+1
       720: 1
       721: q+1
       722: q+1
       723: q+1
       724: q^2+q+1
       725: q+1
       726: q^2+q+1
       727: q+1
       728: q+1
       729: q+1
       730: 1
       731: 2q+1
       732: 2q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: q+1
       741: 2q+1
       742: q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: q+1
       749: 1
       750: q+1
       751: 1
       752: q+1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: 2q+1
       758: q+1
       759: 2q+1
       760: 2q+1
       761: q+1
       762: q+1
       763: q+1
       764: q+1
       765: 2q+1
       766: 2q+1
       767: q^2+2q+1
       768: q+1
       769: 2q+1
       770: 2q+1
       771: 2q+1
       772: 1
       773: q+1
       774: q+1
       775: q+1
       776: q^2+q+1
       777: q+1
       778: q^2+q+1
       779: q+1
       780: q+1
       781: q+1
       782: 1
       783: 2q+1
       784: 2q+1
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: 2q+1
       791: q+1
       792: q+1
       793: 2q+1
       794: q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: q+1
       801: 1
       802: q+1
       803: 1
       804: q+1
       805: 1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: q^2+2q+1
       811: q+1
       812: 2q+1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: 2q+1
       818: 2q+1
       819: q^2+2q+1
       820: 2q+1
       821: q^2+2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: q+1
       827: q^2+2q+1
       828: q+1
       829: q^2+q+1
       830: q^2+q+1
       831: q+1
       832: q+1
       833: q+1
       834: 2q+1
       835: 2q+1
       836: 2q+1
       837: q+1
       838: q+1
       839: q+1
       840: 2q+1
       841: 2q+1
       842: 2q+1
       843: q+1
       844: 2q+1
       845: 1
       846: 2q+1
       847: q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       854: q+1
       855: 1
       856: q+1
       857: q+1
       858: 1
       859: q+1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: 2q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: 1
       870: 1
       871: q+1
       872: q+1
       873: q+1
       874: q+1
       875: q+1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: q+1
       882: q+1
       883: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: q+1
       909: 2q+1
       910: q+1
       911: q+1
       912: 1
       913: q+1
       914: q+1
       915: 1
       916: 2q+1
       917: q+1
       918: 2q+1
       919: 2q+1
       920: q+1
       921: 1
       922: 1
       923: 1
       924: q+1
       925: q+1
       926: q^2+q+1
       927: q+1
       928: q+1
       929: q+1
       930: q+1
       931: 1
       932: 1
       933: q+1
       934: 2q+1
       935: q+1
       936: q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: q+1
       963: 2q+1
       964: q+1
       965: q+1
       966: 1
       967: q+1
       968: q+1
       969: 1
       970: 2q+1
       971: q+1
       972: 2q+1
       973: 2q+1
       974: q+1
       975: 1
       976: 1
       977: 1
       978: q+1
       979: q+1
       980: q^2+q+1
       981: q+1
       982: q+1
       983: q+1
       984: q+1
       985: 1
       986: 1
       987: q+1
       988: 2q+1
       989: q+1
       990: q+1
       992: q+1
       993: q+1
       994: q+1
       995: 1
       996: q+1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 2q+1
      1017: q+1
      1018: 2q+1
      1019: 2q+1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: 2q+1
      1025: 2q+1
      1026: q^2+2q+1
      1027: q+1
      1028: 2q+1
      1029: 2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: q+1
      1034: q+1
      1035: q^2+q+1
      1036: q+1
      1037: q^2+q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: 1
      1042: 2q+1
      1043: 2q+1
      1044: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1051: q+1
      1052: 2q+1
      1053: q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: q+1
      1060: 1
      1061: q+1
      1062: 1
      1063: q+1
      1064: 1
      1065: 1
      1066: 1
      1067: q+1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1089: q+1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1108: 1
      1109: 1
      1110: 1
      1112: 1
      1113: q+1
      1114: 1
      1115: q+1
      1116: q+1
      1117: 1
      1118: q+1
      1119: 1
      1120: 1
      1121: 1
      1122: q+1
      1123: 2q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: q+1
      1131: q+1
      1132: q+1
      1133: q+1
      1134: q+1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: q+1
      1141: q+1
      1142: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: 1
      1167: q+1
      1168: q+1
      1169: 1
      1170: q+1
      1171: 1
      1172: 1
      1173: 1
      1174: q+1
      1175: 2q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: q+1
      1183: q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: q+1
      1190: 1
      1191: q+1
      1193: q+1
      1194: q+1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1219: q+1
      1220: 2q+1
      1221: q+1
      1222: q+1
      1223: 1
      1224: q+1
      1225: q+1
      1226: 1
      1227: 2q+1
      1228: q+1
      1229: 2q+1
      1230: 2q+1
      1231: q+1
      1232: 1
      1233: 1
      1234: 1
      1235: q+1
      1236: q+1
      1237: q^2+q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: 1
      1244: q+1
      1245: 2q+1
      1246: q+1
      1247: q+1
      1249: q+1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: q+1
      1255: q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1303: 1
      1305: 1
      1306: 1
      1310: 1
      1311: q+1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: q+1
      1325: q+1
      1326: q+1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1333: q+1
      1335: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1352: 1
      1353: 1
      1354: 1
      1356: 1
      1357: 1
      1358: q+1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1380: q+1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1403: 1
      1404: q+1
      1405: 1
      1406: q+1
      1407: q+1
      1408: 1
      1409: q+1
      1410: 1
      1411: 1
      1412: 1
      1413: q+1
      1414: 2q+1
      1415: q+1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: q+1
      1422: q+1
      1423: q+1
      1424: q+1
      1425: q+1
      1426: 1
      1427: 1
      1428: q+1
      1429: 1
      1430: q+1
      1432: q+1
      1433: q+1
      1435: 1
      1436: 1
      1437: 1
      1438: q+1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1481: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: q+1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1503: 1
      1506: 1
      1508: 1
      1509: 1
      1511: 1
      1513: 1
      1515: 1
      1516: 1
      1518: 1
      1520: 1
      1521: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1557: 1
      1559: 1
      1560: 1
      1564: 1
      1565: q+1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: q+1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: q+1
      1579: q+1
      1580: q+1
      1581: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1587: q+1
      1589: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1606: 1
      1607: 1
      1608: 1
      1610: 1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1621: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1643: 1
      1647: 1
      1649: 1
      1652: 1
      1657: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1687: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: q+1
      1704: 1
      1705: 1
      1706: 1
      1707: 1
      1709: 1
      1712: 1
      1714: 1
      1715: 1
      1717: 1
      1719: 1
      1721: 1
      1722: 1
      1724: 1
      1726: 1
      1727: 1
      1732: 1
      1745: 1
      1747: 1
      1748: 1
      1749: 1
      1754: 1
      1766: 1
      1768: 1
      1769: 1
      1770: 1
      1775: 1
      1786: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1792: 1
      1793: 1
      1794: 1
      1795: 1
      1797: 1
      1801: 1
      1803: 1
      1806: 1
      1811: 1
      1824: 1
      1837: 1
      1850: 1
      1852: 1
      1853: 1
      1854: 1
      1859: 1
      1888: 1

1889:    0: q^3+2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: 2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^2+2q+1
        13: 2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: 2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: 2q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^3+2q^2+2q+1
        28: 2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: 2q^2+2q+1
        37: q^3+2q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: 2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: 2q^2+2q+1
        51: q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 2q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^3+2q^2+2q+1
        61: q^2+2q+1
        62: 2q^2+2q+1
        63: q^2+2q+1
        64: q^3+2q^2+2q+1
        65: q^2+2q+1
        66: 2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: 2q^2+2q+1
        74: q^3+2q^2+2q+1
        75: q^2+2q+1
        76: 2q^2+2q+1
        77: q^2+2q+1
        78: q^3+2q^2+2q+1
        79: 2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^2+2q+1
        89: 2q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: 2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+2q^2+2q+1
       100: 2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^2+2q+1
       104: q+1
       105: 2q^2+2q+1
       106: q+1
       107: 2q^2+2q+1
       108: 2q^2+2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 2q^2+2q+1
       113: q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: q^2+2q+1
       117: 2q+1
       118: q^2+2q+1
       119: 2q^2+2q+1
       120: q^2+2q+1
       121: q^2+2q+1
       122: q^3+2q^2+2q+1
       123: q+1
       124: q^2+2q+1
       125: 2q+1
       126: 2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^2+2q+1
       130: 2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+2q+1
       135: q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: 2q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 2q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^3+2q^2+2q+1
       145: q^2+2q+1
       146: 2q^2+2q+1
       147: q^2+2q+1
       148: q^3+2q^2+2q+1
       149: q^2+2q+1
       150: 2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q^2+2q+1
       156: q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^3+2q^2+2q+1
       166: q^2+2q+1
       167: 2q^2+2q+1
       168: q^2+2q+1
       169: q^3+2q^2+2q+1
       170: q^2+2q+1
       171: 2q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: 2q^2+2q+1
       178: 2q^2+2q+1
       179: q^3+2q^2+2q+1
       180: q^2+2q+1
       181: 2q^2+2q+1
       182: q^2+2q+1
       183: q^3+2q^2+2q+1
       184: 2q^2+2q+1
       185: q^3+2q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: 2q^2+2q+1
       192: q+1
       193: 2q^2+2q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: q+1
       199: q^2+2q+1
       200: q+1
       201: q^2+2q+1
       202: q^2+2q+1
       203: 2q+1
       204: 2q+1
       205: q^2+2q+1
       206: 2q^2+2q+1
       207: 1
       208: q^2+2q+1
       209: q^2+2q+1
       210: q^2+2q+1
       211: q+1
       212: q+1
       213: q^2+2q+1
       214: q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: 2q+1
       222: 2q+1
       223: q^2+2q+1
       224: q+1
       225: q^2+2q+1
       226: q+1
       227: q^2+2q+1
       228: q+1
       229: 2q^2+2q+1
       230: q+1
       231: 2q^2+2q+1
       232: 2q^2+2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q^2+2q+1
       237: q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: q^2+2q+1
       241: 2q+1
       242: q^2+2q+1
       243: 2q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: q^3+2q^2+2q+1
       247: q+1
       248: q^2+2q+1
       249: 2q+1
       250: 2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^2+2q+1
       254: 2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q+1
       259: 2q^2+2q+1
       260: q+1
       261: 2q^2+2q+1
       262: 2q^2+2q+1
       263: q^2+2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q^2+2q+1
       267: q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: q^2+2q+1
       271: 2q+1
       272: q^2+2q+1
       273: 2q^2+2q+1
       274: q^2+2q+1
       275: q^2+2q+1
       276: q^3+2q^2+2q+1
       277: q+1
       278: q^2+2q+1
       279: 2q+1
       280: 2q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: q^2+2q+1
       284: 2q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q^2+2q+1
       289: q+1
       290: 2q^2+2q+1
       291: 2q^2+2q+1
       292: 2q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q^3+2q^2+2q+1
       299: q^2+2q+1
       300: 2q^2+2q+1
       301: q^2+2q+1
       302: q^3+2q^2+2q+1
       303: q^2+2q+1
       304: 2q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q+1
       312: 2q^2+2q+1
       313: 1
       314: q^2+2q+1
       315: q+1
       316: q^2+2q+1
       317: q^2+2q+1
       318: q+1
       319: q+1
       320: q+1
       321: q^2+2q+1
       322: q+1
       323: q^2+2q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: q^2+2q+1
       328: 1
       329: q^2+2q+1
       330: 1
       331: q^2+2q+1
       332: q^2+2q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: 2q+1
       338: q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q^2+2q+1
       344: q^2+2q+1
       345: 1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: q+1
       350: q+1
       351: q^2+2q+1
       352: q+1
       353: q+1
       354: q^2+2q+1
       355: q+1
       356: q+1
       357: q+1
       358: 2q^2+2q+1
       359: q+1
       360: 2q^2+2q+1
       361: q^2+2q+1
       362: q^2+2q+1
       363: q^2+2q+1
       364: q^2+2q+1
       365: q+1
       366: q^2+2q+1
       367: q+1
       368: q^2+2q+1
       369: q^2+2q+1
       370: 2q+1
       371: 2q+1
       372: q^2+2q+1
       373: 2q^2+2q+1
       374: 1
       375: q^2+2q+1
       376: q^2+2q+1
       377: q^2+2q+1
       378: q+1
       379: q+1
       380: q^2+2q+1
       381: q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: q^2+2q+1
       387: q^2+2q+1
       388: 2q+1
       389: 2q+1
       390: q^2+2q+1
       391: q+1
       392: q^2+2q+1
       393: q+1
       394: q^2+2q+1
       395: q+1
       396: q+1
       397: 2q^2+2q+1
       398: q+1
       399: 2q^2+2q+1
       400: q^2+2q+1
       401: q^2+2q+1
       402: q^2+2q+1
       403: q^2+2q+1
       404: q+1
       405: q^2+2q+1
       406: q+1
       407: q^2+2q+1
       408: q^2+2q+1
       409: 2q+1
       410: 2q+1
       411: q^2+2q+1
       412: 2q^2+2q+1
       413: 1
       414: q^2+2q+1
       415: q^2+2q+1
       416: q^2+2q+1
       417: q+1
       418: q+1
       419: q^2+2q+1
       420: q+1
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: q^2+2q+1
       426: q^2+2q+1
       427: 2q+1
       428: 2q+1
       429: q^2+2q+1
       430: q+1
       431: q^2+2q+1
       432: q+1
       433: q^2+2q+1
       434: q+1
       435: 2q^2+2q+1
       436: q+1
       437: 2q^2+2q+1
       438: 2q^2+2q+1
       439: q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q^2+2q+1
       443: q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: q^2+2q+1
       447: 2q+1
       448: q^2+2q+1
       449: 2q^2+2q+1
       450: q^2+2q+1
       451: q^2+2q+1
       452: q^3+2q^2+2q+1
       453: q+1
       454: q^2+2q+1
       455: 2q+1
       456: 2q+1
       457: q^2+2q+1
       458: q^2+2q+1
       459: q^2+2q+1
       460: 2q+1
       461: q^2+2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: q+1
       467: 1
       468: q+1
       469: q^2+2q+1
       470: 1
       471: q^2+2q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q^2+2q+1
       477: 1
       478: 2q+1
       479: q+1
       480: 2q+1
       481: 2q+1
       482: q+1
       483: 1
       484: 1
       485: q^2+2q+1
       486: 1
       487: q^2+2q+1
       488: q+1
       489: q+1
       490: q+1
       491: q+1
       492: q+1
       493: q+1
       494: 2q+1
       495: q+1
       496: 2q+1
       497: 2q+1
       498: 2q+1
       499: 2q+1
       500: q^2+2q+1
       501: 1
       502: 2q+1
       503: 1
       504: 2q+1
       505: 2q+1
       506: q+1
       507: q+1
       508: q+1
       509: q^2+2q+1
       510: 1
       511: q+1
       512: q+1
       513: q+1
       514: 1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: 2q^2+2q+1
       520: 1
       521: q^2+2q+1
       522: q+1
       523: q^2+2q+1
       524: q^2+2q+1
       525: q+1
       526: q+1
       527: q+1
       528: q^2+2q+1
       529: q+1
       530: q^2+2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q^2+2q+1
       535: 1
       536: q^2+2q+1
       537: 1
       538: q^2+2q+1
       539: q^2+2q+1
       540: q+1
       541: q+1
       542: q+1
       543: q+1
       544: 2q+1
       545: q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q^2+2q+1
       551: q^2+2q+1
       552: 1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: q+1
       557: q+1
       558: q^2+2q+1
       559: q+1
       560: q+1
       561: q^2+2q+1
       562: q+1
       563: q+1
       564: q+1
       565: q+1
       566: 2q^2+2q+1
       567: 1
       568: q^2+2q+1
       569: q+1
       570: q^2+2q+1
       571: q^2+2q+1
       572: q+1
       573: q+1
       574: q+1
       575: q^2+2q+1
       576: q+1
       577: q^2+2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q^2+2q+1
       582: 1
       583: q^2+2q+1
       584: 1
       585: q^2+2q+1
       586: q^2+2q+1
       587: q+1
       588: q+1
       589: q+1
       590: q+1
       591: 2q+1
       592: q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q^2+2q+1
       598: q^2+2q+1
       599: 1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: q+1
       604: q+1
       605: q^2+2q+1
       606: q+1
       607: q+1
       608: q^2+2q+1
       609: q+1
       610: q+1
       611: q+1
       612: 2q^2+2q+1
       613: q+1
       614: 2q^2+2q+1
       615: q^2+2q+1
       616: q^2+2q+1
       617: q^2+2q+1
       618: q^2+2q+1
       619: q+1
       620: q^2+2q+1
       621: q+1
       622: q^2+2q+1
       623: q^2+2q+1
       624: 2q+1
       625: 2q+1
       626: q^2+2q+1
       627: 2q^2+2q+1
       628: 1
       629: q^2+2q+1
       630: q^2+2q+1
       631: q^2+2q+1
       632: q+1
       633: q+1
       634: q^2+2q+1
       635: q+1
       636: 2q+1
       637: 2q+1
       638: 2q+1
       639: 2q+1
       640: q^2+2q+1
       641: q^2+2q+1
       642: 2q+1
       643: 2q+1
       644: q^2+2q+1
       645: q+1
       646: q^2+2q+1
       647: q+1
       648: q^2+2q+1
       650: q+1
       651: 1
       652: q+1
       653: 1
       654: q^2+2q+1
       655: 1
       656: q+1
       658: q+1
       659: q+1
       660: 1
       661: q+1
       662: 2q+1
       663: 1
       664: 2q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q^2+2q+1
       670: 1
       671: q+1
       672: 1
       673: q+1
       674: q+1
       675: 1
       676: q+1
       677: q+1
       678: q+1
       679: 2q+1
       681: 2q+1
       682: q+1
       683: 2q+1
       684: 2q+1
       685: q+1
       686: 1
       687: 1
       688: 2q+1
       689: 1
       690: 2q+1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       702: q+1
       704: q+1
       705: q+1
       706: 1
       707: q+1
       708: q^2+2q+1
       709: 1
       710: q^2+2q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q^2+2q+1
       716: 1
       717: 2q+1
       718: q+1
       719: 2q+1
       720: 2q+1
       721: q+1
       722: 1
       723: 1
       724: q^2+2q+1
       725: 1
       726: q^2+2q+1
       727: q+1
       728: q+1
       729: q+1
       730: q+1
       731: q+1
       732: q+1
       733: 2q+1
       734: q+1
       735: 2q+1
       736: 2q+1
       737: 2q+1
       738: 2q+1
       739: q^2+2q+1
       740: 1
       741: 2q+1
       742: 1
       743: 2q+1
       744: 2q+1
       745: q+1
       746: q+1
       747: q+1
       748: q^2+2q+1
       749: 1
       750: q+1
       751: q+1
       752: q+1
       753: 1
       754: q+1
       756: q+1
       757: q+1
       758: 1
       759: q+1
       760: q^2+2q+1
       761: 1
       762: q^2+2q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q^2+2q+1
       768: 1
       769: 2q+1
       770: q+1
       771: 2q+1
       772: 2q+1
       773: q+1
       774: 1
       775: 1
       776: q^2+2q+1
       777: 1
       778: q^2+2q+1
       779: q+1
       780: q+1
       781: q+1
       782: q+1
       783: q+1
       784: q+1
       785: 2q+1
       786: q+1
       787: 2q+1
       788: 2q+1
       789: 2q+1
       790: 2q+1
       791: q^2+2q+1
       792: 1
       793: 2q+1
       794: 1
       795: 2q+1
       796: 2q+1
       797: q+1
       798: q+1
       799: q+1
       800: q^2+2q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: q+1
       807: q+1
       808: q+1
       809: q+1
       810: 2q^2+2q+1
       811: 1
       812: q^2+2q+1
       813: q+1
       814: q^2+2q+1
       815: q^2+2q+1
       816: q+1
       817: q+1
       818: q+1
       819: q^2+2q+1
       820: q+1
       821: q^2+2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q^2+2q+1
       826: 1
       827: q^2+2q+1
       828: 1
       829: q^2+2q+1
       830: q^2+2q+1
       831: q+1
       832: q+1
       833: q+1
       834: q+1
       835: 2q+1
       836: q+1
       837: 2q+1
       838: 2q+1
       839: 2q+1
       840: 2q+1
       841: q^2+2q+1
       842: q^2+2q+1
       843: 1
       844: 2q+1
       845: 2q+1
       846: 2q+1
       847: q+1
       848: q+1
       849: q^2+2q+1
       850: q+1
       851: q+1
       852: q^2+2q+1
       853: q+1
       855: 1
       856: q+1
       857: 1
       858: 1
       859: q+1
       860: 1
       862: q+1
       863: 1
       864: q+1
       865: 1
       866: 2q+1
       867: 1
       868: q+1
       870: 1
       871: 1
       872: 1
       873: 1
       874: q+1
       875: 1
       876: q+1
       877: 1
       879: q+1
       880: q+1
       882: q+1
       883: 2q+1
       885: 2q+1
       886: q+1
       887: 1
       888: 1
       889: 1
       890: 2q+1
       892: q+1
       893: 1
       894: q+1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: 1
       903: 1
       904: 1
       905: q+1
       907: q+1
       908: 1
       909: q+1
       910: 1
       911: q^2+2q+1
       912: 1
       913: q+1
       915: q+1
       916: q+1
       917: 1
       918: q+1
       919: 2q+1
       920: 1
       921: 2q+1
       922: q+1
       923: 1
       924: 1
       925: 1
       926: q^2+2q+1
       927: 1
       928: q+1
       929: 1
       930: q+1
       931: q+1
       932: 1
       933: q+1
       934: q+1
       935: q+1
       936: 2q+1
       938: 2q+1
       939: q+1
       940: 2q+1
       941: 2q+1
       942: q+1
       943: 1
       944: 1
       945: 2q+1
       946: 1
       947: 2q+1
       948: q+1
       949: q+1
       950: q+1
       951: q+1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       959: q+1
       961: q+1
       962: 1
       963: q+1
       964: 1
       965: q^2+2q+1
       966: 1
       967: q+1
       969: q+1
       970: q+1
       971: 1
       972: q+1
       973: 2q+1
       974: 1
       975: 2q+1
       976: q+1
       977: 1
       978: 1
       979: 1
       980: q^2+2q+1
       981: 1
       982: q+1
       983: 1
       984: q+1
       985: q+1
       986: 1
       987: q+1
       988: q+1
       989: q+1
       990: 2q+1
       992: 2q+1
       993: q+1
       994: 2q+1
       995: 2q+1
       996: q+1
       997: 1
       998: 1
       999: 2q+1
      1000: 1
      1001: 2q+1
      1002: q+1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: q+1
      1015: q+1
      1016: q+1
      1017: 1
      1018: q+1
      1019: q^2+2q+1
      1020: 1
      1021: q^2+2q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q^2+2q+1
      1027: 1
      1028: 2q+1
      1029: q+1
      1030: 2q+1
      1031: 2q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q^2+2q+1
      1036: 1
      1037: q^2+2q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: q+1
      1042: q+1
      1043: q+1
      1044: 2q+1
      1045: q+1
      1046: 2q+1
      1047: 2q+1
      1048: 2q+1
      1049: 2q+1
      1050: q^2+2q+1
      1051: 1
      1052: 2q+1
      1053: 1
      1054: 2q+1
      1055: 2q+1
      1056: q+1
      1057: q+1
      1058: q+1
      1059: q^2+2q+1
      1060: 1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: 1
      1065: q+1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1076: q+1
      1077: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: q+1
      1084: 1
      1085: 1
      1087: q+1
      1089: q+1
      1091: 2q+1
      1093: q+1
      1095: 1
      1096: 1
      1098: 1
      1099: q+1
      1101: q+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: q+1
      1116: 1
      1117: 1
      1118: q+1
      1119: 1
      1121: q+1
      1122: 1
      1123: q+1
      1124: 1
      1125: 2q+1
      1126: 1
      1127: q+1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: q+1
      1134: 1
      1135: q+1
      1136: 1
      1138: q+1
      1139: q+1
      1141: q+1
      1142: 2q+1
      1144: 2q+1
      1145: q+1
      1146: 1
      1147: 1
      1148: 1
      1149: 2q+1
      1151: q+1
      1152: 1
      1153: q+1
      1154: q+1
      1155: 1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: 1
      1162: 1
      1163: 1
      1164: q+1
      1166: 1
      1167: q+1
      1168: 1
      1169: 1
      1170: q+1
      1171: 1
      1173: q+1
      1174: 1
      1175: q+1
      1176: 1
      1177: 2q+1
      1178: 1
      1179: q+1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: q+1
      1186: 1
      1187: q+1
      1188: 1
      1190: q+1
      1191: q+1
      1193: q+1
      1194: 2q+1
      1196: 2q+1
      1197: q+1
      1198: 1
      1199: 1
      1200: 1
      1201: 2q+1
      1203: q+1
      1204: 1
      1205: q+1
      1206: q+1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1212: q+1
      1213: 1
      1214: 1
      1215: 1
      1216: q+1
      1218: q+1
      1219: 1
      1220: q+1
      1221: 1
      1222: q^2+2q+1
      1223: 1
      1224: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1229: q+1
      1230: 2q+1
      1231: 1
      1232: 2q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: 1
      1237: q^2+2q+1
      1238: 1
      1239: q+1
      1240: 1
      1241: q+1
      1242: q+1
      1243: 1
      1244: q+1
      1245: q+1
      1246: q+1
      1247: 2q+1
      1249: 2q+1
      1250: q+1
      1251: 2q+1
      1252: 2q+1
      1253: q+1
      1254: 1
      1255: 1
      1256: 2q+1
      1257: 1
      1258: 2q+1
      1259: q+1
      1260: q+1
      1261: q+1
      1262: q+1
      1263: 1
      1264: q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1270: q+1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1288: q+1
      1291: q+1
      1294: 1
      1296: 1
      1298: q+1
      1300: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: q+1
      1318: 1
      1319: 1
      1320: q+1
      1321: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: q+1
      1328: 1
      1329: 1
      1331: q+1
      1333: q+1
      1335: 2q+1
      1337: q+1
      1339: 1
      1340: 1
      1342: 1
      1343: q+1
      1345: q+1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: q+1
      1365: 1
      1366: 1
      1367: q+1
      1368: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: q+1
      1375: 1
      1376: 1
      1378: q+1
      1380: q+1
      1382: 2q+1
      1384: q+1
      1386: 1
      1387: 1
      1389: 1
      1390: q+1
      1392: q+1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: q+1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1405: 1
      1406: q+1
      1407: 1
      1408: 1
      1409: q+1
      1410: 1
      1412: q+1
      1413: 1
      1414: q+1
      1415: 1
      1416: 2q+1
      1417: 1
      1418: q+1
      1420: 1
      1421: 1
      1422: 1
      1423: 1
      1424: q+1
      1425: 1
      1426: q+1
      1427: 1
      1429: q+1
      1430: q+1
      1432: q+1
      1433: 2q+1
      1435: 2q+1
      1436: q+1
      1437: 1
      1438: 1
      1439: 1
      1440: 2q+1
      1442: q+1
      1443: 1
      1444: q+1
      1445: q+1
      1446: 1
      1447: 1
      1448: 1
      1449: q+1
      1450: 1
      1451: q+1
      1452: 1
      1453: 1
      1454: 1
      1455: q+1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1473: 1
      1476: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1492: 1
      1493: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1503: q+1
      1506: q+1
      1509: 1
      1511: 1
      1513: q+1
      1515: 1
      1517: 1
      1518: 1
      1520: 1
      1521: 1
      1523: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1531: 1
      1532: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1542: q+1
      1545: q+1
      1548: 1
      1550: 1
      1552: q+1
      1554: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: q+1
      1572: 1
      1573: 1
      1574: q+1
      1575: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: q+1
      1582: 1
      1583: 1
      1585: q+1
      1587: q+1
      1589: 2q+1
      1591: q+1
      1593: 1
      1594: 1
      1596: 1
      1597: q+1
      1599: q+1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: q+1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1613: 1
      1615: 1
      1616: 1
      1627: 1
      1630: 1
      1633: 1
      1635: 1
      1636: 1
      1639: 1
      1640: 1
      1641: 1
      1649: 1
      1652: 1
      1655: 1
      1657: 1
      1659: 1
      1661: 1
      1663: 1
      1665: 1
      1666: 1
      1669: 1
      1670: 1
      1671: 1
      1679: 1
      1682: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1693: 1
      1694: 1
      1697: 1
      1698: 1
      1699: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1709: q+1
      1712: q+1
      1715: 1
      1717: 1
      1719: q+1
      1721: 1
      1723: 1
      1724: 1
      1726: 1
      1727: 1
      1729: 1
      1730: 1
      1733: 1
      1746: 1
      1748: 1
      1749: 1
      1760: 1
      1763: 1
      1767: 1
      1769: 1
      1770: 1
      1781: 1
      1784: 1
      1787: 1
      1789: 1
      1790: 1
      1793: 1
      1794: 1
      1795: 1
      1803: 1
      1806: 1
      1809: 1
      1811: 1
      1813: 1
      1815: 1
      1825: 1
      1838: 1
      1851: 1
      1853: 1
      1854: 1
      1865: 1
      1868: 1
      1889: 1

1890:    0: 2q^2+2q+1
         1: 2q^2+2q+1
         2: 2q^2+2q+1
         3: 2q^2+2q+1
         4: 2q^2+2q+1
         5: 2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: 2q^2+2q+1
        13: 2q^2+2q+1
        14: 2q^2+2q+1
        15: 2q^2+2q+1
        16: 2q^2+2q+1
        17: 2q^2+2q+1
        18: 2q^2+2q+1
        19: 2q^2+2q+1
        20: 2q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: q^2+2q+1
        24: 2q^2+2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^2+2q+1
        29: 2q+1
        30: 2q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: 2q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: 2q^2+2q+1
        47: 2q^2+2q+1
        48: 2q^2+2q+1
        49: 2q^2+2q+1
        50: q^2+2q+1
        51: 2q^2+2q+1
        52: 2q^2+2q+1
        53: q^2+2q+1
        54: q^2+2q+1
        55: 2q^2+2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: 2q+1
        61: q^2+2q+1
        62: 2q+1
        63: 2q+1
        64: 2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        75: 2q^2+2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^2+2q+1
        80: 2q+1
        81: 2q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: 2q^2+2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^2+2q+1
        93: 2q+1
        94: 2q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: 2q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: 2q^2+2q+1
       107: q^2+2q+1
       108: 2q+1
       109: q^2+2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 2q+1
       113: q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: 2q+1
       117: q^2+2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^2+2q+1
       129: 2q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: 2q^2+2q+1
       136: 2q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: 2q+1
       145: q^2+2q+1
       146: 2q+1
       147: 2q+1
       148: 2q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: 2q^2+2q+1
       157: 2q^2+2q+1
       158: q^2+2q+1
       159: q^2+2q+1
       160: 2q^2+2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: 2q+1
       166: q^2+2q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: 2q^2+2q+1
       178: 2q^2+2q+1
       179: q^2+2q+1
       180: 2q^2+2q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^2+2q+1
       185: 2q+1
       186: 2q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: 2q+1
       192: q^2+2q+1
       193: 2q+1
       194: q^2+2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: 2q+1
       203: q^2+2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: q+1
       214: q^2+2q+1
       215: q^2+2q+1
       216: q^2+q+1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: 2q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 2q^2+2q+1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: q^2+2q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: 2q+1
       241: q^2+2q+1
       242: 2q+1
       243: 2q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q+1
       252: q^2+2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: 2q^2+2q+1
       261: q^2+2q+1
       262: 2q+1
       263: q^2+2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: q^2+2q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: 2q+1
       271: q^2+2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: q^2+2q+1
       279: q^2+2q+1
       280: q^2+2q+1
       281: q+1
       282: q^2+2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: 2q^2+2q+1
       290: 2q^2+2q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q^2+2q+1
       295: q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: 2q+1
       299: q^2+2q+1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       309: q+1
       310: q^2+2q+1
       311: 2q+1
       312: 2q+1
       313: 2q+1
       314: q+1
       315: q^2+2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: q^2+2q+1
       323: 2q+1
       324: q^2+2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: q+1
       337: q+1
       338: q^2+2q+1
       339: q^2+q+1
       340: q+1
       341: q^2+q+1
       342: q+1
       343: q+1
       344: q+1
       345: 2q+1
       346: 2q+1
       347: 1
       348: q+1
       349: 2q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q+1
       359: q^2+2q+1
       360: 2q+1
       361: q^2+2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: q+1
       381: q^2+2q+1
       382: q^2+2q+1
       383: q^2+q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: q+1
       391: 2q+1
       392: q+1
       393: q+1
       394: q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q+1
       398: q^2+2q+1
       399: 2q+1
       400: q^2+2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: q^2+2q+1
       407: q^2+2q+1
       408: 2q+1
       409: q^2+2q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: q+1
       420: q^2+2q+1
       421: q^2+2q+1
       422: q^2+q+1
       423: q+1
       424: q^2+2q+1
       425: q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       429: q+1
       430: 2q+1
       431: q+1
       432: q+1
       433: q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: 2q^2+2q+1
       437: q^2+2q+1
       438: 2q+1
       439: q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: q^2+2q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: 2q+1
       447: q^2+2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: q^2+2q+1
       455: q^2+2q+1
       456: q^2+2q+1
       457: q+1
       458: q^2+2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: q+1
       466: 2q+1
       467: 2q+1
       468: q+1
       469: q+1
       470: 2q+1
       471: q+1
       472: q+1
       473: q+1
       474: 2q+1
       475: 2q+1
       476: 2q+1
       477: 2q+1
       478: q+1
       479: q^2+2q+1
       480: 2q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: q+1
       493: q+1
       494: q+1
       495: q^2+q+1
       496: q+1
       497: q^2+q+1
       498: q+1
       499: q+1
       500: 1
       501: q+1
       502: q+1
       503: 2q+1
       504: 1
       505: 1
       506: 1
       507: q+1
       508: q+1
       509: 1
       510: q+1
       511: q+1
       512: 1
       513: 1
       514: q+1
       515: 1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: 2q+1
       521: q+1
       522: q^2+2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: 2q+1
       529: q^2+2q+1
       530: 2q+1
       531: q^2+2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: q+1
       539: q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: q+1
       544: q+1
       545: q^2+2q+1
       546: q^2+q+1
       547: q+1
       548: q^2+q+1
       549: q+1
       550: q+1
       551: q+1
       552: 2q+1
       553: 2q+1
       554: 1
       555: q+1
       556: 2q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       568: q+1
       569: q^2+2q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: q^2+2q+1
       577: 2q+1
       578: q^2+2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: q+1
       591: q+1
       592: q^2+2q+1
       593: q^2+q+1
       594: q+1
       595: q^2+q+1
       596: q+1
       597: q+1
       598: q+1
       599: 2q+1
       600: 2q+1
       601: 1
       602: q+1
       603: 2q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: 2q+1
       613: q^2+2q+1
       614: 2q+1
       615: q^2+2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: q^2+2q+1
       622: q^2+2q+1
       623: 2q+1
       624: q^2+2q+1
       625: 2q+1
       626: 2q+1
       627: 2q+1
       628: 2q+1
       629: 2q+1
       630: q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: q+1
       635: q^2+2q+1
       636: q^2+2q+1
       637: q^2+q+1
       638: q+1
       639: q^2+2q+1
       640: q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: q+1
       645: 2q+1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: 2q+1
       652: q+1
       653: q+1
       654: 1
       655: q+1
       656: q+1
       657: q+1
       658: 1
       659: 2q+1
       660: 2q+1
       661: q+1
       662: q+1
       663: 2q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: q+1
       669: q+1
       670: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       676: 1
       677: q+1
       678: q+1
       679: q+1
       680: q+1
       681: q+1
       682: q^2+q+1
       683: q+1
       684: 1
       685: 1
       686: q+1
       687: q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q+1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: 2q+1
       706: 2q+1
       707: q+1
       708: q+1
       709: 2q+1
       710: q+1
       711: q+1
       712: q+1
       713: 2q+1
       714: 2q+1
       715: 2q+1
       716: 2q+1
       717: q+1
       718: q^2+2q+1
       719: 2q+1
       720: 1
       721: q+1
       722: 2q+1
       723: 2q+1
       724: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       731: q+1
       732: q+1
       733: q+1
       734: q^2+q+1
       735: q+1
       736: q^2+q+1
       737: q+1
       738: q+1
       739: 1
       740: q+1
       741: q+1
       742: 2q+1
       743: 1
       744: 1
       745: 1
       746: q+1
       747: q+1
       748: 1
       749: q+1
       750: q+1
       751: 1
       752: 1
       753: q+1
       754: 1
       755: q+1
       756: q+1
       757: 2q+1
       758: 2q+1
       759: q+1
       760: q+1
       761: 2q+1
       762: q+1
       763: q+1
       764: q+1
       765: 2q+1
       766: 2q+1
       767: 2q+1
       768: 2q+1
       769: q+1
       770: q^2+2q+1
       771: 2q+1
       772: 1
       773: q+1
       774: 2q+1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: q+1
       784: q+1
       785: q+1
       786: q^2+q+1
       787: q+1
       788: q^2+q+1
       789: q+1
       790: q+1
       791: 1
       792: q+1
       793: q+1
       794: 2q+1
       795: 1
       796: 1
       797: 1
       798: q+1
       799: q+1
       800: 1
       801: q+1
       802: q+1
       803: 1
       804: 1
       805: q+1
       806: 1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: 2q+1
       811: 2q+1
       812: q+1
       813: q^2+2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: 2q+1
       818: 2q+1
       819: 2q+1
       820: q^2+2q+1
       821: 2q+1
       822: q^2+2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: 2q+1
       827: 2q+1
       828: 2q+1
       829: q+1
       830: q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       834: q+1
       835: q+1
       836: q^2+2q+1
       837: q^2+q+1
       838: q+1
       839: q^2+q+1
       840: q+1
       841: q+1
       842: q+1
       843: 2q+1
       844: 2q+1
       845: 1
       846: q+1
       847: 2q+1
       848: q+1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       854: q+1
       855: q+1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: q+1
       861: 1
       862: 1
       863: 2q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: q+1
       870: 1
       871: q+1
       872: q+1
       875: q+1
       876: 1
       877: 1
       878: 1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       885: 1
       886: 1
       887: 1
       888: q+1
       889: 1
       890: 1
       891: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: 2q+1
       909: q+1
       910: q+1
       911: 1
       912: q+1
       913: q+1
       914: q+1
       915: 1
       916: 2q+1
       917: 2q+1
       918: q+1
       919: q+1
       920: 2q+1
       921: 1
       922: 1
       923: q+1
       924: 2q+1
       925: q+1
       926: q+1
       927: q+1
       929: q+1
       930: q+1
       931: 1
       932: q+1
       933: 1
       934: q+1
       935: q+1
       936: q+1
       937: q+1
       938: q+1
       939: q^2+q+1
       940: q+1
       941: 1
       942: 1
       943: q+1
       944: q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q+1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: 2q+1
       963: q+1
       964: q+1
       965: 1
       966: q+1
       967: q+1
       968: q+1
       969: 1
       970: 2q+1
       971: 2q+1
       972: q+1
       973: q+1
       974: 2q+1
       975: 1
       976: 1
       977: q+1
       978: 2q+1
       979: q+1
       980: q+1
       981: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       987: 1
       988: q+1
       989: q+1
       990: q+1
       991: q+1
       992: q+1
       993: q^2+q+1
       994: q+1
       995: 1
       996: 1
       997: q+1
       998: q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q+1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 2q+1
      1017: 2q+1
      1018: q+1
      1019: q+1
      1020: 2q+1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: 2q+1
      1025: 2q+1
      1026: 2q+1
      1027: 2q+1
      1028: q+1
      1029: q^2+2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: 2q+1
      1034: 2q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1042: q+1
      1043: q+1
      1044: q+1
      1045: q^2+q+1
      1046: q+1
      1047: q^2+q+1
      1048: q+1
      1049: q+1
      1050: 1
      1051: q+1
      1052: q+1
      1053: 2q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q+1
      1058: q+1
      1059: 1
      1060: q+1
      1061: q+1
      1062: 1
      1063: 1
      1064: q+1
      1065: 1
      1066: q+1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: 1
      1110: 1
      1112: 1
      1113: q+1
      1114: q+1
      1115: 1
      1116: q+1
      1117: 1
      1118: 1
      1119: q+1
      1120: 1
      1121: 1
      1122: 2q+1
      1123: q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1128: q+1
      1129: 1
      1130: q+1
      1131: q+1
      1134: q+1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: q+1
      1140: q+1
      1141: q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: 1
      1146: 1
      1147: q+1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: q+1
      1167: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: q+1
      1172: 1
      1173: 1
      1174: 2q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1180: q+1
      1181: 1
      1182: q+1
      1183: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: q+1
      1192: q+1
      1193: q+1
      1194: q+1
      1195: q+1
      1196: 1
      1197: 1
      1198: 1
      1199: q+1
      1200: 1
      1201: 1
      1202: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1219: 2q+1
      1220: q+1
      1221: q+1
      1222: 1
      1223: q+1
      1224: q+1
      1225: q+1
      1226: 1
      1227: 2q+1
      1228: 2q+1
      1229: q+1
      1230: q+1
      1231: 2q+1
      1232: 1
      1233: 1
      1234: q+1
      1235: 2q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: q+1
      1244: 1
      1245: q+1
      1246: q+1
      1247: q+1
      1248: q+1
      1249: q+1
      1250: q^2+q+1
      1251: q+1
      1252: 1
      1253: 1
      1254: q+1
      1255: q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q+1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1303: 1
      1304: 1
      1307: 1
      1310: q+1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: q+1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1356: 1
      1357: q+1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1379: q+1
      1380: q+1
      1381: q+1
      1382: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: 1
      1401: 1
      1403: 1
      1404: q+1
      1405: q+1
      1406: 1
      1407: q+1
      1408: 1
      1409: 1
      1410: q+1
      1411: 1
      1412: 1
      1413: 2q+1
      1414: q+1
      1415: q+1
      1416: 1
      1417: 1
      1418: 1
      1419: q+1
      1420: 1
      1421: q+1
      1422: q+1
      1425: q+1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1430: q+1
      1431: q+1
      1432: q+1
      1433: q+1
      1434: q+1
      1435: 1
      1436: 1
      1437: 1
      1438: q+1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1477: 1
      1480: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1518: 1
      1519: 1
      1522: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1541: 1
      1542: 1
      1543: q+1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1553: 1
      1554: 1
      1555: 1
      1557: 1
      1558: 1
      1561: 1
      1564: q+1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: q+1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: q+1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1586: q+1
      1587: q+1
      1588: q+1
      1589: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: 1
      1608: 1
      1610: 1
      1612: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1653: 1
      1656: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1683: 1
      1686: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1706: 1
      1707: 1
      1708: 1
      1709: 1
      1710: q+1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1715: 1
      1716: 1
      1720: 1
      1721: 1
      1722: 1
      1724: 1
      1725: 1
      1728: 1
      1734: 1
      1745: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1766: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1786: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1796: 1
      1797: 1
      1798: 1
      1799: 1
      1800: 1
      1801: 1
      1802: 1
      1807: 1
      1810: 1
      1826: 1
      1839: 1
      1850: 1
      1855: 1
      1856: 1
      1857: 1
      1858: 1
      1890: 1

1891:    0: q^3+2q^2+2q+1
         1: 2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: 2q^2+2q+1
         7: 2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: 2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^2+2q+1
        12: q^3+2q^2+2q+1
        13: 2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: 2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: 2q^2+2q+1
        21: 2q^2+2q+1
        22: 2q^2+2q+1
        23: q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q^2+2q+1
        26: q^2+2q+1
        27: q^3+2q^2+2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: 2q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^2+2q+1
        33: 2q^2+2q+1
        34: 2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: 2q^2+2q+1
        37: q^3+2q^2+2q+1
        38: q^2+2q+1
        39: q^3+2q^2+2q+1
        40: 2q^2+2q+1
        41: 2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: 2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^2+2q+1
        46: q^3+2q^2+2q+1
        47: 2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q+1
        51: 2q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: q^2+2q+1
        55: 2q^2+2q+1
        56: q^2+2q+1
        57: 2q^2+2q+1
        58: q^2+2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^3+2q^2+2q+1
        62: q^2+2q+1
        63: 2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: q^2+2q+1
        67: q^3+2q^2+2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: 2q^2+2q+1
        73: 2q^2+2q+1
        74: q^2+2q+1
        75: q^3+2q^2+2q+1
        76: 2q^2+2q+1
        77: q^2+2q+1
        78: q^3+2q^2+2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: 2q^2+2q+1
        82: q^3+2q^2+2q+1
        83: q^2+2q+1
        84: 2q^2+2q+1
        85: 2q^2+2q+1
        86: 2q^2+2q+1
        87: q^2+2q+1
        88: q^3+2q^2+2q+1
        89: 2q^2+2q+1
        90: q^2+2q+1
        91: q^3+2q^2+2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: 2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: q^2+2q+1
        97: 2q^2+2q+1
        98: 2q^2+2q+1
        99: q^3+2q^2+2q+1
       100: 2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^2+2q+1
       103: q^3+2q^2+2q+1
       104: q+1
       105: q+1
       106: 2q^2+2q+1
       107: 2q^2+2q+1
       108: q^2+2q+1
       109: 2q^2+2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: q+1
       113: 2q^2+2q+1
       114: q^2+2q+1
       115: q^2+2q+1
       116: 2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       120: 2q+1
       121: 2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 2q^2+2q+1
       125: q^2+2q+1
       126: q^2+2q+1
       127: q+1
       128: q^3+2q^2+2q+1
       129: q^2+2q+1
       130: 2q+1
       131: q^2+2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: q+1
       135: 2q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: q^2+2q+1
       139: 2q^2+2q+1
       140: q^2+2q+1
       141: 2q^2+2q+1
       142: q^2+2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q^3+2q^2+2q+1
       146: q^2+2q+1
       147: 2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: q^2+2q+1
       151: q^3+2q^2+2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: q+1
       156: 2q^2+2q+1
       157: 2q^2+2q+1
       158: 2q^2+2q+1
       159: q^2+2q+1
       160: 2q^2+2q+1
       161: q^2+2q+1
       162: 2q^2+2q+1
       163: q^2+2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^3+2q^2+2q+1
       167: q^2+2q+1
       168: 2q+1
       169: q^2+2q+1
       170: 2q^2+2q+1
       171: q^2+2q+1
       172: q^3+2q^2+2q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: 2q^2+2q+1
       178: 2q^2+2q+1
       179: q^2+2q+1
       180: q^3+2q^2+2q+1
       181: 2q^2+2q+1
       182: q^2+2q+1
       183: q^3+2q^2+2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: 2q^2+2q+1
       187: q^3+2q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: q+1
       191: q+1
       192: 2q^2+2q+1
       193: q^2+2q+1
       194: 2q^2+2q+1
       195: q^2+2q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: q+1
       199: q+1
       200: q^2+2q+1
       201: q^2+2q+1
       202: 2q+1
       203: q^2+2q+1
       204: 2q+1
       205: q^2+2q+1
       206: q+1
       207: q^2+2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: q^2+2q+1
       213: 1
       214: 2q^2+2q+1
       215: q^2+2q+1
       216: q^2+2q+1
       217: q+1
       218: q^2+2q+1
       219: q+1
       220: q^2+2q+1
       221: 2q+1
       222: 2q+1
       223: q+1
       224: q^2+2q+1
       225: q^2+2q+1
       226: q+1
       227: q^2+2q+1
       228: q+1
       229: q+1
       230: 2q^2+2q+1
       231: 2q^2+2q+1
       232: q^2+2q+1
       233: 2q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: q+1
       237: 2q^2+2q+1
       238: q^2+2q+1
       239: q^2+2q+1
       240: 2q+1
       241: q^2+2q+1
       242: q^2+2q+1
       243: q^2+2q+1
       244: 2q+1
       245: 2q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: 2q^2+2q+1
       249: q^2+2q+1
       250: q^2+2q+1
       251: q+1
       252: q^3+2q^2+2q+1
       253: q^2+2q+1
       254: 2q+1
       255: q^2+2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: q+1
       259: q+1
       260: 2q^2+2q+1
       261: 2q^2+2q+1
       262: q^2+2q+1
       263: 2q^2+2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: q+1
       267: 2q^2+2q+1
       268: q^2+2q+1
       269: q^2+2q+1
       270: 2q+1
       271: q^2+2q+1
       272: q^2+2q+1
       273: q^2+2q+1
       274: 2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 2q^2+2q+1
       279: q^2+2q+1
       280: q^2+2q+1
       281: q+1
       282: q^3+2q^2+2q+1
       283: q^2+2q+1
       284: 2q+1
       285: q^2+2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: q+1
       289: 2q^2+2q+1
       290: 2q^2+2q+1
       291: 2q^2+2q+1
       292: q^2+2q+1
       293: 2q^2+2q+1
       294: q^2+2q+1
       295: 2q^2+2q+1
       296: q^2+2q+1
       297: q^2+2q+1
       298: q^2+2q+1
       299: q^3+2q^2+2q+1
       300: q^2+2q+1
       301: 2q+1
       302: q^2+2q+1
       303: 2q^2+2q+1
       304: q^2+2q+1
       305: q^3+2q^2+2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: q^2+2q+1
       314: 1
       315: 2q^2+2q+1
       316: q^2+2q+1
       317: q^2+2q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q^2+2q+1
       323: 2q+1
       324: q^2+2q+1
       325: 2q+1
       326: 2q+1
       327: q^2+2q+1
       328: q+1
       329: q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q^2+2q+1
       336: 1
       337: 1
       338: q^2+2q+1
       339: q^2+2q+1
       340: q+1
       341: q^2+2q+1
       342: q+1
       343: q+1
       344: 1
       345: q^2+2q+1
       346: 2q+1
       347: 2q+1
       348: q+1
       349: 2q+1
       350: q+1
       351: q^2+2q+1
       352: q+1
       353: q+1
       354: q+1
       355: q^2+2q+1
       356: q+1
       357: q+1
       358: q+1
       359: 2q^2+2q+1
       360: q^2+2q+1
       361: 2q^2+2q+1
       362: q^2+2q+1
       363: q^2+2q+1
       364: q^2+2q+1
       365: q+1
       366: q+1
       367: q^2+2q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+2q+1
       371: 2q+1
       372: q^2+2q+1
       373: q+1
       374: q^2+2q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: q^2+2q+1
       380: 1
       381: 2q^2+2q+1
       382: q^2+2q+1
       383: q^2+2q+1
       384: q+1
       385: q^2+2q+1
       386: q+1
       387: q^2+2q+1
       388: 2q+1
       389: 2q+1
       390: q+1
       391: q^2+2q+1
       392: q^2+2q+1
       393: q+1
       394: q^2+2q+1
       395: q+1
       396: q+1
       397: q+1
       398: 2q^2+2q+1
       399: q^2+2q+1
       400: 2q^2+2q+1
       401: q^2+2q+1
       402: q^2+2q+1
       403: q^2+2q+1
       404: q+1
       405: q+1
       406: q^2+2q+1
       407: q^2+2q+1
       408: 2q+1
       409: q^2+2q+1
       410: 2q+1
       411: q^2+2q+1
       412: q+1
       413: q^2+2q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: q^2+2q+1
       419: 1
       420: 2q^2+2q+1
       421: q^2+2q+1
       422: q^2+2q+1
       423: q+1
       424: q^2+2q+1
       425: q+1
       426: q^2+2q+1
       427: 2q+1
       428: 2q+1
       429: q+1
       430: q^2+2q+1
       431: q^2+2q+1
       432: q+1
       433: q^2+2q+1
       434: q+1
       435: q+1
       436: 2q^2+2q+1
       437: 2q^2+2q+1
       438: q^2+2q+1
       439: 2q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: q+1
       443: 2q^2+2q+1
       444: q^2+2q+1
       445: q^2+2q+1
       446: 2q+1
       447: q^2+2q+1
       448: q^2+2q+1
       449: q^2+2q+1
       450: 2q+1
       451: 2q+1
       452: q^2+2q+1
       453: q^2+2q+1
       454: 2q^2+2q+1
       455: q^2+2q+1
       456: q^2+2q+1
       457: q+1
       458: q^3+2q^2+2q+1
       459: q^2+2q+1
       460: 2q+1
       461: q^2+2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       465: q+1
       466: q+1
       467: q+1
       468: 1
       469: 1
       470: q^2+2q+1
       471: q^2+2q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: 2q+1
       478: 1
       479: q^2+2q+1
       480: 2q+1
       481: 2q+1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: 2q+1
       487: 2q+1
       488: 2q+1
       489: 2q+1
       490: 2q+1
       491: q^2+2q+1
       492: 1
       493: 1
       494: 1
       495: q^2+2q+1
       496: q+1
       497: q^2+2q+1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: 1
       503: 2q+1
       504: 2q+1
       505: q+1
       506: 2q+1
       507: q+1
       508: q+1
       509: 1
       510: q^2+2q+1
       511: q+1
       512: q+1
       513: 1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q^2+2q+1
       521: 1
       522: 2q^2+2q+1
       523: q^2+2q+1
       524: q^2+2q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q^2+2q+1
       530: 2q+1
       531: q^2+2q+1
       532: 2q+1
       533: 2q+1
       534: q^2+2q+1
       535: q+1
       536: q+1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q^2+2q+1
       543: 1
       544: 1
       545: q^2+2q+1
       546: q^2+2q+1
       547: q+1
       548: q^2+2q+1
       549: q+1
       550: q+1
       551: 1
       552: q^2+2q+1
       553: 2q+1
       554: 2q+1
       555: q+1
       556: 2q+1
       557: q+1
       558: q^2+2q+1
       559: q+1
       560: q+1
       561: q+1
       562: q^2+2q+1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q^2+2q+1
       568: 1
       569: 2q^2+2q+1
       570: q^2+2q+1
       571: q^2+2q+1
       572: q+1
       573: q+1
       574: q+1
       575: q+1
       576: q^2+2q+1
       577: 2q+1
       578: q^2+2q+1
       579: 2q+1
       580: 2q+1
       581: q^2+2q+1
       582: q+1
       583: q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q^2+2q+1
       590: 1
       591: 1
       592: q^2+2q+1
       593: q^2+2q+1
       594: q+1
       595: q^2+2q+1
       596: q+1
       597: q+1
       598: 1
       599: q^2+2q+1
       600: 2q+1
       601: 2q+1
       602: q+1
       603: 2q+1
       604: q+1
       605: q^2+2q+1
       606: q+1
       607: q+1
       608: q+1
       609: q^2+2q+1
       610: q+1
       611: q+1
       612: q+1
       613: 2q^2+2q+1
       614: q^2+2q+1
       615: 2q^2+2q+1
       616: q^2+2q+1
       617: q^2+2q+1
       618: q^2+2q+1
       619: q+1
       620: q+1
       621: q^2+2q+1
       622: q^2+2q+1
       623: 2q+1
       624: q^2+2q+1
       625: 2q+1
       626: q^2+2q+1
       627: q+1
       628: q^2+2q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: 2q+1
       633: q^2+2q+1
       634: 1
       635: 2q^2+2q+1
       636: q^2+2q+1
       637: q^2+2q+1
       638: q+1
       639: q^2+2q+1
       640: q+1
       641: q^2+2q+1
       642: 2q+1
       643: 2q+1
       644: q+1
       645: q^2+2q+1
       646: q^2+2q+1
       647: q+1
       648: q^2+2q+1
       650: q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q^2+2q+1
       656: q+1
       658: q+1
       659: q+1
       660: q+1
       661: 1
       662: 1
       663: 2q+1
       664: 2q+1
       665: q+1
       666: q+1
       667: q+1
       668: q+1
       669: q+1
       670: 2q+1
       672: 2q+1
       673: 2q+1
       674: 2q+1
       675: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q+1
       681: 1
       682: q^2+2q+1
       683: q+1
       684: q+1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 2q+1
       690: q+1
       691: 2q+1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       702: q+1
       704: q+1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: q^2+2q+1
       710: q^2+2q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       716: 2q+1
       717: 1
       718: q^2+2q+1
       719: 2q+1
       720: 2q+1
       721: q+1
       722: q+1
       723: q+1
       724: q+1
       725: 2q+1
       726: 2q+1
       727: 2q+1
       728: 2q+1
       729: 2q+1
       730: q^2+2q+1
       731: 1
       732: 1
       733: 1
       734: q^2+2q+1
       735: q+1
       736: q^2+2q+1
       737: q+1
       738: q+1
       739: q+1
       740: 1
       741: 1
       742: 2q+1
       743: 2q+1
       744: q+1
       745: 2q+1
       746: q+1
       747: q+1
       748: 1
       749: q^2+2q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: q+1
       756: q+1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: q^2+2q+1
       762: q^2+2q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q+1
       768: 2q+1
       769: 1
       770: q^2+2q+1
       771: 2q+1
       772: 2q+1
       773: q+1
       774: q+1
       775: q+1
       776: q+1
       777: 2q+1
       778: 2q+1
       779: 2q+1
       780: 2q+1
       781: 2q+1
       782: q^2+2q+1
       783: 1
       784: 1
       785: 1
       786: q^2+2q+1
       787: q+1
       788: q^2+2q+1
       789: q+1
       790: q+1
       791: q+1
       792: 1
       793: 1
       794: 2q+1
       795: 2q+1
       796: q+1
       797: 2q+1
       798: q+1
       799: q+1
       800: 1
       801: q^2+2q+1
       802: q+1
       803: q+1
       804: 1
       805: q+1
       806: q+1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: q^2+2q+1
       812: 1
       813: 2q^2+2q+1
       814: q^2+2q+1
       815: q^2+2q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q^2+2q+1
       821: 2q+1
       822: q^2+2q+1
       823: 2q+1
       824: 2q+1
       825: q^2+2q+1
       826: q+1
       827: q+1
       828: 2q+1
       829: 2q+1
       830: 2q+1
       831: 2q+1
       832: 2q+1
       833: q^2+2q+1
       834: 1
       835: 1
       836: q^2+2q+1
       837: q^2+2q+1
       838: q+1
       839: q^2+2q+1
       840: q+1
       841: q+1
       842: 1
       843: q^2+2q+1
       844: 2q+1
       845: 2q+1
       846: q+1
       847: 2q+1
       848: q+1
       849: q^2+2q+1
       850: q+1
       851: q+1
       852: q+1
       853: q^2+2q+1
       855: q+1
       856: 1
       857: 1
       858: 1
       859: 1
       860: q+1
       862: q+1
       863: q+1
       864: 1
       865: 1
       866: 1
       867: 2q+1
       868: q+1
       870: q+1
       871: q+1
       872: q+1
       875: 2q+1
       876: 2q+1
       877: q+1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q+1
       885: q+1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: q+1
       893: 2q+1
       894: q+1
       895: q+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       902: q+1
       903: 1
       904: 1
       905: q+1
       907: q+1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q^2+2q+1
       913: q+1
       915: q+1
       916: q+1
       917: q+1
       918: 1
       919: 1
       920: 2q+1
       921: 2q+1
       922: q+1
       923: q+1
       924: q+1
       925: q+1
       926: q+1
       927: 2q+1
       929: 2q+1
       930: 2q+1
       931: 2q+1
       932: q+1
       933: 1
       934: 1
       935: 1
       936: 1
       937: q+1
       938: 1
       939: q^2+2q+1
       940: q+1
       941: q+1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 2q+1
       947: q+1
       948: 2q+1
       949: q+1
       950: q+1
       951: q+1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: q+1
       961: q+1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q^2+2q+1
       967: q+1
       969: q+1
       970: q+1
       971: q+1
       972: 1
       973: 1
       974: 2q+1
       975: 2q+1
       976: q+1
       977: q+1
       978: q+1
       979: q+1
       980: q+1
       981: 2q+1
       983: 2q+1
       984: 2q+1
       985: 2q+1
       986: q+1
       987: 1
       988: 1
       989: 1
       990: 1
       991: q+1
       992: 1
       993: q^2+2q+1
       994: q+1
       995: q+1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 2q+1
      1001: q+1
      1002: 2q+1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1013: q+1
      1015: q+1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: q^2+2q+1
      1021: q^2+2q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 2q+1
      1028: 1
      1029: q^2+2q+1
      1030: 2q+1
      1031: 2q+1
      1032: q+1
      1033: q+1
      1034: q+1
      1035: q+1
      1036: 2q+1
      1037: 2q+1
      1038: 2q+1
      1039: 2q+1
      1040: 2q+1
      1041: q^2+2q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q^2+2q+1
      1046: q+1
      1047: q^2+2q+1
      1048: q+1
      1049: q+1
      1050: q+1
      1051: 1
      1052: 1
      1053: 2q+1
      1054: 2q+1
      1055: q+1
      1056: 2q+1
      1057: q+1
      1058: q+1
      1059: 1
      1060: q^2+2q+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: q+1
      1065: q+1
      1068: 1
      1069: 1
      1070: 1
      1072: q+1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: q+1
      1079: q+1
      1080: q+1
      1084: 2q+1
      1085: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: q+1
      1093: 1
      1095: 1
      1096: 1
      1097: 1
      1100: q+1
      1101: q+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1114: q+1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: q+1
      1121: q+1
      1122: q+1
      1123: 1
      1124: 1
      1125: 1
      1126: 2q+1
      1127: q+1
      1129: q+1
      1130: q+1
      1131: q+1
      1134: 2q+1
      1135: 2q+1
      1136: q+1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: q+1
      1144: q+1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: q+1
      1152: 2q+1
      1153: q+1
      1154: q+1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1161: q+1
      1162: 1
      1163: 1
      1164: q+1
      1166: q+1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: q+1
      1173: q+1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: 2q+1
      1179: q+1
      1181: q+1
      1182: q+1
      1183: q+1
      1186: 2q+1
      1187: 2q+1
      1188: q+1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: q+1
      1196: q+1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: q+1
      1204: 2q+1
      1205: q+1
      1206: q+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1213: q+1
      1214: 1
      1215: 1
      1216: q+1
      1218: q+1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q^2+2q+1
      1224: q+1
      1226: q+1
      1227: q+1
      1228: q+1
      1229: 1
      1230: 1
      1231: 2q+1
      1232: 2q+1
      1233: q+1
      1234: q+1
      1235: q+1
      1236: q+1
      1237: q+1
      1238: 2q+1
      1240: 2q+1
      1241: 2q+1
      1242: 2q+1
      1243: q+1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: q+1
      1249: 1
      1250: q^2+2q+1
      1251: q+1
      1252: q+1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 2q+1
      1258: q+1
      1259: 2q+1
      1260: q+1
      1261: q+1
      1262: q+1
      1263: 1
      1264: 1
      1265: q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1270: q+1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: q+1
      1285: q+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1294: 1
      1295: 1
      1299: q+1
      1300: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: q+1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: q+1
      1323: q+1
      1324: q+1
      1328: 2q+1
      1329: q+1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: q+1
      1337: 1
      1339: 1
      1340: 1
      1341: 1
      1344: q+1
      1345: q+1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: q+1
      1354: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: q+1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: q+1
      1370: q+1
      1371: q+1
      1375: 2q+1
      1376: q+1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: q+1
      1384: 1
      1386: 1
      1387: 1
      1388: 1
      1391: q+1
      1392: q+1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1405: q+1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: q+1
      1412: q+1
      1413: q+1
      1414: 1
      1415: 1
      1416: 1
      1417: 2q+1
      1418: q+1
      1420: q+1
      1421: q+1
      1422: q+1
      1425: 2q+1
      1426: 2q+1
      1427: q+1
      1429: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: q+1
      1435: q+1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: q+1
      1443: 2q+1
      1444: q+1
      1445: q+1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1452: q+1
      1453: 1
      1454: 1
      1455: q+1
      1457: 1
      1459: 1
      1460: 1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1477: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1492: 1
      1493: 1
      1495: q+1
      1500: q+1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1509: 1
      1510: 1
      1514: q+1
      1515: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1531: 1
      1532: 1
      1534: q+1
      1539: q+1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1548: 1
      1549: 1
      1553: q+1
      1554: 1
      1556: 1
      1557: 1
      1558: 1
      1561: 1
      1562: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: q+1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: q+1
      1577: q+1
      1578: q+1
      1582: 2q+1
      1583: q+1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: q+1
      1591: 1
      1593: 1
      1594: 1
      1595: 1
      1598: q+1
      1599: q+1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: q+1
      1608: 1
      1609: 1
      1610: 1
      1613: 1
      1618: 1
      1619: 1
      1626: 1
      1631: 1
      1633: 1
      1635: 1
      1636: 1
      1644: 1
      1645: 1
      1646: 1
      1648: 1
      1653: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1663: 1
      1665: 1
      1666: 1
      1674: 1
      1675: 1
      1676: 1
      1678: 1
      1683: 1
      1685: 1
      1686: 1
      1690: 1
      1691: 1
      1693: 1
      1694: 1
      1697: 1
      1698: 1
      1699: 1
      1701: q+1
      1706: q+1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1715: 1
      1716: 1
      1720: q+1
      1721: 1
      1723: 1
      1724: 1
      1725: 1
      1728: 1
      1729: 1
      1730: 1
      1735: 1
      1746: 1
      1751: 1
      1752: 1
      1759: 1
      1764: 1
      1767: 1
      1772: 1
      1773: 1
      1780: 1
      1785: 1
      1787: 1
      1789: 1
      1790: 1
      1798: 1
      1799: 1
      1800: 1
      1802: 1
      1807: 1
      1809: 1
      1810: 1
      1814: 1
      1815: 1
      1827: 1
      1840: 1
      1851: 1
      1856: 1
      1857: 1
      1864: 1
      1869: 1
      1891: 1

1892:    0: 2q^4+6q^3+7q^2+4q+1
         1: 2q^4+6q^3+7q^2+4q+1
         2: q^4+5q^3+7q^2+4q+1
         3: q^4+5q^3+7q^2+4q+1
         4: 2q^4+6q^3+7q^2+4q+1
         5: 2q^4+6q^3+7q^2+4q+1
         6: q^4+5q^3+7q^2+4q+1
         7: q^4+5q^3+7q^2+4q+1
         8: 2q^3+6q^2+4q+1
         9: q^4+5q^3+7q^2+4q+1
        10: 2q^3+6q^2+4q+1
        11: q^4+5q^3+7q^2+4q+1
        12: q^4+5q^3+7q^2+4q+1
        13: 2q^4+6q^3+7q^2+4q+1
        14: q^4+5q^3+7q^2+4q+1
        15: q^4+5q^3+7q^2+4q+1
        16: 2q^4+6q^3+7q^2+4q+1
        17: q^4+5q^3+7q^2+4q+1
        18: q^4+5q^3+7q^2+4q+1
        19: 2q^4+6q^3+7q^2+4q+1
        20: 2q^3+6q^2+4q+1
        21: q^4+5q^3+7q^2+4q+1
        22: 2q^3+6q^2+4q+1
        23: 2q^3+6q^2+4q+1
        24: 2q^3+6q^2+4q+1
        25: 2q^3+6q^2+4q+1
        26: 2q^3+6q^2+4q+1
        27: 5q^2+4q+1
        28: q^4+5q^3+7q^2+4q+1
        29: 2q^3+6q^2+4q+1
        30: q^4+5q^3+7q^2+4q+1
        31: 2q^3+6q^2+4q+1
        32: q^4+5q^3+7q^2+4q+1
        33: q^4+5q^3+7q^2+4q+1
        34: q^4+5q^3+7q^2+4q+1
        35: 2q^3+6q^2+4q+1
        36: q^4+5q^3+7q^2+4q+1
        37: 2q^3+6q^2+4q+1
        38: q^4+5q^3+7q^2+4q+1
        39: q^4+5q^3+7q^2+4q+1
        40: q^4+5q^3+7q^2+4q+1
        41: q^4+5q^3+7q^2+4q+1
        42: 2q^3+6q^2+4q+1
        43: q^4+5q^3+7q^2+4q+1
        44: 2q^3+6q^2+4q+1
        45: q^4+5q^3+7q^2+4q+1
        46: q^4+5q^3+7q^2+4q+1
        47: 2q^4+6q^3+7q^2+4q+1
        48: q^4+5q^3+7q^2+4q+1
        49: q^4+5q^3+7q^2+4q+1
        50: 2q^3+6q^2+4q+1
        51: 2q^3+6q^2+4q+1
        52: 2q^3+6q^2+4q+1
        53: 4q^2+4q+1
        54: 2q^3+6q^2+4q+1
        55: 2q^3+6q^2+4q+1
        56: 2q^3+6q^2+4q+1
        57: 5q^2+4q+1
        58: 2q^3+6q^2+4q+1
        59: 5q^2+4q+1
        60: 5q^2+4q+1
        61: 5q^2+4q+1
        62: 2q^3+6q^2+4q+1
        63: 2q^3+6q^2+4q+1
        64: 4q^2+4q+1
        65: 2q^3+6q^2+4q+1
        66: 2q^3+6q^2+4q+1
        67: 4q^2+4q+1
        68: q^4+5q^3+7q^2+4q+1
        69: 2q^3+6q^2+4q+1
        70: q^4+4q^3+6q^2+4q+1
        71: 2q^3+6q^2+4q+1
        72: q^4+5q^3+7q^2+4q+1
        73: 2q^3+6q^2+4q+1
        74: 2q^3+6q^2+4q+1
        75: 2q^3+6q^2+4q+1
        76: 2q^3+6q^2+4q+1
        77: 2q^3+6q^2+4q+1
        78: 5q^2+4q+1
        79: q^4+5q^3+7q^2+4q+1
        80: 2q^3+6q^2+4q+1
        81: q^4+5q^3+7q^2+4q+1
        82: 2q^3+6q^2+4q+1
        83: q^4+5q^3+7q^2+4q+1
        84: 2q^3+6q^2+4q+1
        85: q^4+5q^3+7q^2+4q+1
        86: 2q^3+6q^2+4q+1
        87: 2q^3+6q^2+4q+1
        88: 2q^3+6q^2+4q+1
        89: 2q^3+6q^2+4q+1
        90: 2q^3+6q^2+4q+1
        91: 5q^2+4q+1
        92: q^4+5q^3+7q^2+4q+1
        93: 2q^3+6q^2+4q+1
        94: q^4+5q^3+7q^2+4q+1
        95: 2q^3+6q^2+4q+1
        96: q^4+5q^3+7q^2+4q+1
        97: q^4+5q^3+7q^2+4q+1
        98: q^4+5q^3+7q^2+4q+1
        99: 2q^3+6q^2+4q+1
       100: q^4+5q^3+7q^2+4q+1
       101: 2q^3+6q^2+4q+1
       102: q^4+5q^3+7q^2+4q+1
       103: q^4+5q^3+7q^2+4q+1
       104: 2q^3+6q^2+4q+1
       105: 2q^3+6q^2+4q+1
       106: 2q^3+6q^2+4q+1
       107: 4q^2+4q+1
       108: 4q^2+4q+1
       109: 4q^2+4q+1
       110: 2q^3+6q^2+4q+1
       111: q^3+3q^2+3q+1
       112: 5q^2+4q+1
       113: 5q^2+4q+1
       114: 5q^2+4q+1
       115: 4q^2+4q+1
       116: 5q^2+4q+1
       117: 5q^2+4q+1
       118: 5q^2+4q+1
       119: 4q^2+4q+1
       120: 2q^3+6q^2+4q+1
       121: 4q^2+4q+1
       122: 4q^2+4q+1
       123: 4q^2+4q+1
       124: 4q^2+4q+1
       125: 2q^3+6q^2+4q+1
       126: 4q^2+4q+1
       127: 4q^2+4q+1
       128: 4q^2+4q+1
       129: 2q^3+6q^2+4q+1
       130: 2q^3+6q^2+4q+1
       131: 3q^2+4q+1
       132: q^4+4q^3+6q^2+4q+1
       133: q^3+3q^2+3q+1
       134: 2q^3+6q^2+4q+1
       135: 2q^3+6q^2+4q+1
       136: 2q^3+6q^2+4q+1
       137: 4q^2+4q+1
       138: 2q^3+6q^2+4q+1
       139: 2q^3+6q^2+4q+1
       140: 2q^3+6q^2+4q+1
       141: 5q^2+4q+1
       142: 2q^3+6q^2+4q+1
       143: 5q^2+4q+1
       144: 5q^2+4q+1
       145: 5q^2+4q+1
       146: 2q^3+6q^2+4q+1
       147: 2q^3+6q^2+4q+1
       148: 4q^2+4q+1
       149: 2q^3+6q^2+4q+1
       150: 2q^3+6q^2+4q+1
       151: 4q^2+4q+1
       152: q^4+5q^3+7q^2+4q+1
       153: 2q^3+6q^2+4q+1
       154: q^4+4q^3+6q^2+4q+1
       155: 2q^3+6q^2+4q+1
       156: 2q^3+6q^2+4q+1
       157: 2q^3+6q^2+4q+1
       158: 4q^2+4q+1
       159: 2q^3+6q^2+4q+1
       160: 2q^3+6q^2+4q+1
       161: 2q^3+6q^2+4q+1
       162: 5q^2+4q+1
       163: 2q^3+6q^2+4q+1
       164: 5q^2+4q+1
       165: 5q^2+4q+1
       166: 5q^2+4q+1
       167: 2q^3+6q^2+4q+1
       168: 2q^3+6q^2+4q+1
       169: 4q^2+4q+1
       170: 2q^3+6q^2+4q+1
       171: 2q^3+6q^2+4q+1
       172: 4q^2+4q+1
       173: q^4+5q^3+7q^2+4q+1
       174: 2q^3+6q^2+4q+1
       175: q^4+4q^3+6q^2+4q+1
       176: 2q^3+6q^2+4q+1
       177: q^4+5q^3+7q^2+4q+1
       178: 2q^3+6q^2+4q+1
       179: 2q^3+6q^2+4q+1
       180: 2q^3+6q^2+4q+1
       181: 2q^3+6q^2+4q+1
       182: 2q^3+6q^2+4q+1
       183: 5q^2+4q+1
       184: q^4+5q^3+7q^2+4q+1
       185: 2q^3+6q^2+4q+1
       186: q^4+5q^3+7q^2+4q+1
       187: 2q^3+6q^2+4q+1
       188: q^4+5q^3+7q^2+4q+1
       189: q^3+3q^2+3q+1
       190: 2q^3+6q^2+4q+1
       191: 4q^2+4q+1
       192: 4q^2+4q+1
       193: 2q^2+3q+1
       194: 2q^2+3q+1
       195: 4q^2+4q+1
       196: q^3+3q^2+3q+1
       197: q^2+2q+1
       198: 5q^2+4q+1
       199: 5q^2+4q+1
       200: 5q^2+4q+1
       201: 4q^2+4q+1
       202: 4q^2+4q+1
       203: 4q^2+4q+1
       204: 5q^2+4q+1
       205: q^2+3q+1
       206: 4q^2+4q+1
       207: 4q^2+4q+1
       208: 4q^2+4q+1
       209: 2q^2+3q+1
       210: 4q^2+4q+1
       211: 4q^2+4q+1
       212: 4q^2+4q+1
       213: 4q^2+4q+1
       214: 4q^2+4q+1
       215: 4q^2+4q+1
       216: 2q^2+3q+1
       217: 4q^2+4q+1
       218: 4q^2+4q+1
       219: 4q^2+4q+1
       220: 3q^2+4q+1
       221: 2q^3+6q^2+4q+1
       222: 3q^2+4q+1
       223: 3q^2+4q+1
       224: 3q^2+4q+1
       225: q^3+3q^2+3q+1
       226: q^3+3q^2+3q+1
       227: q^2+3q+1
       228: 2q^3+6q^2+4q+1
       229: 2q^3+6q^2+4q+1
       230: 2q^3+6q^2+4q+1
       231: 4q^2+4q+1
       232: 4q^2+4q+1
       233: 4q^2+4q+1
       234: 2q^3+6q^2+4q+1
       235: q^3+3q^2+3q+1
       236: 5q^2+4q+1
       237: 5q^2+4q+1
       238: 5q^2+4q+1
       239: 4q^2+4q+1
       240: 5q^2+4q+1
       241: 5q^2+4q+1
       242: 5q^2+4q+1
       243: 4q^2+4q+1
       244: 2q^3+6q^2+4q+1
       245: 4q^2+4q+1
       246: 4q^2+4q+1
       247: 4q^2+4q+1
       248: 4q^2+4q+1
       249: 2q^3+6q^2+4q+1
       250: 4q^2+4q+1
       251: 4q^2+4q+1
       252: 4q^2+4q+1
       253: 2q^3+6q^2+4q+1
       254: 2q^3+6q^2+4q+1
       255: 3q^2+4q+1
       256: q^4+4q^3+6q^2+4q+1
       257: q^3+3q^2+3q+1
       258: 2q^3+6q^2+4q+1
       259: 2q^3+6q^2+4q+1
       260: 2q^3+6q^2+4q+1
       261: 4q^2+4q+1
       262: 4q^2+4q+1
       263: 4q^2+4q+1
       264: 2q^3+6q^2+4q+1
       265: q^3+3q^2+3q+1
       266: 5q^2+4q+1
       267: 5q^2+4q+1
       268: 5q^2+4q+1
       269: 4q^2+4q+1
       270: 5q^2+4q+1
       271: 5q^2+4q+1
       272: 5q^2+4q+1
       273: 4q^2+4q+1
       274: 2q^3+6q^2+4q+1
       275: 4q^2+4q+1
       276: 4q^2+4q+1
       277: 4q^2+4q+1
       278: 4q^2+4q+1
       279: 2q^3+6q^2+4q+1
       280: 4q^2+4q+1
       281: 4q^2+4q+1
       282: 4q^2+4q+1
       283: 2q^3+6q^2+4q+1
       284: 2q^3+6q^2+4q+1
       285: 3q^2+4q+1
       286: q^4+4q^3+6q^2+4q+1
       287: q^3+3q^2+3q+1
       288: 2q^3+6q^2+4q+1
       289: 2q^3+6q^2+4q+1
       290: 2q^3+6q^2+4q+1
       291: 4q^2+4q+1
       292: 2q^3+6q^2+4q+1
       293: 2q^3+6q^2+4q+1
       294: 2q^3+6q^2+4q+1
       295: 5q^2+4q+1
       296: 2q^3+6q^2+4q+1
       297: 5q^2+4q+1
       298: 5q^2+4q+1
       299: 5q^2+4q+1
       300: 2q^3+6q^2+4q+1
       301: 2q^3+6q^2+4q+1
       302: 4q^2+4q+1
       303: 2q^3+6q^2+4q+1
       304: 2q^3+6q^2+4q+1
       305: 4q^2+4q+1
       306: q^4+5q^3+7q^2+4q+1
       307: 2q^3+6q^2+4q+1
       308: q^4+4q^3+6q^2+4q+1
       309: q^2+2q+1
       310: q^3+3q^2+3q+1
       311: 4q^2+4q+1
       312: 2q^2+3q+1
       313: 2q^2+3q+1
       314: 2q^2+3q+1
       315: 2q^2+3q+1
       316: 2q+1
       317: q^2+2q+1
       318: q^2+2q+1
       319: q^2+3q+1
       320: 5q^2+4q+1
       321: 4q^2+4q+1
       322: 4q^2+4q+1
       323: 2q^2+3q+1
       324: 2q^2+3q+1
       325: 4q^2+4q+1
       326: q^2+3q+1
       327: 2q+1
       328: 4q^2+4q+1
       329: 4q^2+4q+1
       330: 4q^2+4q+1
       331: 2q^2+3q+1
       332: 2q^2+3q+1
       333: 2q^2+3q+1
       334: 4q^2+4q+1
       335: q^2+3q+1
       336: 4q^2+4q+1
       337: 4q^2+4q+1
       338: 4q^2+4q+1
       339: 2q^2+3q+1
       340: 2q^2+3q+1
       341: 2q^2+3q+1
       342: 4q^2+4q+1
       343: q^2+3q+1
       344: 3q^2+4q+1
       345: 3q^2+4q+1
       346: 3q^2+4q+1
       347: 2q+1
       348: 3q^2+4q+1
       349: 3q^2+4q+1
       350: 3q^2+4q+1
       351: q^2+3q+1
       352: q^3+3q^2+3q+1
       353: q^2+3q+1
       354: q^2+3q+1
       355: q^2+3q+1
       356: q^3+3q^2+3q+1
       357: 2q^3+6q^2+4q+1
       358: 4q^2+4q+1
       359: 4q^2+4q+1
       360: 2q^2+3q+1
       361: 2q^2+3q+1
       362: 4q^2+4q+1
       363: q^3+3q^2+3q+1
       364: q^2+2q+1
       365: 5q^2+4q+1
       366: 5q^2+4q+1
       367: 5q^2+4q+1
       368: 4q^2+4q+1
       369: 4q^2+4q+1
       370: 4q^2+4q+1
       371: 5q^2+4q+1
       372: q^2+3q+1
       373: 4q^2+4q+1
       374: 4q^2+4q+1
       375: 4q^2+4q+1
       376: 2q^2+3q+1
       377: 4q^2+4q+1
       378: 4q^2+4q+1
       379: 4q^2+4q+1
       380: 4q^2+4q+1
       381: 4q^2+4q+1
       382: 4q^2+4q+1
       383: 2q^2+3q+1
       384: 4q^2+4q+1
       385: 4q^2+4q+1
       386: 4q^2+4q+1
       387: 3q^2+4q+1
       388: 2q^3+6q^2+4q+1
       389: 3q^2+4q+1
       390: 3q^2+4q+1
       391: 3q^2+4q+1
       392: q^3+3q^2+3q+1
       393: q^3+3q^2+3q+1
       394: q^2+3q+1
       395: q^3+3q^2+3q+1
       396: 2q^3+6q^2+4q+1
       397: 4q^2+4q+1
       398: 4q^2+4q+1
       399: 2q^2+3q+1
       400: 2q^2+3q+1
       401: 4q^2+4q+1
       402: q^3+3q^2+3q+1
       403: q^2+2q+1
       404: 5q^2+4q+1
       405: 5q^2+4q+1
       406: 5q^2+4q+1
       407: 4q^2+4q+1
       408: 4q^2+4q+1
       409: 4q^2+4q+1
       410: 5q^2+4q+1
       411: q^2+3q+1
       412: 4q^2+4q+1
       413: 4q^2+4q+1
       414: 4q^2+4q+1
       415: 2q^2+3q+1
       416: 4q^2+4q+1
       417: 4q^2+4q+1
       418: 4q^2+4q+1
       419: 4q^2+4q+1
       420: 4q^2+4q+1
       421: 4q^2+4q+1
       422: 2q^2+3q+1
       423: 4q^2+4q+1
       424: 4q^2+4q+1
       425: 4q^2+4q+1
       426: 3q^2+4q+1
       427: 2q^3+6q^2+4q+1
       428: 3q^2+4q+1
       429: 3q^2+4q+1
       430: 3q^2+4q+1
       431: q^3+3q^2+3q+1
       432: q^3+3q^2+3q+1
       433: q^2+3q+1
       434: 2q^3+6q^2+4q+1
       435: 2q^3+6q^2+4q+1
       436: 2q^3+6q^2+4q+1
       437: 4q^2+4q+1
       438: 4q^2+4q+1
       439: 4q^2+4q+1
       440: 2q^3+6q^2+4q+1
       441: q^3+3q^2+3q+1
       442: 5q^2+4q+1
       443: 5q^2+4q+1
       444: 5q^2+4q+1
       445: 4q^2+4q+1
       446: 5q^2+4q+1
       447: 5q^2+4q+1
       448: 5q^2+4q+1
       449: 4q^2+4q+1
       450: 2q^3+6q^2+4q+1
       451: 4q^2+4q+1
       452: 4q^2+4q+1
       453: 4q^2+4q+1
       454: 4q^2+4q+1
       455: 2q^3+6q^2+4q+1
       456: 4q^2+4q+1
       457: 4q^2+4q+1
       458: 4q^2+4q+1
       459: 2q^3+6q^2+4q+1
       460: 2q^3+6q^2+4q+1
       461: 3q^2+4q+1
       462: q^4+4q^3+6q^2+4q+1
       463: q^3+3q^2+3q+1
       464: q^2+2q+1
       465: q^2+2q+1
       466: 2q+1
       467: 2q^2+3q+1
       468: 2q^2+3q+1
       469: 2q+1
       470: 2q+1
       471: q+1
       472: q^2+2q+1
       473: 2q+1
       474: q^2+3q+1
       475: 4q^2+4q+1
       476: 2q^2+3q+1
       477: 2q^2+3q+1
       478: 2q^2+3q+1
       479: 2q^2+3q+1
       480: 2q+1
       481: q+1
       482: 2q+1
       483: q^2+3q+1
       484: 4q^2+4q+1
       485: 2q^2+3q+1
       486: 2q^2+3q+1
       487: q^2+2q+1
       488: q^2+2q+1
       489: 2q^2+3q+1
       490: q^2+3q+1
       491: 2q+1
       492: q^2+3q+1
       493: 4q^2+4q+1
       494: 2q^2+3q+1
       495: 2q^2+3q+1
       496: q^2+2q+1
       497: q^2+2q+1
       498: 2q^2+3q+1
       499: q^2+3q+1
       500: 2q+1
       501: 3q^2+4q+1
       502: 3q^2+4q+1
       503: 3q^2+4q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 3q^2+4q+1
       508: q^2+3q+1
       509: q^2+3q+1
       510: q^2+3q+1
       511: q^2+3q+1
       512: 2q+1
       513: q^2+3q+1
       514: q^2+3q+1
       515: q^2+3q+1
       516: q^2+2q+1
       517: q^3+3q^2+3q+1
       518: 4q^2+4q+1
       519: 2q^2+3q+1
       520: 2q^2+3q+1
       521: 2q^2+3q+1
       522: 2q^2+3q+1
       523: 2q+1
       524: q^2+2q+1
       525: q^2+2q+1
       526: q^2+3q+1
       527: 5q^2+4q+1
       528: 4q^2+4q+1
       529: 4q^2+4q+1
       530: 2q^2+3q+1
       531: 2q^2+3q+1
       532: 4q^2+4q+1
       533: q^2+3q+1
       534: 2q+1
       535: 4q^2+4q+1
       536: 4q^2+4q+1
       537: 4q^2+4q+1
       538: 2q^2+3q+1
       539: 2q^2+3q+1
       540: 2q^2+3q+1
       541: 4q^2+4q+1
       542: q^2+3q+1
       543: 4q^2+4q+1
       544: 4q^2+4q+1
       545: 4q^2+4q+1
       546: 2q^2+3q+1
       547: 2q^2+3q+1
       548: 2q^2+3q+1
       549: 4q^2+4q+1
       550: q^2+3q+1
       551: 3q^2+4q+1
       552: 3q^2+4q+1
       553: 3q^2+4q+1
       554: 2q+1
       555: 3q^2+4q+1
       556: 3q^2+4q+1
       557: 3q^2+4q+1
       558: q^2+3q+1
       559: q^3+3q^2+3q+1
       560: q^2+3q+1
       561: q^2+3q+1
       562: q^2+3q+1
       563: q^2+2q+1
       564: q^3+3q^2+3q+1
       565: 4q^2+4q+1
       566: 2q^2+3q+1
       567: 2q^2+3q+1
       568: 2q^2+3q+1
       569: 2q^2+3q+1
       570: 2q+1
       571: q^2+2q+1
       572: q^2+2q+1
       573: q^2+3q+1
       574: 5q^2+4q+1
       575: 4q^2+4q+1
       576: 4q^2+4q+1
       577: 2q^2+3q+1
       578: 2q^2+3q+1
       579: 4q^2+4q+1
       580: q^2+3q+1
       581: 2q+1
       582: 4q^2+4q+1
       583: 4q^2+4q+1
       584: 4q^2+4q+1
       585: 2q^2+3q+1
       586: 2q^2+3q+1
       587: 2q^2+3q+1
       588: 4q^2+4q+1
       589: q^2+3q+1
       590: 4q^2+4q+1
       591: 4q^2+4q+1
       592: 4q^2+4q+1
       593: 2q^2+3q+1
       594: 2q^2+3q+1
       595: 2q^2+3q+1
       596: 4q^2+4q+1
       597: q^2+3q+1
       598: 3q^2+4q+1
       599: 3q^2+4q+1
       600: 3q^2+4q+1
       601: 2q+1
       602: 3q^2+4q+1
       603: 3q^2+4q+1
       604: 3q^2+4q+1
       605: q^2+3q+1
       606: q^3+3q^2+3q+1
       607: q^2+3q+1
       608: q^2+3q+1
       609: q^2+3q+1
       610: q^3+3q^2+3q+1
       611: 2q^3+6q^2+4q+1
       612: 4q^2+4q+1
       613: 4q^2+4q+1
       614: 2q^2+3q+1
       615: 2q^2+3q+1
       616: 4q^2+4q+1
       617: q^3+3q^2+3q+1
       618: q^2+2q+1
       619: 5q^2+4q+1
       620: 5q^2+4q+1
       621: 5q^2+4q+1
       622: 4q^2+4q+1
       623: 4q^2+4q+1
       624: 4q^2+4q+1
       625: 5q^2+4q+1
       626: q^2+3q+1
       627: 4q^2+4q+1
       628: 4q^2+4q+1
       629: 4q^2+4q+1
       630: 2q^2+3q+1
       631: 4q^2+4q+1
       632: 4q^2+4q+1
       633: 4q^2+4q+1
       634: 4q^2+4q+1
       635: 4q^2+4q+1
       636: 4q^2+4q+1
       637: 2q^2+3q+1
       638: 4q^2+4q+1
       639: 4q^2+4q+1
       640: 4q^2+4q+1
       641: 3q^2+4q+1
       642: 2q^3+6q^2+4q+1
       643: 3q^2+4q+1
       644: 3q^2+4q+1
       645: 3q^2+4q+1
       646: q^3+3q^2+3q+1
       647: q^3+3q^2+3q+1
       648: q^2+3q+1
       649: q^2+2q+1
       650: q+1
       651: 2q+1
       652: 2q+1
       653: 2q+1
       654: q+1
       655: q+1
       656: q+1
       657: 2q+1
       658: q+1
       659: 2q+1
       660: 2q^2+3q+1
       661: 2q^2+3q+1
       662: 2q+1
       663: 2q+1
       664: 1
       665: q+1
       666: 2q+1
       667: q^2+3q+1
       668: 2q^2+3q+1
       669: q^2+2q+1
       670: q^2+2q+1
       671: q^2+2q+1
       672: q^2+2q+1
       673: q+1
       674: q+1
       675: 2q+1
       676: 2q+1
       677: q^2+3q+1
       678: 2q^2+3q+1
       679: q^2+2q+1
       680: q^2+2q+1
       681: q^2+2q+1
       682: q^2+2q+1
       683: q+1
       684: q+1
       685: 2q+1
       686: q^2+3q+1
       687: 3q^2+4q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q^2+3q+1
       694: 2q+1
       695: q^2+3q+1
       696: q^2+3q+1
       697: q^2+3q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: q^2+3q+1
       702: q+1
       703: q^2+2q+1
       704: q^2+2q+1
       705: 2q+1
       706: 2q^2+3q+1
       707: 2q^2+3q+1
       708: 2q+1
       709: 2q+1
       710: q+1
       711: q^2+2q+1
       712: 2q+1
       713: q^2+3q+1
       714: 4q^2+4q+1
       715: 2q^2+3q+1
       716: 2q^2+3q+1
       717: 2q^2+3q+1
       718: 2q^2+3q+1
       719: 2q+1
       720: q+1
       721: 2q+1
       722: q^2+3q+1
       723: 4q^2+4q+1
       724: 2q^2+3q+1
       725: 2q^2+3q+1
       726: q^2+2q+1
       727: q^2+2q+1
       728: 2q^2+3q+1
       729: q^2+3q+1
       730: 2q+1
       731: q^2+3q+1
       732: 4q^2+4q+1
       733: 2q^2+3q+1
       734: 2q^2+3q+1
       735: q^2+2q+1
       736: q^2+2q+1
       737: 2q^2+3q+1
       738: q^2+3q+1
       739: 2q+1
       740: 3q^2+4q+1
       741: 3q^2+4q+1
       742: 3q^2+4q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 3q^2+4q+1
       747: q^2+3q+1
       748: q^2+3q+1
       749: q^2+3q+1
       750: q^2+3q+1
       751: 2q+1
       752: q^2+3q+1
       753: q^2+3q+1
       754: q^2+3q+1
       755: q^2+2q+1
       756: q^2+2q+1
       757: 2q+1
       758: 2q^2+3q+1
       759: 2q^2+3q+1
       760: 2q+1
       761: 2q+1
       762: q+1
       763: q^2+2q+1
       764: 2q+1
       765: q^2+3q+1
       766: 4q^2+4q+1
       767: 2q^2+3q+1
       768: 2q^2+3q+1
       769: 2q^2+3q+1
       770: 2q^2+3q+1
       771: 2q+1
       772: q+1
       773: 2q+1
       774: q^2+3q+1
       775: 4q^2+4q+1
       776: 2q^2+3q+1
       777: 2q^2+3q+1
       778: q^2+2q+1
       779: q^2+2q+1
       780: 2q^2+3q+1
       781: q^2+3q+1
       782: 2q+1
       783: q^2+3q+1
       784: 4q^2+4q+1
       785: 2q^2+3q+1
       786: 2q^2+3q+1
       787: q^2+2q+1
       788: q^2+2q+1
       789: 2q^2+3q+1
       790: q^2+3q+1
       791: 2q+1
       792: 3q^2+4q+1
       793: 3q^2+4q+1
       794: 3q^2+4q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 3q^2+4q+1
       799: q^2+3q+1
       800: q^2+3q+1
       801: q^2+3q+1
       802: q^2+3q+1
       803: 2q+1
       804: q^2+3q+1
       805: q^2+3q+1
       806: q^2+3q+1
       807: q^2+2q+1
       808: q^3+3q^2+3q+1
       809: 4q^2+4q+1
       810: 2q^2+3q+1
       811: 2q^2+3q+1
       812: 2q^2+3q+1
       813: 2q^2+3q+1
       814: 2q+1
       815: q^2+2q+1
       816: q^2+2q+1
       817: q^2+3q+1
       818: 5q^2+4q+1
       819: 4q^2+4q+1
       820: 4q^2+4q+1
       821: 2q^2+3q+1
       822: 2q^2+3q+1
       823: 4q^2+4q+1
       824: q^2+3q+1
       825: 2q+1
       826: 4q^2+4q+1
       827: 4q^2+4q+1
       828: 4q^2+4q+1
       829: 2q^2+3q+1
       830: 2q^2+3q+1
       831: 2q^2+3q+1
       832: 4q^2+4q+1
       833: q^2+3q+1
       834: 4q^2+4q+1
       835: 4q^2+4q+1
       836: 4q^2+4q+1
       837: 2q^2+3q+1
       838: 2q^2+3q+1
       839: 2q^2+3q+1
       840: 4q^2+4q+1
       841: q^2+3q+1
       842: 3q^2+4q+1
       843: 3q^2+4q+1
       844: 3q^2+4q+1
       845: 2q+1
       846: 3q^2+4q+1
       847: 3q^2+4q+1
       848: 3q^2+4q+1
       849: q^2+3q+1
       850: q^3+3q^2+3q+1
       851: q^2+3q+1
       852: q^2+3q+1
       853: q^2+3q+1
       854: q+1
       855: q+1
       856: q+1
       857: 2q+1
       858: q+1
       859: q+1
       860: q+1
       861: q+1
       862: 1
       863: 2q+1
       864: 2q+1
       865: 2q+1
       866: 1
       867: 1
       868: 1
       869: 2q+1
       870: q+1
       871: q+1
       872: q^2+2q+1
       873: q^2+2q+1
       874: q+1
       875: q+1
       876: 1
       877: q+1
       878: 2q+1
       879: q+1
       880: q+1
       881: q^2+2q+1
       882: q^2+2q+1
       883: q+1
       884: q+1
       885: 1
       886: q+1
       887: 2q+1
       888: q^2+3q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       896: 2q+1
       897: q+1
       898: q^2+3q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: q+1
       905: q+1
       906: q^2+2q+1
       907: q+1
       908: 2q+1
       909: 2q+1
       910: 2q+1
       911: q+1
       912: q+1
       913: q+1
       914: 2q+1
       915: q+1
       916: 2q+1
       917: 2q^2+3q+1
       918: 2q^2+3q+1
       919: 2q+1
       920: 2q+1
       921: 1
       922: q+1
       923: 2q+1
       924: q^2+3q+1
       925: 2q^2+3q+1
       926: q^2+2q+1
       927: q^2+2q+1
       928: q^2+2q+1
       929: q^2+2q+1
       930: q+1
       931: q+1
       932: 2q+1
       933: 2q+1
       934: q^2+3q+1
       935: 2q^2+3q+1
       936: q^2+2q+1
       937: q^2+2q+1
       938: q^2+2q+1
       939: q^2+2q+1
       940: q+1
       941: q+1
       942: 2q+1
       943: q^2+3q+1
       944: 3q^2+4q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: q^2+3q+1
       951: 2q+1
       952: q^2+3q+1
       953: q^2+3q+1
       954: q^2+3q+1
       955: 2q+1
       956: 2q+1
       957: 2q+1
       958: q^2+3q+1
       959: q+1
       960: q^2+2q+1
       961: q+1
       962: 2q+1
       963: 2q+1
       964: 2q+1
       965: q+1
       966: q+1
       967: q+1
       968: 2q+1
       969: q+1
       970: 2q+1
       971: 2q^2+3q+1
       972: 2q^2+3q+1
       973: 2q+1
       974: 2q+1
       975: 1
       976: q+1
       977: 2q+1
       978: q^2+3q+1
       979: 2q^2+3q+1
       980: q^2+2q+1
       981: q^2+2q+1
       982: q^2+2q+1
       983: q^2+2q+1
       984: q+1
       985: q+1
       986: 2q+1
       987: 2q+1
       988: q^2+3q+1
       989: 2q^2+3q+1
       990: q^2+2q+1
       991: q^2+2q+1
       992: q^2+2q+1
       993: q^2+2q+1
       994: q+1
       995: q+1
       996: 2q+1
       997: q^2+3q+1
       998: 3q^2+4q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: q^2+3q+1
      1005: 2q+1
      1006: q^2+3q+1
      1007: q^2+3q+1
      1008: q^2+3q+1
      1009: 2q+1
      1010: 2q+1
      1011: 2q+1
      1012: q^2+3q+1
      1013: q+1
      1014: q^2+2q+1
      1015: q^2+2q+1
      1016: 2q+1
      1017: 2q^2+3q+1
      1018: 2q^2+3q+1
      1019: 2q+1
      1020: 2q+1
      1021: q+1
      1022: q^2+2q+1
      1023: 2q+1
      1024: q^2+3q+1
      1025: 4q^2+4q+1
      1026: 2q^2+3q+1
      1027: 2q^2+3q+1
      1028: 2q^2+3q+1
      1029: 2q^2+3q+1
      1030: 2q+1
      1031: q+1
      1032: 2q+1
      1033: q^2+3q+1
      1034: 4q^2+4q+1
      1035: 2q^2+3q+1
      1036: 2q^2+3q+1
      1037: q^2+2q+1
      1038: q^2+2q+1
      1039: 2q^2+3q+1
      1040: q^2+3q+1
      1041: 2q+1
      1042: q^2+3q+1
      1043: 4q^2+4q+1
      1044: 2q^2+3q+1
      1045: 2q^2+3q+1
      1046: q^2+2q+1
      1047: q^2+2q+1
      1048: 2q^2+3q+1
      1049: q^2+3q+1
      1050: 2q+1
      1051: 3q^2+4q+1
      1052: 3q^2+4q+1
      1053: 3q^2+4q+1
      1054: 2q+1
      1055: 2q+1
      1056: 2q+1
      1057: 3q^2+4q+1
      1058: q^2+3q+1
      1059: q^2+3q+1
      1060: q^2+3q+1
      1061: q^2+3q+1
      1062: 2q+1
      1063: q^2+3q+1
      1064: q^2+3q+1
      1065: q^2+3q+1
      1066: q+1
      1067: q+1
      1068: q+1
      1070: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 2q+1
      1075: 1
      1076: 1
      1077: 1
      1078: q+1
      1079: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1094: 2q+1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: q+1
      1104: q+1
      1105: 2q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1112: q+1
      1113: q+1
      1114: q+1
      1115: q+1
      1116: 2q+1
      1117: q+1
      1118: q+1
      1119: q+1
      1120: q+1
      1121: 1
      1122: 2q+1
      1123: 2q+1
      1124: 2q+1
      1125: 1
      1126: 1
      1127: 1
      1128: 2q+1
      1129: q+1
      1130: q+1
      1131: q^2+2q+1
      1132: q^2+2q+1
      1133: q+1
      1134: q+1
      1135: 1
      1136: q+1
      1137: 2q+1
      1138: q+1
      1139: q+1
      1140: q^2+2q+1
      1141: q^2+2q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: q+1
      1146: 2q+1
      1147: q^2+3q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1155: 2q+1
      1156: q+1
      1157: q^2+3q+1
      1158: 2q+1
      1159: 2q+1
      1160: q+1
      1161: q+1
      1162: 2q+1
      1163: q+1
      1164: q+1
      1165: q+1
      1166: q+1
      1167: q+1
      1168: 2q+1
      1169: q+1
      1170: q+1
      1171: q+1
      1172: q+1
      1173: 1
      1174: 2q+1
      1175: 2q+1
      1176: 2q+1
      1177: 1
      1178: 1
      1179: 1
      1180: 2q+1
      1181: q+1
      1182: q+1
      1183: q^2+2q+1
      1184: q^2+2q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: q+1
      1189: 2q+1
      1190: q+1
      1191: q+1
      1192: q^2+2q+1
      1193: q^2+2q+1
      1194: q+1
      1195: q+1
      1196: 1
      1197: q+1
      1198: 2q+1
      1199: q^2+3q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1203: q+1
      1204: q+1
      1205: 1
      1206: q+1
      1207: 2q+1
      1208: q+1
      1209: q^2+3q+1
      1210: 2q+1
      1211: 2q+1
      1212: q+1
      1213: q+1
      1214: 2q+1
      1215: q+1
      1216: q+1
      1217: q^2+2q+1
      1218: q+1
      1219: 2q+1
      1220: 2q+1
      1221: 2q+1
      1222: q+1
      1223: q+1
      1224: q+1
      1225: 2q+1
      1226: q+1
      1227: 2q+1
      1228: 2q^2+3q+1
      1229: 2q^2+3q+1
      1230: 2q+1
      1231: 2q+1
      1232: 1
      1233: q+1
      1234: 2q+1
      1235: q^2+3q+1
      1236: 2q^2+3q+1
      1237: q^2+2q+1
      1238: q^2+2q+1
      1239: q^2+2q+1
      1240: q^2+2q+1
      1241: q+1
      1242: q+1
      1243: 2q+1
      1244: 2q+1
      1245: q^2+3q+1
      1246: 2q^2+3q+1
      1247: q^2+2q+1
      1248: q^2+2q+1
      1249: q^2+2q+1
      1250: q^2+2q+1
      1251: q+1
      1252: q+1
      1253: 2q+1
      1254: q^2+3q+1
      1255: 3q^2+4q+1
      1256: 2q+1
      1257: 2q+1
      1258: q+1
      1259: q+1
      1260: 2q+1
      1261: q^2+3q+1
      1262: 2q+1
      1263: q^2+3q+1
      1264: q^2+3q+1
      1265: q^2+3q+1
      1266: 2q+1
      1267: 2q+1
      1268: 2q+1
      1269: q^2+3q+1
      1270: q+1
      1271: q+1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: q+1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1310: q+1
      1311: q+1
      1312: q+1
      1314: q+1
      1315: 1
      1316: 1
      1317: 1
      1318: 2q+1
      1319: 1
      1320: 1
      1321: 1
      1322: q+1
      1323: 1
      1324: q+1
      1325: q+1
      1326: q+1
      1327: 1
      1328: 1
      1329: 1
      1330: q+1
      1331: 1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1338: 2q+1
      1339: q+1
      1340: 1
      1341: q+1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1346: q+1
      1347: q+1
      1348: q+1
      1349: 2q+1
      1350: q+1
      1351: q+1
      1352: q+1
      1353: q+1
      1354: 1
      1356: q+1
      1357: q+1
      1358: q+1
      1359: q+1
      1361: q+1
      1362: 1
      1363: 1
      1364: 1
      1365: 2q+1
      1366: 1
      1367: 1
      1368: 1
      1369: q+1
      1370: 1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1377: q+1
      1378: 1
      1379: q+1
      1380: q+1
      1381: q+1
      1382: 1
      1383: 1
      1384: 1
      1385: 2q+1
      1386: q+1
      1387: 1
      1388: q+1
      1389: q+1
      1390: 1
      1391: 1
      1392: 1
      1393: q+1
      1394: q+1
      1395: q+1
      1396: 2q+1
      1397: q+1
      1398: q+1
      1399: q+1
      1400: q+1
      1401: 1
      1403: q+1
      1404: q+1
      1405: q+1
      1406: q+1
      1407: 2q+1
      1408: q+1
      1409: q+1
      1410: q+1
      1411: q+1
      1412: 1
      1413: 2q+1
      1414: 2q+1
      1415: 2q+1
      1416: 1
      1417: 1
      1418: 1
      1419: 2q+1
      1420: q+1
      1421: q+1
      1422: q^2+2q+1
      1423: q^2+2q+1
      1424: q+1
      1425: q+1
      1426: 1
      1427: q+1
      1428: 2q+1
      1429: q+1
      1430: q+1
      1431: q^2+2q+1
      1432: q^2+2q+1
      1433: q+1
      1434: q+1
      1435: 1
      1436: q+1
      1437: 2q+1
      1438: q^2+3q+1
      1439: 2q+1
      1440: q+1
      1441: q+1
      1442: q+1
      1443: q+1
      1444: 1
      1445: q+1
      1446: 2q+1
      1447: q+1
      1448: q^2+3q+1
      1449: 2q+1
      1450: 2q+1
      1451: q+1
      1452: q+1
      1453: 2q+1
      1454: q+1
      1455: q+1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1486: q+1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: q+1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1508: q+1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: q+1
      1518: 1
      1519: q+1
      1520: q+1
      1521: 1
      1522: 1
      1525: q+1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1541: 1
      1542: 1
      1543: q+1
      1544: 1
      1545: 1
      1546: 1
      1547: q+1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: q+1
      1557: 1
      1558: q+1
      1559: q+1
      1560: 1
      1561: 1
      1564: q+1
      1565: q+1
      1566: q+1
      1568: q+1
      1569: 1
      1570: 1
      1571: 1
      1572: 2q+1
      1573: 1
      1574: 1
      1575: 1
      1576: q+1
      1577: 1
      1578: q+1
      1579: q+1
      1580: q+1
      1581: 1
      1582: 1
      1583: 1
      1584: q+1
      1585: 1
      1586: q+1
      1587: q+1
      1588: q+1
      1589: 1
      1590: 1
      1591: 1
      1592: 2q+1
      1593: q+1
      1594: 1
      1595: q+1
      1596: q+1
      1597: 1
      1598: 1
      1599: 1
      1600: q+1
      1601: q+1
      1602: q+1
      1603: 2q+1
      1604: q+1
      1605: q+1
      1606: q+1
      1607: q+1
      1608: 1
      1610: q+1
      1614: 1
      1617: 1
      1620: 1
      1621: 1
      1622: 1
      1624: 1
      1628: 1
      1634: 1
      1637: 1
      1638: 1
      1639: 1
      1641: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1656: 1
      1657: 1
      1658: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1672: 1
      1673: 1
      1674: 1
      1676: 1
      1677: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1686: 1
      1687: 1
      1688: 1
      1692: q+1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: q+1
      1704: 1
      1705: 1
      1706: 1
      1707: 1
      1708: 1
      1709: 1
      1710: q+1
      1711: 1
      1712: 1
      1713: 1
      1714: q+1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1722: q+1
      1724: 1
      1725: q+1
      1726: q+1
      1727: 1
      1728: 1
      1736: 1
      1747: 1
      1750: 1
      1753: 1
      1754: 1
      1755: 1
      1757: 1
      1761: 1
      1768: 1
      1771: 1
      1774: 1
      1775: 1
      1776: 1
      1778: 1
      1782: 1
      1788: 1
      1791: 1
      1792: 1
      1793: 1
      1795: 1
      1796: 1
      1797: 1
      1798: 1
      1800: 1
      1801: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1806: 1
      1807: 1
      1810: 1
      1811: 1
      1812: 1
      1828: 1
      1841: 1
      1852: 1
      1855: 1
      1858: 1
      1859: 1
      1860: 1
      1862: 1
      1866: 1
      1892: 1

1893:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
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        34: q+1
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        54: q+1
        55: q+1
        56: q+1
        57: q+1
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        60: q+1
        61: q+1
        62: q+1
        63: 1
        64: q+1
        65: q+1
        66: 1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
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        78: q+1
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        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: 1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
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       102: q+1
       103: q+1
       104: q+1
       105: q+1
       106: q+1
       107: q+1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: q+1
       113: q+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q+1
       119: q+1
       120: 1
       121: 1
       122: q+1
       123: q+1
       124: q+1
       125: 1
       126: 1
       127: q+1
       128: q+1
       129: q+1
       130: 1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: 1
       143: 1
       144: q+1
       145: q+1
       146: q+1
       147: 1
       148: q+1
       149: q+1
       150: 1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: 1
       164: 1
       165: q+1
       166: q+1
       167: q+1
       168: 1
       169: q+1
       170: q+1
       171: 1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: 1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q+1
       206: q+1
       207: q+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q+1
       213: q+1
       214: q+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q+1
       220: q+1
       221: 1
       222: 1
       223: q+1
       224: q+1
       225: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q+1
       243: q+1
       244: 1
       245: 1
       246: q+1
       247: q+1
       248: q+1
       249: 1
       250: 1
       251: q+1
       252: q+1
       253: q+1
       254: 1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q+1
       273: q+1
       274: 1
       275: 1
       276: q+1
       277: q+1
       278: q+1
       279: 1
       280: 1
       281: q+1
       282: q+1
       283: q+1
       284: 1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: 1
       297: 1
       298: q+1
       299: q+1
       300: q+1
       301: 1
       302: q+1
       303: q+1
       304: 1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       319: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q+1
       328: q+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q+1
       336: q+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q+1
       344: q+1
       345: q+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: q+1
       351: q+1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q+1
       373: q+1
       374: q+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q+1
       380: q+1
       381: q+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q+1
       387: q+1
       388: 1
       389: 1
       390: q+1
       391: q+1
       392: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q+1
       412: q+1
       413: q+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q+1
       419: q+1
       420: q+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q+1
       426: q+1
       427: 1
       428: 1
       429: q+1
       430: q+1
       431: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q+1
       449: q+1
       450: 1
       451: 1
       452: q+1
       453: q+1
       454: q+1
       455: 1
       456: 1
       457: q+1
       458: q+1
       459: q+1
       460: 1
       461: q+1
       462: q+1
       463: q+1
       465: q+1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       473: q+1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q+1
       492: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q+1
       501: q+1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: q+1
       509: q+1
       510: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       524: q+1
       526: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q+1
       535: q+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q+1
       543: q+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q+1
       551: q+1
       552: q+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q+1
       558: q+1
       561: q+1
       562: q+1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       573: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q+1
       582: q+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q+1
       590: q+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q+1
       598: q+1
       599: q+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q+1
       605: q+1
       608: q+1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q+1
       627: q+1
       628: q+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q+1
       634: q+1
       635: q+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q+1
       641: q+1
       642: 1
       643: 1
       644: q+1
       645: q+1
       646: q+1
       648: q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: q+1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: q+1
       695: q+1
       702: q+1
       704: q+1
       705: q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: q+1
       712: q+1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: q+1
       731: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q+1
       740: q+1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: q+1
       748: q+1
       749: q+1
       754: q+1
       756: q+1
       757: q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: q+1
       764: q+1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q+1
       783: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: q+1
       792: q+1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: q+1
       800: q+1
       801: q+1
       806: q+1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: q+1
       815: q+1
       817: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: q+1
       826: q+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q+1
       834: q+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q+1
       842: q+1
       843: q+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q+1
       849: q+1
       852: q+1
       853: q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       887: q+1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: q+1
       905: q+1
       907: q+1
       908: q+1
       909: q+1
       910: q+1
       911: q+1
       912: q+1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: q+1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       933: q+1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: q+1
       952: q+1
       959: q+1
       961: q+1
       962: q+1
       963: q+1
       964: q+1
       965: q+1
       966: q+1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: q+1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       987: q+1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: q+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: q+1
      1006: q+1
      1013: q+1
      1015: q+1
      1016: q+1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1021: q+1
      1023: q+1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q+1
      1042: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q+1
      1051: q+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q+1
      1059: q+1
      1060: q+1
      1065: q+1
      1068: q+1
      1069: q+1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1103: q+1
      1114: q+1
      1115: q+1
      1116: q+1
      1117: q+1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1146: q+1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: q+1
      1164: q+1
      1166: q+1
      1167: q+1
      1168: q+1
      1169: q+1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1198: q+1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: q+1
      1216: q+1
      1218: q+1
      1219: q+1
      1220: q+1
      1221: q+1
      1222: q+1
      1223: q+1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: q+1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: q+1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q+1
      1263: q+1
      1270: q+1
      1272: q+1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1312: q+1
      1313: q+1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1347: q+1
      1359: q+1
      1360: q+1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1394: q+1
      1405: q+1
      1406: q+1
      1407: q+1
      1408: q+1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1437: q+1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q+1
      1455: q+1
      1459: 1
      1463: 1
      1464: 1
      1468: 1
      1469: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1487: q+1
      1491: 1
      1492: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1526: q+1
      1530: 1
      1531: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1566: q+1
      1567: q+1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1593: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1601: q+1
      1615: 1
      1618: 1
      1622: 1
      1623: 1
      1635: 1
      1639: 1
      1640: 1
      1644: 1
      1645: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1665: 1
      1669: 1
      1670: 1
      1674: 1
      1675: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1693: q+1
      1697: 1
      1698: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1737: 1
      1748: 1
      1751: 1
      1755: 1
      1756: 1
      1769: 1
      1772: 1
      1776: 1
      1777: 1
      1789: 1
      1793: 1
      1794: 1
      1798: 1
      1799: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1829: 1
      1842: 1
      1853: 1
      1856: 1
      1860: 1
      1861: 1
      1893: 1

1894:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^2+2q+1
         7: q^3+2q^2+2q+1
         8: q^3+2q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^3+2q^2+2q+1
        23: q^3+2q^2+2q+1
        24: q^3+2q^2+2q+1
        25: 2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+2q^2+2q+1
        29: q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^2+2q+1
        34: q^3+2q^2+2q+1
        35: q^3+2q^2+2q+1
        36: q^3+2q^2+2q+1
        37: q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        40: q^2+2q+1
        41: q^3+2q^2+2q+1
        42: q^3+2q^2+2q+1
        43: q^3+2q^2+2q+1
        44: q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q^3+2q^2+2q+1
        55: q^3+2q^2+2q+1
        56: q^3+2q^2+2q+1
        57: 2q+1
        58: 2q+1
        59: q^2+2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: 2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: 2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^3+2q^2+2q+1
        69: q^2+2q+1
        70: q^3+2q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^3+2q^2+2q+1
        74: q^3+2q^2+2q+1
        75: q^3+2q^2+2q+1
        76: 2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^3+2q^2+2q+1
        80: q^2+2q+1
        81: q^3+2q^2+2q+1
        82: q^2+2q+1
        83: q^3+2q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^3+2q^2+2q+1
        87: q^3+2q^2+2q+1
        88: q^3+2q^2+2q+1
        89: 2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^2+2q+1
        96: q^3+2q^2+2q+1
        97: q^2+2q+1
        98: q^3+2q^2+2q+1
        99: q^3+2q^2+2q+1
       100: q^3+2q^2+2q+1
       101: q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^3+2q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^3+2q^2+2q+1
       111: q^3+2q^2+2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: q^2+2q+1
       117: q^2+2q+1
       118: q^2+2q+1
       119: 2q+1
       120: 2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: 2q+1
       125: 2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^3+2q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^3+2q^2+2q+1
       139: q^3+2q^2+2q+1
       140: q^3+2q^2+2q+1
       141: 2q+1
       142: 2q+1
       143: q^2+2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: 2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^3+2q^2+2q+1
       153: q^2+2q+1
       154: q^3+2q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: q^3+2q^2+2q+1
       160: q^3+2q^2+2q+1
       161: q^3+2q^2+2q+1
       162: 2q+1
       163: 2q+1
       164: q^2+2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: 2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: 2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^3+2q^2+2q+1
       174: q^2+2q+1
       175: q^3+2q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^3+2q^2+2q+1
       179: q^3+2q^2+2q+1
       180: q^3+2q^2+2q+1
       181: 2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^3+2q^2+2q+1
       185: q^2+2q+1
       186: q^3+2q^2+2q+1
       187: q^2+2q+1
       188: q^3+2q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: 2q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^3+2q^2+2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: q^2+2q+1
       205: q^2+2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: q^2+2q+1
       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q+1
       221: 2q+1
       222: q^2+2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^3+2q^2+2q+1
       235: q^3+2q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: q^2+2q+1
       241: q^2+2q+1
       242: q^2+2q+1
       243: 2q+1
       244: 2q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: 2q+1
       249: 2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^3+2q^2+2q+1
       257: q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^3+2q^2+2q+1
       265: q^3+2q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: q^2+2q+1
       271: q^2+2q+1
       272: q^2+2q+1
       273: 2q+1
       274: 2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: 2q+1
       279: 2q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: 2q+1
       284: q^2+2q+1
       285: q^2+2q+1
       286: q^3+2q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: q^3+2q^2+2q+1
       293: q^3+2q^2+2q+1
       294: q^3+2q^2+2q+1
       295: 2q+1
       296: 2q+1
       297: q^2+2q+1
       298: q^2+2q+1
       299: q^2+2q+1
       300: 2q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: 2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^3+2q^2+2q+1
       307: q^2+2q+1
       308: q^3+2q^2+2q+1
       310: q^2+2q+1
       311: 2q+1
       312: 2q+1
       313: 2q+1
       314: 2q+1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: q^2+2q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+2q+1
       343: q^2+2q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 1
       348: q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^3+2q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: q^2+2q+1
       372: q^2+2q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       377: q^2+2q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: q^2+2q+1
       385: q^2+2q+1
       386: q^2+2q+1
       387: 2q+1
       388: 2q+1
       389: q^2+2q+1
       390: q^2+2q+1
       391: q^2+2q+1
       392: q+1
       393: q+1
       394: q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^3+2q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: q^2+2q+1
       411: q^2+2q+1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: q^2+2q+1
       417: q^2+2q+1
       418: q^2+2q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: q+1
       423: q^2+2q+1
       424: q^2+2q+1
       425: q^2+2q+1
       426: 2q+1
       427: 2q+1
       428: q^2+2q+1
       429: q^2+2q+1
       430: q^2+2q+1
       431: q+1
       432: q+1
       433: q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^3+2q^2+2q+1
       441: q^3+2q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: q^2+2q+1
       447: q^2+2q+1
       448: q^2+2q+1
       449: 2q+1
       450: 2q+1
       451: q^2+2q+1
       452: q^2+2q+1
       453: q^2+2q+1
       454: 2q+1
       455: 2q+1
       456: q^2+2q+1
       457: q^2+2q+1
       458: q^2+2q+1
       459: 2q+1
       460: q^2+2q+1
       461: q^2+2q+1
       462: q^3+2q^2+2q+1
       463: q+1
       466: 2q+1
       467: 2q+1
       468: 2q+1
       469: 2q+1
       470: 2q+1
       471: q+1
       472: q+1
       474: 2q+1
       475: 2q+1
       476: 2q+1
       477: 2q+1
       478: 2q+1
       479: 2q+1
       480: 2q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: q^2+2q+1
       491: q+1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q^2+2q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 1
       505: 1
       506: 1
       507: q^2+2q+1
       508: q^2+2q+1
       509: q+1
       510: q+1
       511: q+1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       517: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: 2q+1
       521: 2q+1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: q^2+2q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: q+1
       539: q+1
       540: q+1
       541: q^2+2q+1
       542: q^2+2q+1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: q^2+2q+1
       550: q^2+2q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: 1
       555: q^2+2q+1
       556: q^2+2q+1
       557: q^2+2q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       564: q^2+2q+1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       568: 2q+1
       569: 2q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: q^2+2q+1
       581: q+1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: q^2+2q+1
       589: q^2+2q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: q+1
       594: q+1
       595: q+1
       596: q^2+2q+1
       597: q^2+2q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: 1
       602: q^2+2q+1
       603: q^2+2q+1
       604: q^2+2q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: 2q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^3+2q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: q^2+2q+1
       626: q^2+2q+1
       627: 2q+1
       628: 2q+1
       629: 2q+1
       630: q+1
       631: q^2+2q+1
       632: q^2+2q+1
       633: q^2+2q+1
       634: 2q+1
       635: 2q+1
       636: 2q+1
       637: q+1
       638: q^2+2q+1
       639: q^2+2q+1
       640: q^2+2q+1
       641: 2q+1
       642: 2q+1
       643: q^2+2q+1
       644: q^2+2q+1
       645: q^2+2q+1
       646: q+1
       647: q+1
       648: q+1
       651: 2q+1
       652: 2q+1
       653: 2q+1
       654: q+1
       655: q+1
       656: q+1
       659: 2q+1
       660: 2q+1
       661: 2q+1
       662: 2q+1
       663: 2q+1
       664: 1
       665: 1
       667: 2q+1
       668: q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       677: 2q+1
       678: q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: 2q+1
       687: 2q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+2q+1
       694: q+1
       695: q+1
       696: q+1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: q+1
       702: q+1
       705: 2q+1
       706: 2q+1
       707: 2q+1
       708: 2q+1
       709: 2q+1
       710: q+1
       711: q+1
       713: 2q+1
       714: 2q+1
       715: 2q+1
       716: 2q+1
       717: 2q+1
       718: 2q+1
       719: 2q+1
       720: 1
       721: q+1
       722: 2q+1
       723: 2q+1
       724: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: q^2+2q+1
       730: q+1
       731: 2q+1
       732: 2q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q^2+2q+1
       739: q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 1
       744: 1
       745: 1
       746: q^2+2q+1
       747: q^2+2q+1
       748: q+1
       749: q+1
       750: q+1
       751: 1
       752: q+1
       753: q+1
       754: q+1
       757: 2q+1
       758: 2q+1
       759: 2q+1
       760: 2q+1
       761: 2q+1
       762: q+1
       763: q+1
       765: 2q+1
       766: 2q+1
       767: 2q+1
       768: 2q+1
       769: 2q+1
       770: 2q+1
       771: 2q+1
       772: 1
       773: q+1
       774: 2q+1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: q^2+2q+1
       782: q+1
       783: 2q+1
       784: 2q+1
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: q^2+2q+1
       791: q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 1
       796: 1
       797: 1
       798: q^2+2q+1
       799: q^2+2q+1
       800: q+1
       801: q+1
       802: q+1
       803: 1
       804: q+1
       805: q+1
       806: q+1
       808: q^2+2q+1
       809: 2q+1
       810: 2q+1
       811: 2q+1
       812: 2q+1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: 2q+1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: q^2+2q+1
       825: q+1
       826: 2q+1
       827: 2q+1
       828: 2q+1
       829: q+1
       830: q+1
       831: q+1
       832: q^2+2q+1
       833: q^2+2q+1
       834: 2q+1
       835: 2q+1
       836: 2q+1
       837: q+1
       838: q+1
       839: q+1
       840: q^2+2q+1
       841: q^2+2q+1
       842: 2q+1
       843: 2q+1
       844: 2q+1
       845: 1
       846: q^2+2q+1
       847: q^2+2q+1
       848: q^2+2q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: q+1
       857: 2q+1
       858: q+1
       859: q+1
       860: q+1
       863: 2q+1
       864: 2q+1
       865: 2q+1
       866: 1
       867: 1
       868: 1
       871: q+1
       872: q+1
       873: q+1
       874: q+1
       875: q+1
       876: 1
       877: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       885: 1
       886: 1
       888: 2q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: q+1
       897: q+1
       898: q+1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: q+1
       905: q+1
       908: 2q+1
       909: 2q+1
       910: 2q+1
       911: q+1
       912: q+1
       913: q+1
       916: 2q+1
       917: 2q+1
       918: 2q+1
       919: 2q+1
       920: 2q+1
       921: 1
       922: 1
       924: 2q+1
       925: q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: q+1
       931: 1
       932: q+1
       934: 2q+1
       935: q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: 2q+1
       944: 2q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q^2+2q+1
       951: q+1
       952: q+1
       953: q+1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: q+1
       959: q+1
       962: 2q+1
       963: 2q+1
       964: 2q+1
       965: q+1
       966: q+1
       967: q+1
       970: 2q+1
       971: 2q+1
       972: 2q+1
       973: 2q+1
       974: 2q+1
       975: 1
       976: 1
       978: 2q+1
       979: q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       988: 2q+1
       989: q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: q+1
       995: 1
       996: q+1
       997: 2q+1
       998: 2q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q^2+2q+1
      1005: q+1
      1006: q+1
      1007: q+1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: q+1
      1013: q+1
      1016: 2q+1
      1017: 2q+1
      1018: 2q+1
      1019: 2q+1
      1020: 2q+1
      1021: q+1
      1022: q+1
      1024: 2q+1
      1025: 2q+1
      1026: 2q+1
      1027: 2q+1
      1028: 2q+1
      1029: 2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: 2q+1
      1034: 2q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: q^2+2q+1
      1041: q+1
      1042: 2q+1
      1043: 2q+1
      1044: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: q^2+2q+1
      1050: q+1
      1051: 2q+1
      1052: 2q+1
      1053: 2q+1
      1054: 1
      1055: 1
      1056: 1
      1057: q^2+2q+1
      1058: q^2+2q+1
      1059: q+1
      1060: q+1
      1061: q+1
      1062: 1
      1063: q+1
      1064: q+1
      1065: q+1
      1069: q+1
      1070: q+1
      1074: 2q+1
      1075: 1
      1076: 1
      1077: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1104: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: q+1
      1116: 2q+1
      1117: q+1
      1118: q+1
      1119: q+1
      1122: 2q+1
      1123: 2q+1
      1124: 2q+1
      1125: 1
      1126: 1
      1127: 1
      1130: q+1
      1131: q+1
      1132: q+1
      1133: q+1
      1134: q+1
      1135: 1
      1136: 1
      1139: q+1
      1140: q+1
      1141: q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: 1
      1147: 2q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: q+1
      1156: q+1
      1157: q+1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: q+1
      1164: q+1
      1168: 2q+1
      1169: q+1
      1170: q+1
      1171: q+1
      1174: 2q+1
      1175: 2q+1
      1176: 2q+1
      1177: 1
      1178: 1
      1179: 1
      1182: q+1
      1183: q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: 1
      1191: q+1
      1192: q+1
      1193: q+1
      1194: q+1
      1195: q+1
      1196: 1
      1197: 1
      1199: 2q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: q+1
      1208: q+1
      1209: q+1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: q+1
      1216: q+1
      1219: 2q+1
      1220: 2q+1
      1221: 2q+1
      1222: q+1
      1223: q+1
      1224: q+1
      1227: 2q+1
      1228: 2q+1
      1229: 2q+1
      1230: 2q+1
      1231: 2q+1
      1232: 1
      1233: 1
      1235: 2q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: q+1
      1245: 2q+1
      1246: q+1
      1247: q+1
      1248: q+1
      1249: q+1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: 2q+1
      1255: 2q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q^2+2q+1
      1262: q+1
      1263: q+1
      1264: q+1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: q+1
      1270: q+1
      1273: q+1
      1277: 1
      1278: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1313: q+1
      1314: q+1
      1318: 2q+1
      1319: 1
      1320: 1
      1321: 1
      1324: q+1
      1325: q+1
      1326: q+1
      1327: 1
      1328: 1
      1329: 1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: 1
      1348: q+1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1356: q+1
      1360: q+1
      1361: q+1
      1365: 2q+1
      1366: 1
      1367: 1
      1368: 1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1379: q+1
      1380: q+1
      1381: q+1
      1382: 1
      1383: 1
      1384: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: 1
      1395: q+1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1403: q+1
      1407: 2q+1
      1408: q+1
      1409: q+1
      1410: q+1
      1413: 2q+1
      1414: 2q+1
      1415: 2q+1
      1416: 1
      1417: 1
      1418: 1
      1421: q+1
      1422: q+1
      1423: q+1
      1424: q+1
      1425: q+1
      1426: 1
      1427: 1
      1430: q+1
      1431: q+1
      1432: q+1
      1433: q+1
      1434: q+1
      1435: 1
      1436: 1
      1438: 2q+1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: q+1
      1447: q+1
      1448: q+1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q+1
      1455: q+1
      1460: 1
      1464: 1
      1465: 1
      1469: 1
      1470: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1488: q+1
      1492: 1
      1493: 1
      1497: q+1
      1498: 1
      1499: 1
      1500: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1527: q+1
      1531: 1
      1532: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: 1
      1543: q+1
      1544: 1
      1545: 1
      1546: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1567: q+1
      1568: q+1
      1572: 2q+1
      1573: 1
      1574: 1
      1575: 1
      1578: q+1
      1579: q+1
      1580: q+1
      1581: 1
      1582: 1
      1583: 1
      1586: q+1
      1587: q+1
      1588: q+1
      1589: 1
      1590: 1
      1591: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1600: 1
      1602: q+1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1610: q+1
      1616: 1
      1619: 1
      1623: 1
      1624: 1
      1628: 1
      1636: 1
      1640: 1
      1641: 1
      1645: 1
      1646: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1656: 1
      1657: 1
      1658: 1
      1666: 1
      1670: 1
      1671: 1
      1675: 1
      1676: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1686: 1
      1687: 1
      1688: 1
      1694: q+1
      1698: 1
      1699: 1
      1703: q+1
      1704: 1
      1705: 1
      1706: 1
      1710: q+1
      1711: 1
      1712: 1
      1713: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1724: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1738: 1
      1749: 1
      1752: 1
      1756: 1
      1757: 1
      1761: 1
      1770: 1
      1773: 1
      1777: 1
      1778: 1
      1782: 1
      1790: 1
      1794: 1
      1795: 1
      1799: 1
      1800: 1
      1804: 1
      1805: 1
      1806: 1
      1807: 1
      1810: 1
      1811: 1
      1812: 1
      1830: 1
      1843: 1
      1854: 1
      1857: 1
      1861: 1
      1862: 1
      1866: 1
      1894: 1

1895:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: 1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
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       828: q+1
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       830: 1
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       844: q+1
       845: q+1
       846: 1
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       849: q+1
       850: q+1
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       867: 1
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       900: q+1
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       902: q+1
       903: 1
       904: 1
       905: 1
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       913: 1
       914: 1
       915: 1
       916: 1
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       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: q+1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
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       946: q+1
       947: 1
       948: q+1
       949: 1
       950: 1
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       962: 1
       966: 1
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       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       983: q+1
       984: 1
       985: 1
       986: 1
       987: 1
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       990: 1
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      1020: 1
      1021: 1
      1022: 1
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      1025: 1
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      1032: 1
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      1100: 1
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      1102: 1
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      1104: 1
      1105: 1
      1106: 1
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      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1126: 1
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      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
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      1138: 1
      1139: 1
      1140: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
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      1153: 1
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      1155: 1
      1156: 1
      1157: 1
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      1159: q+1
      1160: 1
      1161: q+1
      1162: 1
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      1166: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1178: 1
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      1182: 1
      1183: 1
      1186: 1
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      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: q+1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1213: q+1
      1214: 1
      1215: 1
      1216: 1
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      1218: 1
      1219: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: q+1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: q+1
      1258: 1
      1259: q+1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1270: 1
      1274: 1
      1279: 1
      1280: 1
      1285: 1
      1286: 1
      1287: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1315: 1
      1316: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: q+1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1362: 1
      1363: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1379: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1431: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: q+1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1452: q+1
      1453: 1
      1454: 1
      1455: 1
      1461: 1
      1466: 1
      1471: 1
      1472: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1489: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1502: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1528: 1
      1533: 1
      1534: 1
      1539: 1
      1540: 1
      1541: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1553: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1558: 1
      1561: 1
      1562: 1
      1563: 1
      1564: 1
      1569: 1
      1570: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1586: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: q+1
      1608: 1
      1609: 1
      1610: 1
      1620: 1
      1625: 1
      1626: 1
      1631: 1
      1637: 1
      1642: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1667: 1
      1672: 1
      1677: 1
      1678: 1
      1683: 1
      1684: 1
      1685: 1
      1686: 1
      1690: 1
      1691: 1
      1695: 1
      1700: 1
      1701: 1
      1706: 1
      1707: 1
      1708: 1
      1713: 1
      1714: 1
      1715: 1
      1716: 1
      1720: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1725: 1
      1728: 1
      1729: 1
      1730: 1
      1739: 1
      1753: 1
      1758: 1
      1759: 1
      1764: 1
      1774: 1
      1779: 1
      1780: 1
      1785: 1
      1791: 1
      1796: 1
      1801: 1
      1802: 1
      1807: 1
      1808: 1
      1809: 1
      1810: 1
      1814: 1
      1815: 1
      1831: 1
      1844: 1
      1858: 1
      1863: 1
      1864: 1
      1869: 1
      1895: 1

1896:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: q+1
        21: q+1
        22: q+1
        23: q+1
        24: 1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: q+1
        51: 1
        52: q+1
        53: q+1
        54: q+1
        55: 1
        56: 1
        57: q+1
        58: q+1
        59: q+1
        60: q+1
        61: 1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q+1
        72: q+1
        73: q+1
        74: q+1
        75: 1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q+1
        85: q+1
        86: q+1
        87: q+1
        88: 1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: q+1
       106: 1
       107: q+1
       108: q+1
       109: 1
       110: 1
       111: 1
       112: q+1
       113: 1
       114: q+1
       115: q+1
       116: q+1
       117: 1
       118: 1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: 1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: 1
       136: q+1
       137: q+1
       138: q+1
       139: 1
       140: 1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: 1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: 1
       157: q+1
       158: q+1
       159: q+1
       160: 1
       161: 1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: 1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q+1
       178: q+1
       179: q+1
       180: 1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: 1
       190: 1
       191: q+1
       192: 1
       193: q+1
       194: 1
       195: 1
       196: 1
       197: 1
       198: 1
       199: q+1
       200: 1
       201: q+1
       202: q+1
       203: 1
       204: 1
       205: 1
       206: q+1
       207: 1
       208: q+1
       209: q+1
       210: q+1
       211: 1
       212: 1
       213: q+1
       214: 1
       215: q+1
       216: q+1
       217: q+1
       218: 1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: q+1
       230: 1
       231: q+1
       232: q+1
       233: 1
       234: 1
       235: 1
       236: q+1
       237: 1
       238: q+1
       239: q+1
       240: q+1
       241: 1
       242: 1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: 1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: q+1
       260: 1
       261: q+1
       262: q+1
       263: 1
       264: 1
       265: 1
       266: q+1
       267: 1
       268: q+1
       269: q+1
       270: q+1
       271: 1
       272: 1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: 1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: 1
       290: q+1
       291: q+1
       292: q+1
       293: 1
       294: 1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: 1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: 1
       310: 1
       311: 1
       312: q+1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: q+1
       322: 1
       323: q+1
       324: 1
       325: 1
       326: 1
       327: 1
       328: 1
       329: q+1
       330: 1
       331: q+1
       332: q+1
       333: 1
       334: 1
       335: 1
       336: 1
       337: q+1
       338: 1
       339: q+1
       340: q+1
       341: 1
       342: 1
       343: 1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: 1
       357: 1
       358: q+1
       359: 1
       360: q+1
       361: 1
       362: 1
       363: 1
       364: 1
       365: 1
       366: q+1
       367: 1
       368: q+1
       369: q+1
       370: 1
       371: 1
       372: 1
       373: q+1
       374: 1
       375: q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       380: q+1
       381: 1
       382: q+1
       383: q+1
       384: q+1
       385: 1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       395: 1
       396: 1
       397: q+1
       398: 1
       399: q+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q+1
       406: 1
       407: q+1
       408: q+1
       409: 1
       410: 1
       411: 1
       412: q+1
       413: 1
       414: q+1
       415: q+1
       416: q+1
       417: 1
       418: 1
       419: q+1
       420: 1
       421: q+1
       422: q+1
       423: q+1
       424: 1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: q+1
       436: 1
       437: q+1
       438: q+1
       439: 1
       440: 1
       441: 1
       442: q+1
       443: 1
       444: q+1
       445: q+1
       446: q+1
       447: 1
       448: 1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: 1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: 1
       465: 1
       466: 1
       468: 1
       469: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: q+1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: q+1
       486: 1
       487: q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: 1
       493: 1
       494: q+1
       495: 1
       496: q+1
       497: 1
       498: 1
       499: 1
       500: 1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       511: q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       516: 1
       517: 1
       518: 1
       519: q+1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: q+1
       529: 1
       530: q+1
       531: 1
       532: 1
       533: 1
       534: 1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: 1
       541: 1
       542: 1
       543: 1
       544: q+1
       545: 1
       546: q+1
       547: q+1
       548: 1
       549: 1
       550: 1
       551: q+1
       552: 1
       553: q+1
       554: q+1
       555: q+1
       556: 1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       563: 1
       564: 1
       565: 1
       566: q+1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q+1
       576: 1
       577: q+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q+1
       584: 1
       585: q+1
       586: q+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: q+1
       592: 1
       593: q+1
       594: q+1
       595: 1
       596: 1
       597: 1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: 1
       611: 1
       612: q+1
       613: 1
       614: q+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q+1
       621: 1
       622: q+1
       623: q+1
       624: 1
       625: 1
       626: 1
       627: q+1
       628: 1
       629: q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       634: q+1
       635: 1
       636: q+1
       637: q+1
       638: q+1
       639: 1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: 1
       650: 1
       652: 1
       654: 1
       656: 1
       657: 1
       658: 1
       659: 1
       661: 1
       662: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: q+1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: q+1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       707: 1
       708: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: q+1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: q+1
       734: 1
       735: q+1
       736: 1
       737: 1
       738: 1
       739: 1
       740: 1
       741: q+1
       742: 1
       743: q+1
       744: q+1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       750: q+1
       751: q+1
       752: q+1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       759: 1
       760: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q+1
       777: 1
       778: q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: q+1
       786: 1
       787: q+1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: q+1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q+1
       820: 1
       821: q+1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 1
       834: 1
       835: q+1
       836: 1
       837: q+1
       838: q+1
       839: 1
       840: 1
       841: 1
       842: q+1
       843: 1
       844: q+1
       845: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       854: 1
       856: 1
       859: 1
       861: 1
       862: 1
       864: 1
       866: 1
       868: 1
       869: 1
       870: 1
       871: 1
       873: 1
       874: 1
       876: 1
       877: 1
       878: 1
       879: 1
       880: 1
       882: 1
       883: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: 1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       909: 1
       911: 1
       913: 1
       914: 1
       915: 1
       916: 1
       918: 1
       919: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: q+1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: q+1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: q+1
       946: 1
       947: q+1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       959: 1
       960: 1
       961: 1
       963: 1
       965: 1
       967: 1
       968: 1
       969: 1
       970: 1
       972: 1
       973: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: q+1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1018: 1
      1019: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: q+1
      1045: 1
      1046: q+1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: q+1
      1053: 1
      1054: q+1
      1055: q+1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: 1
      1065: 1
      1067: 1
      1071: 1
      1073: 1
      1076: 1
      1078: 1
      1079: 1
      1081: 1
      1083: 1
      1085: 1
      1086: 1
      1087: 1
      1089: 1
      1091: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1115: 1
      1118: 1
      1120: 1
      1121: 1
      1123: 1
      1125: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1132: 1
      1133: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1141: 1
      1142: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1167: 1
      1170: 1
      1172: 1
      1173: 1
      1175: 1
      1177: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1184: 1
      1185: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1212: q+1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1220: 1
      1222: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1229: 1
      1230: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: q+1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: q+1
      1257: 1
      1258: q+1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1270: 1
      1275: 1
      1279: 1
      1281: 1
      1284: 1
      1286: 1
      1288: 1
      1291: 1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1311: 1
      1315: 1
      1317: 1
      1320: 1
      1322: 1
      1323: 1
      1325: 1
      1327: 1
      1329: 1
      1330: 1
      1331: 1
      1333: 1
      1335: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1358: 1
      1362: 1
      1364: 1
      1367: 1
      1369: 1
      1370: 1
      1372: 1
      1374: 1
      1376: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: q+1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1406: 1
      1409: 1
      1411: 1
      1412: 1
      1414: 1
      1416: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1423: 1
      1424: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: q+1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: q+1
      1450: 1
      1451: q+1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1462: 1
      1467: 1
      1471: 1
      1473: 1
      1476: 1
      1478: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1490: 1
      1494: 1
      1496: 1
      1499: 1
      1501: 1
      1503: 1
      1506: 1
      1508: 1
      1509: 1
      1511: 1
      1513: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1520: 1
      1521: 1
      1523: 1
      1524: 1
      1529: 1
      1533: 1
      1535: 1
      1538: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1565: 1
      1569: 1
      1571: 1
      1574: 1
      1576: 1
      1577: 1
      1579: 1
      1581: 1
      1583: 1
      1584: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: q+1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1621: 1
      1625: 1
      1627: 1
      1630: 1
      1638: 1
      1643: 1
      1647: 1
      1649: 1
      1652: 1
      1654: 1
      1655: 1
      1657: 1
      1659: 1
      1661: 1
      1668: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1684: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1696: 1
      1700: 1
      1702: 1
      1705: 1
      1707: 1
      1709: 1
      1712: 1
      1714: 1
      1715: 1
      1717: 1
      1719: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1726: 1
      1727: 1
      1729: 1
      1730: 1
      1740: 1
      1754: 1
      1758: 1
      1760: 1
      1763: 1
      1775: 1
      1779: 1
      1781: 1
      1784: 1
      1792: 1
      1797: 1
      1801: 1
      1803: 1
      1806: 1
      1808: 1
      1809: 1
      1811: 1
      1813: 1
      1815: 1
      1832: 1
      1845: 1
      1859: 1
      1863: 1
      1865: 1
      1868: 1
      1896: 1

1897:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: q^3+2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^3+2q^2+2q+1
        10: q^3+2q^2+2q+1
        11: q^3+2q^2+2q+1
        12: q^3+2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: q^3+2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: q^3+2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: 2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: q^3+2q^2+2q+1
        26: q^2+2q+1
        27: q^2+2q+1
        28: q^3+2q^2+2q+1
        29: q^3+2q^2+2q+1
        30: q^3+2q^2+2q+1
        31: q^3+2q^2+2q+1
        32: q^3+2q^2+2q+1
        33: q^3+2q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^3+2q^2+2q+1
        37: q^3+2q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^3+2q^2+2q+1
        40: q^3+2q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^3+2q^2+2q+1
        44: q^3+2q^2+2q+1
        45: q^3+2q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: q^3+2q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: q^2+2q+1
        57: q^2+2q+1
        58: q^2+2q+1
        59: 2q+1
        60: q^2+2q+1
        61: q^2+2q+1
        62: q^3+2q^2+2q+1
        63: q^2+2q+1
        64: q^2+2q+1
        65: q^3+2q^2+2q+1
        66: q^2+2q+1
        67: q^2+2q+1
        68: q^3+2q^2+2q+1
        69: q^3+2q^2+2q+1
        70: q^3+2q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: 2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: q^3+2q^2+2q+1
        77: q^2+2q+1
        78: q^2+2q+1
        79: q^3+2q^2+2q+1
        80: q^3+2q^2+2q+1
        81: q^3+2q^2+2q+1
        82: q^3+2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: 2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: q^3+2q^2+2q+1
        90: q^2+2q+1
        91: q^2+2q+1
        92: q^3+2q^2+2q+1
        93: q^3+2q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^3+2q^2+2q+1
        96: q^3+2q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^3+2q^2+2q+1
       101: q^3+2q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^3+2q^2+2q+1
       104: q^2+2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: q^2+2q+1
       113: q^2+2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: q^2+2q+1
       119: q^2+2q+1
       120: q^2+2q+1
       121: 2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: q^2+2q+1
       126: 2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: q^3+2q^2+2q+1
       130: q^2+2q+1
       131: q^2+2q+1
       132: q^3+2q^2+2q+1
       133: q^3+2q^2+2q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: q^2+2q+1
       141: q^2+2q+1
       142: q^2+2q+1
       143: 2q+1
       144: q^2+2q+1
       145: q^2+2q+1
       146: q^3+2q^2+2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: q^3+2q^2+2q+1
       150: q^2+2q+1
       151: q^2+2q+1
       152: q^3+2q^2+2q+1
       153: q^3+2q^2+2q+1
       154: q^3+2q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: q^2+2q+1
       162: q^2+2q+1
       163: q^2+2q+1
       164: 2q+1
       165: q^2+2q+1
       166: q^2+2q+1
       167: q^3+2q^2+2q+1
       168: q^2+2q+1
       169: q^2+2q+1
       170: q^3+2q^2+2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^3+2q^2+2q+1
       174: q^3+2q^2+2q+1
       175: q^3+2q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: 2q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: q^3+2q^2+2q+1
       182: q^2+2q+1
       183: q^2+2q+1
       184: q^3+2q^2+2q+1
       185: q^3+2q^2+2q+1
       186: q^3+2q^2+2q+1
       187: q^3+2q^2+2q+1
       188: q^3+2q^2+2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: q^2+2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: q^2+2q+1
       207: q^2+2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: q^2+2q+1
       213: q^2+2q+1
       214: q^2+2q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: q^2+2q+1
       220: q^2+2q+1
       221: q^2+2q+1
       222: 2q+1
       223: q^2+2q+1
       224: q^2+2q+1
       225: q^3+2q^2+2q+1
       226: q^2+2q+1
       227: q^2+2q+1
       228: q^2+2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: q^2+2q+1
       237: q^2+2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: q^2+2q+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: 2q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: q^2+2q+1
       250: 2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: q^3+2q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^3+2q^2+2q+1
       257: q^3+2q^2+2q+1
       258: q^2+2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: q^2+2q+1
       267: q^2+2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: q^2+2q+1
       273: q^2+2q+1
       274: q^2+2q+1
       275: 2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q^2+2q+1
       279: q^2+2q+1
       280: 2q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: q^3+2q^2+2q+1
       284: q^2+2q+1
       285: q^2+2q+1
       286: q^3+2q^2+2q+1
       287: q^3+2q^2+2q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: q^2+2q+1
       295: q^2+2q+1
       296: q^2+2q+1
       297: 2q+1
       298: q^2+2q+1
       299: q^2+2q+1
       300: q^3+2q^2+2q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: q^3+2q^2+2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^3+2q^2+2q+1
       307: q^3+2q^2+2q+1
       308: q^3+2q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       319: q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       328: q^2+2q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: q^2+2q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: q^2+2q+1
       345: q^2+2q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: q^2+2q+1
       351: q^2+2q+1
       352: q^2+2q+1
       353: 2q+1
       354: q^2+2q+1
       355: q^2+2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: q^2+2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: q^2+2q+1
       374: q^2+2q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: q^2+2q+1
       380: q^2+2q+1
       381: q^2+2q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: q^2+2q+1
       387: q^2+2q+1
       388: q^2+2q+1
       389: 2q+1
       390: q^2+2q+1
       391: q^2+2q+1
       392: q^3+2q^2+2q+1
       393: q^2+2q+1
       394: q^2+2q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: q^2+2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q+1
       412: q^2+2q+1
       413: q^2+2q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: q^2+2q+1
       419: q^2+2q+1
       420: q^2+2q+1
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: q^2+2q+1
       426: q^2+2q+1
       427: q^2+2q+1
       428: 2q+1
       429: q^2+2q+1
       430: q^2+2q+1
       431: q^3+2q^2+2q+1
       432: q^2+2q+1
       433: q^2+2q+1
       434: q^2+2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: q^2+2q+1
       443: q^2+2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: q^2+2q+1
       449: q^2+2q+1
       450: q^2+2q+1
       451: 2q+1
       452: q^2+2q+1
       453: q^2+2q+1
       454: q^2+2q+1
       455: q^2+2q+1
       456: 2q+1
       457: q^2+2q+1
       458: q^2+2q+1
       459: q^3+2q^2+2q+1
       460: q^2+2q+1
       461: q^2+2q+1
       462: q^3+2q^2+2q+1
       463: q^3+2q^2+2q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       473: q+1
       474: q+1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: q^2+2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: q^2+2q+1
       510: q^2+2q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: 2q+1
       515: q^2+2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       526: q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       535: q^2+2q+1
       536: 2q+1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       543: q^2+2q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: q^2+2q+1
       552: q^2+2q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: q^2+2q+1
       558: q^2+2q+1
       559: q^2+2q+1
       560: 2q+1
       561: q^2+2q+1
       562: q^2+2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       573: q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: q+1
       581: q+1
       582: q^2+2q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q+1
       590: q^2+2q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q+1
       598: q^2+2q+1
       599: q^2+2q+1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: q^2+2q+1
       605: q^2+2q+1
       606: q^2+2q+1
       607: 2q+1
       608: q^2+2q+1
       609: q^2+2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: q^2+2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: q+1
       627: q^2+2q+1
       628: q^2+2q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: 2q+1
       633: q^2+2q+1
       634: q^2+2q+1
       635: q^2+2q+1
       636: 2q+1
       637: 2q+1
       638: 2q+1
       639: 2q+1
       640: q^2+2q+1
       641: q^2+2q+1
       642: q^2+2q+1
       643: 2q+1
       644: q^2+2q+1
       645: q^2+2q+1
       646: q^3+2q^2+2q+1
       647: q^2+2q+1
       648: q^2+2q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: q+1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       666: q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: q^2+2q+1
       696: 2q+1
       697: 2q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: 2q+1
       702: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       712: q+1
       713: q+1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       722: q+1
       723: 2q+1
       724: 2q+1
       725: 2q+1
       726: q+1
       727: q+1
       728: 2q+1
       729: q+1
       730: q+1
       731: q+1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       740: q^2+2q+1
       741: 2q+1
       742: 2q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: q^2+2q+1
       749: q^2+2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: 2q+1
       754: q^2+2q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       764: q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       772: q+1
       774: q+1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: q+1
       782: q+1
       783: q+1
       784: 2q+1
       785: 2q+1
       786: 2q+1
       787: q+1
       788: q+1
       789: 2q+1
       790: q+1
       791: q+1
       792: q^2+2q+1
       793: 2q+1
       794: 2q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: q+1
       800: q^2+2q+1
       801: q^2+2q+1
       802: 2q+1
       803: 2q+1
       804: 2q+1
       805: 2q+1
       806: q^2+2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       817: q+1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: q+1
       825: q+1
       826: q^2+2q+1
       827: 2q+1
       828: 2q+1
       829: 2q+1
       830: 2q+1
       831: 2q+1
       832: 2q+1
       833: q+1
       834: q^2+2q+1
       835: 2q+1
       836: 2q+1
       837: 2q+1
       838: 2q+1
       839: 2q+1
       840: 2q+1
       841: q+1
       842: q^2+2q+1
       843: q^2+2q+1
       844: 2q+1
       845: 2q+1
       846: 2q+1
       847: 2q+1
       848: q^2+2q+1
       849: q^2+2q+1
       850: q^2+2q+1
       851: 2q+1
       852: q^2+2q+1
       853: q^2+2q+1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       897: q+1
       898: 2q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: q+1
       905: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: q+1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       921: 1
       923: q+1
       924: q+1
       925: 2q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: 1
       931: q+1
       933: q+1
       934: q+1
       935: 2q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       943: q+1
       944: 2q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: q+1
       951: q+1
       952: q^2+2q+1
       953: 2q+1
       954: 2q+1
       955: 2q+1
       956: 2q+1
       957: 2q+1
       958: 2q+1
       959: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: q+1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       977: q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: 1
       985: q+1
       987: q+1
       988: q+1
       989: 2q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: 1
       995: q+1
       997: q+1
       998: 2q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1006: q^2+2q+1
      1007: 2q+1
      1008: 2q+1
      1009: 2q+1
      1010: 2q+1
      1011: 2q+1
      1012: 2q+1
      1013: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1023: q+1
      1024: q+1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: q+1
      1033: q+1
      1034: 2q+1
      1035: 2q+1
      1036: 2q+1
      1037: q+1
      1038: q+1
      1039: 2q+1
      1040: q+1
      1041: q+1
      1042: q+1
      1043: 2q+1
      1044: 2q+1
      1045: 2q+1
      1046: q+1
      1047: q+1
      1048: 2q+1
      1049: q+1
      1050: q+1
      1051: q^2+2q+1
      1052: 2q+1
      1053: 2q+1
      1054: 2q+1
      1055: 2q+1
      1056: 2q+1
      1057: 2q+1
      1058: q+1
      1059: q^2+2q+1
      1060: q^2+2q+1
      1061: 2q+1
      1062: 2q+1
      1063: 2q+1
      1064: 2q+1
      1065: q^2+2q+1
      1068: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1103: q+1
      1104: q+1
      1105: 2q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1111: q+1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: q+1
      1130: 1
      1131: q+1
      1132: q+1
      1133: 1
      1134: 1
      1135: 1
      1138: q+1
      1139: 1
      1140: q+1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1146: q+1
      1147: q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1156: q+1
      1157: 2q+1
      1158: 2q+1
      1159: 2q+1
      1160: q+1
      1161: q+1
      1162: 2q+1
      1163: q+1
      1164: q+1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: q+1
      1182: 1
      1183: q+1
      1184: q+1
      1185: 1
      1186: 1
      1187: 1
      1190: q+1
      1191: 1
      1192: q+1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1198: q+1
      1199: q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1203: q+1
      1204: q+1
      1205: 1
      1206: q+1
      1208: q+1
      1209: 2q+1
      1210: 2q+1
      1211: 2q+1
      1212: q+1
      1213: q+1
      1214: 2q+1
      1215: q+1
      1216: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1226: q+1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1234: q+1
      1235: q+1
      1236: 2q+1
      1237: q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: 1
      1242: q+1
      1244: q+1
      1245: q+1
      1246: 2q+1
      1247: q+1
      1248: q+1
      1249: q+1
      1250: q+1
      1251: 1
      1252: q+1
      1254: q+1
      1255: 2q+1
      1256: 2q+1
      1257: 2q+1
      1258: q+1
      1259: q+1
      1260: 2q+1
      1261: q+1
      1262: q+1
      1263: q^2+2q+1
      1264: 2q+1
      1265: 2q+1
      1266: 2q+1
      1267: 2q+1
      1268: 2q+1
      1269: 2q+1
      1270: q+1
      1276: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1302: q+1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1312: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: q+1
      1340: 1
      1341: q+1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1347: q+1
      1348: q+1
      1349: 2q+1
      1350: q+1
      1351: q+1
      1352: q+1
      1353: q+1
      1354: 1
      1355: q+1
      1359: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: q+1
      1387: 1
      1388: q+1
      1389: q+1
      1390: 1
      1391: 1
      1392: 1
      1394: q+1
      1395: q+1
      1396: 2q+1
      1397: q+1
      1398: q+1
      1399: q+1
      1400: q+1
      1401: 1
      1402: q+1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: q+1
      1421: 1
      1422: q+1
      1423: q+1
      1424: 1
      1425: 1
      1426: 1
      1429: q+1
      1430: 1
      1431: q+1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1437: q+1
      1438: q+1
      1439: 2q+1
      1440: q+1
      1441: q+1
      1442: q+1
      1443: q+1
      1444: 1
      1445: q+1
      1447: q+1
      1448: 2q+1
      1449: 2q+1
      1450: 2q+1
      1451: q+1
      1452: q+1
      1453: 2q+1
      1454: q+1
      1455: q+1
      1463: 1
      1468: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1491: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1517: q+1
      1518: 1
      1519: q+1
      1520: q+1
      1521: 1
      1522: 1
      1523: 1
      1530: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1556: q+1
      1557: 1
      1558: q+1
      1559: q+1
      1560: 1
      1561: 1
      1562: 1
      1566: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1593: q+1
      1594: 1
      1595: q+1
      1596: q+1
      1597: 1
      1598: 1
      1599: 1
      1601: q+1
      1602: q+1
      1603: 2q+1
      1604: q+1
      1605: q+1
      1606: q+1
      1607: q+1
      1608: 1
      1609: q+1
      1622: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1639: 1
      1644: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1669: 1
      1674: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1697: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1723: q+1
      1724: 1
      1725: q+1
      1726: q+1
      1727: 1
      1728: 1
      1729: 1
      1741: 1
      1755: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1776: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1793: 1
      1798: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1809: 1
      1810: 1
      1811: 1
      1812: 1
      1813: 1
      1814: 1
      1833: 1
      1846: 1
      1860: 1
      1864: 1
      1865: 1
      1866: 1
      1867: 1
      1897: 1

1898:    0: q^4+2q^2+1
         1: q^4+2q^2+1
         2: 2q^2+1
         3: q^4+2q^2+1
         4: q^4+2q^2+1
         5: q^4+2q^2+1
         6: q^2+1
         7: q^2+1
         8: 2q^2+1
         9: q^4+2q^2+1
        10: 2q^2+1
        11: q^4+2q^2+1
        12: q^4+2q^2+1
        13: q^4+2q^2+1
        14: 2q^2+1
        15: q^4+2q^2+1
        16: q^4+2q^2+1
        17: 2q^2+1
        18: q^4+2q^2+1
        19: q^4+2q^2+1
        20: q^2+1
        21: 1
        22: q^2+1
        23: 2q^2+1
        24: 2q^2+1
        25: q^2+1
        26: q^2+1
        27: 2q^2+1
        28: q^4+2q^2+1
        29: 2q^2+1
        30: q^4+2q^2+1
        31: 2q^2+1
        32: q^4+2q^2+1
        33: q^2+1
        34: q^2+1
        35: 2q^2+1
        36: q^4+2q^2+1
        37: 2q^2+1
        38: q^4+2q^2+1
        39: q^4+2q^2+1
        40: q^2+1
        41: q^2+1
        42: 2q^2+1
        43: q^4+2q^2+1
        44: 2q^2+1
        45: q^4+2q^2+1
        46: q^4+2q^2+1
        47: q^4+2q^2+1
        48: 2q^2+1
        49: q^4+2q^2+1
        50: q^2+1
        51: q^2+1
        52: 1
        53: 1
        54: q^2+1
        55: q^2+1
        56: 2q^2+1
        57: q^2+1
        58: 1
        59: q^2+1
        60: 2q^2+1
        61: 2q^2+1
        62: q^2+1
        63: q^2+1
        64: 2q^2+1
        65: q^2+1
        66: q^2+1
        67: 2q^2+1
        68: q^4+2q^2+1
        69: 2q^2+1
        70: q^4+2q^2+1
        71: q^2+1
        72: 1
        73: q^2+1
        74: 2q^2+1
        75: 2q^2+1
        76: q^2+1
        77: q^2+1
        78: 2q^2+1
        79: q^4+2q^2+1
        80: 2q^2+1
        81: q^4+2q^2+1
        82: 2q^2+1
        83: q^4+2q^2+1
        84: q^2+1
        85: 1
        86: q^2+1
        87: 2q^2+1
        88: 2q^2+1
        89: q^2+1
        90: q^2+1
        91: 2q^2+1
        92: q^4+2q^2+1
        93: 2q^2+1
        94: q^4+2q^2+1
        95: 2q^2+1
        96: q^4+2q^2+1
        97: q^2+1
        98: q^2+1
        99: 2q^2+1
       100: q^4+2q^2+1
       101: 2q^2+1
       102: q^4+2q^2+1
       103: q^4+2q^2+1
       104: q^2+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: q^2+1
       111: 2q^2+1
       112: q^2+1
       113: q^2+1
       114: 1
       115: 1
       116: q^2+1
       117: q^2+1
       118: 2q^2+1
       119: q^2+1
       120: 1
       121: q^2+1
       122: 2q^2+1
       123: 2q^2+1
       124: q^2+1
       125: 1
       126: q^2+1
       127: 2q^2+1
       128: 2q^2+1
       129: q^2+1
       130: q^2+1
       131: 2q^2+1
       132: q^4+2q^2+1
       133: 2q^2+1
       134: q^2+1
       135: q^2+1
       136: 1
       137: 1
       138: q^2+1
       139: q^2+1
       140: 2q^2+1
       141: q^2+1
       142: 1
       143: q^2+1
       144: 2q^2+1
       145: 2q^2+1
       146: q^2+1
       147: q^2+1
       148: 2q^2+1
       149: q^2+1
       150: q^2+1
       151: 2q^2+1
       152: q^4+2q^2+1
       153: 2q^2+1
       154: q^4+2q^2+1
       155: q^2+1
       156: q^2+1
       157: 1
       158: 1
       159: q^2+1
       160: q^2+1
       161: 2q^2+1
       162: q^2+1
       163: 1
       164: q^2+1
       165: 2q^2+1
       166: 2q^2+1
       167: q^2+1
       168: q^2+1
       169: 2q^2+1
       170: q^2+1
       171: q^2+1
       172: 2q^2+1
       173: q^4+2q^2+1
       174: 2q^2+1
       175: q^4+2q^2+1
       176: q^2+1
       177: 1
       178: q^2+1
       179: 2q^2+1
       180: 2q^2+1
       181: q^2+1
       182: q^2+1
       183: 2q^2+1
       184: q^4+2q^2+1
       185: 2q^2+1
       186: q^4+2q^2+1
       187: 2q^2+1
       188: q^4+2q^2+1
       189: q^2+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q^2+1
       197: q^2+1
       198: q^2+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: q^2+1
       205: 2q^2+1
       206: q^2+1
       207: q^2+1
       208: 1
       209: 1
       210: q^2+1
       211: q^2+1
       212: 2q^2+1
       213: q^2+1
       214: q^2+1
       215: 1
       216: 1
       217: q^2+1
       218: q^2+1
       219: 2q^2+1
       220: q^2+1
       221: 1
       222: q^2+1
       223: 2q^2+1
       224: 2q^2+1
       225: q^2+1
       226: q^2+1
       227: 2q^2+1
       228: q^2+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q^2+1
       235: 2q^2+1
       236: q^2+1
       237: q^2+1
       238: 1
       239: 1
       240: q^2+1
       241: q^2+1
       242: 2q^2+1
       243: q^2+1
       244: 1
       245: q^2+1
       246: 2q^2+1
       247: 2q^2+1
       248: q^2+1
       249: 1
       250: q^2+1
       251: 2q^2+1
       252: 2q^2+1
       253: q^2+1
       254: q^2+1
       255: 2q^2+1
       256: q^4+2q^2+1
       257: 2q^2+1
       258: q^2+1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: q^2+1
       265: 2q^2+1
       266: q^2+1
       267: q^2+1
       268: 1
       269: 1
       270: q^2+1
       271: q^2+1
       272: 2q^2+1
       273: q^2+1
       274: 1
       275: q^2+1
       276: 2q^2+1
       277: 2q^2+1
       278: q^2+1
       279: 1
       280: q^2+1
       281: 2q^2+1
       282: 2q^2+1
       283: q^2+1
       284: q^2+1
       285: 2q^2+1
       286: q^4+2q^2+1
       287: 2q^2+1
       288: q^2+1
       289: q^2+1
       290: 1
       291: 1
       292: q^2+1
       293: q^2+1
       294: 2q^2+1
       295: q^2+1
       296: 1
       297: q^2+1
       298: 2q^2+1
       299: 2q^2+1
       300: q^2+1
       301: q^2+1
       302: 2q^2+1
       303: q^2+1
       304: q^2+1
       305: 2q^2+1
       306: q^4+2q^2+1
       307: 2q^2+1
       308: q^4+2q^2+1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: q^2+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q^2+1
       327: q^2+1
       328: q^2+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: q^2+1
       335: 2q^2+1
       336: q^2+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q^2+1
       343: 2q^2+1
       344: q^2+1
       345: q^2+1
       346: 1
       347: 1
       348: q^2+1
       349: q^2+1
       350: 2q^2+1
       351: q^2+1
       352: 1
       353: q^2+1
       354: 2q^2+1
       355: 2q^2+1
       356: q^2+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q^2+1
       364: q^2+1
       365: q^2+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q^2+1
       372: 2q^2+1
       373: q^2+1
       374: q^2+1
       375: 1
       376: 1
       377: q^2+1
       378: q^2+1
       379: 2q^2+1
       380: q^2+1
       381: q^2+1
       382: 1
       383: 1
       384: q^2+1
       385: q^2+1
       386: 2q^2+1
       387: q^2+1
       388: 1
       389: q^2+1
       390: 2q^2+1
       391: 2q^2+1
       392: q^2+1
       393: q^2+1
       394: 2q^2+1
       395: q^2+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q^2+1
       403: q^2+1
       404: q^2+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q^2+1
       411: 2q^2+1
       412: q^2+1
       413: q^2+1
       414: 1
       415: 1
       416: q^2+1
       417: q^2+1
       418: 2q^2+1
       419: q^2+1
       420: q^2+1
       421: 1
       422: 1
       423: q^2+1
       424: q^2+1
       425: 2q^2+1
       426: q^2+1
       427: 1
       428: q^2+1
       429: 2q^2+1
       430: 2q^2+1
       431: q^2+1
       432: q^2+1
       433: 2q^2+1
       434: q^2+1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q^2+1
       441: 2q^2+1
       442: q^2+1
       443: q^2+1
       444: 1
       445: 1
       446: q^2+1
       447: q^2+1
       448: 2q^2+1
       449: q^2+1
       450: 1
       451: q^2+1
       452: 2q^2+1
       453: 2q^2+1
       454: q^2+1
       455: 1
       456: q^2+1
       457: 2q^2+1
       458: 2q^2+1
       459: q^2+1
       460: q^2+1
       461: 2q^2+1
       462: q^4+2q^2+1
       463: 2q^2+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: q^2+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q^2+1
       491: q^2+1
       492: q^2+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q^2+1
       500: q^2+1
       501: q^2+1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q^2+1
       508: 2q^2+1
       509: q^2+1
       510: q^2+1
       511: 1
       512: 1
       513: q^2+1
       514: q^2+1
       515: 2q^2+1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: q^2+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q^2+1
       534: q^2+1
       535: q^2+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: q^2+1
       542: 2q^2+1
       543: q^2+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: q^2+1
       550: 2q^2+1
       551: q^2+1
       552: q^2+1
       553: 1
       554: 1
       555: q^2+1
       556: q^2+1
       557: 2q^2+1
       558: q^2+1
       559: 1
       560: q^2+1
       561: 2q^2+1
       562: 2q^2+1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: q^2+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q^2+1
       581: q^2+1
       582: q^2+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: q^2+1
       589: 2q^2+1
       590: q^2+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: q^2+1
       597: 2q^2+1
       598: q^2+1
       599: q^2+1
       600: 1
       601: 1
       602: q^2+1
       603: q^2+1
       604: 2q^2+1
       605: q^2+1
       606: 1
       607: q^2+1
       608: 2q^2+1
       609: 2q^2+1
       610: q^2+1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+1
       618: q^2+1
       619: q^2+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: q^2+1
       626: 2q^2+1
       627: q^2+1
       628: q^2+1
       629: 1
       630: 1
       631: q^2+1
       632: q^2+1
       633: 2q^2+1
       634: q^2+1
       635: q^2+1
       636: 1
       637: 1
       638: q^2+1
       639: q^2+1
       640: 2q^2+1
       641: q^2+1
       642: 1
       643: q^2+1
       644: 2q^2+1
       645: 2q^2+1
       646: q^2+1
       647: q^2+1
       648: 2q^2+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: q^2+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+1
       694: q^2+1
       695: q^2+1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: q^2+1
       702: 2q^2+1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: q^2+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q^2+1
       730: q^2+1
       731: q^2+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q^2+1
       739: q^2+1
       740: q^2+1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: q^2+1
       747: 2q^2+1
       748: q^2+1
       749: q^2+1
       750: 1
       751: 1
       752: q^2+1
       753: q^2+1
       754: 2q^2+1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: q^2+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q^2+1
       782: q^2+1
       783: q^2+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q^2+1
       791: q^2+1
       792: q^2+1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q^2+1
       799: 2q^2+1
       800: q^2+1
       801: q^2+1
       802: 1
       803: 1
       804: q^2+1
       805: q^2+1
       806: 2q^2+1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: q^2+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: q^2+1
       825: q^2+1
       826: q^2+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: q^2+1
       833: 2q^2+1
       834: q^2+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: q^2+1
       841: 2q^2+1
       842: q^2+1
       843: q^2+1
       844: 1
       845: 1
       846: q^2+1
       847: q^2+1
       848: 2q^2+1
       849: q^2+1
       850: 1
       851: q^2+1
       852: 2q^2+1
       853: 2q^2+1
       857: 1
       858: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: q^2+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: q^2+1
       905: q^2+1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: q^2+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q^2+1
       951: q^2+1
       952: q^2+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: q^2+1
       959: 2q^2+1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: q^2+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q^2+1
      1005: q^2+1
      1006: q^2+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: q^2+1
      1013: 2q^2+1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: q^2+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: q^2+1
      1041: q^2+1
      1042: q^2+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: q^2+1
      1050: q^2+1
      1051: q^2+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: q^2+1
      1058: 2q^2+1
      1059: q^2+1
      1060: q^2+1
      1061: 1
      1062: 1
      1063: q^2+1
      1064: q^2+1
      1065: 2q^2+1
      1069: 1
      1074: 1
      1075: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1116: 1
      1117: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: q^2+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: q^2+1
      1164: q^2+1
      1168: 1
      1169: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: q^2+1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: q^2+1
      1216: q^2+1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: q^2+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q^2+1
      1262: q^2+1
      1263: q^2+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: q^2+1
      1270: 2q^2+1
      1277: 1
      1282: 1
      1283: 1
      1289: 1
      1290: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1313: 1
      1318: 1
      1319: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1360: 1
      1365: 1
      1366: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1407: 1
      1408: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q^2+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q^2+1
      1455: q^2+1
      1464: 1
      1469: 1
      1474: 1
      1475: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1492: 1
      1497: 1
      1498: 1
      1504: 1
      1505: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1531: 1
      1536: 1
      1537: 1
      1543: 1
      1544: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1567: 1
      1572: 1
      1573: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1623: 1
      1628: 1
      1629: 1
      1640: 1
      1645: 1
      1650: 1
      1651: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1670: 1
      1675: 1
      1680: 1
      1681: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1698: 1
      1703: 1
      1704: 1
      1710: 1
      1711: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1724: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1729: 1
      1742: 1
      1756: 1
      1761: 1
      1762: 1
      1777: 1
      1782: 1
      1783: 1
      1794: 1
      1799: 1
      1804: 1
      1805: 1
      1810: 1
      1811: 1
      1812: 1
      1813: 1
      1814: 1
      1834: 1
      1847: 1
      1861: 1
      1866: 1
      1867: 1
      1898: 1

1899:    0: q+1
         1: q+1
         2: q+1
         3: q+1
         4: q+1
         5: q+1
         6: q+1
         7: q+1
         8: q+1
         9: q+1
        10: q+1
        11: q+1
        12: q+1
        13: q+1
        14: q+1
        15: q+1
        16: q+1
        17: q+1
        18: q+1
        19: q+1
        20: 1
        21: q+1
        22: q+1
        23: q+1
        24: q+1
        25: q+1
        26: q+1
        27: q+1
        28: q+1
        29: q+1
        30: q+1
        31: q+1
        32: q+1
        33: q+1
        34: q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q+1
        41: q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q+1
        48: q+1
        49: q+1
        50: 1
        51: 1
        52: 1
        53: q+1
        54: q+1
        55: q+1
        56: q+1
        57: 1
        58: q+1
        59: q+1
        60: q+1
        61: q+1
        62: q+1
        63: q+1
        64: q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: 1
        72: q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: 1
        85: q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q+1
        98: q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: q+1
       109: q+1
       110: q+1
       111: q+1
       112: 1
       113: 1
       114: 1
       115: q+1
       116: q+1
       117: q+1
       118: q+1
       119: 1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: 1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: 1
       135: 1
       136: 1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: 1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: 1
       156: 1
       157: 1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: 1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: 1
       177: q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: q+1
       196: q+1
       197: q+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: q+1
       203: q+1
       204: q+1
       205: q+1
       206: 1
       207: 1
       208: 1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: 1
       215: 1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: 1
       221: q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: 1
       237: 1
       238: 1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: 1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: 1
       267: 1
       268: 1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: 1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: 1
       289: 1
       290: 1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: 1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: q+1
       318: q+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: 1
       330: 1
       331: 1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: 1
       345: 1
       346: 1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: 1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: q+1
       363: q+1
       364: q+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: q+1
       370: q+1
       371: q+1
       372: q+1
       373: 1
       374: 1
       375: 1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: 1
       382: 1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: q+1
       409: q+1
       410: q+1
       411: q+1
       412: 1
       413: 1
       414: 1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: 1
       427: q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: 1
       443: 1
       444: 1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: q+1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: q+1
       482: q+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: 1
       510: 1
       511: 1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: q+1
       525: q+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: 1
       537: 1
       538: 1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: 1
       552: 1
       553: 1
       554: q+1
       555: q+1
       556: q+1
       557: q+1
       558: 1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: 1
       584: 1
       585: 1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: 1
       599: 1
       600: 1
       601: q+1
       602: q+1
       603: q+1
       604: q+1
       605: 1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: 1
       628: 1
       629: 1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: q+1
       644: q+1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       653: 1
       654: 1
       655: 1
       656: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: q+1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: q+1
       685: q+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: q+1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: q+1
       721: q+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: q+1
       729: q+1
       730: q+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: q+1
       738: q+1
       739: q+1
       740: 1
       741: 1
       742: 1
       743: 1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: 1
       749: 1
       750: 1
       751: q+1
       752: q+1
       753: q+1
       754: q+1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: q+1
       773: q+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: q+1
       781: q+1
       782: q+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: q+1
       790: q+1
       791: q+1
       792: 1
       793: 1
       794: 1
       795: 1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       800: 1
       801: 1
       802: 1
       803: q+1
       804: q+1
       805: q+1
       806: q+1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: 1
       828: 1
       829: 1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       842: 1
       843: 1
       844: 1
       845: q+1
       846: q+1
       847: q+1
       848: q+1
       849: 1
       850: q+1
       851: q+1
       852: q+1
       853: q+1
       858: 1
       859: 1
       860: 1
       865: 1
       866: 1
       867: 1
       868: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: q+1
       904: q+1
       905: q+1
       910: 1
       911: 1
       912: 1
       913: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: q+1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: q+1
       932: q+1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: q+1
       942: q+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: q+1
       950: q+1
       951: q+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: q+1
       957: q+1
       958: q+1
       959: q+1
       964: 1
       965: 1
       966: 1
       967: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: q+1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: q+1
       986: q+1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: q+1
       996: q+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: q+1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: q+1
      1032: q+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: q+1
      1040: q+1
      1041: q+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: q+1
      1049: q+1
      1050: q+1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: q+1
      1056: q+1
      1057: q+1
      1058: q+1
      1059: 1
      1060: 1
      1061: 1
      1062: q+1
      1063: q+1
      1064: q+1
      1065: q+1
      1070: 1
      1075: 1
      1076: 1
      1077: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: q+1
      1112: q+1
      1117: 1
      1118: 1
      1119: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: q+1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1155: q+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: q+1
      1163: q+1
      1164: q+1
      1169: 1
      1170: 1
      1171: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: q+1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: q+1
      1207: q+1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: q+1
      1215: q+1
      1216: q+1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: q+1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: q+1
      1243: q+1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: q+1
      1253: q+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: q+1
      1261: q+1
      1262: q+1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: q+1
      1268: q+1
      1269: q+1
      1270: q+1
      1278: 1
      1283: 1
      1284: 1
      1285: 1
      1290: 1
      1291: 1
      1292: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: q+1
      1314: 1
      1319: 1
      1320: 1
      1321: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: q+1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: q+1
      1356: q+1
      1361: 1
      1366: 1
      1367: 1
      1368: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: q+1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1402: q+1
      1403: q+1
      1408: 1
      1409: 1
      1410: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: q+1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1436: q+1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: q+1
      1446: q+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: q+1
      1454: q+1
      1455: q+1
      1465: 1
      1470: 1
      1475: 1
      1476: 1
      1477: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1493: 1
      1498: 1
      1499: 1
      1500: 1
      1505: 1
      1506: 1
      1507: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1524: q+1
      1532: 1
      1537: 1
      1538: 1
      1539: 1
      1544: 1
      1545: 1
      1546: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1563: q+1
      1568: 1
      1573: 1
      1574: 1
      1575: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1600: q+1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1609: q+1
      1610: q+1
      1624: 1
      1629: 1
      1630: 1
      1631: 1
      1641: 1
      1646: 1
      1651: 1
      1652: 1
      1653: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1671: 1
      1676: 1
      1681: 1
      1682: 1
      1683: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1699: 1
      1704: 1
      1705: 1
      1706: 1
      1711: 1
      1712: 1
      1713: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1729: 1
      1730: q+1
      1743: 1
      1757: 1
      1762: 1
      1763: 1
      1764: 1
      1778: 1
      1783: 1
      1784: 1
      1785: 1
      1795: 1
      1800: 1
      1805: 1
      1806: 1
      1807: 1
      1812: 1
      1813: 1
      1814: 1
      1815: 1
      1835: 1
      1848: 1
      1862: 1
      1867: 1
      1868: 1
      1869: 1
      1899: 1

1900:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^3+q^2+q+1
         3: q^3+q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^3+q^2+q+1
         7: q^3+q^2+q+1
         8: q^3+q^2+q+1
         9: q^3+q^2+q+1
        10: q^3+q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^3+q^2+q+1
        21: q^3+q^2+q+1
        22: q^3+q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^3+q^2+q+1
        26: q^3+q^2+q+1
        27: q^3+q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^3+q^2+q+1
        53: q^3+q^2+q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^3+q^2+q+1
        58: q^3+q^2+q+1
        59: q^3+q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q+1
       103: q+1
       104: q^2+q+1
       105: q^2+q+1
       106: q^2+q+1
       107: q^3+q^2+q+1
       108: q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q^2+q+1
       112: q^2+q+1
       113: q^2+q+1
       114: q^3+q^2+q+1
       115: q^3+q^2+q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q+1
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q+1
       128: q^2+q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q^2+q+1
       132: q^2+q+1
       133: q^2+q+1
       134: q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q+1
       180: q+1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q^2+q+1
       190: q^2+q+1
       191: q^2+q+1
       192: q^2+q+1
       193: q^2+q+1
       194: q^2+q+1
       195: q^2+q+1
       196: q^2+q+1
       197: q^2+q+1
       198: q^2+q+1
       199: q^2+q+1
       200: q^2+q+1
       201: q^3+q^2+q+1
       202: q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q^2+q+1
       206: q^2+q+1
       207: q+1
       208: q^2+q+1
       209: q^2+q+1
       210: q^2+q+1
       211: q+1
       212: q+1
       213: q+1
       214: q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: q+1
       218: q^2+q+1
       219: q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q+1
       224: q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q+1
       229: q+1
       230: q^2+q+1
       231: q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: 1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: q+1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q+1
       260: q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+q+1
       267: q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q+1
       278: q+1
       279: q+1
       280: q+1
       281: 1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q+1
       293: q+1
       294: q+1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q^2+q+1
       310: q^2+q+1
       311: q^2+q+1
       312: q^2+q+1
       313: q+1
       314: q+1
       315: q^2+q+1
       316: q^2+q+1
       317: q^2+q+1
       318: q^2+q+1
       319: q^2+q+1
       320: q^2+q+1
       321: q^2+q+1
       322: q^2+q+1
       323: q^2+q+1
       324: q^2+q+1
       325: q^2+q+1
       326: q^2+q+1
       327: q^2+q+1
       328: q+1
       329: q^2+q+1
       330: q+1
       331: q^2+q+1
       332: q^2+q+1
       333: q+1
       334: q+1
       335: q+1
       336: q+1
       337: q+1
       338: q^2+q+1
       339: q^2+q+1
       340: q+1
       341: q^2+q+1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q^2+q+1
       347: q^2+q+1
       348: q+1
       349: q+1
       350: q+1
       351: q^2+q+1
       352: q^2+q+1
       353: q^2+q+1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q^2+q+1
       368: q^2+q+1
       369: q+1
       370: q^2+q+1
       371: q+1
       372: q+1
       373: q+1
       374: 1
       375: q+1
       376: q+1
       377: q+1
       378: 1
       379: 1
       380: q+1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+q+1
       384: q+1
       385: q^2+q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q+1
       399: q^2+q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q^2+q+1
       406: q+1
       407: q^2+q+1
       408: q^2+q+1
       409: q+1
       410: q+1
       411: q+1
       412: q^2+q+1
       413: q+1
       414: q^2+q+1
       415: q^2+q+1
       416: q^2+q+1
       417: q+1
       418: q+1
       419: 1
       420: q+1
       421: q+1
       422: q+1
       423: 1
       424: q+1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q^2+q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q+1
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: 1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: q^2+q+1
       465: q^2+q+1
       466: q^2+q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: q^2+q+1
       472: q^2+q+1
       473: q^2+q+1
       474: q^2+q+1
       475: q^2+q+1
       476: q^2+q+1
       477: q+1
       478: q+1
       479: q^2+q+1
       480: q^2+q+1
       481: q^2+q+1
       482: q^2+q+1
       483: q+1
       484: q+1
       485: q^2+q+1
       486: q+1
       487: q^2+q+1
       488: q+1
       489: q+1
       490: q+1
       491: q+1
       492: q+1
       493: q+1
       494: q+1
       495: q^2+q+1
       496: q+1
       497: q^2+q+1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: q^2+q+1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q^2+q+1
       512: q^2+q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: 1
       521: q+1
       522: q^2+q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q^2+q+1
       530: q+1
       531: q^2+q+1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: q+1
       537: 1
       538: q+1
       539: q+1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q^2+q+1
       546: q^2+q+1
       547: q+1
       548: q^2+q+1
       549: q+1
       550: q+1
       551: q+1
       552: 1
       553: q+1
       554: q+1
       555: q+1
       556: 1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: q+1
       568: 1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: q^2+q+1
       576: q+1
       577: q^2+q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: q+1
       583: q^2+q+1
       584: q+1
       585: q^2+q+1
       586: q^2+q+1
       587: q+1
       588: q+1
       589: q+1
       590: 1
       591: 1
       592: q+1
       593: q+1
       594: 1
       595: q+1
       596: 1
       597: 1
       598: 1
       599: q+1
       600: q+1
       601: q+1
       602: 1
       603: q+1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q^2+q+1
       623: q+1
       624: q+1
       625: q+1
       626: q+1
       627: q+1
       628: 1
       629: q+1
       630: q+1
       631: q+1
       632: 1
       633: 1
       634: 1
       635: q+1
       636: q+1
       637: q+1
       638: 1
       639: q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: q^2+q+1
       650: q^2+q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       656: q^2+q+1
       657: q^2+q+1
       658: q^2+q+1
       659: q^2+q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: q^2+q+1
       665: q^2+q+1
       666: q+1
       667: q+1
       668: q+1
       669: q^2+q+1
       670: q+1
       671: 1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: q+1
       679: q+1
       680: 1
       681: q+1
       682: q^2+q+1
       683: q+1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q+1
       697: q+1
       698: q^2+q+1
       699: q+1
       700: q+1
       701: q+1
       702: q+1
       703: q+1
       704: q+1
       705: q+1
       706: 1
       707: q+1
       708: q+1
       709: 1
       710: q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       716: 1
       717: q+1
       718: q^2+q+1
       719: q+1
       720: q+1
       721: q+1
       722: 1
       723: 1
       724: q+1
       725: 1
       726: q+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: q+1
       732: q+1
       733: q+1
       734: q^2+q+1
       735: q+1
       736: q^2+q+1
       737: q+1
       738: q+1
       739: q+1
       740: 1
       741: q+1
       742: 1
       743: q+1
       744: q+1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       750: q+1
       751: q+1
       752: q+1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: q+1
       762: q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q^2+q+1
       768: q+1
       769: 1
       770: q+1
       771: q+1
       772: q+1
       773: q+1
       774: q+1
       775: q+1
       776: q^2+q+1
       777: q+1
       778: q^2+q+1
       779: q+1
       780: q+1
       781: q+1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q+1
       787: 1
       788: q+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: q+1
       796: 1
       797: q+1
       798: 1
       799: 1
       800: 1
       801: q+1
       802: q+1
       803: q+1
       804: 1
       805: q+1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: 1
       812: 1
       813: q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: q+1
       828: 1
       829: q+1
       830: q+1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: q+1
       837: q+1
       838: 1
       839: q+1
       840: 1
       841: 1
       842: 1
       843: 1
       844: q+1
       845: q+1
       846: 1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: 1
       854: q^2+q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       859: q+1
       860: q+1
       861: q^2+q+1
       862: q^2+q+1
       863: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q^2+q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       873: 1
       874: 1
       875: q+1
       876: q+1
       877: q+1
       878: q+1
       879: q+1
       880: q+1
       881: 1
       882: q+1
       883: q+1
       884: 1
       885: q+1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: q+1
       891: 1
       892: 1
       893: q+1
       894: q+1
       895: q+1
       896: q+1
       897: q+1
       898: q+1
       899: q+1
       900: q+1
       901: q+1
       902: q+1
       903: q+1
       904: q+1
       905: q+1
       906: q+1
       907: q+1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       913: q+1
       914: q+1
       915: q+1
       916: q+1
       917: 1
       918: q+1
       919: q+1
       920: 1
       921: q+1
       922: q+1
       923: 1
       924: 1
       925: 1
       926: q+1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: q+1
       934: q+1
       935: q+1
       936: q+1
       937: 1
       938: q+1
       939: q^2+q+1
       940: q+1
       941: q+1
       942: q+1
       943: 1
       944: 1
       945: q+1
       946: 1
       947: q+1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       967: q+1
       968: q+1
       969: q+1
       970: q+1
       971: q+1
       972: 1
       973: 1
       974: q+1
       975: q+1
       976: q+1
       977: q+1
       978: q+1
       979: q+1
       980: q^2+q+1
       981: q+1
       982: 1
       983: q+1
       984: q+1
       985: q+1
       986: q+1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: q+1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: 1
      1002: q+1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: 1
      1028: 1
      1029: q+1
      1030: q+1
      1031: q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q+1
      1036: 1
      1037: q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: q+1
      1046: 1
      1047: q+1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: q+1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: q+1
      1062: q+1
      1063: 1
      1064: 1
      1065: 1
      1066: q+1
      1067: q+1
      1068: q+1
      1069: q+1
      1070: q+1
      1071: q^2+q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: q+1
      1081: 1
      1082: 1
      1083: 1
      1084: q+1
      1085: q+1
      1086: q+1
      1087: q+1
      1088: 1
      1089: q+1
      1090: 1
      1091: q+1
      1092: 1
      1093: q+1
      1094: q+1
      1095: q+1
      1096: q+1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: q+1
      1102: q+1
      1103: q+1
      1104: q+1
      1105: q+1
      1106: q+1
      1107: 1
      1108: 1
      1109: q+1
      1110: q+1
      1111: q+1
      1112: q+1
      1113: q+1
      1114: 1
      1115: q+1
      1116: 1
      1117: 1
      1118: q+1
      1119: 1
      1120: q+1
      1121: q+1
      1122: 1
      1123: q+1
      1124: 1
      1125: q+1
      1126: 1
      1127: q+1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1137: q+1
      1138: q+1
      1139: q+1
      1140: 1
      1141: q+1
      1142: q+1
      1143: 1
      1144: q+1
      1145: q+1
      1146: 1
      1147: 1
      1148: 1
      1149: q+1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: q+1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: q+1
      1172: q+1
      1173: q+1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: q+1
      1179: q+1
      1180: q+1
      1181: q+1
      1182: q+1
      1183: q+1
      1184: 1
      1185: 1
      1186: q+1
      1187: q+1
      1188: q+1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: q+1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1213: q+1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: q+1
      1225: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: 1
      1237: q+1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: q+1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: q+1
      1272: q+1
      1273: q+1
      1274: q+1
      1275: q+1
      1276: q+1
      1277: q+1
      1278: q+1
      1279: q+1
      1280: q+1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: 1
      1288: q+1
      1289: 1
      1290: 1
      1291: q+1
      1292: 1
      1293: q+1
      1294: q+1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: q+1
      1301: q+1
      1302: q+1
      1303: q+1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: q+1
      1309: q+1
      1310: 1
      1311: q+1
      1312: 1
      1313: 1
      1314: 1
      1315: q+1
      1316: 1
      1317: q+1
      1318: 1
      1319: 1
      1320: q+1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: q+1
      1331: q+1
      1332: 1
      1333: q+1
      1334: 1
      1335: q+1
      1336: 1
      1337: q+1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q+1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1357: q+1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: q+1
      1363: q+1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: q+1
      1369: q+1
      1370: q+1
      1371: q+1
      1372: 1
      1373: 1
      1374: 1
      1375: q+1
      1376: q+1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1404: q+1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: q+1
      1412: q+1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: q+1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: q+1
      1457: q+1
      1458: q+1
      1459: q+1
      1460: q+1
      1461: q+1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: q+1
      1468: 1
      1469: 1
      1470: 1
      1471: q+1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: q+1
      1479: q+1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: q+1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: q+1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: q+1
      1502: 1
      1503: q+1
      1504: 1
      1505: 1
      1506: q+1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: q+1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: q+1
      1534: q+1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: q+1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: q+1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1611: q+1
      1612: q+1
      1613: q+1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: q+1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1642: 1
      1643: q+1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1662: 1
      1663: 1
      1664: 1
      1665: 1
      1666: 1
      1667: q+1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1684: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1706: 1
      1707: 1
      1709: 1
      1712: 1
      1714: 1
      1715: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1729: 1
      1730: 1
      1731: q+1
      1732: 1
      1733: 1
      1734: 1
      1735: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1742: 1
      1743: 1
      1744: 1
      1745: 1
      1746: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1758: 1
      1759: 1
      1764: 1
      1765: 1
      1766: 1
      1767: 1
      1768: 1
      1769: 1
      1770: 1
      1775: 1
      1779: 1
      1781: 1
      1784: 1
      1786: 1
      1787: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1797: 1
      1801: 1
      1808: 1
      1809: 1
      1815: 1
      1816: 1
      1817: 1
      1818: 1
      1819: 1
      1820: 1
      1821: 1
      1822: 1
      1823: 1
      1826: 1
      1827: 1
      1831: 1
      1836: 1
      1837: 1
      1838: 1
      1845: 1
      1849: 1
      1850: 1
      1851: 1
      1863: 1
      1870: 1
      1871: 1
      1872: 1
      1874: 1
      1880: 1
      1887: 1
      1900: 1

1901:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q+1
        43: q+1
        44: q+1
        45: q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q^2+q+1
        84: q+1
        85: q^2+q+1
        86: q+1
        87: q+1
        88: q+1
        89: q+1
        90: q+1
        91: q+1
        92: q+1
        93: q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+q+1
       105: q^2+q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q+1
       112: q^2+q+1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q+1
       120: q^2+q+1
       121: q+1
       122: q+1
       123: q+1
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q+1
       132: q+1
       133: q+1
       134: q^2+q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q^2+q+1
       140: q^2+q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q^2+q+1
       153: q^2+q+1
       154: q+1
       155: q+1
       156: q+1
       157: q+1
       158: q+1
       159: q+1
       160: q+1
       161: q+1
       162: q+1
       163: q+1
       164: q+1
       165: q+1
       166: q+1
       167: q+1
       168: q+1
       169: q+1
       170: q+1
       171: q+1
       172: 1
       173: q+1
       174: q+1
       175: q+1
       176: q+1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q^2+q+1
       191: q^2+q+1
       192: q^2+q+1
       193: q+1
       194: q^2+q+1
       195: q^2+q+1
       196: q+1
       197: q+1
       198: q^2+q+1
       199: q^2+q+1
       200: q^2+q+1
       201: q^2+q+1
       202: q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: q^2+q+1
       214: q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+q+1
       220: q+1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+q+1
       229: q^2+q+1
       230: q^2+q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q^2+q+1
       234: q^2+q+1
       235: q+1
       236: q^2+q+1
       237: q^2+q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q^2+q+1
       241: q^2+q+1
       242: q^2+q+1
       243: q+1
       244: q^2+q+1
       245: q+1
       246: q+1
       247: q+1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q^2+q+1
       254: q^2+q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q+1
       261: q+1
       262: q+1
       263: q+1
       264: q+1
       265: q+1
       266: q+1
       267: q+1
       268: q+1
       269: q+1
       270: q+1
       271: q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: 1
       279: q+1
       280: 1
       281: 1
       282: 1
       283: q+1
       284: q+1
       285: 1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: q+1
       303: q+1
       304: q+1
       305: 1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q^2+q+1
       312: q+1
       313: q+1
       314: q^2+q+1
       315: q^2+q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+q+1
       321: q^2+q+1
       322: q^2+q+1
       323: q+1
       324: q^2+q+1
       325: q^2+q+1
       326: q+1
       327: q+1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: q^2+q+1
       337: q^2+q+1
       338: q^2+q+1
       339: q^2+q+1
       340: q^2+q+1
       341: q^2+q+1
       342: q^2+q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: q^2+q+1
       358: q^2+q+1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q^2+q+1
       363: q+1
       364: q+1
       365: q^2+q+1
       366: q^2+q+1
       367: q^2+q+1
       368: q^2+q+1
       369: q^2+q+1
       370: q^2+q+1
       371: q^2+q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: q^2+q+1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+q+1
       384: q^2+q+1
       385: q^2+q+1
       386: q^2+q+1
       387: q+1
       388: q^2+q+1
       389: q+1
       390: q+1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q+1
       399: q+1
       400: 1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q+1
       407: q+1
       408: q+1
       409: q+1
       410: q+1
       411: 1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: q+1
       428: 1
       429: 1
       430: 1
       431: q+1
       432: q+1
       433: 1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: 1
       455: q+1
       456: 1
       457: 1
       458: 1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: q+1
       468: q^2+q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+q+1
       476: q+1
       477: q+1
       478: q^2+q+1
       479: q^2+q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: 1
       489: q+1
       490: q+1
       491: q+1
       492: q+1
       493: q^2+q+1
       494: q^2+q+1
       495: q^2+q+1
       496: q+1
       497: q^2+q+1
       498: q^2+q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q^2+q+1
       519: q+1
       520: q+1
       521: q^2+q+1
       522: q^2+q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q^2+q+1
       528: q^2+q+1
       529: q^2+q+1
       530: q+1
       531: q^2+q+1
       532: q^2+q+1
       533: q+1
       534: q+1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: q^2+q+1
       544: q^2+q+1
       545: q^2+q+1
       546: q^2+q+1
       547: q^2+q+1
       548: q^2+q+1
       549: q^2+q+1
       550: q+1
       551: q+1
       552: q+1
       553: q+1
       554: q+1
       555: q+1
       556: q+1
       557: q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: 1
       570: 1
       571: q+1
       572: q+1
       573: 1
       574: q+1
       575: q+1
       576: q+1
       577: q+1
       578: 1
       579: q+1
       580: 1
       581: 1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: q+1
       607: 1
       608: 1
       609: 1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: q+1
       615: 1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: q+1
       661: q^2+q+1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       666: q+1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       671: 1
       672: 1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: q^2+q+1
       679: q+1
       680: q+1
       681: q^2+q+1
       682: q^2+q+1
       683: q+1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: q+1
       691: 1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       703: q+1
       704: q+1
       705: q+1
       706: q+1
       707: q^2+q+1
       708: q+1
       709: q+1
       710: q+1
       711: q+1
       712: q+1
       713: q+1
       714: q^2+q+1
       715: q+1
       716: q+1
       717: q^2+q+1
       718: q^2+q+1
       719: q+1
       720: q+1
       721: q+1
       722: q+1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       727: 1
       728: q+1
       729: q+1
       730: q+1
       731: q+1
       732: q^2+q+1
       733: q^2+q+1
       734: q^2+q+1
       735: q+1
       736: q^2+q+1
       737: q^2+q+1
       738: q+1
       739: q+1
       740: q+1
       741: q+1
       742: q+1
       743: q+1
       744: q+1
       745: q+1
       746: q+1
       747: q+1
       748: q+1
       749: q+1
       750: q+1
       751: q+1
       752: q+1
       753: q+1
       754: q+1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: 1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: 1
       765: 1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: 1
       780: q+1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: 1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: q+1
       822: 1
       823: q+1
       824: 1
       825: 1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       854: q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       859: q+1
       860: q+1
       861: q+1
       862: q+1
       863: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: 1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: q+1
       881: q+1
       882: q^2+q+1
       883: q+1
       884: q+1
       885: q+1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: q+1
       891: q+1
       892: 1
       893: 1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: q+1
       902: 1
       903: q+1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: q+1
       909: q+1
       910: q+1
       911: q+1
       912: q+1
       913: q+1
       914: q+1
       915: q+1
       916: q+1
       917: q+1
       918: q^2+q+1
       919: q+1
       920: q+1
       921: q+1
       922: q+1
       923: q+1
       924: q+1
       925: q+1
       926: q+1
       927: q+1
       928: 1
       929: 1
       930: 1
       931: q+1
       932: q+1
       933: q+1
       934: q+1
       935: q^2+q+1
       936: q+1
       937: q+1
       938: q^2+q+1
       939: q^2+q+1
       940: q+1
       941: q+1
       942: q+1
       943: q+1
       944: q+1
       945: q+1
       946: q+1
       947: q+1
       948: 1
       949: q+1
       950: q+1
       951: q+1
       952: q+1
       953: q+1
       954: q+1
       955: q+1
       956: q+1
       957: q+1
       958: q+1
       959: 1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: q+1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: q+1
       980: q+1
       981: q+1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       992: 1
       993: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: q+1
      1027: q+1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: 1
      1039: q+1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1066: q+1
      1067: q+1
      1068: q+1
      1069: 1
      1070: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: q+1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: q+1
      1092: q+1
      1093: q+1
      1094: q+1
      1095: q+1
      1096: 1
      1097: q+1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: q+1
      1107: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: q+1
      1114: q+1
      1115: q+1
      1116: q+1
      1117: q+1
      1118: q+1
      1119: q+1
      1120: q+1
      1121: q+1
      1122: q+1
      1123: q+1
      1124: q+1
      1125: q+1
      1126: q+1
      1127: q+1
      1128: q+1
      1129: q+1
      1130: 1
      1131: q+1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: q+1
      1137: q+1
      1138: q+1
      1139: q+1
      1140: q+1
      1141: q^2+q+1
      1142: q+1
      1143: q+1
      1144: q+1
      1145: q+1
      1146: q+1
      1147: q+1
      1148: q+1
      1149: q+1
      1150: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: q+1
      1155: q+1
      1156: 1
      1157: q+1
      1158: q+1
      1159: q+1
      1160: q+1
      1161: 1
      1162: q+1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: q+1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1193: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1203: 1
      1204: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: q+1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1249: 1
      1250: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: q+1
      1272: 1
      1273: 1
      1274: q+1
      1275: q+1
      1276: q+1
      1277: 1
      1278: q+1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: q+1
      1287: q+1
      1288: q+1
      1289: q+1
      1290: q+1
      1291: q+1
      1292: q+1
      1293: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: q+1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1310: q+1
      1311: q+1
      1312: q+1
      1313: 1
      1314: q+1
      1315: q+1
      1316: q+1
      1317: q+1
      1318: q+1
      1319: q+1
      1320: q+1
      1321: q+1
      1322: q+1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: q+1
      1331: q+1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: q+1
      1336: q+1
      1337: q+1
      1338: q+1
      1339: q+1
      1340: 1
      1341: q+1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: q+1
      1347: 1
      1348: 1
      1349: q+1
      1350: q+1
      1351: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1385: 1
      1386: 1
      1389: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1399: 1
      1400: 1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1422: q+1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1432: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1442: 1
      1443: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: q+1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: q+1
      1467: q+1
      1468: q+1
      1469: 1
      1470: q+1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: q+1
      1487: 1
      1488: 1
      1489: q+1
      1490: q+1
      1491: q+1
      1492: 1
      1493: q+1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: q+1
      1502: q+1
      1503: q+1
      1504: q+1
      1505: q+1
      1506: q+1
      1507: q+1
      1508: q+1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: q+1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1547: 1
      1555: 1
      1556: 1
      1559: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1584: 1
      1592: 1
      1593: 1
      1596: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1606: 1
      1607: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1614: 1
      1615: 1
      1616: 1
      1617: q+1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1633: 1
      1634: q+1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1642: q+1
      1643: q+1
      1644: q+1
      1645: 1
      1646: q+1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1662: 1
      1663: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1684: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1714: 1
      1722: 1
      1723: 1
      1726: 1
      1730: 1
      1731: 1
      1732: 1
      1733: 1
      1734: 1
      1735: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1743: 1
      1744: 1
      1745: 1
      1746: 1
      1747: 1
      1748: 1
      1749: 1
      1750: q+1
      1751: 1
      1752: 1
      1753: 1
      1754: 1
      1755: 1
      1756: 1
      1757: 1
      1758: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1765: 1
      1768: 1
      1786: 1
      1787: 1
      1788: 1
      1791: 1
      1792: 1
      1793: 1
      1795: 1
      1808: 1
      1816: 1
      1817: 1
      1818: 1
      1819: 1
      1820: 1
      1823: 1
      1824: 1
      1825: 1
      1826: 1
      1827: 1
      1828: 1
      1829: 1
      1830: 1
      1831: 1
      1832: 1
      1833: 1
      1835: 1
      1849: 1
      1852: 1
      1870: 1
      1873: 1
      1874: 1
      1875: 1
      1876: 1
      1877: 1
      1901: 1

1902:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: q^3+3q^2+2q+1
         5: q^3+3q^2+2q+1
         6: 3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+3q^2+2q+1
        10: 3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: 3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: q^3+3q^2+2q+1
        17: 3q^2+2q+1
        18: q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: 3q^2+2q+1
        21: 3q^2+2q+1
        22: 3q^2+2q+1
        23: 3q^2+2q+1
        24: 2q^2+2q+1
        25: 3q^2+2q+1
        26: 3q^2+2q+1
        27: 3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: 3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: 3q^2+2q+1
        34: 3q^2+2q+1
        35: 3q^2+2q+1
        36: q^3+3q^2+2q+1
        37: 3q^2+2q+1
        38: q^3+3q^2+2q+1
        39: q^3+3q^2+2q+1
        40: 3q^2+2q+1
        41: 3q^2+2q+1
        42: 3q^2+2q+1
        43: q^3+3q^2+2q+1
        44: 2q^2+2q+1
        45: q^3+3q^2+2q+1
        46: q^3+2q^2+2q+1
        47: q^3+3q^2+2q+1
        48: 3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: 3q^2+2q+1
        51: 2q^2+2q+1
        52: 3q^2+2q+1
        53: 2q^2+2q+1
        54: 3q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: 3q^2+2q+1
        58: 3q^2+2q+1
        59: 3q^2+2q+1
        60: 3q^2+2q+1
        61: 2q^2+2q+1
        62: 3q^2+2q+1
        63: 3q^2+2q+1
        64: 3q^2+2q+1
        65: 3q^2+2q+1
        66: 3q^2+2q+1
        67: 3q^2+2q+1
        68: q^3+3q^2+2q+1
        69: 3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: 3q^2+2q+1
        72: 3q^2+2q+1
        73: 3q^2+2q+1
        74: 3q^2+2q+1
        75: 2q^2+2q+1
        76: 3q^2+2q+1
        77: 3q^2+2q+1
        78: 3q^2+2q+1
        79: q^3+3q^2+2q+1
        80: 3q^2+2q+1
        81: q^3+3q^2+2q+1
        82: 3q^2+2q+1
        83: q^3+3q^2+2q+1
        84: 3q^2+2q+1
        85: 3q^2+2q+1
        86: 3q^2+2q+1
        87: 3q^2+2q+1
        88: q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: 2q^2+2q+1
        92: q^3+3q^2+2q+1
        93: 2q^2+2q+1
        94: q^3+2q^2+2q+1
        95: q^2+2q+1
        96: q^3+2q^2+2q+1
        97: 3q^2+2q+1
        98: 3q^2+2q+1
        99: 3q^2+2q+1
       100: q^3+3q^2+2q+1
       101: 2q^2+2q+1
       102: q^3+3q^2+2q+1
       103: q^3+2q^2+2q+1
       104: 2q^2+2q+1
       105: 3q^2+2q+1
       106: 2q^2+2q+1
       107: 2q^2+2q+1
       108: 2q^2+2q+1
       109: q^2+2q+1
       110: 2q^2+2q+1
       111: 2q^2+2q+1
       112: 3q^2+2q+1
       113: 2q^2+2q+1
       114: 3q^2+2q+1
       115: 2q^2+2q+1
       116: 3q^2+2q+1
       117: 2q^2+2q+1
       118: 2q^2+2q+1
       119: 3q^2+2q+1
       120: 3q^2+2q+1
       121: 3q^2+2q+1
       122: 3q^2+2q+1
       123: q^2+2q+1
       124: 3q^2+2q+1
       125: 3q^2+2q+1
       126: 3q^2+2q+1
       127: 3q^2+2q+1
       128: 2q^2+2q+1
       129: 3q^2+2q+1
       130: 3q^2+2q+1
       131: 3q^2+2q+1
       132: q^3+3q^2+2q+1
       133: 2q^2+2q+1
       134: 3q^2+2q+1
       135: 2q^2+2q+1
       136: 3q^2+2q+1
       137: 2q^2+2q+1
       138: 3q^2+2q+1
       139: 2q^2+2q+1
       140: 2q^2+2q+1
       141: 3q^2+2q+1
       142: 3q^2+2q+1
       143: 3q^2+2q+1
       144: 3q^2+2q+1
       145: 2q^2+2q+1
       146: 3q^2+2q+1
       147: 3q^2+2q+1
       148: 3q^2+2q+1
       149: 3q^2+2q+1
       150: 3q^2+2q+1
       151: 3q^2+2q+1
       152: q^3+3q^2+2q+1
       153: 3q^2+2q+1
       154: q^3+3q^2+2q+1
       155: 3q^2+2q+1
       156: q^2+2q+1
       157: 3q^2+2q+1
       158: q^2+2q+1
       159: 3q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q^2+2q+1
       163: 2q^2+2q+1
       164: 2q^2+2q+1
       165: 2q^2+2q+1
       166: 2q+1
       167: 2q^2+2q+1
       168: 2q^2+2q+1
       169: 2q^2+2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: q^2+2q+1
       173: q^3+2q^2+2q+1
       174: q^2+2q+1
       175: q^3+2q^2+2q+1
       176: 3q^2+2q+1
       177: 3q^2+2q+1
       178: 3q^2+2q+1
       179: 3q^2+2q+1
       180: q^2+2q+1
       181: 2q^2+2q+1
       182: 2q^2+2q+1
       183: 2q^2+2q+1
       184: q^3+3q^2+2q+1
       185: 2q^2+2q+1
       186: q^3+2q^2+2q+1
       187: q^2+2q+1
       188: q^3+2q^2+2q+1
       189: 2q^2+2q+1
       190: 2q^2+2q+1
       191: 2q^2+2q+1
       192: q^2+2q+1
       193: 2q^2+2q+1
       194: q^2+2q+1
       195: q^2+2q+1
       196: 2q^2+2q+1
       197: q^2+q+1
       198: 2q^2+2q+1
       199: 3q^2+2q+1
       200: 2q^2+2q+1
       201: 2q^2+2q+1
       202: 2q^2+2q+1
       203: q^2+2q+1
       204: 2q^2+2q+1
       205: 2q^2+2q+1
       206: 3q^2+2q+1
       207: q^2+2q+1
       208: 3q^2+2q+1
       209: q^2+2q+1
       210: 3q^2+2q+1
       211: q^2+2q+1
       212: q^2+2q+1
       213: 3q^2+2q+1
       214: 2q^2+2q+1
       215: 3q^2+2q+1
       216: 2q^2+2q+1
       217: 3q^2+2q+1
       218: 2q^2+2q+1
       219: 2q^2+2q+1
       220: 3q^2+2q+1
       221: 3q^2+2q+1
       222: 3q^2+2q+1
       223: 3q^2+2q+1
       224: q^2+2q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 2q^2+2q+1
       228: 2q^2+2q+1
       229: 3q^2+2q+1
       230: 2q^2+2q+1
       231: 2q^2+2q+1
       232: 2q^2+2q+1
       233: q^2+2q+1
       234: 2q^2+2q+1
       235: 2q^2+2q+1
       236: 3q^2+2q+1
       237: 2q^2+2q+1
       238: 3q^2+2q+1
       239: 2q^2+2q+1
       240: 3q^2+2q+1
       241: 2q^2+2q+1
       242: 2q^2+2q+1
       243: 3q^2+2q+1
       244: 3q^2+2q+1
       245: 3q^2+2q+1
       246: 3q^2+2q+1
       247: q^2+2q+1
       248: 3q^2+2q+1
       249: 3q^2+2q+1
       250: 3q^2+2q+1
       251: 3q^2+2q+1
       252: 2q^2+2q+1
       253: 3q^2+2q+1
       254: 3q^2+2q+1
       255: 3q^2+2q+1
       256: q^3+3q^2+2q+1
       257: 2q^2+2q+1
       258: q^2+2q+1
       259: 3q^2+2q+1
       260: q^2+2q+1
       261: q^2+2q+1
       262: q^2+2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q^2+2q+1
       267: 2q+1
       268: 2q^2+2q+1
       269: q^2+2q+1
       270: 2q^2+2q+1
       271: 2q+1
       272: 2q+1
       273: 2q^2+2q+1
       274: 2q^2+2q+1
       275: 2q^2+2q+1
       276: 2q^2+2q+1
       277: 2q+1
       278: q^2+2q+1
       279: q^2+2q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: 2q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: q^2+2q+1
       286: q^3+2q^2+2q+1
       287: q^2+2q+1
       288: 3q^2+2q+1
       289: q^2+2q+1
       290: 3q^2+2q+1
       291: q^2+2q+1
       292: 3q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q^2+2q+1
       296: 2q^2+2q+1
       297: 2q^2+2q+1
       298: 2q^2+2q+1
       299: 2q+1
       300: 2q^2+2q+1
       301: 2q^2+2q+1
       302: 2q^2+2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: q^2+2q+1
       306: q^3+2q^2+2q+1
       307: q^2+2q+1
       308: q^3+2q^2+2q+1
       309: q^2+q+1
       310: 2q^2+2q+1
       311: q^2+2q+1
       312: 2q^2+2q+1
       313: q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: q^2+2q+1
       317: q+1
       318: q^2+q+1
       319: 2q^2+2q+1
       320: 2q^2+2q+1
       321: 2q^2+2q+1
       322: q^2+2q+1
       323: 2q^2+2q+1
       324: q^2+2q+1
       325: q^2+2q+1
       326: 2q^2+2q+1
       327: q^2+q+1
       328: q^2+2q+1
       329: 3q^2+2q+1
       330: q^2+2q+1
       331: q^2+2q+1
       332: q^2+2q+1
       333: 2q+1
       334: q^2+2q+1
       335: q^2+2q+1
       336: 2q^2+2q+1
       337: 3q^2+2q+1
       338: 2q^2+2q+1
       339: 2q^2+2q+1
       340: 2q^2+2q+1
       341: q^2+2q+1
       342: 2q^2+2q+1
       343: 2q^2+2q+1
       344: 3q^2+2q+1
       345: q^2+2q+1
       346: 3q^2+2q+1
       347: q^2+2q+1
       348: 3q^2+2q+1
       349: q^2+2q+1
       350: q^2+2q+1
       351: 2q^2+2q+1
       352: 2q^2+2q+1
       353: 2q^2+2q+1
       354: 2q^2+2q+1
       355: 2q+1
       356: 2q^2+2q+1
       357: 2q^2+2q+1
       358: 2q^2+2q+1
       359: q^2+2q+1
       360: 2q^2+2q+1
       361: q^2+2q+1
       362: q^2+2q+1
       363: 2q^2+2q+1
       364: q^2+q+1
       365: 2q^2+2q+1
       366: 3q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: 2q^2+2q+1
       370: q^2+2q+1
       371: 2q^2+2q+1
       372: 2q^2+2q+1
       373: 3q^2+2q+1
       374: q^2+2q+1
       375: 3q^2+2q+1
       376: q^2+2q+1
       377: 3q^2+2q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: 3q^2+2q+1
       381: 2q^2+2q+1
       382: 3q^2+2q+1
       383: 2q^2+2q+1
       384: 3q^2+2q+1
       385: 2q^2+2q+1
       386: 2q^2+2q+1
       387: 3q^2+2q+1
       388: 3q^2+2q+1
       389: 3q^2+2q+1
       390: 3q^2+2q+1
       391: q^2+2q+1
       392: 2q^2+2q+1
       393: 2q^2+2q+1
       394: 2q^2+2q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: q^2+2q+1
       398: 2q+1
       399: q^2+2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q^2+2q+1
       406: 2q+1
       407: q^2+2q+1
       408: q^2+2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: 2q^2+2q+1
       413: 2q+1
       414: 2q^2+2q+1
       415: q^2+2q+1
       416: 2q^2+2q+1
       417: 2q+1
       418: 2q+1
       419: q^2+2q+1
       420: 2q+1
       421: q^2+2q+1
       422: q+1
       423: q^2+2q+1
       424: 2q+1
       425: 2q+1
       426: q^2+2q+1
       427: q^2+2q+1
       428: q^2+2q+1
       429: q^2+2q+1
       430: 2q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: q^2+2q+1
       434: q^2+2q+1
       435: 3q^2+2q+1
       436: q^2+2q+1
       437: q^2+2q+1
       438: q^2+2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q^2+2q+1
       443: 2q+1
       444: 2q^2+2q+1
       445: q^2+2q+1
       446: 2q^2+2q+1
       447: 2q+1
       448: 2q+1
       449: 2q^2+2q+1
       450: 2q^2+2q+1
       451: 2q^2+2q+1
       452: 2q^2+2q+1
       453: 2q+1
       454: q^2+2q+1
       455: q^2+2q+1
       456: q^2+2q+1
       457: q^2+2q+1
       458: 2q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q^2+2q+1
       462: q^3+2q^2+2q+1
       463: q^2+2q+1
       464: q^2+q+1
       465: q+1
       466: q^2+2q+1
       467: q+1
       468: q^2+2q+1
       469: q^2+2q+1
       470: q+1
       471: q+1
       472: q+1
       473: q^2+q+1
       474: 2q^2+2q+1
       475: q^2+2q+1
       476: 2q^2+2q+1
       477: q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: q^2+2q+1
       481: q+1
       482: q^2+q+1
       483: q^2+2q+1
       484: q^2+2q+1
       485: q^2+2q+1
       486: 2q+1
       487: q^2+2q+1
       488: 2q+1
       489: 2q+1
       490: q^2+2q+1
       491: q+1
       492: 2q^2+2q+1
       493: 2q^2+2q+1
       494: 2q^2+2q+1
       495: q^2+2q+1
       496: 2q^2+2q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 2q^2+2q+1
       500: q^2+q+1
       501: q^2+2q+1
       502: 3q^2+2q+1
       503: q^2+2q+1
       504: q^2+2q+1
       505: q^2+2q+1
       506: 2q+1
       507: q^2+2q+1
       508: q^2+2q+1
       509: 2q^2+2q+1
       510: 2q+1
       511: 2q^2+2q+1
       512: q^2+2q+1
       513: 2q^2+2q+1
       514: 2q+1
       515: 2q+1
       516: q^2+q+1
       517: 2q^2+2q+1
       518: q^2+2q+1
       519: 2q^2+2q+1
       520: q+1
       521: q^2+2q+1
       522: q^2+2q+1
       523: q^2+2q+1
       524: q+1
       525: q^2+q+1
       526: 2q^2+2q+1
       527: 2q^2+2q+1
       528: 2q^2+2q+1
       529: q^2+2q+1
       530: 2q^2+2q+1
       531: q^2+2q+1
       532: q^2+2q+1
       533: 2q^2+2q+1
       534: q^2+q+1
       535: q^2+2q+1
       536: 3q^2+2q+1
       537: q^2+2q+1
       538: q^2+2q+1
       539: q^2+2q+1
       540: 2q+1
       541: q^2+2q+1
       542: q^2+2q+1
       543: 2q^2+2q+1
       544: 3q^2+2q+1
       545: 2q^2+2q+1
       546: 2q^2+2q+1
       547: 2q^2+2q+1
       548: q^2+2q+1
       549: 2q^2+2q+1
       550: 2q^2+2q+1
       551: 3q^2+2q+1
       552: q^2+2q+1
       553: 3q^2+2q+1
       554: q^2+2q+1
       555: 3q^2+2q+1
       556: q^2+2q+1
       557: q^2+2q+1
       558: 2q^2+2q+1
       559: 2q^2+2q+1
       560: 2q^2+2q+1
       561: 2q^2+2q+1
       562: 2q+1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: q^2+2q+1
       567: q+1
       568: 2q+1
       569: 2q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: q^2+2q+1
       576: 2q+1
       577: q^2+2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: 2q+1
       583: 2q^2+2q+1
       584: 2q+1
       585: q^2+2q+1
       586: q^2+2q+1
       587: 2q+1
       588: 2q+1
       589: 2q+1
       590: 2q+1
       591: q^2+2q+1
       592: 2q+1
       593: q+1
       594: q+1
       595: q+1
       596: 2q+1
       597: 2q+1
       598: q^2+2q+1
       599: 2q+1
       600: q^2+2q+1
       601: q+1
       602: q^2+2q+1
       603: 2q+1
       604: 2q+1
       605: q^2+2q+1
       606: q^2+2q+1
       607: q^2+2q+1
       608: q^2+2q+1
       609: 2q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: q^2+2q+1
       613: 2q+1
       614: q^2+2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q^2+2q+1
       621: 2q+1
       622: q^2+2q+1
       623: q^2+2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: 2q^2+2q+1
       628: 2q+1
       629: 2q^2+2q+1
       630: q^2+2q+1
       631: 2q^2+2q+1
       632: 2q+1
       633: 2q+1
       634: q^2+2q+1
       635: 2q+1
       636: q^2+2q+1
       637: q+1
       638: q^2+2q+1
       639: 2q+1
       640: 2q+1
       641: q^2+2q+1
       642: q^2+2q+1
       643: q^2+2q+1
       644: q^2+2q+1
       645: 2q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q^2+2q+1
       649: q+1
       650: q+1
       651: q+1
       652: q^2+2q+1
       653: q+1
       654: q+1
       655: 1
       656: q+1
       657: q^2+q+1
       658: q+1
       659: q^2+2q+1
       660: q+1
       661: q^2+2q+1
       662: q^2+2q+1
       663: q+1
       664: q+1
       665: q+1
       666: q+1
       667: q^2+2q+1
       668: 2q+1
       669: q^2+2q+1
       670: q+1
       671: 2q+1
       672: 2q+1
       673: 2q+1
       674: q+1
       675: q+1
       676: q^2+q+1
       677: 2q^2+2q+1
       678: q^2+2q+1
       679: 2q^2+2q+1
       680: q+1
       681: q^2+2q+1
       682: q^2+2q+1
       683: q^2+2q+1
       684: q+1
       685: q^2+q+1
       686: q^2+2q+1
       687: q^2+2q+1
       688: q^2+2q+1
       689: 2q+1
       690: q^2+2q+1
       691: 2q+1
       692: 2q+1
       693: q^2+2q+1
       694: q+1
       695: 2q+1
       696: 2q^2+2q+1
       697: 2q+1
       698: q^2+2q+1
       699: q^2+2q+1
       700: 2q+1
       701: 2q+1
       702: 2q+1
       703: q^2+q+1
       704: q+1
       705: q^2+2q+1
       706: q+1
       707: q^2+2q+1
       708: q^2+2q+1
       709: q+1
       710: q+1
       711: q+1
       712: q^2+q+1
       713: 2q^2+2q+1
       714: q^2+2q+1
       715: 2q^2+2q+1
       716: q+1
       717: q^2+2q+1
       718: q^2+2q+1
       719: q^2+2q+1
       720: q+1
       721: q^2+q+1
       722: q^2+2q+1
       723: q^2+2q+1
       724: q^2+2q+1
       725: 2q+1
       726: q^2+2q+1
       727: 2q+1
       728: 2q+1
       729: q^2+2q+1
       730: q+1
       731: 2q^2+2q+1
       732: 2q^2+2q+1
       733: 2q^2+2q+1
       734: q^2+2q+1
       735: 2q^2+2q+1
       736: q^2+2q+1
       737: q^2+2q+1
       738: 2q^2+2q+1
       739: q^2+q+1
       740: q^2+2q+1
       741: 3q^2+2q+1
       742: q^2+2q+1
       743: q^2+2q+1
       744: q^2+2q+1
       745: 2q+1
       746: q^2+2q+1
       747: q^2+2q+1
       748: 2q^2+2q+1
       749: 2q+1
       750: 2q^2+2q+1
       751: q^2+2q+1
       752: 2q^2+2q+1
       753: 2q+1
       754: 2q+1
       755: q+1
       756: q+1
       757: 2q+1
       758: q+1
       759: 2q+1
       760: 2q+1
       761: q+1
       762: q+1
       763: q+1
       764: q+1
       765: 2q+1
       766: 2q+1
       767: q^2+2q+1
       768: q+1
       769: 2q+1
       770: 2q+1
       771: 2q+1
       772: 1
       773: q+1
       774: 2q+1
       775: 2q+1
       776: q^2+2q+1
       777: 2q+1
       778: q^2+2q+1
       779: 2q+1
       780: 2q+1
       781: 2q+1
       782: q+1
       783: 2q+1
       784: 2q+1
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: 2q+1
       791: q+1
       792: 2q+1
       793: q^2+2q+1
       794: 2q+1
       795: q+1
       796: q+1
       797: q+1
       798: 2q+1
       799: 2q+1
       800: q^2+2q+1
       801: 2q+1
       802: q^2+2q+1
       803: q+1
       804: q^2+2q+1
       805: 2q+1
       806: 2q+1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: q^2+2q+1
       811: q+1
       812: 2q+1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: 2q+1
       818: 2q+1
       819: q^2+2q+1
       820: 2q+1
       821: q^2+2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: 2q+1
       827: 2q^2+2q+1
       828: 2q+1
       829: q^2+2q+1
       830: q^2+2q+1
       831: 2q+1
       832: 2q+1
       833: 2q+1
       834: 2q+1
       835: q^2+2q+1
       836: 2q+1
       837: q+1
       838: q+1
       839: q+1
       840: 2q+1
       841: 2q+1
       842: q^2+2q+1
       843: 2q+1
       844: q^2+2q+1
       845: q+1
       846: q^2+2q+1
       847: 2q+1
       848: 2q+1
       849: q^2+2q+1
       850: q^2+2q+1
       851: q^2+2q+1
       852: q^2+2q+1
       853: 2q+1
       854: q+1
       855: 1
       856: q+1
       857: q+1
       858: 1
       859: q+1
       860: 1
       861: q+1
       862: q+1
       863: q+1
       864: q^2+2q+1
       865: q+1
       866: q+1
       867: 1
       868: q+1
       869: q+1
       870: q+1
       871: 2q+1
       872: q+1
       873: 2q+1
       874: 2q+1
       875: q+1
       876: q+1
       877: q+1
       878: q^2+q+1
       879: q+1
       880: q^2+2q+1
       881: q+1
       882: q^2+2q+1
       883: q^2+2q+1
       884: q+1
       885: q+1
       886: q+1
       887: q+1
       888: q^2+2q+1
       889: 2q+1
       890: q^2+2q+1
       891: q+1
       892: 2q+1
       893: 2q+1
       894: 2q+1
       895: q+1
       896: q+1
       897: 2q+1
       898: 2q+1
       899: q^2+2q+1
       900: 2q+1
       901: q^2+2q+1
       902: 2q+1
       903: 2q+1
       904: 2q+1
       905: q+1
       906: q+1
       907: q+1
       908: q+1
       909: q^2+2q+1
       910: q+1
       911: q+1
       912: 1
       913: q+1
       914: q^2+q+1
       915: q+1
       916: q^2+2q+1
       917: q+1
       918: q^2+2q+1
       919: q^2+2q+1
       920: q+1
       921: q+1
       922: q+1
       923: q+1
       924: q^2+2q+1
       925: 2q+1
       926: q^2+2q+1
       927: q+1
       928: 2q+1
       929: 2q+1
       930: 2q+1
       931: q+1
       932: q+1
       933: q^2+q+1
       934: 2q^2+2q+1
       935: q^2+2q+1
       936: 2q^2+2q+1
       937: q+1
       938: q^2+2q+1
       939: q^2+2q+1
       940: q^2+2q+1
       941: q+1
       942: q^2+q+1
       943: q^2+2q+1
       944: q^2+2q+1
       945: q^2+2q+1
       946: 2q+1
       947: q^2+2q+1
       948: 2q+1
       949: 2q+1
       950: q^2+2q+1
       951: q+1
       952: 2q+1
       953: 2q^2+2q+1
       954: 2q+1
       955: q^2+2q+1
       956: q^2+2q+1
       957: 2q+1
       958: 2q+1
       959: 2q+1
       960: q+1
       961: q+1
       962: q+1
       963: 2q+1
       964: q+1
       965: q+1
       966: 1
       967: q+1
       968: q+1
       969: 1
       970: 2q+1
       971: q+1
       972: 2q+1
       973: 2q+1
       974: q+1
       975: 1
       976: 1
       977: q+1
       978: 2q+1
       979: 2q+1
       980: q^2+2q+1
       981: q+1
       982: 2q+1
       983: 2q+1
       984: 2q+1
       985: 1
       986: q+1
       987: q+1
       988: 2q+1
       989: q+1
       990: q+1
       992: q+1
       993: q+1
       994: q+1
       995: 1
       996: q+1
       997: 2q+1
       998: 2q+1
       999: q+1
      1000: q+1
      1001: q+1
      1002: q+1
      1003: q+1
      1004: 2q+1
      1005: q+1
      1006: 2q+1
      1007: q^2+2q+1
      1008: 2q+1
      1009: q+1
      1010: q+1
      1011: q+1
      1012: 2q+1
      1013: 2q+1
      1014: q+1
      1015: q+1
      1016: 2q+1
      1017: q+1
      1018: 2q+1
      1019: 2q+1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: 2q+1
      1025: 2q+1
      1026: q^2+2q+1
      1027: q+1
      1028: 2q+1
      1029: 2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: 2q+1
      1034: 2q+1
      1035: q^2+2q+1
      1036: 2q+1
      1037: q^2+2q+1
      1038: 2q+1
      1039: 2q+1
      1040: 2q+1
      1041: q+1
      1042: 2q+1
      1043: 2q+1
      1044: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1051: 2q+1
      1052: q^2+2q+1
      1053: 2q+1
      1054: q+1
      1055: q+1
      1056: q+1
      1057: 2q+1
      1058: 2q+1
      1059: q^2+2q+1
      1060: 2q+1
      1061: q^2+2q+1
      1062: q+1
      1063: q^2+2q+1
      1064: 2q+1
      1065: 2q+1
      1066: 1
      1067: q+1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: q+1
      1074: q+1
      1075: 1
      1076: q+1
      1077: 1
      1078: q+1
      1079: q+1
      1080: q+1
      1081: 2q+1
      1082: q+1
      1083: q+1
      1084: 1
      1085: q+1
      1086: q+1
      1087: q+1
      1088: q+1
      1089: q^2+2q+1
      1090: q+1
      1091: q+1
      1092: 1
      1093: q+1
      1094: q+1
      1095: q+1
      1096: 2q+1
      1097: q+1
      1098: 2q+1
      1099: 2q+1
      1100: q+1
      1101: q+1
      1102: q+1
      1103: q+1
      1104: 2q+1
      1105: 2q+1
      1106: q^2+2q+1
      1107: q+1
      1108: 2q+1
      1109: 2q+1
      1110: 2q+1
      1111: 1
      1112: q+1
      1113: q+1
      1114: 1
      1115: q+1
      1116: q+1
      1117: 1
      1118: q+1
      1119: 1
      1120: q+1
      1121: q+1
      1122: q+1
      1123: q^2+2q+1
      1124: q+1
      1125: q+1
      1126: 1
      1127: q+1
      1128: q+1
      1129: q+1
      1130: 2q+1
      1131: q+1
      1132: 2q+1
      1133: 2q+1
      1134: q+1
      1135: q+1
      1136: q+1
      1137: q^2+q+1
      1138: q+1
      1139: q^2+2q+1
      1140: q+1
      1141: q^2+2q+1
      1142: q^2+2q+1
      1143: q+1
      1144: q+1
      1145: q+1
      1146: q+1
      1147: q^2+2q+1
      1148: 2q+1
      1149: q^2+2q+1
      1150: q+1
      1151: 2q+1
      1152: 2q+1
      1153: 2q+1
      1154: q+1
      1155: q+1
      1156: 2q+1
      1157: 2q+1
      1158: q^2+2q+1
      1159: 2q+1
      1160: q^2+2q+1
      1161: 2q+1
      1162: 2q+1
      1163: 2q+1
      1164: q+1
      1165: q+1
      1166: 1
      1167: q+1
      1168: q+1
      1169: 1
      1170: q+1
      1171: 1
      1172: 1
      1173: 1
      1174: q+1
      1175: 2q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1180: q+1
      1181: 1
      1182: 2q+1
      1183: q+1
      1184: 2q+1
      1185: 2q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: q+1
      1190: 1
      1191: q+1
      1193: q+1
      1194: q+1
      1196: 1
      1197: 1
      1198: q+1
      1199: 2q+1
      1200: q+1
      1201: q+1
      1203: q+1
      1204: q+1
      1205: q+1
      1206: 1
      1207: q+1
      1208: 2q+1
      1209: 2q+1
      1210: q+1
      1211: q+1
      1212: q+1
      1213: q+1
      1214: q+1
      1215: 2q+1
      1216: q+1
      1217: q+1
      1218: q+1
      1219: q+1
      1220: 2q+1
      1221: q+1
      1222: q+1
      1223: 1
      1224: q+1
      1225: q+1
      1226: 1
      1227: 2q+1
      1228: q+1
      1229: 2q+1
      1230: 2q+1
      1231: q+1
      1232: 1
      1233: 1
      1234: q+1
      1235: 2q+1
      1236: 2q+1
      1237: q^2+2q+1
      1238: q+1
      1239: 2q+1
      1240: 2q+1
      1241: 2q+1
      1242: 1
      1243: q+1
      1244: q+1
      1245: 2q+1
      1246: q+1
      1247: q+1
      1249: q+1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: 2q+1
      1255: 2q+1
      1256: q+1
      1257: q+1
      1258: q+1
      1259: q+1
      1260: q+1
      1261: 2q+1
      1262: q+1
      1263: 2q+1
      1264: q^2+2q+1
      1265: 2q+1
      1266: q+1
      1267: q+1
      1268: q+1
      1269: 2q+1
      1270: 2q+1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: q+1
      1276: 1
      1277: 1
      1278: 1
      1279: q+1
      1280: 1
      1281: q+1
      1282: q+1
      1283: 1
      1284: q+1
      1285: 1
      1286: q+1
      1287: 1
      1288: q+1
      1289: q+1
      1290: 1
      1291: q+1
      1292: 1
      1293: q+1
      1294: q+1
      1295: q+1
      1296: 2q+1
      1297: q+1
      1298: q+1
      1299: 1
      1300: q+1
      1301: q+1
      1302: 1
      1303: 2q+1
      1304: q+1
      1305: 2q+1
      1306: 2q+1
      1307: q+1
      1308: 1
      1309: 1
      1310: 1
      1311: q+1
      1312: 1
      1313: 1
      1314: 1
      1315: q+1
      1316: 1
      1317: q+1
      1318: q+1
      1319: 1
      1320: q+1
      1321: 1
      1322: q+1
      1323: q+1
      1324: q+1
      1325: 2q+1
      1326: q+1
      1327: q+1
      1328: 1
      1329: q+1
      1330: q+1
      1331: q+1
      1332: q+1
      1333: q^2+2q+1
      1334: q+1
      1335: q+1
      1336: 1
      1337: q+1
      1338: q+1
      1339: q+1
      1340: 2q+1
      1341: q+1
      1342: 2q+1
      1343: 2q+1
      1344: q+1
      1345: q+1
      1346: q+1
      1347: q+1
      1348: 2q+1
      1349: 2q+1
      1350: q^2+2q+1
      1351: q+1
      1352: 2q+1
      1353: 2q+1
      1354: 2q+1
      1355: 1
      1356: q+1
      1357: 1
      1358: q+1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1372: 2q+1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1380: q+1
      1382: 1
      1384: 1
      1385: q+1
      1386: 1
      1387: q+1
      1389: q+1
      1390: q+1
      1392: 1
      1393: 1
      1394: q+1
      1395: 2q+1
      1396: q+1
      1397: q+1
      1399: q+1
      1400: q+1
      1401: q+1
      1402: 1
      1403: q+1
      1404: q+1
      1405: 1
      1406: q+1
      1407: q+1
      1408: 1
      1409: q+1
      1410: 1
      1411: 1
      1412: 1
      1413: q+1
      1414: 2q+1
      1415: q+1
      1416: 1
      1417: 1
      1418: 1
      1419: q+1
      1420: 1
      1421: 2q+1
      1422: q+1
      1423: 2q+1
      1424: 2q+1
      1425: q+1
      1426: 1
      1427: 1
      1428: q+1
      1429: 1
      1430: q+1
      1432: q+1
      1433: q+1
      1435: 1
      1436: 1
      1437: q+1
      1438: 2q+1
      1439: q+1
      1440: q+1
      1442: q+1
      1443: q+1
      1444: q+1
      1445: 1
      1446: q+1
      1447: 2q+1
      1448: 2q+1
      1449: q+1
      1450: q+1
      1451: q+1
      1452: q+1
      1453: q+1
      1454: 2q+1
      1455: q+1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: q+1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: q+1
      1468: 1
      1469: 1
      1470: 1
      1471: q+1
      1472: 1
      1473: q+1
      1474: q+1
      1475: 1
      1476: q+1
      1477: 1
      1478: 1
      1479: 1
      1480: q+1
      1481: 2q+1
      1482: q+1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: q+1
      1491: 1
      1492: 1
      1493: 1
      1494: q+1
      1495: 1
      1496: q+1
      1497: q+1
      1498: 1
      1499: q+1
      1500: 1
      1501: q+1
      1502: 1
      1503: q+1
      1504: q+1
      1505: 1
      1506: q+1
      1507: 1
      1508: q+1
      1509: q+1
      1510: q+1
      1511: 2q+1
      1512: q+1
      1513: q+1
      1514: 1
      1515: q+1
      1516: q+1
      1517: 1
      1518: 2q+1
      1519: q+1
      1520: 2q+1
      1521: 2q+1
      1522: q+1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: q+1
      1552: 1
      1554: 1
      1555: q+1
      1556: 1
      1557: q+1
      1559: q+1
      1560: q+1
      1562: 1
      1563: 1
      1564: 1
      1565: q+1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: q+1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: q+1
      1579: 2q+1
      1580: q+1
      1581: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1587: q+1
      1589: 1
      1591: 1
      1592: q+1
      1593: 1
      1594: q+1
      1596: q+1
      1597: q+1
      1599: 1
      1600: 1
      1601: q+1
      1602: 2q+1
      1603: q+1
      1604: q+1
      1606: q+1
      1607: q+1
      1608: q+1
      1609: 1
      1610: q+1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: q+1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: q+1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1638: q+1
      1639: 1
      1640: 1
      1641: 1
      1642: 1
      1643: q+1
      1644: 1
      1645: 1
      1646: 1
      1647: q+1
      1648: 1
      1649: q+1
      1650: q+1
      1651: 1
      1652: q+1
      1653: 1
      1654: 1
      1655: 1
      1656: q+1
      1657: 2q+1
      1658: q+1
      1659: 1
      1660: 1
      1661: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1684: 1
      1685: 1
      1687: q+1
      1689: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: q+1
      1704: 1
      1705: 1
      1706: 1
      1707: 1
      1709: 1
      1712: 1
      1714: 1
      1715: 1
      1717: q+1
      1719: 1
      1721: 1
      1722: q+1
      1723: 1
      1724: q+1
      1726: q+1
      1727: q+1
      1729: 1
      1730: 1
      1732: 1
      1734: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1742: 1
      1743: 1
      1745: 1
      1747: 1
      1748: 1
      1749: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1754: q+1
      1755: 1
      1756: 1
      1757: 1
      1758: 1
      1759: 1
      1760: 1
      1761: q+1
      1762: 1
      1763: 1
      1764: 1
      1766: 1
      1768: 1
      1769: 1
      1770: 1
      1775: 1
      1779: 1
      1781: 1
      1784: 1
      1786: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1792: 1
      1793: 1
      1794: 1
      1795: 1
      1797: 1
      1801: 1
      1803: 1
      1806: 1
      1808: 1
      1809: 1
      1811: q+1
      1813: 1
      1815: 1
      1818: 1
      1820: 1
      1821: 1
      1822: 1
      1824: 1
      1826: 1
      1828: 1
      1829: 1
      1830: 1
      1831: 1
      1832: 1
      1833: 1
      1834: 1
      1835: 1
      1837: 1
      1845: 1
      1850: 1
      1852: 1
      1853: 1
      1854: 1
      1859: 1
      1863: 1
      1865: 1
      1868: 1
      1871: 1
      1875: 1
      1877: 1
      1878: 1
      1879: 1
      1888: 1
      1896: 1
      1902: 1

1903:    0: q^3+2q^2+1
         1: 2q^2+1
         2: q^3+2q^2+1
         3: q^3+2q^2+1
         4: q^3+2q^2+1
         5: q^3+2q^2+1
         6: 2q^2+1
         7: 2q^2+1
         8: q^3+2q^2+1
         9: 2q^2+1
        10: q^3+2q^2+1
        11: q^3+2q^2+1
        12: q^3+2q^2+1
        13: 2q^2+1
        14: q^3+2q^2+1
        15: q^3+2q^2+1
        16: 2q^2+1
        17: q^3+2q^2+1
        18: q^3+2q^2+1
        19: q^3+2q^2+1
        20: 2q^2+1
        21: 2q^2+1
        22: 2q^2+1
        23: q^3+2q^2+1
        24: q^3+2q^2+1
        25: 2q^2+1
        26: 2q^2+1
        27: q^3+2q^2+1
        28: 2q^2+1
        29: q^3+2q^2+1
        30: 2q^2+1
        31: q^3+2q^2+1
        32: q^3+2q^2+1
        33: 2q^2+1
        34: 2q^2+1
        35: q^3+2q^2+1
        36: 2q^2+1
        37: q^3+2q^2+1
        38: q^3+2q^2+1
        39: q^3+2q^2+1
        40: 2q^2+1
        41: 2q^2+1
        42: q^3+2q^2+1
        43: 2q^2+1
        44: q^3+2q^2+1
        45: q^3+2q^2+1
        46: q^2+1
        47: 2q^2+1
        48: q^3+2q^2+1
        49: q^3+2q^2+1
        50: 2q^2+1
        51: q^2+1
        52: 2q^2+1
        53: 2q^2+1
        54: 2q^2+1
        55: 2q^2+1
        56: q^3+2q^2+1
        57: 2q^2+1
        58: 2q^2+1
        59: 2q^2+1
        60: q^3+2q^2+1
        61: q^3+2q^2+1
        62: 2q^2+1
        63: 2q^2+1
        64: q^3+2q^2+1
        65: 2q^2+1
        66: 2q^2+1
        67: q^3+2q^2+1
        68: 2q^2+1
        69: q^3+2q^2+1
        70: q^3+2q^2+1
        71: 2q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: q^3+2q^2+1
        75: q^3+2q^2+1
        76: 2q^2+1
        77: 2q^2+1
        78: q^3+2q^2+1
        79: 2q^2+1
        80: q^3+2q^2+1
        81: 2q^2+1
        82: q^3+2q^2+1
        83: q^3+2q^2+1
        84: 2q^2+1
        85: 2q^2+1
        86: 2q^2+1
        87: q^3+2q^2+1
        88: q^2+1
        89: 2q^2+1
        90: q^2+1
        91: q^3+2q^2+1
        92: 2q^2+1
        93: q^3+2q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: q^3+2q^2+1
       100: 2q^2+1
       101: q^3+2q^2+1
       102: q^3+2q^2+1
       103: q^2+1
       104: q^2+1
       105: 2q^2+1
       106: q^2+1
       107: 2q^2+1
       108: 2q^2+1
       109: 2q^2+1
       110: 2q^2+1
       111: q^3+2q^2+1
       112: 2q^2+1
       113: q^2+1
       114: 2q^2+1
       115: 2q^2+1
       116: 2q^2+1
       117: 2q^2+1
       118: q^3+2q^2+1
       119: 2q^2+1
       120: 2q^2+1
       121: 2q^2+1
       122: q^3+2q^2+1
       123: q^2+1
       124: 2q^2+1
       125: 2q^2+1
       126: 2q^2+1
       127: q^3+2q^2+1
       128: q^3+2q^2+1
       129: 2q^2+1
       130: 2q^2+1
       131: q^3+2q^2+1
       132: 2q^2+1
       133: q^3+2q^2+1
       134: 2q^2+1
       135: q^2+1
       136: 2q^2+1
       137: 2q^2+1
       138: 2q^2+1
       139: 2q^2+1
       140: q^3+2q^2+1
       141: 2q^2+1
       142: 2q^2+1
       143: 2q^2+1
       144: q^3+2q^2+1
       145: q^3+2q^2+1
       146: 2q^2+1
       147: 2q^2+1
       148: q^3+2q^2+1
       149: 2q^2+1
       150: 2q^2+1
       151: q^3+2q^2+1
       152: 2q^2+1
       153: q^3+2q^2+1
       154: q^3+2q^2+1
       155: 2q^2+1
       156: 1
       157: 2q^2+1
       158: 2q^2+1
       159: 2q^2+1
       160: q^2+1
       161: q^2+1
       162: 2q^2+1
       163: q^2+1
       164: q^2+1
       165: q^3+2q^2+1
       166: q^2+1
       167: 2q^2+1
       168: q^2+1
       169: q^3+2q^2+1
       170: q^2+1
       171: 1
       172: q^2+1
       173: q^2+1
       174: q^2+1
       175: q^2+1
       176: 2q^2+1
       177: 2q^2+1
       178: 2q^2+1
       179: q^3+2q^2+1
       180: q^2+1
       181: 2q^2+1
       182: q^2+1
       183: q^3+2q^2+1
       184: 2q^2+1
       185: q^3+2q^2+1
       186: q^2+1
       187: q^2+1
       188: q^2+1
       189: q^2+1
       190: q^2+1
       191: 2q^2+1
       192: q^2+1
       193: 2q^2+1
       194: 2q^2+1
       195: 2q^2+1
       196: 2q^2+1
       197: q^3+2q^2+1
       198: q^2+1
       199: 2q^2+1
       200: q^2+1
       201: 2q^2+1
       202: 2q^2+1
       203: 2q^2+1
       204: 2q^2+1
       205: q^3+2q^2+1
       206: 2q^2+1
       207: 1
       208: 2q^2+1
       209: 2q^2+1
       210: 2q^2+1
       211: q^2+1
       212: q^2+1
       213: 2q^2+1
       214: q^2+1
       215: 2q^2+1
       216: 2q^2+1
       217: 2q^2+1
       218: 2q^2+1
       219: q^3+2q^2+1
       220: 2q^2+1
       221: 2q^2+1
       222: 2q^2+1
       223: q^3+2q^2+1
       224: q^2+1
       225: 2q^2+1
       226: q^2+1
       227: q^3+2q^2+1
       228: q^2+1
       229: 2q^2+1
       230: q^2+1
       231: 2q^2+1
       232: 2q^2+1
       233: 2q^2+1
       234: 2q^2+1
       235: q^3+2q^2+1
       236: 2q^2+1
       237: q^2+1
       238: 2q^2+1
       239: 2q^2+1
       240: 2q^2+1
       241: 2q^2+1
       242: q^3+2q^2+1
       243: 2q^2+1
       244: 2q^2+1
       245: 2q^2+1
       246: q^3+2q^2+1
       247: q^2+1
       248: 2q^2+1
       249: 2q^2+1
       250: 2q^2+1
       251: q^3+2q^2+1
       252: q^3+2q^2+1
       253: 2q^2+1
       254: 2q^2+1
       255: q^3+2q^2+1
       256: 2q^2+1
       257: q^3+2q^2+1
       258: 1
       259: 2q^2+1
       260: 1
       261: 2q^2+1
       262: 2q^2+1
       263: q^2+1
       264: q^2+1
       265: q^2+1
       266: 2q^2+1
       267: 1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: q^2+1
       273: 2q^2+1
       274: q^2+1
       275: q^2+1
       276: q^3+2q^2+1
       277: q^2+1
       278: q^2+1
       279: 1
       280: 1
       281: q^2+1
       282: q^2+1
       283: q^2+1
       284: 1
       285: q^2+1
       286: q^2+1
       287: q^2+1
       288: 2q^2+1
       289: 1
       290: 2q^2+1
       291: 2q^2+1
       292: 2q^2+1
       293: q^2+1
       294: q^2+1
       295: 2q^2+1
       296: q^2+1
       297: q^2+1
       298: q^3+2q^2+1
       299: q^2+1
       300: 2q^2+1
       301: q^2+1
       302: q^3+2q^2+1
       303: q^2+1
       304: 1
       305: q^2+1
       306: q^2+1
       307: q^2+1
       308: q^2+1
       309: q^2+1
       310: q^2+1
       311: q^2+1
       312: 2q^2+1
       313: 1
       314: 2q^2+1
       315: q^2+1
       316: 2q^2+1
       317: 2q^2+1
       318: q^2+1
       319: q^2+1
       320: q^2+1
       321: 2q^2+1
       322: q^2+1
       323: 2q^2+1
       324: 2q^2+1
       325: 2q^2+1
       326: 2q^2+1
       327: q^3+2q^2+1
       328: 1
       329: 2q^2+1
       330: 1
       331: 2q^2+1
       332: 2q^2+1
       333: q^2+1
       334: q^2+1
       335: q^2+1
       336: q^2+1
       337: 2q^2+1
       338: q^2+1
       339: 2q^2+1
       340: 2q^2+1
       341: 2q^2+1
       342: 2q^2+1
       343: q^3+2q^2+1
       344: 2q^2+1
       345: 1
       346: 2q^2+1
       347: 2q^2+1
       348: 2q^2+1
       349: q^2+1
       350: q^2+1
       351: 2q^2+1
       352: q^2+1
       353: q^2+1
       354: q^3+2q^2+1
       355: q^2+1
       356: q^2+1
       357: q^2+1
       358: 2q^2+1
       359: q^2+1
       360: 2q^2+1
       361: 2q^2+1
       362: 2q^2+1
       363: 2q^2+1
       364: q^3+2q^2+1
       365: q^2+1
       366: 2q^2+1
       367: q^2+1
       368: 2q^2+1
       369: 2q^2+1
       370: 2q^2+1
       371: 2q^2+1
       372: q^3+2q^2+1
       373: 2q^2+1
       374: 1
       375: 2q^2+1
       376: 2q^2+1
       377: 2q^2+1
       378: q^2+1
       379: q^2+1
       380: 2q^2+1
       381: q^2+1
       382: 2q^2+1
       383: 2q^2+1
       384: 2q^2+1
       385: 2q^2+1
       386: q^3+2q^2+1
       387: 2q^2+1
       388: 2q^2+1
       389: 2q^2+1
       390: q^3+2q^2+1
       391: q^2+1
       392: 2q^2+1
       393: q^2+1
       394: q^3+2q^2+1
       395: 1
       396: 1
       397: 2q^2+1
       398: 1
       399: 2q^2+1
       400: q^2+1
       401: q^2+1
       402: q^2+1
       403: q^2+1
       404: 1
       405: q^2+1
       406: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: q^2+1
       412: 2q^2+1
       413: 1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: q^2+1
       419: q^2+1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q^2+1
       426: q^2+1
       427: 1
       428: 1
       429: q^2+1
       430: q^2+1
       431: q^2+1
       432: 1
       433: q^2+1
       434: 1
       435: 2q^2+1
       436: 1
       437: 2q^2+1
       438: 2q^2+1
       439: q^2+1
       440: q^2+1
       441: q^2+1
       442: 2q^2+1
       443: 1
       444: q^2+1
       445: q^2+1
       446: q^2+1
       447: 1
       448: q^2+1
       449: 2q^2+1
       450: q^2+1
       451: q^2+1
       452: q^3+2q^2+1
       453: q^2+1
       454: q^2+1
       455: 1
       456: 1
       457: q^2+1
       458: q^2+1
       459: q^2+1
       460: 1
       461: q^2+1
       462: q^2+1
       463: q^2+1
       465: q^2+1
       466: q^2+1
       467: 1
       468: q^2+1
       469: 2q^2+1
       470: 1
       471: 2q^2+1
       472: q^2+1
       473: q^2+1
       474: q^2+1
       475: q^2+1
       476: 2q^2+1
       477: 1
       478: 2q^2+1
       479: q^2+1
       480: 2q^2+1
       481: 2q^2+1
       482: q^2+1
       483: 1
       484: 1
       485: 2q^2+1
       486: 1
       487: 2q^2+1
       488: q^2+1
       489: q^2+1
       490: q^2+1
       491: q^2+1
       492: q^2+1
       493: q^2+1
       494: 2q^2+1
       495: q^2+1
       496: 2q^2+1
       497: 2q^2+1
       498: 2q^2+1
       499: 2q^2+1
       500: q^3+2q^2+1
       501: 1
       502: 2q^2+1
       503: 1
       504: 2q^2+1
       505: 2q^2+1
       506: q^2+1
       507: q^2+1
       508: q^2+1
       509: 2q^2+1
       510: 1
       511: q^2+1
       512: q^2+1
       513: q^2+1
       514: 1
       515: q^2+1
       516: q^2+1
       517: q^2+1
       518: q^2+1
       519: 2q^2+1
       520: 1
       521: 2q^2+1
       522: q^2+1
       523: 2q^2+1
       524: 2q^2+1
       525: q^2+1
       526: q^2+1
       527: q^2+1
       528: 2q^2+1
       529: q^2+1
       530: 2q^2+1
       531: 2q^2+1
       532: 2q^2+1
       533: 2q^2+1
       534: q^3+2q^2+1
       535: 1
       536: 2q^2+1
       537: 1
       538: 2q^2+1
       539: 2q^2+1
       540: q^2+1
       541: q^2+1
       542: q^2+1
       543: q^2+1
       544: 2q^2+1
       545: q^2+1
       546: 2q^2+1
       547: 2q^2+1
       548: 2q^2+1
       549: 2q^2+1
       550: q^3+2q^2+1
       551: 2q^2+1
       552: 1
       553: 2q^2+1
       554: 2q^2+1
       555: 2q^2+1
       556: q^2+1
       557: q^2+1
       558: 2q^2+1
       559: q^2+1
       560: q^2+1
       561: q^3+2q^2+1
       562: q^2+1
       563: 1
       564: 1
       565: 1
       566: 2q^2+1
       567: 1
       568: q^2+1
       569: 1
       570: q^2+1
       571: q^2+1
       572: 1
       573: 1
       574: 1
       575: q^2+1
       576: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: q^2+1
       582: 1
       583: q^2+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: q^2+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q^2+1
       598: q^2+1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q^2+1
       605: q^2+1
       606: 1
       607: 1
       608: q^2+1
       609: q^2+1
       610: 1
       611: 1
       612: 2q^2+1
       613: 1
       614: 2q^2+1
       615: q^2+1
       616: q^2+1
       617: q^2+1
       618: q^2+1
       619: 1
       620: q^2+1
       621: 1
       622: q^2+1
       623: q^2+1
       624: 1
       625: 1
       626: q^2+1
       627: 2q^2+1
       628: 1
       629: q^2+1
       630: q^2+1
       631: q^2+1
       632: 1
       633: q^2+1
       634: q^2+1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q^2+1
       641: q^2+1
       642: 1
       643: 1
       644: q^2+1
       645: q^2+1
       646: q^2+1
       647: 1
       648: q^2+1
       650: q^2+1
       651: 1
       652: q^2+1
       653: 1
       654: 2q^2+1
       655: 1
       656: q^2+1
       658: q^2+1
       659: q^2+1
       660: 1
       661: q^2+1
       662: 2q^2+1
       663: 1
       664: 2q^2+1
       665: q^2+1
       666: 1
       667: 1
       668: 1
       669: 2q^2+1
       670: 1
       671: q^2+1
       672: 1
       673: q^2+1
       674: q^2+1
       675: 1
       676: q^2+1
       677: q^2+1
       678: q^2+1
       679: 2q^2+1
       680: 1
       681: 2q^2+1
       682: q^2+1
       683: 2q^2+1
       684: 2q^2+1
       685: q^2+1
       686: 1
       687: 1
       688: 2q^2+1
       689: 1
       690: 2q^2+1
       691: q^2+1
       692: q^2+1
       693: q^2+1
       694: q^2+1
       695: 1
       696: q^2+1
       697: 1
       698: q^2+1
       699: q^2+1
       700: 1
       701: 1
       702: q^2+1
       704: q^2+1
       705: q^2+1
       706: 1
       707: q^2+1
       708: 2q^2+1
       709: 1
       710: 2q^2+1
       711: q^2+1
       712: q^2+1
       713: q^2+1
       714: q^2+1
       715: 2q^2+1
       716: 1
       717: 2q^2+1
       718: q^2+1
       719: 2q^2+1
       720: 2q^2+1
       721: q^2+1
       722: 1
       723: 1
       724: 2q^2+1
       725: 1
       726: 2q^2+1
       727: q^2+1
       728: q^2+1
       729: q^2+1
       730: q^2+1
       731: q^2+1
       732: q^2+1
       733: 2q^2+1
       734: q^2+1
       735: 2q^2+1
       736: 2q^2+1
       737: 2q^2+1
       738: 2q^2+1
       739: q^3+2q^2+1
       740: 1
       741: 2q^2+1
       742: 1
       743: 2q^2+1
       744: 2q^2+1
       745: q^2+1
       746: q^2+1
       747: q^2+1
       748: 2q^2+1
       749: 1
       750: q^2+1
       751: q^2+1
       752: q^2+1
       753: 1
       754: q^2+1
       756: 1
       757: 1
       758: 1
       759: 1
       760: q^2+1
       761: 1
       762: q^2+1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q^2+1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: q^2+1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: q^2+1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: q^2+1
       800: q^2+1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q^2+1
       807: 1
       808: 1
       809: 1
       810: 2q^2+1
       811: 1
       812: q^2+1
       813: 1
       814: q^2+1
       815: q^2+1
       816: 1
       817: 1
       818: 1
       819: q^2+1
       820: 1
       821: q^2+1
       822: 1
       823: 1
       824: 1
       825: q^2+1
       826: 1
       827: q^2+1
       828: 1
       829: q^2+1
       830: q^2+1
       831: 1
       832: 1
       833: q^2+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q^2+1
       842: q^2+1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q^2+1
       849: q^2+1
       850: 1
       851: 1
       852: q^2+1
       853: q^2+1
       855: 1
       856: q^2+1
       857: 1
       858: 1
       859: q^2+1
       860: 1
       862: q^2+1
       863: 1
       864: q^2+1
       865: 1
       866: 2q^2+1
       867: 1
       868: q^2+1
       870: 1
       871: 1
       872: 1
       873: 1
       874: q^2+1
       875: 1
       876: q^2+1
       877: 1
       879: q^2+1
       880: q^2+1
       881: 1
       882: q^2+1
       883: 2q^2+1
       884: 1
       885: 2q^2+1
       886: q^2+1
       887: 1
       888: 1
       889: 1
       890: 2q^2+1
       891: 1
       892: q^2+1
       893: 1
       894: q^2+1
       895: q^2+1
       896: 1
       897: 1
       898: 1
       899: q^2+1
       900: 1
       901: q^2+1
       902: 1
       903: 1
       904: 1
       905: q^2+1
       907: q^2+1
       908: 1
       909: q^2+1
       910: 1
       911: 2q^2+1
       912: 1
       913: q^2+1
       915: q^2+1
       916: q^2+1
       917: 1
       918: q^2+1
       919: 2q^2+1
       920: 1
       921: 2q^2+1
       922: q^2+1
       923: 1
       924: 1
       925: 1
       926: 2q^2+1
       927: 1
       928: q^2+1
       929: 1
       930: q^2+1
       931: q^2+1
       932: 1
       933: q^2+1
       934: q^2+1
       935: q^2+1
       936: 2q^2+1
       937: 1
       938: 2q^2+1
       939: q^2+1
       940: 2q^2+1
       941: 2q^2+1
       942: q^2+1
       943: 1
       944: 1
       945: 2q^2+1
       946: 1
       947: 2q^2+1
       948: q^2+1
       949: q^2+1
       950: q^2+1
       951: q^2+1
       952: 1
       953: q^2+1
       954: 1
       955: q^2+1
       956: q^2+1
       957: 1
       958: 1
       959: q^2+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: q^2+1
       966: 1
       967: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q^2+1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: q^2+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q^2+1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: q^2+1
      1020: 1
      1021: q^2+1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q^2+1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: q^2+1
      1036: 1
      1037: q^2+1
      1038: 1
      1039: 1
      1040: 1
      1041: q^2+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q^2+1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q^2+1
      1059: q^2+1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q^2+1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: q^2+1
      1074: 1
      1075: 1
      1076: q^2+1
      1077: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: q^2+1
      1084: 1
      1085: 1
      1087: q^2+1
      1088: 1
      1089: q^2+1
      1090: 1
      1091: 2q^2+1
      1092: 1
      1093: q^2+1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: q^2+1
      1100: 1
      1101: q^2+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q^2+1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: q^2+1
      1116: 1
      1117: 1
      1118: q^2+1
      1119: 1
      1121: q^2+1
      1122: 1
      1123: q^2+1
      1124: 1
      1125: 2q^2+1
      1126: 1
      1127: q^2+1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: q^2+1
      1134: 1
      1135: q^2+1
      1136: 1
      1138: q^2+1
      1139: q^2+1
      1140: 1
      1141: q^2+1
      1142: 2q^2+1
      1143: 1
      1144: 2q^2+1
      1145: q^2+1
      1146: 1
      1147: 1
      1148: 1
      1149: 2q^2+1
      1150: 1
      1151: q^2+1
      1152: 1
      1153: q^2+1
      1154: q^2+1
      1155: 1
      1156: 1
      1157: 1
      1158: q^2+1
      1159: 1
      1160: q^2+1
      1161: 1
      1162: 1
      1163: 1
      1164: q^2+1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q^2+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: q^2+1
      1223: 1
      1224: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: q^2+1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q^2+1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q^2+1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1287: 1
      1288: q^2+1
      1289: 1
      1290: 1
      1291: q^2+1
      1292: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: q^2+1
      1299: 1
      1300: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: q^2+1
      1318: 1
      1319: 1
      1320: q^2+1
      1321: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: q^2+1
      1328: 1
      1329: 1
      1331: q^2+1
      1332: 1
      1333: q^2+1
      1334: 1
      1335: 2q^2+1
      1336: 1
      1337: q^2+1
      1339: 1
      1340: 1
      1341: 1
      1342: 1
      1343: q^2+1
      1344: 1
      1345: q^2+1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q^2+1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1420: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q^2+1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1492: 1
      1493: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1502: 1
      1503: q^2+1
      1504: 1
      1505: 1
      1506: q^2+1
      1507: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: q^2+1
      1514: 1
      1515: 1
      1517: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1531: 1
      1532: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1542: 1
      1545: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1613: 1
      1615: 1
      1616: 1
      1618: 1
      1619: 1
      1622: 1
      1623: 1
      1624: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1633: 1
      1635: 1
      1636: 1
      1639: 1
      1640: 1
      1641: 1
      1644: 1
      1645: 1
      1646: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1663: 1
      1665: 1
      1666: 1
      1669: 1
      1670: 1
      1671: 1
      1679: 1
      1682: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1693: 1
      1694: 1
      1697: 1
      1698: 1
      1699: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1709: 1
      1712: 1
      1715: 1
      1717: 1
      1719: 1
      1721: 1
      1723: 1
      1724: 1
      1726: 1
      1727: 1
      1729: 1
      1730: 1
      1733: 1
      1735: 1
      1737: 1
      1738: 1
      1741: 1
      1742: 1
      1743: 1
      1746: 1
      1748: 1
      1749: 1
      1751: 1
      1752: 1
      1755: 1
      1756: 1
      1757: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1767: 1
      1769: 1
      1770: 1
      1781: 1
      1784: 1
      1787: 1
      1789: 1
      1790: 1
      1793: 1
      1794: 1
      1795: 1
      1803: 1
      1806: 1
      1809: 1
      1811: 1
      1813: 1
      1815: 1
      1819: 1
      1821: 1
      1822: 1
      1825: 1
      1827: 1
      1829: 1
      1830: 1
      1833: 1
      1834: 1
      1835: 1
      1838: 1
      1851: 1
      1853: 1
      1854: 1
      1865: 1
      1868: 1
      1872: 1
      1876: 1
      1878: 1
      1879: 1
      1889: 1
      1903: 1

1904:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q+1
        36: q+1
        37: q+1
        38: q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q+1
        68: q^2+q+1
        69: q^2+q+1
        70: q+1
        71: q+1
        72: q^2+q+1
        73: q+1
        74: q+1
        75: q+1
        76: q+1
        77: q+1
        78: q+1
        79: q+1
        80: q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q^2+q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q+1
       100: q+1
       101: q+1
       102: q+1
       103: q+1
       104: q^2+q+1
       105: q^2+q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q^2+q+1
       110: q^2+q+1
       111: q+1
       112: q^2+q+1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q^2+q+1
       124: q+1
       125: q^2+q+1
       126: q+1
       127: q+1
       128: q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q+1
       136: q+1
       137: q+1
       138: q+1
       139: q+1
       140: q+1
       141: q+1
       142: q+1
       143: q+1
       144: q+1
       145: q+1
       146: q+1
       147: q+1
       148: 1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: q^2+q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q^2+q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q^2+q+1
       171: q^2+q+1
       172: q+1
       173: q^2+q+1
       174: q^2+q+1
       175: q+1
       176: q+1
       177: q^2+q+1
       178: q+1
       179: q+1
       180: q+1
       181: q+1
       182: q+1
       183: q+1
       184: q+1
       185: q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q^2+q+1
       191: q^2+q+1
       192: q^2+q+1
       193: q^2+q+1
       194: q+1
       195: q^2+q+1
       196: q+1
       197: q+1
       198: q^2+q+1
       199: q^2+q+1
       200: q^2+q+1
       201: q^2+q+1
       202: q^2+q+1
       203: q^2+q+1
       204: q^2+q+1
       205: q+1
       206: q^2+q+1
       207: q^2+q+1
       208: q^2+q+1
       209: q^2+q+1
       210: q^2+q+1
       211: q^2+q+1
       212: q^2+q+1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q^2+q+1
       222: q+1
       223: q+1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q+1
       231: q+1
       232: q+1
       233: q+1
       234: q+1
       235: q+1
       236: q+1
       237: q+1
       238: q+1
       239: q+1
       240: q+1
       241: q+1
       242: q+1
       243: 1
       244: q+1
       245: 1
       246: 1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: 1
       256: q+1
       257: q+1
       258: q^2+q+1
       259: q^2+q+1
       260: q^2+q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q^2+q+1
       264: q^2+q+1
       265: q+1
       266: q^2+q+1
       267: q^2+q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q^2+q+1
       271: q^2+q+1
       272: q^2+q+1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q^2+q+1
       278: q+1
       279: q^2+q+1
       280: q+1
       281: q+1
       282: q+1
       283: q^2+q+1
       284: q^2+q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q+1
       290: q+1
       291: q+1
       292: q+1
       293: q+1
       294: q+1
       295: q+1
       296: q+1
       297: q+1
       298: q+1
       299: q+1
       300: q+1
       301: q+1
       302: 1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q^2+q+1
       312: q^2+q+1
       313: q^2+q+1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q^2+q+1
       321: q^2+q+1
       322: q^2+q+1
       323: q^2+q+1
       324: q+1
       325: q^2+q+1
       326: q+1
       327: q+1
       328: q^2+q+1
       329: q^2+q+1
       330: q^2+q+1
       331: q^2+q+1
       332: q^2+q+1
       333: q^2+q+1
       334: q^2+q+1
       335: q+1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: q+1
       346: q+1
       347: q+1
       348: q+1
       349: q+1
       350: q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q+1
       360: 1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q+1
       368: q+1
       369: q+1
       370: q+1
       371: q+1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: 1
       388: q+1
       389: 1
       390: 1
       391: 1
       392: q+1
       393: q+1
       394: 1
       395: q+1
       396: q^2+q+1
       397: q^2+q+1
       398: q^2+q+1
       399: q^2+q+1
       400: q+1
       401: q^2+q+1
       402: q+1
       403: q+1
       404: q^2+q+1
       405: q^2+q+1
       406: q^2+q+1
       407: q^2+q+1
       408: q^2+q+1
       409: q^2+q+1
       410: q^2+q+1
       411: q+1
       412: q^2+q+1
       413: q^2+q+1
       414: q^2+q+1
       415: q^2+q+1
       416: q^2+q+1
       417: q^2+q+1
       418: q^2+q+1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q^2+q+1
       428: q+1
       429: q+1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q+1
       437: q+1
       438: q+1
       439: q+1
       440: q+1
       441: q+1
       442: q+1
       443: q+1
       444: q+1
       445: q+1
       446: q+1
       447: q+1
       448: q+1
       449: 1
       450: q+1
       451: 1
       452: 1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: 1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: q^2+q+1
       468: q+1
       469: q+1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q^2+q+1
       476: q^2+q+1
       477: q^2+q+1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: q^2+q+1
       485: q^2+q+1
       486: q^2+q+1
       487: q^2+q+1
       488: q+1
       489: q^2+q+1
       490: q+1
       491: q+1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: 1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: q+1
       502: q+1
       503: q+1
       504: q+1
       505: q+1
       506: q+1
       507: q+1
       508: q+1
       509: q+1
       510: q+1
       511: q+1
       512: q+1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q+1
       518: q+1
       519: 1
       520: 1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: 1
       527: q+1
       528: q+1
       529: q+1
       530: 1
       531: q+1
       532: q+1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: q+1
       560: 1
       561: 1
       562: 1
       563: q+1
       564: q+1
       565: q^2+q+1
       566: q^2+q+1
       567: q^2+q+1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q^2+q+1
       575: q^2+q+1
       576: q^2+q+1
       577: q^2+q+1
       578: q+1
       579: q^2+q+1
       580: q+1
       581: q+1
       582: q^2+q+1
       583: q^2+q+1
       584: q^2+q+1
       585: q^2+q+1
       586: q^2+q+1
       587: q^2+q+1
       588: q^2+q+1
       589: q+1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: q+1
       599: q+1
       600: q+1
       601: q+1
       602: q+1
       603: q+1
       604: q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: q+1
       614: 1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q+1
       622: q+1
       623: q+1
       624: q+1
       625: q+1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: 1
       642: q+1
       643: 1
       644: 1
       645: 1
       646: q+1
       647: q+1
       648: 1
       649: q+1
       650: q+1
       651: q+1
       652: q+1
       653: q+1
       654: q+1
       655: q+1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: q^2+q+1
       661: q+1
       662: q+1
       663: q+1
       664: q+1
       665: q+1
       666: q+1
       667: q+1
       668: q^2+q+1
       669: q^2+q+1
       670: q^2+q+1
       671: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: q+1
       679: 1
       680: 1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: q+1
       688: q+1
       689: q+1
       690: 1
       691: q+1
       692: q+1
       693: q+1
       694: q+1
       695: q+1
       696: q+1
       697: q+1
       698: q+1
       699: q+1
       700: q+1
       701: q+1
       702: 1
       703: q+1
       704: q+1
       705: 1
       706: 1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: 1
       713: 1
       714: q+1
       715: 1
       716: 1
       717: q+1
       718: q+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: q+1
       733: q+1
       734: q+1
       735: 1
       736: q+1
       737: q+1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: q+1
       758: q^2+q+1
       759: q+1
       760: q+1
       761: q+1
       762: q+1
       763: q+1
       764: q+1
       765: q+1
       766: q^2+q+1
       767: q^2+q+1
       768: q^2+q+1
       769: q+1
       770: q+1
       771: q+1
       772: q+1
       773: q+1
       774: q+1
       775: q^2+q+1
       776: q^2+q+1
       777: q^2+q+1
       778: q^2+q+1
       779: q+1
       780: q^2+q+1
       781: q+1
       782: q+1
       783: q+1
       784: q+1
       785: q+1
       786: q+1
       787: 1
       788: q+1
       789: q+1
       790: q+1
       791: q+1
       792: q+1
       793: q+1
       794: q+1
       795: q+1
       796: q+1
       797: q+1
       798: q+1
       799: q+1
       800: q+1
       801: q+1
       802: q+1
       803: q+1
       804: q+1
       805: q+1
       806: q+1
       807: q+1
       808: q+1
       809: q+1
       810: 1
       811: 1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: 1
       818: q+1
       819: q+1
       820: q+1
       821: 1
       822: q+1
       823: q+1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: q+1
       851: 1
       852: 1
       853: 1
       854: q+1
       855: q+1
       856: q+1
       857: q+1
       858: q+1
       859: q+1
       860: q+1
       861: q+1
       862: q+1
       863: q+1
       864: q+1
       865: q+1
       866: q+1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q^2+q+1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       881: 1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: q+1
       890: 1
       891: 1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       896: q+1
       897: 1
       898: q+1
       899: q+1
       900: q+1
       901: 1
       902: q+1
       903: q+1
       904: 1
       905: 1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: q+1
       936: 1
       937: 1
       938: q+1
       939: q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: q+1
       963: q+1
       964: q+1
       965: q+1
       966: q+1
       967: q+1
       968: q+1
       969: q+1
       970: q+1
       971: q^2+q+1
       972: q+1
       973: q+1
       974: q+1
       975: q+1
       976: q+1
       977: q+1
       978: q+1
       979: q^2+q+1
       980: q^2+q+1
       981: q^2+q+1
       982: q+1
       983: q+1
       984: q+1
       985: q+1
       986: q+1
       987: q+1
       988: q+1
       989: q+1
       990: 1
       991: 1
       992: q+1
       993: q+1
       994: 1
       995: q+1
       996: q+1
       997: q+1
       998: q+1
       999: q+1
      1000: q+1
      1001: 1
      1002: q+1
      1003: q+1
      1004: q+1
      1005: q+1
      1006: q+1
      1007: q+1
      1008: q+1
      1009: q+1
      1010: q+1
      1011: q+1
      1012: q+1
      1013: 1
      1014: q+1
      1015: q+1
      1016: 1
      1017: 1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: 1
      1024: 1
      1025: q+1
      1026: 1
      1027: 1
      1028: q+1
      1029: q+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: q+1
      1044: q+1
      1045: q+1
      1046: 1
      1047: q+1
      1048: q+1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1066: q+1
      1067: q+1
      1068: q+1
      1069: 1
      1070: q+1
      1071: q+1
      1072: q+1
      1073: q+1
      1074: q+1
      1075: q+1
      1076: q+1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: q+1
      1084: q+1
      1085: q+1
      1086: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: 1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: 1
      1104: 1
      1105: q+1
      1106: 1
      1107: 1
      1108: q+1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1131: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: q+1
      1167: q+1
      1168: q+1
      1169: q+1
      1170: q+1
      1171: q+1
      1172: q+1
      1173: q+1
      1174: q+1
      1175: q+1
      1176: q+1
      1177: q+1
      1178: q+1
      1179: q+1
      1180: q+1
      1181: q+1
      1182: q+1
      1183: q^2+q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: q+1
      1188: q+1
      1189: q+1
      1190: q+1
      1191: 1
      1192: 1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1197: q+1
      1198: q+1
      1199: q+1
      1200: q+1
      1201: 1
      1202: 1
      1203: q+1
      1204: q+1
      1205: 1
      1206: q+1
      1207: q+1
      1208: 1
      1209: q+1
      1210: q+1
      1211: q+1
      1212: 1
      1213: q+1
      1214: q+1
      1215: 1
      1216: 1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: q+1
      1247: 1
      1248: 1
      1249: q+1
      1250: q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: q+1
      1272: 1
      1273: 1
      1274: q+1
      1275: q+1
      1276: q+1
      1277: 1
      1278: q+1
      1279: q+1
      1280: q+1
      1281: q+1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: q+1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1341: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1355: 1
      1356: 1
      1357: q+1
      1358: q+1
      1359: q+1
      1360: 1
      1361: q+1
      1362: q+1
      1363: q+1
      1364: q+1
      1365: q+1
      1366: q+1
      1367: q+1
      1368: q+1
      1369: q+1
      1370: q+1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: q+1
      1375: q+1
      1376: q+1
      1377: q+1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: q+1
      1386: q+1
      1387: 1
      1388: 1
      1389: q+1
      1390: 1
      1391: 1
      1392: 1
      1393: q+1
      1394: 1
      1395: 1
      1396: q+1
      1397: 1
      1398: 1
      1399: q+1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1422: 1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1431: 1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: q+1
      1459: 1
      1460: 1
      1461: q+1
      1462: q+1
      1463: q+1
      1464: 1
      1465: q+1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1516: 1
      1517: 1
      1519: 1
      1524: 1
      1525: q+1
      1526: 1
      1527: 1
      1528: q+1
      1529: q+1
      1530: q+1
      1531: 1
      1532: q+1
      1533: q+1
      1534: q+1
      1535: q+1
      1536: q+1
      1537: q+1
      1538: q+1
      1539: q+1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: q+1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1558: 1
      1559: q+1
      1560: 1
      1561: 1
      1562: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1584: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1595: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1614: q+1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1654: 1
      1662: 1
      1663: 1
      1664: q+1
      1665: 1
      1666: 1
      1667: q+1
      1668: q+1
      1669: q+1
      1670: 1
      1671: q+1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1684: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1707: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1722: 1
      1723: 1
      1725: 1
      1730: 1
      1731: 1
      1732: 1
      1733: 1
      1734: 1
      1735: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1743: 1
      1744: 1
      1750: 1
      1765: 1
      1766: 1
      1767: 1
      1768: q+1
      1769: 1
      1770: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1775: 1
      1776: 1
      1777: 1
      1778: 1
      1779: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1786: 1
      1787: 1
      1788: 1
      1796: 1
      1797: 1
      1798: 1
      1800: 1
      1808: 1
      1816: 1
      1817: 1
      1818: 1
      1819: 1
      1820: 1
      1836: 1
      1837: 1
      1838: 1
      1839: 1
      1840: 1
      1841: 1
      1842: 1
      1843: 1
      1844: 1
      1845: 1
      1846: 1
      1848: 1
      1849: 1
      1855: 1
      1870: 1
      1880: 1
      1881: 1
      1882: 1
      1883: 1
      1884: 1
      1904: 1

1905:    0: q^3+3q^2+2q+1
         1: q^3+3q^2+2q+1
         2: 3q^2+2q+1
         3: q^3+3q^2+2q+1
         4: q^3+3q^2+2q+1
         5: q^3+3q^2+2q+1
         6: 3q^2+2q+1
         7: 3q^2+2q+1
         8: 3q^2+2q+1
         9: q^3+3q^2+2q+1
        10: 3q^2+2q+1
        11: q^3+3q^2+2q+1
        12: q^3+3q^2+2q+1
        13: q^3+3q^2+2q+1
        14: 3q^2+2q+1
        15: q^3+3q^2+2q+1
        16: q^3+3q^2+2q+1
        17: 3q^2+2q+1
        18: q^3+3q^2+2q+1
        19: q^3+3q^2+2q+1
        20: 3q^2+2q+1
        21: 3q^2+2q+1
        22: 3q^2+2q+1
        23: 2q^2+2q+1
        24: 3q^2+2q+1
        25: 3q^2+2q+1
        26: 3q^2+2q+1
        27: 3q^2+2q+1
        28: q^3+3q^2+2q+1
        29: 3q^2+2q+1
        30: q^3+3q^2+2q+1
        31: 3q^2+2q+1
        32: q^3+3q^2+2q+1
        33: 3q^2+2q+1
        34: 3q^2+2q+1
        35: 3q^2+2q+1
        36: q^3+3q^2+2q+1
        37: 2q^2+2q+1
        38: q^3+2q^2+2q+1
        39: q^3+3q^2+2q+1
        40: 3q^2+2q+1
        41: 3q^2+2q+1
        42: 3q^2+2q+1
        43: q^3+3q^2+2q+1
        44: 3q^2+2q+1
        45: q^3+3q^2+2q+1
        46: q^3+3q^2+2q+1
        47: q^3+3q^2+2q+1
        48: 3q^2+2q+1
        49: q^3+3q^2+2q+1
        50: 2q^2+2q+1
        51: 3q^2+2q+1
        52: 3q^2+2q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: 3q^2+2q+1
        56: 2q^2+2q+1
        57: 3q^2+2q+1
        58: 3q^2+2q+1
        59: 3q^2+2q+1
        60: 2q^2+2q+1
        61: 3q^2+2q+1
        62: 3q^2+2q+1
        63: 3q^2+2q+1
        64: 3q^2+2q+1
        65: 3q^2+2q+1
        66: 3q^2+2q+1
        67: 3q^2+2q+1
        68: q^3+3q^2+2q+1
        69: 3q^2+2q+1
        70: q^3+3q^2+2q+1
        71: 3q^2+2q+1
        72: 3q^2+2q+1
        73: 3q^2+2q+1
        74: q^2+2q+1
        75: 3q^2+2q+1
        76: 2q^2+2q+1
        77: 2q^2+2q+1
        78: 2q^2+2q+1
        79: q^3+2q^2+2q+1
        80: q^2+2q+1
        81: q^3+3q^2+2q+1
        82: 2q^2+2q+1
        83: q^3+2q^2+2q+1
        84: 3q^2+2q+1
        85: 3q^2+2q+1
        86: 3q^2+2q+1
        87: 2q^2+2q+1
        88: 3q^2+2q+1
        89: 3q^2+2q+1
        90: 3q^2+2q+1
        91: 3q^2+2q+1
        92: q^3+3q^2+2q+1
        93: 3q^2+2q+1
        94: q^3+3q^2+2q+1
        95: 3q^2+2q+1
        96: q^3+3q^2+2q+1
        97: 3q^2+2q+1
        98: 3q^2+2q+1
        99: 3q^2+2q+1
       100: q^3+3q^2+2q+1
       101: 2q^2+2q+1
       102: q^3+2q^2+2q+1
       103: q^3+3q^2+2q+1
       104: 2q^2+2q+1
       105: 2q^2+2q+1
       106: 3q^2+2q+1
       107: 2q^2+2q+1
       108: q^2+2q+1
       109: 2q^2+2q+1
       110: 2q^2+2q+1
       111: 2q^2+2q+1
       112: 2q^2+2q+1
       113: 3q^2+2q+1
       114: 3q^2+2q+1
       115: 2q^2+2q+1
       116: 2q^2+2q+1
       117: 3q^2+2q+1
       118: 2q^2+2q+1
       119: 3q^2+2q+1
       120: 3q^2+2q+1
       121: 3q^2+2q+1
       122: 2q^2+2q+1
       123: 3q^2+2q+1
       124: 3q^2+2q+1
       125: 3q^2+2q+1
       126: 3q^2+2q+1
       127: q^2+2q+1
       128: 3q^2+2q+1
       129: 3q^2+2q+1
       130: 3q^2+2q+1
       131: 3q^2+2q+1
       132: q^3+3q^2+2q+1
       133: 2q^2+2q+1
       134: q^2+2q+1
       135: 3q^2+2q+1
       136: 3q^2+2q+1
       137: q^2+2q+1
       138: q^2+2q+1
       139: 3q^2+2q+1
       140: q^2+2q+1
       141: 2q^2+2q+1
       142: 2q^2+2q+1
       143: 2q^2+2q+1
       144: 2q+1
       145: 2q^2+2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: 2q^2+2q+1
       152: q^3+2q^2+2q+1
       153: q^2+2q+1
       154: q^3+2q^2+2q+1
       155: 2q^2+2q+1
       156: 3q^2+2q+1
       157: 3q^2+2q+1
       158: 2q^2+2q+1
       159: 2q^2+2q+1
       160: 3q^2+2q+1
       161: 2q^2+2q+1
       162: 3q^2+2q+1
       163: 3q^2+2q+1
       164: 3q^2+2q+1
       165: 2q^2+2q+1
       166: 3q^2+2q+1
       167: 3q^2+2q+1
       168: 3q^2+2q+1
       169: 3q^2+2q+1
       170: 3q^2+2q+1
       171: 3q^2+2q+1
       172: 3q^2+2q+1
       173: q^3+3q^2+2q+1
       174: 3q^2+2q+1
       175: q^3+3q^2+2q+1
       176: 3q^2+2q+1
       177: 3q^2+2q+1
       178: 3q^2+2q+1
       179: q^2+2q+1
       180: 3q^2+2q+1
       181: 2q^2+2q+1
       182: 2q^2+2q+1
       183: 2q^2+2q+1
       184: q^3+2q^2+2q+1
       185: q^2+2q+1
       186: q^3+3q^2+2q+1
       187: 2q^2+2q+1
       188: q^3+2q^2+2q+1
       189: 2q^2+2q+1
       190: 2q^2+2q+1
       191: q^2+2q+1
       192: 2q^2+2q+1
       193: q^2+2q+1
       194: 2q^2+2q+1
       195: q^2+2q+1
       196: 2q^2+2q+1
       197: q^2+q+1
       198: 2q^2+2q+1
       199: 2q^2+2q+1
       200: 3q^2+2q+1
       201: 2q^2+2q+1
       202: q^2+2q+1
       203: 2q^2+2q+1
       204: 2q^2+2q+1
       205: 2q^2+2q+1
       206: 2q^2+2q+1
       207: 3q^2+2q+1
       208: 3q^2+2q+1
       209: 2q^2+2q+1
       210: 2q^2+2q+1
       211: 3q^2+2q+1
       212: 2q^2+2q+1
       213: q^2+2q+1
       214: 3q^2+2q+1
       215: 3q^2+2q+1
       216: q^2+2q+1
       217: q^2+2q+1
       218: 3q^2+2q+1
       219: q^2+2q+1
       220: 3q^2+2q+1
       221: 3q^2+2q+1
       222: 3q^2+2q+1
       223: q^2+2q+1
       224: 3q^2+2q+1
       225: 2q^2+2q+1
       226: 2q^2+2q+1
       227: 2q^2+2q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: 3q^2+2q+1
       231: q^2+2q+1
       232: 2q+1
       233: q^2+2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: 2q^2+2q+1
       238: 2q^2+2q+1
       239: q^2+2q+1
       240: 2q+1
       241: 2q^2+2q+1
       242: 2q+1
       243: q^2+2q+1
       244: q^2+2q+1
       245: q^2+2q+1
       246: 2q+1
       247: q^2+2q+1
       248: 2q^2+2q+1
       249: 2q^2+2q+1
       250: 2q^2+2q+1
       251: 2q+1
       252: 2q^2+2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: q^2+2q+1
       256: q^3+2q^2+2q+1
       257: q^2+2q+1
       258: 2q^2+2q+1
       259: 2q^2+2q+1
       260: 3q^2+2q+1
       261: 2q^2+2q+1
       262: q^2+2q+1
       263: 2q^2+2q+1
       264: 2q^2+2q+1
       265: 2q^2+2q+1
       266: 2q^2+2q+1
       267: 3q^2+2q+1
       268: 3q^2+2q+1
       269: 2q^2+2q+1
       270: 2q^2+2q+1
       271: 3q^2+2q+1
       272: 2q^2+2q+1
       273: 3q^2+2q+1
       274: 3q^2+2q+1
       275: 3q^2+2q+1
       276: 2q^2+2q+1
       277: 3q^2+2q+1
       278: 3q^2+2q+1
       279: 3q^2+2q+1
       280: 3q^2+2q+1
       281: q^2+2q+1
       282: 3q^2+2q+1
       283: 3q^2+2q+1
       284: 3q^2+2q+1
       285: 3q^2+2q+1
       286: q^3+3q^2+2q+1
       287: 2q^2+2q+1
       288: q^2+2q+1
       289: 3q^2+2q+1
       290: 3q^2+2q+1
       291: q^2+2q+1
       292: q^2+2q+1
       293: 3q^2+2q+1
       294: q^2+2q+1
       295: 2q^2+2q+1
       296: 2q^2+2q+1
       297: 2q^2+2q+1
       298: 2q+1
       299: 2q^2+2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: q^2+2q+1
       303: 2q^2+2q+1
       304: 2q^2+2q+1
       305: 2q^2+2q+1
       306: q^3+2q^2+2q+1
       307: q^2+2q+1
       308: q^3+2q^2+2q+1
       309: q^2+q+1
       310: 2q^2+2q+1
       311: q^2+2q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: q+1
       315: 2q^2+2q+1
       316: q^2+2q+1
       317: q+1
       318: q^2+q+1
       319: 2q^2+2q+1
       320: 2q^2+2q+1
       321: q^2+2q+1
       322: 2q^2+2q+1
       323: q^2+2q+1
       324: 2q^2+2q+1
       325: q^2+2q+1
       326: 2q^2+2q+1
       327: q^2+q+1
       328: 2q^2+2q+1
       329: 2q^2+2q+1
       330: 3q^2+2q+1
       331: 2q^2+2q+1
       332: q^2+2q+1
       333: 2q^2+2q+1
       334: 2q^2+2q+1
       335: 2q^2+2q+1
       336: q^2+2q+1
       337: q^2+2q+1
       338: 3q^2+2q+1
       339: q^2+2q+1
       340: 2q+1
       341: q^2+2q+1
       342: q^2+2q+1
       343: q^2+2q+1
       344: q^2+2q+1
       345: 3q^2+2q+1
       346: 3q^2+2q+1
       347: q^2+2q+1
       348: q^2+2q+1
       349: 3q^2+2q+1
       350: q^2+2q+1
       351: 2q^2+2q+1
       352: 2q^2+2q+1
       353: 2q^2+2q+1
       354: 2q+1
       355: 2q^2+2q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q+1
       359: q^2+2q+1
       360: 2q+1
       361: q^2+2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q^2+2q+1
       368: q^2+2q+1
       369: 2q+1
       370: q^2+2q+1
       371: 2q+1
       372: 2q+1
       373: 2q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q+1
       377: 2q+1
       378: q^2+2q+1
       379: 2q+1
       380: 2q+1
       381: 2q^2+2q+1
       382: 2q^2+2q+1
       383: q^2+2q+1
       384: 2q+1
       385: 2q^2+2q+1
       386: 2q+1
       387: q^2+2q+1
       388: q^2+2q+1
       389: q^2+2q+1
       390: 2q+1
       391: q^2+2q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: q^2+2q+1
       395: 2q^2+2q+1
       396: 2q^2+2q+1
       397: q^2+2q+1
       398: 2q^2+2q+1
       399: q^2+2q+1
       400: 2q^2+2q+1
       401: q^2+2q+1
       402: 2q^2+2q+1
       403: q^2+q+1
       404: 2q^2+2q+1
       405: 2q^2+2q+1
       406: 3q^2+2q+1
       407: 2q^2+2q+1
       408: q^2+2q+1
       409: 2q^2+2q+1
       410: 2q^2+2q+1
       411: 2q^2+2q+1
       412: 2q^2+2q+1
       413: 3q^2+2q+1
       414: 3q^2+2q+1
       415: 2q^2+2q+1
       416: 2q^2+2q+1
       417: 3q^2+2q+1
       418: 2q^2+2q+1
       419: q^2+2q+1
       420: 3q^2+2q+1
       421: 3q^2+2q+1
       422: q^2+2q+1
       423: q^2+2q+1
       424: 3q^2+2q+1
       425: q^2+2q+1
       426: 3q^2+2q+1
       427: 3q^2+2q+1
       428: 3q^2+2q+1
       429: q^2+2q+1
       430: 3q^2+2q+1
       431: 2q^2+2q+1
       432: 2q^2+2q+1
       433: 2q^2+2q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: 3q^2+2q+1
       437: q^2+2q+1
       438: 2q+1
       439: q^2+2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q^2+2q+1
       444: 2q^2+2q+1
       445: q^2+2q+1
       446: 2q+1
       447: 2q^2+2q+1
       448: 2q+1
       449: q^2+2q+1
       450: q^2+2q+1
       451: q^2+2q+1
       452: 2q+1
       453: q^2+2q+1
       454: 2q^2+2q+1
       455: 2q^2+2q+1
       456: 2q^2+2q+1
       457: 2q+1
       458: 2q^2+2q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: q^2+2q+1
       462: q^3+2q^2+2q+1
       463: q^2+2q+1
       464: q^2+q+1
       465: q+1
       466: q^2+2q+1
       467: q^2+2q+1
       468: q+1
       469: q+1
       470: q^2+2q+1
       471: q+1
       472: q+1
       473: q^2+q+1
       474: 2q^2+2q+1
       475: q^2+2q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: q+1
       479: 2q^2+2q+1
       480: q^2+2q+1
       481: q+1
       482: q^2+q+1
       483: 2q^2+2q+1
       484: 2q^2+2q+1
       485: q^2+2q+1
       486: 2q^2+2q+1
       487: q^2+2q+1
       488: 2q^2+2q+1
       489: q^2+2q+1
       490: 2q^2+2q+1
       491: q^2+q+1
       492: q^2+2q+1
       493: q^2+2q+1
       494: 2q+1
       495: q^2+2q+1
       496: 2q+1
       497: q^2+2q+1
       498: 2q+1
       499: q^2+2q+1
       500: q+1
       501: q^2+2q+1
       502: q^2+2q+1
       503: 3q^2+2q+1
       504: q^2+2q+1
       505: 2q+1
       506: q^2+2q+1
       507: q^2+2q+1
       508: q^2+2q+1
       509: 2q+1
       510: 2q^2+2q+1
       511: 2q^2+2q+1
       512: q^2+2q+1
       513: 2q+1
       514: 2q^2+2q+1
       515: 2q+1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: 2q+1
       521: q+1
       522: q^2+2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: 2q+1
       529: q^2+2q+1
       530: 2q+1
       531: q^2+2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: q^2+2q+1
       538: q+1
       539: q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: 2q+1
       544: 2q+1
       545: 2q^2+2q+1
       546: q^2+2q+1
       547: 2q+1
       548: q^2+2q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: q^2+2q+1
       553: q^2+2q+1
       554: q+1
       555: 2q+1
       556: q^2+2q+1
       557: 2q+1
       558: q^2+2q+1
       559: q^2+2q+1
       560: q^2+2q+1
       561: 2q+1
       562: q^2+2q+1
       563: q^2+q+1
       564: 2q^2+2q+1
       565: q^2+2q+1
       566: q^2+2q+1
       567: q^2+2q+1
       568: q+1
       569: 2q^2+2q+1
       570: q^2+2q+1
       571: q+1
       572: q^2+q+1
       573: 2q^2+2q+1
       574: 2q^2+2q+1
       575: q^2+2q+1
       576: 2q^2+2q+1
       577: q^2+2q+1
       578: 2q^2+2q+1
       579: q^2+2q+1
       580: 2q^2+2q+1
       581: q^2+q+1
       582: 2q^2+2q+1
       583: 2q^2+2q+1
       584: 3q^2+2q+1
       585: 2q^2+2q+1
       586: q^2+2q+1
       587: 2q^2+2q+1
       588: 2q^2+2q+1
       589: 2q^2+2q+1
       590: q^2+2q+1
       591: q^2+2q+1
       592: 3q^2+2q+1
       593: q^2+2q+1
       594: 2q+1
       595: q^2+2q+1
       596: q^2+2q+1
       597: q^2+2q+1
       598: q^2+2q+1
       599: 3q^2+2q+1
       600: 3q^2+2q+1
       601: q^2+2q+1
       602: q^2+2q+1
       603: 3q^2+2q+1
       604: q^2+2q+1
       605: 2q^2+2q+1
       606: 2q^2+2q+1
       607: 2q^2+2q+1
       608: 2q+1
       609: 2q^2+2q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: 2q+1
       613: q^2+2q+1
       614: 2q+1
       615: q^2+2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q^2+2q+1
       622: q^2+2q+1
       623: 2q+1
       624: q^2+2q+1
       625: 2q+1
       626: 2q+1
       627: 2q+1
       628: q^2+2q+1
       629: q^2+2q+1
       630: q+1
       631: 2q+1
       632: q^2+2q+1
       633: 2q+1
       634: 2q+1
       635: 2q^2+2q+1
       636: 2q^2+2q+1
       637: q^2+2q+1
       638: 2q+1
       639: 2q^2+2q+1
       640: 2q+1
       641: q^2+2q+1
       642: q^2+2q+1
       643: q^2+2q+1
       644: 2q+1
       645: q^2+2q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: q^2+2q+1
       649: q+1
       650: q+1
       651: q^2+2q+1
       652: q+1
       653: q+1
       654: 1
       655: q+1
       656: q+1
       657: q^2+q+1
       658: q+1
       659: q^2+2q+1
       660: q^2+2q+1
       661: q+1
       662: q+1
       663: q^2+2q+1
       664: q+1
       665: q+1
       666: q^2+q+1
       667: 2q^2+2q+1
       668: q^2+2q+1
       669: q^2+2q+1
       670: q^2+2q+1
       671: q+1
       672: 2q^2+2q+1
       673: q^2+2q+1
       674: q+1
       675: q^2+q+1
       676: q+1
       677: q^2+2q+1
       678: 2q+1
       679: 2q+1
       680: 2q+1
       681: q+1
       682: q^2+2q+1
       683: 2q+1
       684: q+1
       685: q+1
       686: q^2+2q+1
       687: q^2+2q+1
       688: 2q+1
       689: q^2+2q+1
       690: 2q+1
       691: q^2+2q+1
       692: 2q+1
       693: q^2+2q+1
       694: q+1
       695: 2q+1
       696: 2q+1
       697: 2q^2+2q+1
       698: q^2+2q+1
       699: 2q+1
       700: q^2+2q+1
       701: 2q+1
       702: 2q+1
       703: q+1
       704: q+1
       705: 2q+1
       706: 2q+1
       707: q+1
       708: q+1
       709: 2q+1
       710: q+1
       711: q+1
       712: q+1
       713: 2q+1
       714: 2q+1
       715: 2q+1
       716: 2q+1
       717: q+1
       718: q^2+2q+1
       719: 2q+1
       720: 1
       721: q+1
       722: 2q+1
       723: 2q+1
       724: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       731: 2q+1
       732: 2q+1
       733: 2q+1
       734: q^2+2q+1
       735: 2q+1
       736: q^2+2q+1
       737: 2q+1
       738: 2q+1
       739: q+1
       740: 2q+1
       741: 2q+1
       742: q^2+2q+1
       743: q+1
       744: q+1
       745: q+1
       746: 2q+1
       747: 2q+1
       748: 2q+1
       749: q^2+2q+1
       750: q^2+2q+1
       751: q+1
       752: 2q+1
       753: q^2+2q+1
       754: 2q+1
       755: q^2+q+1
       756: q+1
       757: q^2+2q+1
       758: q^2+2q+1
       759: q+1
       760: q+1
       761: q^2+2q+1
       762: q+1
       763: q+1
       764: q^2+q+1
       765: 2q^2+2q+1
       766: q^2+2q+1
       767: q^2+2q+1
       768: q^2+2q+1
       769: q+1
       770: 2q^2+2q+1
       771: q^2+2q+1
       772: q+1
       773: q^2+q+1
       774: 2q^2+2q+1
       775: 2q^2+2q+1
       776: q^2+2q+1
       777: 2q^2+2q+1
       778: q^2+2q+1
       779: 2q^2+2q+1
       780: q^2+2q+1
       781: 2q^2+2q+1
       782: q^2+q+1
       783: q^2+2q+1
       784: q^2+2q+1
       785: 2q+1
       786: q^2+2q+1
       787: 2q+1
       788: q^2+2q+1
       789: 2q+1
       790: q^2+2q+1
       791: q+1
       792: q^2+2q+1
       793: q^2+2q+1
       794: 3q^2+2q+1
       795: q^2+2q+1
       796: 2q+1
       797: q^2+2q+1
       798: q^2+2q+1
       799: q^2+2q+1
       800: 2q+1
       801: 2q^2+2q+1
       802: 2q^2+2q+1
       803: q^2+2q+1
       804: 2q+1
       805: 2q^2+2q+1
       806: 2q+1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: 2q+1
       811: 2q+1
       812: q+1
       813: q^2+2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: 2q+1
       818: 2q+1
       819: 2q+1
       820: q^2+2q+1
       821: 2q+1
       822: q^2+2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: 2q+1
       827: 2q+1
       828: q^2+2q+1
       829: q+1
       830: q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       834: 2q+1
       835: 2q+1
       836: 2q^2+2q+1
       837: q^2+2q+1
       838: 2q+1
       839: q^2+2q+1
       840: 2q+1
       841: 2q+1
       842: 2q+1
       843: q^2+2q+1
       844: q^2+2q+1
       845: q+1
       846: 2q+1
       847: q^2+2q+1
       848: 2q+1
       849: q^2+2q+1
       850: q^2+2q+1
       851: q^2+2q+1
       852: 2q+1
       853: q^2+2q+1
       854: q+1
       855: q+1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: q+1
       861: q+1
       862: q+1
       863: q^2+2q+1
       864: q+1
       865: q+1
       866: 1
       867: q+1
       868: q+1
       869: q^2+q+1
       870: q+1
       871: q^2+2q+1
       872: q^2+2q+1
       873: q+1
       874: q+1
       875: q^2+2q+1
       876: q+1
       877: q+1
       878: q+1
       879: q+1
       880: 2q+1
       881: 2q+1
       882: q+1
       883: q+1
       884: 2q+1
       885: q+1
       886: q+1
       887: q+1
       888: q^2+2q+1
       889: 2q+1
       890: 2q+1
       891: 2q+1
       892: q+1
       893: q^2+2q+1
       894: 2q+1
       895: q+1
       896: q+1
       897: 2q+1
       898: 2q+1
       899: 2q+1
       900: q^2+2q+1
       901: 2q+1
       902: q^2+2q+1
       903: 2q+1
       904: 2q+1
       905: q+1
       906: q+1
       907: q+1
       908: 2q+1
       909: q+1
       910: q+1
       911: 1
       912: q+1
       913: q+1
       914: q+1
       915: 1
       916: 2q+1
       917: 2q+1
       918: q+1
       919: q+1
       920: 2q+1
       921: 1
       922: 1
       923: q+1
       924: 2q+1
       925: q+1
       926: q+1
       927: q+1
       929: q+1
       930: q+1
       931: 1
       932: q+1
       933: q+1
       934: 2q+1
       935: 2q+1
       936: 2q+1
       937: 2q+1
       938: q+1
       939: q^2+2q+1
       940: 2q+1
       941: 1
       942: q+1
       943: 2q+1
       944: 2q+1
       945: q+1
       946: q+1
       947: q+1
       948: q+1
       949: q+1
       950: 2q+1
       951: q+1
       952: 2q+1
       953: 2q+1
       954: q^2+2q+1
       955: q+1
       956: q+1
       957: q+1
       958: 2q+1
       959: 2q+1
       960: q+1
       961: q+1
       962: q^2+2q+1
       963: q+1
       964: q+1
       965: 1
       966: q+1
       967: q+1
       968: q^2+q+1
       969: q+1
       970: q^2+2q+1
       971: q^2+2q+1
       972: q+1
       973: q+1
       974: q^2+2q+1
       975: q+1
       976: q+1
       977: q^2+q+1
       978: 2q^2+2q+1
       979: q^2+2q+1
       980: q^2+2q+1
       981: q^2+2q+1
       982: q+1
       983: 2q^2+2q+1
       984: q^2+2q+1
       985: q+1
       986: q^2+q+1
       987: q+1
       988: q^2+2q+1
       989: 2q+1
       990: 2q+1
       991: 2q+1
       992: q+1
       993: q^2+2q+1
       994: 2q+1
       995: q+1
       996: q+1
       997: q^2+2q+1
       998: q^2+2q+1
       999: 2q+1
      1000: q^2+2q+1
      1001: 2q+1
      1002: q^2+2q+1
      1003: 2q+1
      1004: q^2+2q+1
      1005: q+1
      1006: 2q+1
      1007: 2q+1
      1008: 2q^2+2q+1
      1009: q^2+2q+1
      1010: 2q+1
      1011: q^2+2q+1
      1012: 2q+1
      1013: 2q+1
      1014: q+1
      1015: q+1
      1016: 2q+1
      1017: 2q+1
      1018: q+1
      1019: q+1
      1020: 2q+1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: 2q+1
      1025: 2q+1
      1026: 2q+1
      1027: 2q+1
      1028: q+1
      1029: q^2+2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: 2q+1
      1034: 2q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1042: 2q+1
      1043: 2q+1
      1044: 2q+1
      1045: q^2+2q+1
      1046: 2q+1
      1047: q^2+2q+1
      1048: 2q+1
      1049: 2q+1
      1050: q+1
      1051: 2q+1
      1052: 2q+1
      1053: q^2+2q+1
      1054: q+1
      1055: q+1
      1056: q+1
      1057: 2q+1
      1058: 2q+1
      1059: 2q+1
      1060: q^2+2q+1
      1061: q^2+2q+1
      1062: q+1
      1063: 2q+1
      1064: q^2+2q+1
      1065: 2q+1
      1066: q+1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: q+1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: q^2+2q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: q+1
      1085: q+1
      1086: q+1
      1087: q+1
      1088: 2q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: q+1
      1093: q+1
      1094: q+1
      1095: q+1
      1096: 2q+1
      1097: 2q+1
      1098: q+1
      1099: q+1
      1100: 2q+1
      1101: q+1
      1102: q+1
      1103: q+1
      1104: 2q+1
      1105: 2q+1
      1106: 2q+1
      1107: 2q+1
      1108: q+1
      1109: q^2+2q+1
      1110: 2q+1
      1111: 1
      1112: q+1
      1113: q+1
      1114: q+1
      1115: 1
      1116: q+1
      1117: 1
      1118: 1
      1119: q+1
      1120: 1
      1121: 1
      1122: 2q+1
      1123: q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1128: q+1
      1129: 1
      1130: q+1
      1131: q+1
      1134: q+1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: 2q+1
      1140: 2q+1
      1141: q+1
      1142: q+1
      1143: 2q+1
      1144: 1
      1145: 1
      1146: q+1
      1147: 2q+1
      1148: q+1
      1149: q+1
      1150: q+1
      1152: q+1
      1153: q+1
      1154: 1
      1155: q+1
      1156: 2q+1
      1157: 2q+1
      1158: q+1
      1159: q+1
      1160: q+1
      1161: q+1
      1162: q+1
      1163: 2q+1
      1164: q+1
      1165: q+1
      1166: q+1
      1167: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: q+1
      1172: q+1
      1173: q+1
      1174: q^2+2q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: q+1
      1179: q+1
      1180: q^2+q+1
      1181: q+1
      1182: q^2+2q+1
      1183: q^2+2q+1
      1184: q+1
      1185: q+1
      1186: q^2+2q+1
      1187: q+1
      1188: q+1
      1189: q+1
      1190: q+1
      1191: 2q+1
      1192: 2q+1
      1193: q+1
      1194: q+1
      1195: 2q+1
      1196: q+1
      1197: q+1
      1198: q+1
      1199: q^2+2q+1
      1200: 2q+1
      1201: 2q+1
      1202: 2q+1
      1203: q+1
      1204: q^2+2q+1
      1205: 2q+1
      1206: q+1
      1207: q+1
      1208: 2q+1
      1209: 2q+1
      1210: 2q+1
      1211: q^2+2q+1
      1212: 2q+1
      1213: q^2+2q+1
      1214: 2q+1
      1215: 2q+1
      1216: q+1
      1217: q+1
      1218: q+1
      1219: 2q+1
      1220: q+1
      1221: q+1
      1222: 1
      1223: q+1
      1224: q+1
      1225: q+1
      1226: 1
      1227: 2q+1
      1228: 2q+1
      1229: q+1
      1230: q+1
      1231: 2q+1
      1232: 1
      1233: 1
      1234: q+1
      1235: 2q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: q+1
      1244: q+1
      1245: 2q+1
      1246: 2q+1
      1247: 2q+1
      1248: 2q+1
      1249: q+1
      1250: q^2+2q+1
      1251: 2q+1
      1252: 1
      1253: q+1
      1254: 2q+1
      1255: 2q+1
      1256: q+1
      1257: q+1
      1258: q+1
      1259: q+1
      1260: q+1
      1261: 2q+1
      1262: q+1
      1263: 2q+1
      1264: 2q+1
      1265: q^2+2q+1
      1266: q+1
      1267: q+1
      1268: q+1
      1269: 2q+1
      1270: 2q+1
      1271: 1
      1272: 1
      1273: 1
      1274: q+1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: q+1
      1280: q+1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: q+1
      1286: q+1
      1287: q+1
      1288: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: q+1
      1293: q+1
      1294: q+1
      1295: 2q+1
      1296: q+1
      1297: q+1
      1298: 1
      1299: q+1
      1300: q+1
      1301: q+1
      1302: 1
      1303: 2q+1
      1304: 2q+1
      1305: q+1
      1306: q+1
      1307: 2q+1
      1308: 1
      1309: 1
      1310: q+1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: q+1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: 2q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1338: q+1
      1339: 1
      1340: q+1
      1341: q+1
      1344: q+1
      1345: 1
      1346: 1
      1347: q+1
      1348: 2q+1
      1349: q+1
      1350: q+1
      1351: q+1
      1353: q+1
      1354: q+1
      1355: 1
      1356: q+1
      1357: q+1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: q+1
      1363: q+1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: q+1
      1369: q+1
      1370: q+1
      1371: q^2+2q+1
      1372: q+1
      1373: q+1
      1374: 1
      1375: q+1
      1376: q+1
      1377: q+1
      1378: q+1
      1379: 2q+1
      1380: q+1
      1381: q+1
      1382: 1
      1383: q+1
      1384: q+1
      1385: q+1
      1386: q+1
      1387: 2q+1
      1388: 2q+1
      1389: q+1
      1390: q+1
      1391: 2q+1
      1392: q+1
      1393: q+1
      1394: q+1
      1395: 2q+1
      1396: 2q+1
      1397: 2q+1
      1398: 2q+1
      1399: q+1
      1400: q^2+2q+1
      1401: 2q+1
      1402: 1
      1403: q+1
      1404: q+1
      1405: q+1
      1406: 1
      1407: q+1
      1408: 1
      1409: 1
      1410: q+1
      1411: 1
      1412: 1
      1413: 2q+1
      1414: q+1
      1415: q+1
      1416: 1
      1417: 1
      1418: 1
      1419: q+1
      1420: 1
      1421: q+1
      1422: q+1
      1425: q+1
      1426: 1
      1427: 1
      1428: q+1
      1429: 1
      1430: 2q+1
      1431: 2q+1
      1432: q+1
      1433: q+1
      1434: 2q+1
      1435: 1
      1436: 1
      1437: q+1
      1438: 2q+1
      1439: q+1
      1440: q+1
      1441: q+1
      1443: q+1
      1444: q+1
      1445: 1
      1446: q+1
      1447: 2q+1
      1448: 2q+1
      1449: q+1
      1450: q+1
      1451: q+1
      1452: q+1
      1453: q+1
      1454: 2q+1
      1455: q+1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: q+1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: q+1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: q+1
      1472: q+1
      1473: 1
      1474: q+1
      1475: 1
      1476: 1
      1477: q+1
      1478: 1
      1479: 1
      1480: 2q+1
      1481: q+1
      1482: q+1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: q+1
      1514: 1
      1515: 1
      1516: q+1
      1517: 1
      1518: q+1
      1519: q+1
      1522: q+1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: q+1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: q+1
      1534: q+1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: q+1
      1540: q+1
      1541: q+1
      1542: 1
      1543: q+1
      1544: 1
      1545: 1
      1546: q+1
      1547: q+1
      1548: q+1
      1549: 2q+1
      1550: q+1
      1551: q+1
      1552: 1
      1553: q+1
      1554: q+1
      1555: q+1
      1556: 1
      1557: 2q+1
      1558: 2q+1
      1559: q+1
      1560: q+1
      1561: 2q+1
      1562: 1
      1563: 1
      1564: q+1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: q+1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: q+1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1586: 2q+1
      1587: q+1
      1588: q+1
      1589: 1
      1590: 1
      1591: 1
      1592: q+1
      1593: 1
      1594: q+1
      1595: q+1
      1598: q+1
      1599: 1
      1600: 1
      1601: q+1
      1602: 2q+1
      1603: q+1
      1604: q+1
      1605: q+1
      1607: q+1
      1608: q+1
      1609: 1
      1610: q+1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: q+1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: q+1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1655: 1
      1656: q+1
      1660: 1
      1661: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: q+1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1672: q+1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: q+1
      1678: q+1
      1679: 1
      1680: q+1
      1681: 1
      1682: 1
      1683: q+1
      1684: 1
      1685: 1
      1686: 2q+1
      1687: q+1
      1688: q+1
      1689: 1
      1690: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1706: 1
      1707: 1
      1708: 1
      1709: 1
      1710: q+1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1715: 1
      1716: q+1
      1720: 1
      1721: 1
      1722: q+1
      1723: 1
      1724: q+1
      1725: q+1
      1728: q+1
      1729: 1
      1730: 1
      1732: 1
      1734: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1742: 1
      1743: 1
      1745: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1758: 1
      1759: 1
      1764: 1
      1766: 1
      1768: 1
      1769: 1
      1770: 1
      1771: 1
      1772: 1
      1773: 1
      1774: q+1
      1775: 1
      1776: 1
      1777: 1
      1778: 1
      1779: 1
      1780: 1
      1781: 1
      1782: q+1
      1783: 1
      1784: 1
      1785: 1
      1786: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1796: 1
      1797: 1
      1798: 1
      1799: 1
      1800: 1
      1801: 1
      1802: 1
      1807: 1
      1808: 1
      1809: 1
      1810: q+1
      1814: 1
      1815: 1
      1818: 1
      1820: 1
      1821: 1
      1822: 1
      1826: 1
      1831: 1
      1837: 1
      1839: 1
      1841: 1
      1842: 1
      1843: 1
      1844: 1
      1845: 1
      1846: 1
      1847: 1
      1848: 1
      1850: 1
      1855: 1
      1856: 1
      1857: 1
      1858: 1
      1863: 1
      1864: 1
      1869: 1
      1871: 1
      1882: 1
      1884: 1
      1885: 1
      1886: 1
      1890: 1
      1895: 1
      1905: 1

1906:    0: q^3+2q^2+1
         1: 2q^2+1
         2: q^3+2q^2+1
         3: q^3+2q^2+1
         4: q^3+2q^2+1
         5: q^3+2q^2+1
         6: 2q^2+1
         7: 2q^2+1
         8: q^3+2q^2+1
         9: 2q^2+1
        10: q^3+2q^2+1
        11: q^3+2q^2+1
        12: q^3+2q^2+1
        13: 2q^2+1
        14: q^3+2q^2+1
        15: q^3+2q^2+1
        16: 2q^2+1
        17: q^3+2q^2+1
        18: q^3+2q^2+1
        19: q^3+2q^2+1
        20: 2q^2+1
        21: 2q^2+1
        22: 2q^2+1
        23: q^3+2q^2+1
        24: q^3+2q^2+1
        25: 2q^2+1
        26: 2q^2+1
        27: q^3+2q^2+1
        28: 2q^2+1
        29: q^3+2q^2+1
        30: 2q^2+1
        31: q^3+2q^2+1
        32: q^3+2q^2+1
        33: 2q^2+1
        34: 2q^2+1
        35: q^3+2q^2+1
        36: 2q^2+1
        37: q^3+2q^2+1
        38: q^2+1
        39: q^3+2q^2+1
        40: 2q^2+1
        41: 2q^2+1
        42: q^3+2q^2+1
        43: 2q^2+1
        44: q^3+2q^2+1
        45: q^3+2q^2+1
        46: q^3+2q^2+1
        47: 2q^2+1
        48: q^3+2q^2+1
        49: q^3+2q^2+1
        50: q^2+1
        51: 2q^2+1
        52: 2q^2+1
        53: 2q^2+1
        54: 2q^2+1
        55: 2q^2+1
        56: q^3+2q^2+1
        57: 2q^2+1
        58: 2q^2+1
        59: 2q^2+1
        60: q^3+2q^2+1
        61: q^3+2q^2+1
        62: 2q^2+1
        63: 2q^2+1
        64: q^3+2q^2+1
        65: 2q^2+1
        66: 2q^2+1
        67: q^3+2q^2+1
        68: 2q^2+1
        69: q^3+2q^2+1
        70: q^3+2q^2+1
        71: 2q^2+1
        72: 2q^2+1
        73: 2q^2+1
        74: q^2+1
        75: q^3+2q^2+1
        76: 2q^2+1
        77: q^2+1
        78: q^3+2q^2+1
        79: q^2+1
        80: q^2+1
        81: 2q^2+1
        82: q^3+2q^2+1
        83: q^2+1
        84: 2q^2+1
        85: 2q^2+1
        86: 2q^2+1
        87: q^3+2q^2+1
        88: q^3+2q^2+1
        89: 2q^2+1
        90: 2q^2+1
        91: q^3+2q^2+1
        92: 2q^2+1
        93: q^3+2q^2+1
        94: 2q^2+1
        95: q^3+2q^2+1
        96: q^3+2q^2+1
        97: 2q^2+1
        98: 2q^2+1
        99: q^3+2q^2+1
       100: 2q^2+1
       101: q^3+2q^2+1
       102: q^2+1
       103: q^3+2q^2+1
       104: q^2+1
       105: q^2+1
       106: 2q^2+1
       107: 2q^2+1
       108: 2q^2+1
       109: 2q^2+1
       110: 2q^2+1
       111: q^3+2q^2+1
       112: q^2+1
       113: 2q^2+1
       114: 2q^2+1
       115: 2q^2+1
       116: 2q^2+1
       117: 2q^2+1
       118: q^3+2q^2+1
       119: 2q^2+1
       120: 2q^2+1
       121: 2q^2+1
       122: q^3+2q^2+1
       123: q^3+2q^2+1
       124: 2q^2+1
       125: 2q^2+1
       126: 2q^2+1
       127: q^2+1
       128: q^3+2q^2+1
       129: 2q^2+1
       130: 2q^2+1
       131: q^3+2q^2+1
       132: 2q^2+1
       133: q^3+2q^2+1
       134: 1
       135: 2q^2+1
       136: 2q^2+1
       137: 2q^2+1
       138: q^2+1
       139: 2q^2+1
       140: q^2+1
       141: 2q^2+1
       142: q^2+1
       143: q^2+1
       144: q^2+1
       145: q^3+2q^2+1
       146: q^2+1
       147: 1
       148: q^2+1
       149: 2q^2+1
       150: q^2+1
       151: q^3+2q^2+1
       152: q^2+1
       153: q^2+1
       154: q^2+1
       155: q^2+1
       156: 2q^2+1
       157: 2q^2+1
       158: 2q^2+1
       159: 2q^2+1
       160: 2q^2+1
       161: q^3+2q^2+1
       162: 2q^2+1
       163: 2q^2+1
       164: 2q^2+1
       165: q^3+2q^2+1
       166: q^3+2q^2+1
       167: 2q^2+1
       168: 2q^2+1
       169: q^3+2q^2+1
       170: 2q^2+1
       171: 2q^2+1
       172: q^3+2q^2+1
       173: 2q^2+1
       174: q^3+2q^2+1
       175: q^3+2q^2+1
       176: 2q^2+1
       177: 2q^2+1
       178: 2q^2+1
       179: q^2+1
       180: q^3+2q^2+1
       181: 2q^2+1
       182: q^2+1
       183: q^3+2q^2+1
       184: q^2+1
       185: q^2+1
       186: 2q^2+1
       187: q^3+2q^2+1
       188: q^2+1
       189: q^2+1
       190: q^2+1
       191: q^2+1
       192: 2q^2+1
       193: 2q^2+1
       194: 2q^2+1
       195: 2q^2+1
       196: 2q^2+1
       197: q^3+2q^2+1
       198: q^2+1
       199: q^2+1
       200: 2q^2+1
       201: 2q^2+1
       202: 2q^2+1
       203: 2q^2+1
       204: 2q^2+1
       205: q^3+2q^2+1
       206: q^2+1
       207: 2q^2+1
       208: 2q^2+1
       209: 2q^2+1
       210: 2q^2+1
       211: 2q^2+1
       212: q^3+2q^2+1
       213: 1
       214: 2q^2+1
       215: 2q^2+1
       216: 2q^2+1
       217: q^2+1
       218: 2q^2+1
       219: q^2+1
       220: 2q^2+1
       221: 2q^2+1
       222: 2q^2+1
       223: q^2+1
       224: q^3+2q^2+1
       225: 2q^2+1
       226: q^2+1
       227: q^3+2q^2+1
       228: 1
       229: 1
       230: 2q^2+1
       231: 2q^2+1
       232: q^2+1
       233: 2q^2+1
       234: q^2+1
       235: q^2+1
       236: 1
       237: 2q^2+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: q^2+1
       243: q^2+1
       244: 1
       245: 1
       246: q^2+1
       247: q^2+1
       248: 2q^2+1
       249: q^2+1
       250: q^2+1
       251: q^2+1
       252: q^3+2q^2+1
       253: q^2+1
       254: 1
       255: q^2+1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       259: q^2+1
       260: 2q^2+1
       261: 2q^2+1
       262: 2q^2+1
       263: 2q^2+1
       264: 2q^2+1
       265: q^3+2q^2+1
       266: q^2+1
       267: 2q^2+1
       268: 2q^2+1
       269: 2q^2+1
       270: 2q^2+1
       271: 2q^2+1
       272: q^3+2q^2+1
       273: 2q^2+1
       274: 2q^2+1
       275: 2q^2+1
       276: q^3+2q^2+1
       277: q^3+2q^2+1
       278: 2q^2+1
       279: 2q^2+1
       280: 2q^2+1
       281: q^2+1
       282: q^3+2q^2+1
       283: 2q^2+1
       284: 2q^2+1
       285: q^3+2q^2+1
       286: 2q^2+1
       287: q^3+2q^2+1
       288: 1
       289: 2q^2+1
       290: 2q^2+1
       291: 2q^2+1
       292: q^2+1
       293: 2q^2+1
       294: q^2+1
       295: 2q^2+1
       296: q^2+1
       297: q^2+1
       298: q^2+1
       299: q^3+2q^2+1
       300: q^2+1
       301: 1
       302: q^2+1
       303: 2q^2+1
       304: q^2+1
       305: q^3+2q^2+1
       306: q^2+1
       307: q^2+1
       308: q^2+1
       309: q^2+1
       310: q^2+1
       311: q^2+1
       312: q^2+1
       313: 2q^2+1
       314: 1
       315: 2q^2+1
       316: 2q^2+1
       317: 2q^2+1
       318: q^2+1
       319: q^2+1
       320: q^2+1
       321: q^2+1
       322: 2q^2+1
       323: 2q^2+1
       324: 2q^2+1
       325: 2q^2+1
       326: 2q^2+1
       327: q^3+2q^2+1
       328: q^2+1
       329: q^2+1
       330: 2q^2+1
       331: 2q^2+1
       332: 2q^2+1
       333: 2q^2+1
       334: 2q^2+1
       335: q^3+2q^2+1
       336: 1
       337: 1
       338: 2q^2+1
       339: 2q^2+1
       340: q^2+1
       341: 2q^2+1
       342: q^2+1
       343: q^2+1
       344: 1
       345: 2q^2+1
       346: 2q^2+1
       347: 2q^2+1
       348: q^2+1
       349: 2q^2+1
       350: q^2+1
       351: 2q^2+1
       352: q^2+1
       353: q^2+1
       354: q^2+1
       355: q^3+2q^2+1
       356: 1
       357: 1
       358: 1
       359: 2q^2+1
       360: q^2+1
       361: 2q^2+1
       362: q^2+1
       363: q^2+1
       364: q^2+1
       365: 1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: q^2+1
       373: 1
       374: q^2+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q^2+1
       380: 1
       381: 2q^2+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: q^2+1
       387: q^2+1
       388: 1
       389: 1
       390: q^2+1
       391: q^2+1
       392: q^2+1
       393: 1
       394: q^2+1
       395: q^2+1
       396: q^2+1
       397: q^2+1
       398: 2q^2+1
       399: 2q^2+1
       400: 2q^2+1
       401: 2q^2+1
       402: 2q^2+1
       403: q^3+2q^2+1
       404: q^2+1
       405: q^2+1
       406: 2q^2+1
       407: 2q^2+1
       408: 2q^2+1
       409: 2q^2+1
       410: 2q^2+1
       411: q^3+2q^2+1
       412: q^2+1
       413: 2q^2+1
       414: 2q^2+1
       415: 2q^2+1
       416: 2q^2+1
       417: 2q^2+1
       418: q^3+2q^2+1
       419: 1
       420: 2q^2+1
       421: 2q^2+1
       422: 2q^2+1
       423: q^2+1
       424: 2q^2+1
       425: q^2+1
       426: 2q^2+1
       427: 2q^2+1
       428: 2q^2+1
       429: q^2+1
       430: q^3+2q^2+1
       431: 2q^2+1
       432: q^2+1
       433: q^3+2q^2+1
       434: 1
       435: 1
       436: 2q^2+1
       437: 2q^2+1
       438: q^2+1
       439: 2q^2+1
       440: q^2+1
       441: q^2+1
       442: 1
       443: 2q^2+1
       444: q^2+1
       445: q^2+1
       446: 1
       447: q^2+1
       448: q^2+1
       449: q^2+1
       450: 1
       451: 1
       452: q^2+1
       453: q^2+1
       454: 2q^2+1
       455: q^2+1
       456: q^2+1
       457: q^2+1
       458: q^3+2q^2+1
       459: q^2+1
       460: 1
       461: q^2+1
       462: q^2+1
       463: q^2+1
       465: q^2+1
       466: q^2+1
       467: q^2+1
       468: 1
       469: 1
       470: 2q^2+1
       471: 2q^2+1
       472: q^2+1
       473: q^2+1
       474: q^2+1
       475: q^2+1
       476: q^2+1
       477: 2q^2+1
       478: 1
       479: 2q^2+1
       480: 2q^2+1
       481: 2q^2+1
       482: q^2+1
       483: q^2+1
       484: q^2+1
       485: q^2+1
       486: 2q^2+1
       487: 2q^2+1
       488: 2q^2+1
       489: 2q^2+1
       490: 2q^2+1
       491: q^3+2q^2+1
       492: 1
       493: 1
       494: 1
       495: 2q^2+1
       496: q^2+1
       497: 2q^2+1
       498: q^2+1
       499: q^2+1
       500: q^2+1
       501: 1
       502: 1
       503: 2q^2+1
       504: 2q^2+1
       505: q^2+1
       506: 2q^2+1
       507: q^2+1
       508: q^2+1
       509: 1
       510: 2q^2+1
       511: q^2+1
       512: q^2+1
       513: 1
       514: q^2+1
       515: q^2+1
       516: 1
       517: 1
       518: 1
       519: 1
       520: q^2+1
       521: 1
       522: 2q^2+1
       523: q^2+1
       524: q^2+1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: q^2+1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q^2+1
       543: 1
       544: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: q^2+1
       551: 1
       552: q^2+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q^2+1
       558: q^2+1
       559: 1
       560: 1
       561: q^2+1
       562: q^2+1
       563: q^2+1
       564: q^2+1
       565: q^2+1
       566: q^2+1
       567: 2q^2+1
       568: 1
       569: 2q^2+1
       570: 2q^2+1
       571: 2q^2+1
       572: q^2+1
       573: q^2+1
       574: q^2+1
       575: q^2+1
       576: 2q^2+1
       577: 2q^2+1
       578: 2q^2+1
       579: 2q^2+1
       580: 2q^2+1
       581: q^3+2q^2+1
       582: q^2+1
       583: q^2+1
       584: 2q^2+1
       585: 2q^2+1
       586: 2q^2+1
       587: 2q^2+1
       588: 2q^2+1
       589: q^3+2q^2+1
       590: 1
       591: 1
       592: 2q^2+1
       593: 2q^2+1
       594: q^2+1
       595: 2q^2+1
       596: q^2+1
       597: q^2+1
       598: 1
       599: 2q^2+1
       600: 2q^2+1
       601: 2q^2+1
       602: q^2+1
       603: 2q^2+1
       604: q^2+1
       605: 2q^2+1
       606: q^2+1
       607: q^2+1
       608: q^2+1
       609: q^3+2q^2+1
       610: 1
       611: 1
       612: 1
       613: 2q^2+1
       614: q^2+1
       615: 2q^2+1
       616: q^2+1
       617: q^2+1
       618: q^2+1
       619: 1
       620: 1
       621: q^2+1
       622: q^2+1
       623: 1
       624: q^2+1
       625: 1
       626: q^2+1
       627: 1
       628: q^2+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q^2+1
       634: 1
       635: 2q^2+1
       636: q^2+1
       637: q^2+1
       638: 1
       639: q^2+1
       640: q^2+1
       641: q^2+1
       642: 1
       643: 1
       644: q^2+1
       645: q^2+1
       646: q^2+1
       647: 1
       648: q^2+1
       650: q^2+1
       651: q^2+1
       652: 1
       653: 1
       654: 1
       655: 2q^2+1
       656: q^2+1
       658: q^2+1
       659: q^2+1
       660: q^2+1
       661: 1
       662: 1
       663: 2q^2+1
       664: 2q^2+1
       665: q^2+1
       666: q^2+1
       667: q^2+1
       668: q^2+1
       669: q^2+1
       670: 2q^2+1
       671: 1
       672: 2q^2+1
       673: 2q^2+1
       674: 2q^2+1
       675: q^2+1
       676: 1
       677: 1
       678: 1
       679: 1
       680: q^2+1
       681: 1
       682: 2q^2+1
       683: q^2+1
       684: q^2+1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 2q^2+1
       690: q^2+1
       691: 2q^2+1
       692: q^2+1
       693: q^2+1
       694: q^2+1
       695: 1
       696: 1
       697: q^2+1
       698: q^2+1
       699: 1
       700: q^2+1
       701: 1
       702: q^2+1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: q^2+1
       710: q^2+1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: q^2+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: q^2+1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: q^2+1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: q^2+1
       748: 1
       749: q^2+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q^2+1
       756: q^2+1
       757: q^2+1
       758: q^2+1
       759: 1
       760: 1
       761: 2q^2+1
       762: 2q^2+1
       763: q^2+1
       764: q^2+1
       765: q^2+1
       766: q^2+1
       767: q^2+1
       768: 2q^2+1
       769: 1
       770: 2q^2+1
       771: 2q^2+1
       772: 2q^2+1
       773: q^2+1
       774: q^2+1
       775: q^2+1
       776: q^2+1
       777: 2q^2+1
       778: 2q^2+1
       779: 2q^2+1
       780: 2q^2+1
       781: 2q^2+1
       782: q^3+2q^2+1
       783: 1
       784: 1
       785: 1
       786: 2q^2+1
       787: q^2+1
       788: 2q^2+1
       789: q^2+1
       790: q^2+1
       791: q^2+1
       792: 1
       793: 1
       794: 2q^2+1
       795: 2q^2+1
       796: q^2+1
       797: 2q^2+1
       798: q^2+1
       799: q^2+1
       800: 1
       801: 2q^2+1
       802: q^2+1
       803: q^2+1
       804: 1
       805: q^2+1
       806: q^2+1
       807: 1
       808: 1
       809: 1
       810: 1
       811: q^2+1
       812: 1
       813: 2q^2+1
       814: q^2+1
       815: q^2+1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q^2+1
       821: 1
       822: q^2+1
       823: 1
       824: 1
       825: q^2+1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q^2+1
       834: 1
       835: 1
       836: q^2+1
       837: q^2+1
       838: 1
       839: q^2+1
       840: 1
       841: q^2+1
       842: 1
       843: q^2+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q^2+1
       849: q^2+1
       850: 1
       851: 1
       852: q^2+1
       853: q^2+1
       855: q^2+1
       856: 1
       857: 1
       858: 1
       859: 1
       860: q^2+1
       862: q^2+1
       863: q^2+1
       864: 1
       865: 1
       866: 1
       867: 2q^2+1
       868: q^2+1
       870: q^2+1
       871: q^2+1
       872: q^2+1
       873: 1
       874: 1
       875: 2q^2+1
       876: 2q^2+1
       877: q^2+1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: q^2+1
       885: q^2+1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: q^2+1
       892: 1
       893: 2q^2+1
       894: q^2+1
       895: q^2+1
       896: 1
       897: 1
       898: 1
       899: 1
       900: q^2+1
       901: 1
       902: q^2+1
       903: 1
       904: 1
       905: q^2+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: q^2+1
       913: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: q^2+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: q^2+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q^2+1
       961: q^2+1
       962: q^2+1
       963: 1
       964: 1
       965: 1
       966: 2q^2+1
       967: q^2+1
       969: q^2+1
       970: q^2+1
       971: q^2+1
       972: 1
       973: 1
       974: 2q^2+1
       975: 2q^2+1
       976: q^2+1
       977: q^2+1
       978: q^2+1
       979: q^2+1
       980: q^2+1
       981: 2q^2+1
       982: 1
       983: 2q^2+1
       984: 2q^2+1
       985: 2q^2+1
       986: q^2+1
       987: 1
       988: 1
       989: 1
       990: 1
       991: q^2+1
       992: 1
       993: 2q^2+1
       994: q^2+1
       995: q^2+1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 2q^2+1
      1001: q^2+1
      1002: 2q^2+1
      1003: q^2+1
      1004: q^2+1
      1005: q^2+1
      1006: 1
      1007: 1
      1008: q^2+1
      1009: q^2+1
      1010: 1
      1011: q^2+1
      1012: 1
      1013: q^2+1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: q^2+1
      1021: q^2+1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: q^2+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q^2+1
      1042: 1
      1043: 1
      1044: 1
      1045: q^2+1
      1046: 1
      1047: q^2+1
      1048: 1
      1049: 1
      1050: q^2+1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q^2+1
      1059: 1
      1060: q^2+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q^2+1
      1068: 1
      1069: 1
      1070: 1
      1072: q^2+1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: q^2+1
      1079: q^2+1
      1080: q^2+1
      1081: 1
      1082: 1
      1083: 1
      1084: 2q^2+1
      1085: q^2+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: q^2+1
      1093: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: q^2+1
      1101: q^2+1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: q^2+1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: q^2+1
      1166: q^2+1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: q^2+1
      1173: q^2+1
      1174: q^2+1
      1175: 1
      1176: 1
      1177: 1
      1178: 2q^2+1
      1179: q^2+1
      1181: q^2+1
      1182: q^2+1
      1183: q^2+1
      1184: 1
      1185: 1
      1186: 2q^2+1
      1187: 2q^2+1
      1188: q^2+1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: q^2+1
      1196: q^2+1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: q^2+1
      1203: 1
      1204: 2q^2+1
      1205: q^2+1
      1206: q^2+1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q^2+1
      1212: 1
      1213: q^2+1
      1214: 1
      1215: 1
      1216: q^2+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: q^2+1
      1224: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: q^2+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q^2+1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q^2+1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: q^2+1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: q^2+1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: q^2+1
      1300: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: q^2+1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: q^2+1
      1370: q^2+1
      1371: q^2+1
      1372: 1
      1373: 1
      1374: 1
      1375: 2q^2+1
      1376: q^2+1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: q^2+1
      1384: 1
      1386: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: q^2+1
      1392: q^2+1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: q^2+1
      1401: 1
      1402: 1
      1403: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1429: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q^2+1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1492: 1
      1493: 1
      1495: 1
      1500: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1531: 1
      1532: 1
      1534: q^2+1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: q^2+1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: q^2+1
      1554: 1
      1556: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1613: 1
      1615: 1
      1616: 1
      1618: 1
      1619: 1
      1622: 1
      1623: 1
      1624: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1633: 1
      1635: 1
      1636: 1
      1644: 1
      1645: 1
      1646: 1
      1648: 1
      1653: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1663: 1
      1665: 1
      1666: 1
      1669: 1
      1670: 1
      1671: 1
      1674: 1
      1675: 1
      1676: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1693: 1
      1694: 1
      1697: 1
      1698: 1
      1699: 1
      1701: 1
      1706: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1715: 1
      1716: 1
      1720: 1
      1721: 1
      1723: 1
      1724: 1
      1725: 1
      1728: 1
      1729: 1
      1730: 1
      1733: 1
      1735: 1
      1737: 1
      1738: 1
      1741: 1
      1742: 1
      1743: 1
      1746: 1
      1751: 1
      1752: 1
      1759: 1
      1764: 1
      1767: 1
      1769: 1
      1770: 1
      1772: 1
      1773: 1
      1776: 1
      1777: 1
      1778: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1787: 1
      1789: 1
      1790: 1
      1798: 1
      1799: 1
      1800: 1
      1802: 1
      1807: 1
      1809: 1
      1810: 1
      1814: 1
      1815: 1
      1819: 1
      1821: 1
      1822: 1
      1827: 1
      1838: 1
      1840: 1
      1842: 1
      1843: 1
      1846: 1
      1847: 1
      1848: 1
      1851: 1
      1856: 1
      1857: 1
      1864: 1
      1869: 1
      1872: 1
      1883: 1
      1885: 1
      1886: 1
      1891: 1
      1906: 1

1907:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q^2+q+1
        12: q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^2+q+1
        29: q^2+q+1
        30: q+1
        31: q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q^2+q+1
        39: q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q^2+q+1
        46: q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q^2+q+1
        51: q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q^2+q+1
        55: q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q+1
        66: q+1
        67: q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q^2+q+1
        80: q^2+q+1
        81: q+1
        82: q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^2+q+1
        93: q^2+q+1
        94: q+1
        95: q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q^2+q+1
       103: q+1
       104: q+1
       105: q^2+q+1
       106: q+1
       107: q^2+q+1
       108: q^2+q+1
       109: q+1
       110: q+1
       111: q+1
       112: q^2+q+1
       113: q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q^2+q+1
       117: q+1
       118: q+1
       119: q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: 1
       124: q+1
       125: q+1
       126: q+1
       127: q+1
       128: q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q^2+q+1
       135: q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q^2+q+1
       139: q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q+1
       146: q^2+q+1
       147: q^2+q+1
       148: q^2+q+1
       149: q+1
       150: q+1
       151: q+1
       152: q+1
       153: q+1
       154: q+1
       155: q^2+q+1
       156: q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q^2+q+1
       160: q+1
       161: q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q+1
       171: q+1
       172: q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q^2+q+1
       180: q+1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q^2+q+1
       185: q^2+q+1
       186: q+1
       187: q+1
       188: q+1
       189: q+1
       190: q+1
       191: q^2+q+1
       192: q+1
       193: q^2+q+1
       194: q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q^2+q+1
       200: q+1
       201: q^2+q+1
       202: q^2+q+1
       203: q+1
       204: q+1
       205: q+1
       206: q^2+q+1
       207: 1
       208: q^2+q+1
       209: q^2+q+1
       210: q^2+q+1
       211: 1
       212: 1
       213: q+1
       214: q+1
       215: q+1
       216: q+1
       217: q+1
       218: q+1
       219: q+1
       220: q+1
       221: q+1
       222: q+1
       223: q+1
       224: 1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q^2+q+1
       230: q+1
       231: q^2+q+1
       232: q^2+q+1
       233: q+1
       234: q+1
       235: q+1
       236: q^2+q+1
       237: q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q^2+q+1
       241: q+1
       242: q+1
       243: q^2+q+1
       244: q^2+q+1
       245: q^2+q+1
       246: q^2+q+1
       247: 1
       248: q+1
       249: q+1
       250: q+1
       251: q+1
       252: q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q^2+q+1
       260: q+1
       261: q^2+q+1
       262: q^2+q+1
       263: q+1
       264: q+1
       265: q+1
       266: q^2+q+1
       267: q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q^2+q+1
       271: q+1
       272: q+1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: 1
       278: q+1
       279: q+1
       280: q+1
       281: q+1
       282: q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q^2+q+1
       289: q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q^2+q+1
       293: q+1
       294: q+1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q^2+q+1
       299: q+1
       300: q^2+q+1
       301: q^2+q+1
       302: q^2+q+1
       303: q+1
       304: q+1
       305: q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q^2+q+1
       313: 1
       314: q+1
       315: q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q^2+q+1
       322: q+1
       323: q^2+q+1
       324: q+1
       325: q+1
       326: q+1
       327: q+1
       328: 1
       329: q^2+q+1
       330: 1
       331: q^2+q+1
       332: q^2+q+1
       333: 1
       334: 1
       335: 1
       336: q+1
       337: q+1
       338: q+1
       339: q+1
       340: q+1
       341: q+1
       342: q+1
       343: q+1
       344: q+1
       345: 1
       346: q+1
       347: q+1
       348: q+1
       349: 1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: 1
       356: q+1
       357: q+1
       358: q^2+q+1
       359: q+1
       360: q^2+q+1
       361: q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q^2+q+1
       367: q+1
       368: q^2+q+1
       369: q^2+q+1
       370: q+1
       371: q+1
       372: q+1
       373: q^2+q+1
       374: 1
       375: q^2+q+1
       376: q^2+q+1
       377: q^2+q+1
       378: 1
       379: 1
       380: q+1
       381: q+1
       382: q+1
       383: q+1
       384: q+1
       385: q+1
       386: q+1
       387: q+1
       388: q+1
       389: q+1
       390: q+1
       391: 1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q^2+q+1
       398: q+1
       399: q^2+q+1
       400: q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q^2+q+1
       406: q+1
       407: q^2+q+1
       408: q^2+q+1
       409: q+1
       410: q+1
       411: q+1
       412: q^2+q+1
       413: 1
       414: q^2+q+1
       415: q^2+q+1
       416: q^2+q+1
       417: 1
       418: 1
       419: q+1
       420: q+1
       421: q+1
       422: q+1
       423: q+1
       424: q+1
       425: q+1
       426: q+1
       427: q+1
       428: q+1
       429: q+1
       430: 1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q^2+q+1
       436: q+1
       437: q^2+q+1
       438: q^2+q+1
       439: q+1
       440: q+1
       441: q+1
       442: q^2+q+1
       443: q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q^2+q+1
       447: q+1
       448: q+1
       449: q^2+q+1
       450: q^2+q+1
       451: q^2+q+1
       452: q^2+q+1
       453: 1
       454: q+1
       455: q+1
       456: q+1
       457: q+1
       458: q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: 1
       468: q+1
       469: q+1
       470: 1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q^2+q+1
       477: 1
       478: q+1
       479: q+1
       480: q+1
       481: q+1
       482: q+1
       483: 1
       484: 1
       485: q^2+q+1
       486: 1
       487: q^2+q+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: q+1
       493: q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q+1
       500: q+1
       501: 1
       502: q+1
       503: 1
       504: q+1
       505: q+1
       506: 1
       507: 1
       508: 1
       509: q+1
       510: 1
       511: q+1
       512: q+1
       513: q+1
       514: 1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q^2+q+1
       520: 1
       521: q+1
       522: q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q^2+q+1
       529: q+1
       530: q^2+q+1
       531: q+1
       532: q+1
       533: q+1
       534: q+1
       535: 1
       536: q^2+q+1
       537: 1
       538: q^2+q+1
       539: q^2+q+1
       540: 1
       541: 1
       542: 1
       543: q+1
       544: q+1
       545: q+1
       546: q+1
       547: q+1
       548: q+1
       549: q+1
       550: q+1
       551: q+1
       552: 1
       553: q+1
       554: q+1
       555: q+1
       556: 1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: 1
       563: q+1
       564: q+1
       565: q+1
       566: q^2+q+1
       567: 1
       568: q+1
       569: q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: q^2+q+1
       576: q+1
       577: q^2+q+1
       578: q+1
       579: q+1
       580: q+1
       581: q+1
       582: 1
       583: q^2+q+1
       584: 1
       585: q^2+q+1
       586: q^2+q+1
       587: 1
       588: 1
       589: 1
       590: q+1
       591: q+1
       592: q+1
       593: q+1
       594: q+1
       595: q+1
       596: q+1
       597: q+1
       598: q+1
       599: 1
       600: q+1
       601: q+1
       602: q+1
       603: 1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: 1
       610: q+1
       611: q+1
       612: q^2+q+1
       613: q+1
       614: q^2+q+1
       615: q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q^2+q+1
       621: q+1
       622: q^2+q+1
       623: q^2+q+1
       624: q+1
       625: q+1
       626: q+1
       627: q^2+q+1
       628: 1
       629: q^2+q+1
       630: q^2+q+1
       631: q^2+q+1
       632: 1
       633: 1
       634: q+1
       635: q+1
       636: q+1
       637: q+1
       638: q+1
       639: q+1
       640: q+1
       641: q+1
       642: q+1
       643: q+1
       644: q+1
       645: 1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: 1
       652: q+1
       653: 1
       654: q+1
       655: 1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: 1
       661: q+1
       662: q+1
       663: 1
       664: q+1
       665: q+1
       666: 1
       667: 1
       668: 1
       669: q^2+q+1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q+1
       677: q+1
       678: q+1
       679: q+1
       681: q+1
       682: q+1
       683: q+1
       684: q+1
       685: q+1
       686: 1
       687: 1
       688: q+1
       689: 1
       690: q+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: q+1
       697: 1
       698: q+1
       699: q+1
       700: 1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: q+1
       706: 1
       707: q+1
       708: q+1
       709: 1
       710: q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q^2+q+1
       716: 1
       717: q+1
       718: q+1
       719: q+1
       720: q+1
       721: q+1
       722: 1
       723: 1
       724: q^2+q+1
       725: 1
       726: q^2+q+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: q+1
       732: q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q+1
       739: q+1
       740: 1
       741: q+1
       742: 1
       743: q+1
       744: q+1
       745: 1
       746: 1
       747: 1
       748: q+1
       749: 1
       750: q+1
       751: q+1
       752: q+1
       753: 1
       754: 1
       755: q+1
       756: q+1
       757: q+1
       758: 1
       759: q+1
       760: q+1
       761: 1
       762: q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q^2+q+1
       768: 1
       769: q+1
       770: q+1
       771: q+1
       772: q+1
       773: q+1
       774: 1
       775: 1
       776: q^2+q+1
       777: 1
       778: q^2+q+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: q+1
       784: q+1
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: q+1
       791: q+1
       792: 1
       793: q+1
       794: 1
       795: q+1
       796: q+1
       797: 1
       798: 1
       799: 1
       800: q+1
       801: 1
       802: q+1
       803: q+1
       804: q+1
       805: 1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q^2+q+1
       811: 1
       812: q+1
       813: q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q^2+q+1
       820: q+1
       821: q^2+q+1
       822: q+1
       823: q+1
       824: q+1
       825: q+1
       826: 1
       827: q^2+q+1
       828: 1
       829: q^2+q+1
       830: q^2+q+1
       831: 1
       832: 1
       833: 1
       834: q+1
       835: q+1
       836: q+1
       837: q+1
       838: q+1
       839: q+1
       840: q+1
       841: q+1
       842: q+1
       843: 1
       844: q+1
       845: q+1
       846: q+1
       847: 1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: 1
       854: q+1
       855: 1
       856: q+1
       857: 1
       858: 1
       859: q+1
       860: 1
       861: q+1
       862: q+1
       863: 1
       864: q+1
       865: 1
       866: q+1
       867: 1
       868: q+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: q+1
       879: q+1
       880: q+1
       882: q+1
       883: q+1
       885: q+1
       886: q+1
       887: 1
       888: 1
       889: 1
       890: q+1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: q+1
       900: 1
       901: q+1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: 1
       909: q+1
       910: 1
       911: q+1
       912: 1
       913: q+1
       914: q+1
       915: q+1
       916: q+1
       917: 1
       918: q+1
       919: q+1
       920: 1
       921: q+1
       922: q+1
       923: 1
       924: 1
       925: 1
       926: q^2+q+1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: q+1
       934: q+1
       935: q+1
       936: q+1
       938: q+1
       939: q+1
       940: q+1
       941: q+1
       942: q+1
       943: 1
       944: 1
       945: q+1
       946: 1
       947: q+1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: q+1
       954: 1
       955: q+1
       956: q+1
       957: 1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: 1
       963: q+1
       964: 1
       965: q+1
       966: 1
       967: q+1
       968: q+1
       969: q+1
       970: q+1
       971: 1
       972: q+1
       973: q+1
       974: 1
       975: q+1
       976: q+1
       977: 1
       978: 1
       979: 1
       980: q^2+q+1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: q+1
       988: q+1
       989: q+1
       990: q+1
       992: q+1
       993: q+1
       994: q+1
       995: q+1
       996: q+1
       997: 1
       998: 1
       999: q+1
      1000: 1
      1001: q+1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: q+1
      1008: 1
      1009: q+1
      1010: q+1
      1011: 1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1017: 1
      1018: q+1
      1019: q+1
      1020: 1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q^2+q+1
      1027: 1
      1028: q+1
      1029: q+1
      1030: q+1
      1031: q+1
      1032: q+1
      1033: 1
      1034: 1
      1035: q^2+q+1
      1036: 1
      1037: q^2+q+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: q+1
      1043: q+1
      1044: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: q+1
      1050: q+1
      1051: 1
      1052: q+1
      1053: 1
      1054: q+1
      1055: q+1
      1056: 1
      1057: 1
      1058: 1
      1059: q+1
      1060: 1
      1061: q+1
      1062: q+1
      1063: q+1
      1064: 1
      1065: 1
      1066: 1
      1067: q+1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: 1
      1073: q+1
      1074: 1
      1075: 1
      1076: q+1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: q+1
      1089: q+1
      1091: q+1
      1093: q+1
      1094: 1
      1095: 1
      1096: 1
      1098: 1
      1099: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q+1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: q+1
      1114: 1
      1115: q+1
      1116: 1
      1117: 1
      1118: q+1
      1119: 1
      1120: q+1
      1121: q+1
      1122: 1
      1123: q+1
      1124: 1
      1125: q+1
      1126: 1
      1127: q+1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1137: q+1
      1138: q+1
      1139: q+1
      1141: q+1
      1142: q+1
      1144: q+1
      1145: q+1
      1146: 1
      1147: 1
      1148: 1
      1149: q+1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: q+1
      1159: 1
      1160: q+1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: 1
      1167: q+1
      1168: 1
      1169: 1
      1170: q+1
      1171: 1
      1172: q+1
      1173: q+1
      1174: 1
      1175: q+1
      1176: 1
      1177: q+1
      1178: 1
      1179: q+1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: q+1
      1190: q+1
      1191: q+1
      1193: q+1
      1194: q+1
      1196: q+1
      1197: q+1
      1198: 1
      1199: 1
      1200: 1
      1201: q+1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: q+1
      1211: 1
      1212: q+1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1219: 1
      1220: q+1
      1221: 1
      1222: q+1
      1223: 1
      1224: q+1
      1225: q+1
      1226: q+1
      1227: q+1
      1228: 1
      1229: q+1
      1230: q+1
      1231: 1
      1232: q+1
      1233: q+1
      1234: 1
      1235: 1
      1236: 1
      1237: q^2+q+1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: q+1
      1245: q+1
      1246: q+1
      1247: q+1
      1249: q+1
      1250: q+1
      1251: q+1
      1252: q+1
      1253: q+1
      1254: 1
      1255: 1
      1256: q+1
      1257: 1
      1258: q+1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: q+1
      1265: 1
      1266: q+1
      1267: q+1
      1268: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: q+1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: q+1
      1288: q+1
      1291: q+1
      1293: 1
      1294: 1
      1296: 1
      1298: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1305: 1
      1306: 1
      1308: 1
      1309: 1
      1310: 1
      1311: q+1
      1312: 1
      1313: 1
      1314: 1
      1315: q+1
      1316: 1
      1317: q+1
      1318: 1
      1319: 1
      1320: q+1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: q+1
      1331: q+1
      1333: q+1
      1335: q+1
      1337: q+1
      1338: 1
      1339: 1
      1340: 1
      1342: 1
      1343: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q+1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1358: q+1
      1359: 1
      1360: 1
      1361: 1
      1362: q+1
      1363: 1
      1364: q+1
      1365: 1
      1366: 1
      1367: q+1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: q+1
      1378: q+1
      1380: q+1
      1382: q+1
      1384: q+1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: q+1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1404: q+1
      1405: 1
      1406: q+1
      1407: 1
      1408: 1
      1409: q+1
      1410: 1
      1411: q+1
      1412: q+1
      1413: 1
      1414: q+1
      1415: 1
      1416: q+1
      1417: 1
      1418: q+1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1428: q+1
      1429: q+1
      1430: q+1
      1432: q+1
      1433: q+1
      1435: q+1
      1436: q+1
      1437: 1
      1438: 1
      1439: 1
      1440: q+1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: q+1
      1450: 1
      1451: q+1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1467: q+1
      1471: 1
      1473: 1
      1476: 1
      1478: 1
      1479: 1
      1481: 1
      1483: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: q+1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: q+1
      1503: q+1
      1506: q+1
      1508: 1
      1509: 1
      1511: 1
      1513: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1520: 1
      1521: 1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: q+1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1540: q+1
      1542: q+1
      1545: q+1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1564: 1
      1565: q+1
      1566: 1
      1567: 1
      1568: 1
      1569: q+1
      1570: 1
      1571: q+1
      1572: 1
      1573: 1
      1574: q+1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1584: q+1
      1585: q+1
      1587: q+1
      1589: q+1
      1591: q+1
      1592: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: q+1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1614: 1
      1615: 1
      1616: 1
      1621: 1
      1625: 1
      1627: 1
      1630: 1
      1632: 1
      1633: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1643: q+1
      1647: 1
      1649: 1
      1652: 1
      1654: 1
      1655: 1
      1657: 1
      1659: 1
      1661: 1
      1662: 1
      1663: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1673: q+1
      1677: 1
      1679: 1
      1682: 1
      1684: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: q+1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1707: q+1
      1709: q+1
      1712: q+1
      1714: 1
      1715: 1
      1717: 1
      1719: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1726: 1
      1727: 1
      1729: 1
      1730: 1
      1731: 1
      1732: 1
      1733: 1
      1740: 1
      1744: 1
      1745: 1
      1746: 1
      1747: 1
      1748: 1
      1749: 1
      1754: 1
      1758: 1
      1760: 1
      1763: 1
      1765: 1
      1766: 1
      1767: 1
      1768: 1
      1769: 1
      1770: 1
      1775: 1
      1779: 1
      1781: 1
      1784: 1
      1786: 1
      1787: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1792: 1
      1793: 1
      1794: 1
      1795: 1
      1797: q+1
      1801: 1
      1803: 1
      1806: 1
      1808: 1
      1809: 1
      1811: 1
      1813: 1
      1815: 1
      1816: 1
      1823: 1
      1824: 1
      1825: 1
      1832: 1
      1836: 1
      1837: 1
      1838: 1
      1845: 1
      1849: 1
      1850: 1
      1851: 1
      1852: 1
      1853: 1
      1854: 1
      1859: 1
      1863: 1
      1865: 1
      1868: 1
      1873: 1
      1880: 1
      1887: 1
      1888: 1
      1889: 1
      1896: 1
      1907: 1

1908:    0: q^2+q+1
         1: q^2+q+1
         2: q^2+q+1
         3: q^2+q+1
         4: q^2+q+1
         5: q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^2+q+1
        10: q^2+q+1
        11: q+1
        12: q^2+q+1
        13: q^2+q+1
        14: q^2+q+1
        15: q^2+q+1
        16: q^2+q+1
        17: q^2+q+1
        18: q^2+q+1
        19: q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q+1
        29: q+1
        30: q^2+q+1
        31: q^2+q+1
        32: q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^2+q+1
        37: q^2+q+1
        38: q+1
        39: q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^2+q+1
        44: q^2+q+1
        45: q+1
        46: q^2+q+1
        47: q^2+q+1
        48: q^2+q+1
        49: q^2+q+1
        50: q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q^2+q+1
        54: q+1
        55: q^2+q+1
        56: q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q+1
        61: q^2+q+1
        62: q+1
        63: q+1
        64: q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q+1
        69: q+1
        70: q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q+1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q+1
        80: q+1
        81: q^2+q+1
        82: q^2+q+1
        83: q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q+1
        93: q+1
        94: q^2+q+1
        95: q^2+q+1
        96: q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^2+q+1
       101: q^2+q+1
       102: q+1
       103: q^2+q+1
       104: q+1
       105: q+1
       106: q^2+q+1
       107: q^2+q+1
       108: q+1
       109: q^2+q+1
       110: q+1
       111: q+1
       112: q+1
       113: q^2+q+1
       114: q^2+q+1
       115: q^2+q+1
       116: q+1
       117: q^2+q+1
       118: q+1
       119: q+1
       120: q+1
       121: q+1
       122: q+1
       123: q+1
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: 1
       128: q^2+q+1
       129: q+1
       130: q+1
       131: q+1
       132: q+1
       133: q+1
       134: q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q^2+q+1
       138: q+1
       139: q^2+q+1
       140: q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q+1
       145: q^2+q+1
       146: q+1
       147: q+1
       148: q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q+1
       153: q+1
       154: q+1
       155: q+1
       156: q^2+q+1
       157: q^2+q+1
       158: q^2+q+1
       159: q+1
       160: q^2+q+1
       161: q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q+1
       166: q^2+q+1
       167: q+1
       168: q+1
       169: q+1
       170: q^2+q+1
       171: q^2+q+1
       172: q^2+q+1
       173: q+1
       174: q+1
       175: q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q+1
       180: q^2+q+1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q+1
       185: q+1
       186: q^2+q+1
       187: q^2+q+1
       188: q+1
       189: q+1
       190: q+1
       191: q+1
       192: q^2+q+1
       193: q+1
       194: q^2+q+1
       195: q+1
       196: q+1
       197: q+1
       198: q+1
       199: q+1
       200: q^2+q+1
       201: q^2+q+1
       202: q+1
       203: q^2+q+1
       204: q+1
       205: q+1
       206: q+1
       207: q+1
       208: q+1
       209: q+1
       210: q+1
       211: q+1
       212: q+1
       213: 1
       214: q^2+q+1
       215: q^2+q+1
       216: q^2+q+1
       217: 1
       218: q^2+q+1
       219: 1
       220: q+1
       221: q+1
       222: q+1
       223: 1
       224: q+1
       225: q+1
       226: q+1
       227: q+1
       228: q+1
       229: q+1
       230: q^2+q+1
       231: q^2+q+1
       232: q+1
       233: q^2+q+1
       234: q+1
       235: q+1
       236: q+1
       237: q^2+q+1
       238: q^2+q+1
       239: q^2+q+1
       240: q+1
       241: q^2+q+1
       242: q+1
       243: q+1
       244: q+1
       245: q+1
       246: q+1
       247: q+1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: 1
       252: q^2+q+1
       253: q+1
       254: q+1
       255: q+1
       256: q+1
       257: q+1
       258: q+1
       259: q+1
       260: q^2+q+1
       261: q^2+q+1
       262: q+1
       263: q^2+q+1
       264: q+1
       265: q+1
       266: q+1
       267: q^2+q+1
       268: q^2+q+1
       269: q^2+q+1
       270: q+1
       271: q^2+q+1
       272: q+1
       273: q+1
       274: q+1
       275: q+1
       276: q+1
       277: q+1
       278: q^2+q+1
       279: q^2+q+1
       280: q^2+q+1
       281: 1
       282: q^2+q+1
       283: q+1
       284: q+1
       285: q+1
       286: q+1
       287: q+1
       288: q+1
       289: q^2+q+1
       290: q^2+q+1
       291: q^2+q+1
       292: q+1
       293: q^2+q+1
       294: q+1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q+1
       299: q^2+q+1
       300: q+1
       301: q+1
       302: q+1
       303: q^2+q+1
       304: q^2+q+1
       305: q^2+q+1
       306: q+1
       307: q+1
       308: q+1
       309: q+1
       310: q+1
       311: q+1
       312: q+1
       313: q+1
       314: 1
       315: q^2+q+1
       316: q+1
       317: q+1
       318: q+1
       319: q+1
       320: q+1
       321: q+1
       322: q^2+q+1
       323: q+1
       324: q^2+q+1
       325: q+1
       326: q+1
       327: q+1
       328: q+1
       329: q+1
       330: q+1
       331: q+1
       332: q+1
       333: q+1
       334: q+1
       335: q+1
       336: 1
       337: 1
       338: q^2+q+1
       339: q^2+q+1
       340: 1
       341: q^2+q+1
       342: 1
       343: 1
       344: 1
       345: q+1
       346: q+1
       347: q+1
       348: 1
       349: q+1
       350: 1
       351: q+1
       352: q+1
       353: q+1
       354: 1
       355: q+1
       356: q+1
       357: q+1
       358: q+1
       359: q^2+q+1
       360: q+1
       361: q^2+q+1
       362: q+1
       363: q+1
       364: q+1
       365: q+1
       366: q+1
       367: q^2+q+1
       368: q^2+q+1
       369: q+1
       370: q^2+q+1
       371: q+1
       372: q+1
       373: q+1
       374: q+1
       375: q+1
       376: q+1
       377: q+1
       378: q+1
       379: q+1
       380: 1
       381: q^2+q+1
       382: q^2+q+1
       383: q^2+q+1
       384: 1
       385: q^2+q+1
       386: 1
       387: q+1
       388: q+1
       389: q+1
       390: 1
       391: q+1
       392: q+1
       393: q+1
       394: q+1
       395: q+1
       396: q+1
       397: q+1
       398: q^2+q+1
       399: q+1
       400: q^2+q+1
       401: q+1
       402: q+1
       403: q+1
       404: q+1
       405: q+1
       406: q^2+q+1
       407: q^2+q+1
       408: q+1
       409: q^2+q+1
       410: q+1
       411: q+1
       412: q+1
       413: q+1
       414: q+1
       415: q+1
       416: q+1
       417: q+1
       418: q+1
       419: 1
       420: q^2+q+1
       421: q^2+q+1
       422: q^2+q+1
       423: 1
       424: q^2+q+1
       425: 1
       426: q+1
       427: q+1
       428: q+1
       429: 1
       430: q+1
       431: q+1
       432: q+1
       433: q+1
       434: q+1
       435: q+1
       436: q^2+q+1
       437: q^2+q+1
       438: q+1
       439: q^2+q+1
       440: q+1
       441: q+1
       442: q+1
       443: q^2+q+1
       444: q^2+q+1
       445: q^2+q+1
       446: q+1
       447: q^2+q+1
       448: q+1
       449: q+1
       450: q+1
       451: q+1
       452: q+1
       453: q+1
       454: q^2+q+1
       455: q^2+q+1
       456: q^2+q+1
       457: 1
       458: q^2+q+1
       459: q+1
       460: q+1
       461: q+1
       462: q+1
       463: q+1
       464: q+1
       465: q+1
       466: q+1
       467: q+1
       468: 1
       469: 1
       470: q+1
       471: q+1
       472: q+1
       473: q+1
       474: q+1
       475: q+1
       476: q+1
       477: q+1
       478: 1
       479: q^2+q+1
       480: q+1
       481: q+1
       482: q+1
       483: q+1
       484: q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: q+1
       491: q+1
       492: 1
       493: 1
       494: 1
       495: q^2+q+1
       496: 1
       497: q^2+q+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q+1
       504: q+1
       505: 1
       506: q+1
       507: 1
       508: 1
       509: 1
       510: q+1
       511: q+1
       512: q+1
       513: 1
       514: q+1
       515: 1
       516: q+1
       517: q+1
       518: q+1
       519: q+1
       520: q+1
       521: 1
       522: q^2+q+1
       523: q+1
       524: q+1
       525: q+1
       526: q+1
       527: q+1
       528: q+1
       529: q^2+q+1
       530: q+1
       531: q^2+q+1
       532: q+1
       533: q+1
       534: q+1
       535: q+1
       536: q+1
       537: q+1
       538: q+1
       539: q+1
       540: q+1
       541: q+1
       542: q+1
       543: 1
       544: 1
       545: q^2+q+1
       546: q^2+q+1
       547: 1
       548: q^2+q+1
       549: 1
       550: 1
       551: 1
       552: q+1
       553: q+1
       554: q+1
       555: 1
       556: q+1
       557: 1
       558: q+1
       559: q+1
       560: q+1
       561: 1
       562: q+1
       563: q+1
       564: q+1
       565: q+1
       566: q+1
       567: q+1
       568: 1
       569: q^2+q+1
       570: q+1
       571: q+1
       572: q+1
       573: q+1
       574: q+1
       575: q+1
       576: q^2+q+1
       577: q+1
       578: q^2+q+1
       579: q+1
       580: q+1
       581: q+1
       582: q+1
       583: q+1
       584: q+1
       585: q+1
       586: q+1
       587: q+1
       588: q+1
       589: q+1
       590: 1
       591: 1
       592: q^2+q+1
       593: q^2+q+1
       594: 1
       595: q^2+q+1
       596: 1
       597: 1
       598: 1
       599: q+1
       600: q+1
       601: q+1
       602: 1
       603: q+1
       604: 1
       605: q+1
       606: q+1
       607: q+1
       608: 1
       609: q+1
       610: q+1
       611: q+1
       612: q+1
       613: q^2+q+1
       614: q+1
       615: q^2+q+1
       616: q+1
       617: q+1
       618: q+1
       619: q+1
       620: q+1
       621: q^2+q+1
       622: q^2+q+1
       623: q+1
       624: q^2+q+1
       625: q+1
       626: q+1
       627: q+1
       628: q+1
       629: q+1
       630: q+1
       631: q+1
       632: q+1
       633: q+1
       634: 1
       635: q^2+q+1
       636: q^2+q+1
       637: q^2+q+1
       638: 1
       639: q^2+q+1
       640: 1
       641: q+1
       642: q+1
       643: q+1
       644: 1
       645: q+1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: q+1
       652: 1
       653: 1
       654: 1
       655: q+1
       656: q+1
       657: q+1
       658: q+1
       659: q+1
       660: q+1
       661: 1
       662: 1
       663: q+1
       664: q+1
       665: q+1
       666: q+1
       667: q+1
       668: q+1
       669: q+1
       670: q+1
       672: q+1
       673: q+1
       674: q+1
       675: q+1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: q^2+q+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: q+1
       690: 1
       691: q+1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: q+1
       698: q+1
       699: 1
       700: q+1
       701: 1
       702: 1
       703: q+1
       704: q+1
       705: q+1
       706: q+1
       707: 1
       708: 1
       709: q+1
       710: q+1
       711: q+1
       712: q+1
       713: q+1
       714: q+1
       715: q+1
       716: q+1
       717: 1
       718: q^2+q+1
       719: q+1
       720: q+1
       721: q+1
       722: q+1
       723: q+1
       724: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: q+1
       730: q+1
       731: 1
       732: 1
       733: 1
       734: q^2+q+1
       735: 1
       736: q^2+q+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: q+1
       743: q+1
       744: 1
       745: q+1
       746: 1
       747: 1
       748: 1
       749: q+1
       750: q+1
       751: q+1
       752: 1
       753: q+1
       754: 1
       755: q+1
       756: q+1
       757: q+1
       758: q+1
       759: 1
       760: 1
       761: q+1
       762: q+1
       763: q+1
       764: q+1
       765: q+1
       766: q+1
       767: q+1
       768: q+1
       769: 1
       770: q^2+q+1
       771: q+1
       772: q+1
       773: q+1
       774: q+1
       775: q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: q+1
       782: q+1
       783: 1
       784: 1
       785: 1
       786: q^2+q+1
       787: 1
       788: q^2+q+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: q+1
       795: q+1
       796: 1
       797: q+1
       798: 1
       799: 1
       800: 1
       801: q+1
       802: q+1
       803: q+1
       804: 1
       805: q+1
       806: 1
       807: q+1
       808: q+1
       809: q+1
       810: q+1
       811: q+1
       812: 1
       813: q^2+q+1
       814: q+1
       815: q+1
       816: q+1
       817: q+1
       818: q+1
       819: q+1
       820: q^2+q+1
       821: q+1
       822: q^2+q+1
       823: q+1
       824: q+1
       825: q+1
       826: q+1
       827: q+1
       828: q+1
       829: q+1
       830: q+1
       831: q+1
       832: q+1
       833: q+1
       834: 1
       835: 1
       836: q^2+q+1
       837: q^2+q+1
       838: 1
       839: q^2+q+1
       840: 1
       841: 1
       842: 1
       843: q+1
       844: q+1
       845: q+1
       846: 1
       847: q+1
       848: 1
       849: q+1
       850: q+1
       851: q+1
       852: 1
       853: q+1
       854: q+1
       855: q+1
       856: 1
       857: 1
       858: 1
       859: 1
       860: q+1
       861: q+1
       862: q+1
       863: q+1
       864: 1
       865: 1
       866: 1
       867: q+1
       868: q+1
       869: q+1
       870: q+1
       871: q+1
       872: q+1
       875: q+1
       876: q+1
       877: q+1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       893: q+1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: q+1
       901: 1
       902: q+1
       903: 1
       904: 1
       905: 1
       906: q+1
       907: q+1
       908: q+1
       909: 1
       910: 1
       911: 1
       912: q+1
       913: q+1
       914: q+1
       915: q+1
       916: q+1
       917: q+1
       918: 1
       919: 1
       920: q+1
       921: q+1
       922: q+1
       923: q+1
       924: q+1
       925: q+1
       926: q+1
       927: q+1
       929: q+1
       930: q+1
       931: q+1
       932: q+1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: q^2+q+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: q+1
       947: 1
       948: q+1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: q+1
       955: q+1
       956: 1
       957: q+1
       958: 1
       959: 1
       960: q+1
       961: q+1
       962: q+1
       963: 1
       964: 1
       965: 1
       966: q+1
       967: q+1
       968: q+1
       969: q+1
       970: q+1
       971: q+1
       972: 1
       973: 1
       974: q+1
       975: q+1
       976: q+1
       977: q+1
       978: q+1
       979: q+1
       980: q+1
       981: q+1
       983: q+1
       984: q+1
       985: q+1
       986: q+1
       987: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: q^2+q+1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: q+1
      1001: 1
      1002: q+1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: q+1
      1009: q+1
      1010: 1
      1011: q+1
      1012: 1
      1013: 1
      1014: q+1
      1015: q+1
      1016: q+1
      1017: q+1
      1018: 1
      1019: 1
      1020: q+1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: q+1
      1026: q+1
      1027: q+1
      1028: 1
      1029: q^2+q+1
      1030: q+1
      1031: q+1
      1032: q+1
      1033: q+1
      1034: q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: q+1
      1041: q+1
      1042: 1
      1043: 1
      1044: 1
      1045: q^2+q+1
      1046: 1
      1047: q^2+q+1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: q+1
      1054: q+1
      1055: 1
      1056: q+1
      1057: 1
      1058: 1
      1059: 1
      1060: q+1
      1061: q+1
      1062: q+1
      1063: 1
      1064: q+1
      1065: 1
      1066: q+1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q+1
      1072: q+1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: q+1
      1078: q+1
      1079: q+1
      1080: q+1
      1084: q+1
      1085: q+1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1109: q+1
      1110: 1
      1111: 1
      1112: 1
      1113: q+1
      1114: q+1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: q+1
      1120: q+1
      1121: q+1
      1122: q+1
      1123: 1
      1124: 1
      1125: 1
      1126: q+1
      1127: q+1
      1128: q+1
      1129: q+1
      1130: q+1
      1131: q+1
      1134: q+1
      1135: q+1
      1136: q+1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: q+1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: q+1
      1160: 1
      1161: q+1
      1162: 1
      1163: 1
      1164: 1
      1165: q+1
      1166: q+1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: q+1
      1172: q+1
      1173: q+1
      1174: q+1
      1175: 1
      1176: 1
      1177: 1
      1178: q+1
      1179: q+1
      1180: q+1
      1181: q+1
      1182: q+1
      1183: q+1
      1186: q+1
      1187: q+1
      1188: q+1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1204: q+1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q+1
      1212: 1
      1213: q+1
      1214: 1
      1215: 1
      1216: 1
      1217: q+1
      1218: q+1
      1219: q+1
      1220: 1
      1221: 1
      1222: 1
      1223: q+1
      1224: q+1
      1225: q+1
      1226: q+1
      1227: q+1
      1228: q+1
      1229: 1
      1230: 1
      1231: q+1
      1232: q+1
      1233: q+1
      1234: q+1
      1235: q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1240: q+1
      1241: q+1
      1242: q+1
      1243: q+1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: q^2+q+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: q+1
      1258: 1
      1259: q+1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: q+1
      1266: q+1
      1267: 1
      1268: q+1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: q+1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: q+1
      1280: q+1
      1285: q+1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1307: 1
      1308: 1
      1309: 1
      1310: q+1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: q+1
      1316: q+1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: q+1
      1322: q+1
      1323: q+1
      1324: q+1
      1328: q+1
      1329: q+1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: q+1
      1354: 1
      1355: 1
      1356: 1
      1357: q+1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: q+1
      1363: q+1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: q+1
      1369: q+1
      1370: q+1
      1371: q+1
      1375: q+1
      1376: q+1
      1377: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1388: 1
      1391: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1400: q+1
      1401: 1
      1402: 1
      1403: 1
      1404: q+1
      1405: q+1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: q+1
      1411: q+1
      1412: q+1
      1413: q+1
      1414: 1
      1415: 1
      1416: 1
      1417: q+1
      1418: q+1
      1419: q+1
      1420: q+1
      1421: q+1
      1422: q+1
      1425: q+1
      1426: q+1
      1427: q+1
      1428: 1
      1429: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: q+1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: q+1
      1451: 1
      1452: q+1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: q+1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: q+1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: q+1
      1495: q+1
      1500: q+1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: q+1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: q+1
      1534: q+1
      1539: q+1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1553: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1558: 1
      1561: 1
      1562: 1
      1563: 1
      1564: q+1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: q+1
      1570: q+1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: q+1
      1576: q+1
      1577: q+1
      1578: q+1
      1582: q+1
      1583: q+1
      1584: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: q+1
      1608: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1625: 1
      1626: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1635: 1
      1636: 1
      1637: q+1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1662: 1
      1663: 1
      1664: 1
      1665: 1
      1666: 1
      1667: q+1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1683: 1
      1684: 1
      1685: 1
      1686: 1
      1690: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: q+1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: q+1
      1701: q+1
      1706: q+1
      1707: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1715: 1
      1716: 1
      1720: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1725: 1
      1728: 1
      1729: 1
      1730: 1
      1731: 1
      1734: 1
      1735: 1
      1739: 1
      1744: 1
      1745: 1
      1746: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1758: 1
      1759: 1
      1764: 1
      1765: 1
      1766: 1
      1767: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1779: 1
      1780: 1
      1785: 1
      1786: 1
      1787: 1
      1788: 1
      1789: 1
      1790: 1
      1791: q+1
      1796: 1
      1797: 1
      1798: 1
      1799: 1
      1800: 1
      1801: 1
      1802: 1
      1807: 1
      1808: 1
      1809: 1
      1810: 1
      1814: 1
      1815: 1
      1817: 1
      1823: 1
      1826: 1
      1827: 1
      1831: 1
      1836: 1
      1839: 1
      1840: 1
      1844: 1
      1849: 1
      1850: 1
      1851: 1
      1855: 1
      1856: 1
      1857: 1
      1858: 1
      1863: 1
      1864: 1
      1869: 1
      1874: 1
      1881: 1
      1887: 1
      1890: 1
      1891: 1
      1895: 1
      1908: 1

1909:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: q^2+2q+1
         9: q^2+2q+1
        10: 2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: q^2+2q+1
        21: q^2+2q+1
        22: q^2+2q+1
        23: q^2+2q+1
        24: q^2+2q+1
        25: 2q+1
        26: 2q+1
        27: 2q+1
        28: q^2+2q+1
        29: 2q+1
        30: q^2+2q+1
        31: 2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: q^2+2q+1
        36: q^2+2q+1
        37: 2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: q^2+2q+1
        43: q^2+2q+1
        44: 2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: q^2+2q+1
        51: q^2+2q+1
        52: q^2+2q+1
        53: 2q+1
        54: q^2+2q+1
        55: q^2+2q+1
        56: q^2+2q+1
        57: 2q+1
        58: 2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: 2q+1
        63: 2q+1
        64: 2q+1
        65: 2q+1
        66: 2q+1
        67: 2q+1
        68: q^2+2q+1
        69: 2q+1
        70: q^2+2q+1
        71: q^2+2q+1
        72: q^2+2q+1
        73: q^2+2q+1
        74: q^2+2q+1
        75: q^2+2q+1
        76: 2q+1
        77: 2q+1
        78: 2q+1
        79: q^2+2q+1
        80: 2q+1
        81: q^2+2q+1
        82: 2q+1
        83: q^2+2q+1
        84: q^2+2q+1
        85: q^2+2q+1
        86: q^2+2q+1
        87: q^2+2q+1
        88: q^2+2q+1
        89: 2q+1
        90: 2q+1
        91: 2q+1
        92: q^2+2q+1
        93: 2q+1
        94: q^2+2q+1
        95: 2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: q^2+2q+1
       100: q^2+2q+1
       101: 2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: q^2+2q+1
       105: q^2+2q+1
       106: q^2+2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: q^2+2q+1
       111: q^2+2q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: 2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: 2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: 2q+1
       130: 2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q+1
       134: q^2+2q+1
       135: q^2+2q+1
       136: q^2+2q+1
       137: 2q+1
       138: q^2+2q+1
       139: q^2+2q+1
       140: q^2+2q+1
       141: 2q+1
       142: 2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: 2q+1
       147: 2q+1
       148: 2q+1
       149: 2q+1
       150: 2q+1
       151: 2q+1
       152: q^2+2q+1
       153: 2q+1
       154: q^2+2q+1
       155: q^2+2q+1
       156: q^2+2q+1
       157: q^2+2q+1
       158: 2q+1
       159: q^2+2q+1
       160: q^2+2q+1
       161: q^2+2q+1
       162: 2q+1
       163: 2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: 2q+1
       168: 2q+1
       169: 2q+1
       170: 2q+1
       171: 2q+1
       172: 2q+1
       173: q^2+2q+1
       174: 2q+1
       175: q^2+2q+1
       176: q^2+2q+1
       177: q^2+2q+1
       178: q^2+2q+1
       179: q^2+2q+1
       180: q^2+2q+1
       181: 2q+1
       182: 2q+1
       183: 2q+1
       184: q^2+2q+1
       185: 2q+1
       186: q^2+2q+1
       187: 2q+1
       188: q^2+2q+1
       189: q^2+2q+1
       190: q^2+2q+1
       191: 2q+1
       192: 2q+1
       193: 2q+1
       194: 2q+1
       195: 2q+1
       196: q^2+2q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: 2q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: 2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q+1
       226: q+1
       227: q+1
       228: q^2+2q+1
       229: q^2+2q+1
       230: q^2+2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: q^2+2q+1
       235: q^2+2q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: 2q+1
       244: 2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: 2q+1
       249: 2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: 2q+1
       254: 2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q+1
       258: q^2+2q+1
       259: q^2+2q+1
       260: q^2+2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: q^2+2q+1
       265: q^2+2q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: 2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: 2q+1
       279: 2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: 2q+1
       284: 2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q+1
       288: q^2+2q+1
       289: q^2+2q+1
       290: q^2+2q+1
       291: 2q+1
       292: q^2+2q+1
       293: q^2+2q+1
       294: q^2+2q+1
       295: 2q+1
       296: 2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: 2q+1
       301: 2q+1
       302: 2q+1
       303: 2q+1
       304: 2q+1
       305: 2q+1
       306: q^2+2q+1
       307: 2q+1
       308: q^2+2q+1
       309: q+1
       310: q^2+2q+1
       311: 2q+1
       312: 2q+1
       313: 2q+1
       314: 2q+1
       315: 2q+1
       316: 2q+1
       317: q+1
       318: q+1
       319: 2q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: 2q+1
       324: 2q+1
       325: 2q+1
       326: 2q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: q+1
       332: q+1
       333: q+1
       334: 2q+1
       335: 2q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: q+1
       340: q+1
       341: q+1
       342: 2q+1
       343: 2q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: q+1
       352: q+1
       353: q+1
       354: q+1
       355: q+1
       356: q^2+2q+1
       357: q^2+2q+1
       358: 2q+1
       359: 2q+1
       360: 2q+1
       361: 2q+1
       362: 2q+1
       363: q^2+2q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: 2q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: 2q+1
       388: 2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q+1
       393: q+1
       394: q+1
       395: q^2+2q+1
       396: q^2+2q+1
       397: 2q+1
       398: 2q+1
       399: 2q+1
       400: 2q+1
       401: 2q+1
       402: q^2+2q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: 2q+1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: 2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q+1
       432: q+1
       433: q+1
       434: q^2+2q+1
       435: q^2+2q+1
       436: q^2+2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: q^2+2q+1
       441: q^2+2q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: 2q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: 2q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: 2q+1
       460: 2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q+1
       464: q+1
       465: q+1
       466: 2q+1
       467: 2q+1
       468: 2q+1
       469: 2q+1
       470: 2q+1
       471: q+1
       472: q+1
       473: q+1
       474: 2q+1
       475: 2q+1
       476: 2q+1
       477: 2q+1
       478: 2q+1
       479: 2q+1
       480: 2q+1
       481: 1
       482: q+1
       483: 2q+1
       484: 2q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: 2q+1
       491: q+1
       492: 2q+1
       493: 2q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: 2q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 1
       505: 1
       506: 1
       507: 2q+1
       508: 2q+1
       509: q+1
       510: q+1
       511: q+1
       512: 1
       513: q+1
       514: q+1
       515: q+1
       516: q+1
       517: q^2+2q+1
       518: 2q+1
       519: 2q+1
       520: 2q+1
       521: 2q+1
       522: 2q+1
       523: 2q+1
       524: q+1
       525: q+1
       526: 2q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: 2q+1
       531: 2q+1
       532: 2q+1
       533: 2q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: q+1
       539: q+1
       540: q+1
       541: 2q+1
       542: 2q+1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: q+1
       547: q+1
       548: q+1
       549: 2q+1
       550: 2q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: 1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: q+1
       559: q+1
       560: q+1
       561: q+1
       562: q+1
       563: q+1
       564: q^2+2q+1
       565: 2q+1
       566: 2q+1
       567: 2q+1
       568: 2q+1
       569: 2q+1
       570: 2q+1
       571: q+1
       572: q+1
       573: 2q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: 2q+1
       578: 2q+1
       579: 2q+1
       580: 2q+1
       581: q+1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: q+1
       586: q+1
       587: q+1
       588: 2q+1
       589: 2q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: q+1
       594: q+1
       595: q+1
       596: 2q+1
       597: 2q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: 1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: q+1
       606: q+1
       607: q+1
       608: q+1
       609: q+1
       610: q^2+2q+1
       611: q^2+2q+1
       612: 2q+1
       613: 2q+1
       614: 2q+1
       615: 2q+1
       616: 2q+1
       617: q^2+2q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: 2q+1
       627: 2q+1
       628: 2q+1
       629: 2q+1
       630: q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: 2q+1
       635: 2q+1
       636: 2q+1
       637: q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: 2q+1
       642: 2q+1
       643: 2q+1
       644: 2q+1
       645: 2q+1
       646: q+1
       647: q+1
       648: q+1
       649: q+1
       650: q+1
       651: 2q+1
       652: 2q+1
       653: 2q+1
       654: q+1
       655: q+1
       656: q+1
       657: q+1
       658: 1
       659: 2q+1
       660: 2q+1
       661: 2q+1
       662: 2q+1
       663: 2q+1
       664: 1
       665: 1
       666: q+1
       667: 2q+1
       668: q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: q+1
       676: q+1
       677: 2q+1
       678: q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q+1
       686: 2q+1
       687: 2q+1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 2q+1
       694: q+1
       695: q+1
       696: q+1
       697: q+1
       698: 1
       699: 1
       700: 1
       701: q+1
       702: q+1
       703: q+1
       704: q+1
       705: 2q+1
       706: 2q+1
       707: 2q+1
       708: 2q+1
       709: 2q+1
       710: q+1
       711: q+1
       712: q+1
       713: 2q+1
       714: 2q+1
       715: 2q+1
       716: 2q+1
       717: 2q+1
       718: 2q+1
       719: 2q+1
       720: 1
       721: q+1
       722: 2q+1
       723: 2q+1
       724: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: 2q+1
       730: q+1
       731: 2q+1
       732: 2q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: 2q+1
       739: q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 1
       744: 1
       745: 1
       746: 2q+1
       747: 2q+1
       748: q+1
       749: q+1
       750: q+1
       751: 1
       752: q+1
       753: q+1
       754: q+1
       755: q+1
       756: q+1
       757: 2q+1
       758: 2q+1
       759: 2q+1
       760: 2q+1
       761: 2q+1
       762: q+1
       763: q+1
       764: q+1
       765: 2q+1
       766: 2q+1
       767: 2q+1
       768: 2q+1
       769: 2q+1
       770: 2q+1
       771: 2q+1
       772: 1
       773: q+1
       774: 2q+1
       775: 2q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: 2q+1
       782: q+1
       783: 2q+1
       784: 2q+1
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: 2q+1
       791: q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 1
       796: 1
       797: 1
       798: 2q+1
       799: 2q+1
       800: q+1
       801: q+1
       802: q+1
       803: 1
       804: q+1
       805: q+1
       806: q+1
       807: q+1
       808: q^2+2q+1
       809: 2q+1
       810: 2q+1
       811: 2q+1
       812: 2q+1
       813: 2q+1
       814: 2q+1
       815: q+1
       816: q+1
       817: 2q+1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: 2q+1
       822: 2q+1
       823: 2q+1
       824: 2q+1
       825: q+1
       826: 2q+1
       827: 2q+1
       828: 2q+1
       829: q+1
       830: q+1
       831: q+1
       832: 2q+1
       833: 2q+1
       834: 2q+1
       835: 2q+1
       836: 2q+1
       837: q+1
       838: q+1
       839: q+1
       840: 2q+1
       841: 2q+1
       842: 2q+1
       843: 2q+1
       844: 2q+1
       845: 1
       846: 2q+1
       847: 2q+1
       848: 2q+1
       849: q+1
       850: q+1
       851: q+1
       852: q+1
       853: q+1
       854: q+1
       855: q+1
       856: q+1
       857: 2q+1
       858: q+1
       859: q+1
       860: q+1
       861: 1
       862: 1
       863: 2q+1
       864: 2q+1
       865: 2q+1
       866: 1
       867: 1
       868: 1
       869: q+1
       870: 1
       871: q+1
       872: q+1
       873: q+1
       874: q+1
       875: q+1
       876: 1
       877: 1
       878: q+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       885: 1
       886: 1
       887: q+1
       888: 2q+1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: q+1
       897: q+1
       898: q+1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: q+1
       905: q+1
       906: q+1
       907: q+1
       908: 2q+1
       909: 2q+1
       910: 2q+1
       911: q+1
       912: q+1
       913: q+1
       914: q+1
       915: 1
       916: 2q+1
       917: 2q+1
       918: 2q+1
       919: 2q+1
       920: 2q+1
       921: 1
       922: 1
       923: q+1
       924: 2q+1
       925: q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: q+1
       931: 1
       932: q+1
       933: q+1
       934: 2q+1
       935: q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: q+1
       943: 2q+1
       944: 2q+1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 2q+1
       951: q+1
       952: q+1
       953: q+1
       954: q+1
       955: 1
       956: 1
       957: 1
       958: q+1
       959: q+1
       960: q+1
       961: q+1
       962: 2q+1
       963: 2q+1
       964: 2q+1
       965: q+1
       966: q+1
       967: q+1
       968: q+1
       969: 1
       970: 2q+1
       971: 2q+1
       972: 2q+1
       973: 2q+1
       974: 2q+1
       975: 1
       976: 1
       977: q+1
       978: 2q+1
       979: q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: q+1
       985: 1
       986: q+1
       987: q+1
       988: 2q+1
       989: q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: q+1
       995: 1
       996: q+1
       997: 2q+1
       998: 2q+1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 2q+1
      1005: q+1
      1006: q+1
      1007: q+1
      1008: q+1
      1009: 1
      1010: 1
      1011: 1
      1012: q+1
      1013: q+1
      1014: q+1
      1015: q+1
      1016: 2q+1
      1017: 2q+1
      1018: 2q+1
      1019: 2q+1
      1020: 2q+1
      1021: q+1
      1022: q+1
      1023: q+1
      1024: 2q+1
      1025: 2q+1
      1026: 2q+1
      1027: 2q+1
      1028: 2q+1
      1029: 2q+1
      1030: 2q+1
      1031: 1
      1032: q+1
      1033: 2q+1
      1034: 2q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: 2q+1
      1041: q+1
      1042: 2q+1
      1043: 2q+1
      1044: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: 2q+1
      1050: q+1
      1051: 2q+1
      1052: 2q+1
      1053: 2q+1
      1054: 1
      1055: 1
      1056: 1
      1057: 2q+1
      1058: 2q+1
      1059: q+1
      1060: q+1
      1061: q+1
      1062: 1
      1063: q+1
      1064: q+1
      1065: q+1
      1066: q+1
      1067: q+1
      1068: q+1
      1069: q+1
      1070: q+1
      1071: 1
      1072: 1
      1073: 1
      1074: 2q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1103: q+1
      1104: q+1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1112: q+1
      1113: q+1
      1114: q+1
      1115: q+1
      1116: 2q+1
      1117: q+1
      1118: q+1
      1119: q+1
      1120: 1
      1121: 1
      1122: 2q+1
      1123: 2q+1
      1124: 2q+1
      1125: 1
      1126: 1
      1127: 1
      1128: q+1
      1129: 1
      1130: q+1
      1131: q+1
      1132: q+1
      1133: q+1
      1134: q+1
      1135: 1
      1136: 1
      1137: q+1
      1138: 1
      1139: q+1
      1140: q+1
      1141: q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: 1
      1146: q+1
      1147: 2q+1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: q+1
      1156: q+1
      1157: q+1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: q+1
      1164: q+1
      1165: q+1
      1166: q+1
      1167: q+1
      1168: 2q+1
      1169: q+1
      1170: q+1
      1171: q+1
      1172: 1
      1173: 1
      1174: 2q+1
      1175: 2q+1
      1176: 2q+1
      1177: 1
      1178: 1
      1179: 1
      1180: q+1
      1181: 1
      1182: q+1
      1183: q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: q+1
      1190: 1
      1191: q+1
      1192: q+1
      1193: q+1
      1194: q+1
      1195: q+1
      1196: 1
      1197: 1
      1198: q+1
      1199: 2q+1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: q+1
      1208: q+1
      1209: q+1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: q+1
      1216: q+1
      1217: q+1
      1218: q+1
      1219: 2q+1
      1220: 2q+1
      1221: 2q+1
      1222: q+1
      1223: q+1
      1224: q+1
      1225: q+1
      1226: 1
      1227: 2q+1
      1228: 2q+1
      1229: 2q+1
      1230: 2q+1
      1231: 2q+1
      1232: 1
      1233: 1
      1234: q+1
      1235: 2q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: q+1
      1244: q+1
      1245: 2q+1
      1246: q+1
      1247: q+1
      1248: q+1
      1249: q+1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q+1
      1254: 2q+1
      1255: 2q+1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 2q+1
      1262: q+1
      1263: q+1
      1264: q+1
      1265: q+1
      1266: 1
      1267: 1
      1268: 1
      1269: q+1
      1270: q+1
      1271: q+1
      1272: q+1
      1273: q+1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: q+1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1310: q+1
      1311: q+1
      1312: q+1
      1313: q+1
      1314: q+1
      1315: 1
      1316: 1
      1317: 1
      1318: 2q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: q+1
      1325: q+1
      1326: q+1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1338: q+1
      1339: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: 1
      1347: q+1
      1348: q+1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1356: q+1
      1357: q+1
      1358: q+1
      1359: q+1
      1360: q+1
      1361: q+1
      1362: 1
      1363: 1
      1364: 1
      1365: 2q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1379: q+1
      1380: q+1
      1381: q+1
      1382: 1
      1383: 1
      1384: 1
      1385: q+1
      1386: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: 1
      1394: q+1
      1395: q+1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1403: q+1
      1404: q+1
      1405: q+1
      1406: q+1
      1407: 2q+1
      1408: q+1
      1409: q+1
      1410: q+1
      1411: 1
      1412: 1
      1413: 2q+1
      1414: 2q+1
      1415: 2q+1
      1416: 1
      1417: 1
      1418: 1
      1419: q+1
      1420: 1
      1421: q+1
      1422: q+1
      1423: q+1
      1424: q+1
      1425: q+1
      1426: 1
      1427: 1
      1428: q+1
      1429: 1
      1430: q+1
      1431: q+1
      1432: q+1
      1433: q+1
      1434: q+1
      1435: 1
      1436: 1
      1437: q+1
      1438: 2q+1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: q+1
      1447: q+1
      1448: q+1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q+1
      1455: q+1
      1456: q+1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1486: q+1
      1487: q+1
      1488: q+1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: q+1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: q+1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1525: q+1
      1526: q+1
      1527: q+1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1541: 1
      1542: 1
      1543: q+1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: q+1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1564: q+1
      1565: q+1
      1566: q+1
      1567: q+1
      1568: q+1
      1569: 1
      1570: 1
      1571: 1
      1572: 2q+1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: q+1
      1579: q+1
      1580: q+1
      1581: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1586: q+1
      1587: q+1
      1588: q+1
      1589: 1
      1590: 1
      1591: 1
      1592: q+1
      1593: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1600: 1
      1601: q+1
      1602: q+1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1610: q+1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1628: 1
      1632: q+1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1656: 1
      1657: 1
      1658: 1
      1662: q+1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1686: 1
      1687: 1
      1688: 1
      1692: q+1
      1693: q+1
      1694: q+1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: q+1
      1704: 1
      1705: 1
      1706: 1
      1707: 1
      1708: 1
      1709: 1
      1710: q+1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1722: q+1
      1724: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1732: 1
      1734: 1
      1736: 1
      1737: 1
      1738: 1
      1745: 1
      1747: 1
      1748: 1
      1749: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1754: 1
      1755: 1
      1756: 1
      1757: 1
      1761: 1
      1766: 1
      1768: 1
      1769: 1
      1770: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1775: 1
      1776: 1
      1777: 1
      1778: 1
      1782: 1
      1786: q+1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1792: 1
      1793: 1
      1794: 1
      1795: 1
      1796: 1
      1797: 1
      1798: 1
      1799: 1
      1800: 1
      1801: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1806: 1
      1807: 1
      1810: 1
      1811: 1
      1812: 1
      1818: 1
      1824: 1
      1826: 1
      1828: 1
      1829: 1
      1830: 1
      1837: 1
      1839: 1
      1841: 1
      1842: 1
      1843: 1
      1850: 1
      1852: 1
      1853: 1
      1854: 1
      1855: 1
      1856: 1
      1857: 1
      1858: 1
      1859: 1
      1860: 1
      1861: 1
      1862: 1
      1866: 1
      1875: 1
      1882: 1
      1888: 1
      1890: 1
      1892: 1
      1893: 1
      1894: 1
      1909: 1

1910:    0: q^4+3q^3+4q^2+3q+1
         1: 2q^3+4q^2+3q+1
         2: q^4+3q^3+4q^2+3q+1
         3: 2q^3+4q^2+3q+1
         4: q^4+3q^3+4q^2+3q+1
         5: q^4+3q^3+4q^2+3q+1
         6: 2q^3+4q^2+3q+1
         7: 2q^3+4q^2+3q+1
         8: 2q^3+4q^2+3q+1
         9: q^3+4q^2+3q+1
        10: 2q^3+4q^2+3q+1
        11: 2q^3+4q^2+3q+1
        12: 2q^3+4q^2+3q+1
        13: 2q^3+4q^2+3q+1
        14: q^4+3q^3+4q^2+3q+1
        15: 2q^3+4q^2+3q+1
        16: 2q^3+4q^2+3q+1
        17: q^4+3q^3+4q^2+3q+1
        18: 2q^3+4q^2+3q+1
        19: q^4+3q^3+4q^2+3q+1
        20: 3q^2+3q+1
        21: 2q^3+4q^2+3q+1
        22: q^3+4q^2+3q+1
        23: 2q^3+4q^2+3q+1
        24: 2q^3+4q^2+3q+1
        25: q^3+4q^2+3q+1
        26: 3q^2+3q+1
        27: 2q^3+4q^2+3q+1
        28: q^3+4q^2+3q+1
        29: 2q^3+4q^2+3q+1
        30: q^3+4q^2+3q+1
        31: 2q^3+4q^2+3q+1
        32: 2q^3+4q^2+3q+1
        33: 2q^3+4q^2+3q+1
        34: 2q^3+4q^2+3q+1
        35: 2q^3+4q^2+3q+1
        36: q^3+4q^2+3q+1
        37: 2q^3+4q^2+3q+1
        38: 2q^3+4q^2+3q+1
        39: 2q^3+4q^2+3q+1
        40: 2q^3+4q^2+3q+1
        41: 2q^3+4q^2+3q+1
        42: 2q^3+4q^2+3q+1
        43: q^3+4q^2+3q+1
        44: 2q^3+4q^2+3q+1
        45: 2q^3+4q^2+3q+1
        46: 2q^3+4q^2+3q+1
        47: 2q^3+4q^2+3q+1
        48: q^4+3q^3+4q^2+3q+1
        49: 2q^3+4q^2+3q+1
        50: 3q^2+3q+1
        51: 3q^2+3q+1
        52: 3q^2+3q+1
        53: q^3+4q^2+3q+1
        54: q^3+4q^2+3q+1
        55: q^3+4q^2+3q+1
        56: 2q^3+4q^2+3q+1
        57: 3q^2+3q+1
        58: 3q^2+3q+1
        59: 3q^2+3q+1
        60: 2q^3+4q^2+3q+1
        61: 2q^3+4q^2+3q+1
        62: q^3+4q^2+3q+1
        63: 3q^2+3q+1
        64: q^3+3q^2+3q+1
        65: q^3+4q^2+3q+1
        66: 3q^2+3q+1
        67: q^3+3q^2+3q+1
        68: q^3+4q^2+3q+1
        69: 2q^3+4q^2+3q+1
        70: q^3+3q^2+3q+1
        71: 3q^2+3q+1
        72: 2q^3+4q^2+3q+1
        73: q^3+4q^2+3q+1
        74: 2q^3+4q^2+3q+1
        75: 2q^3+4q^2+3q+1
        76: q^3+4q^2+3q+1
        77: 3q^2+3q+1
        78: 2q^3+4q^2+3q+1
        79: q^3+4q^2+3q+1
        80: 2q^3+4q^2+3q+1
        81: q^3+4q^2+3q+1
        82: 2q^3+4q^2+3q+1
        83: 2q^3+4q^2+3q+1
        84: 3q^2+3q+1
        85: 2q^3+4q^2+3q+1
        86: q^3+4q^2+3q+1
        87: 2q^3+4q^2+3q+1
        88: 2q^3+4q^2+3q+1
        89: q^3+4q^2+3q+1
        90: 3q^2+3q+1
        91: 2q^3+4q^2+3q+1
        92: q^3+4q^2+3q+1
        93: 2q^3+4q^2+3q+1
        94: q^3+4q^2+3q+1
        95: 2q^3+4q^2+3q+1
        96: 2q^3+4q^2+3q+1
        97: 2q^3+4q^2+3q+1
        98: 2q^3+4q^2+3q+1
        99: 2q^3+4q^2+3q+1
       100: q^3+4q^2+3q+1
       101: 2q^3+4q^2+3q+1
       102: 2q^3+4q^2+3q+1
       103: 2q^3+4q^2+3q+1
       104: 3q^2+3q+1
       105: 3q^2+3q+1
       106: 3q^2+3q+1
       107: 3q^2+3q+1
       108: q^3+4q^2+3q+1
       109: q^3+4q^2+3q+1
       110: q^3+4q^2+3q+1
       111: q^3+3q^2+3q+1
       112: 3q^2+3q+1
       113: 3q^2+3q+1
       114: 2q^2+3q+1
       115: 3q^2+3q+1
       116: 3q^2+3q+1
       117: 3q^2+3q+1
       118: 2q^3+4q^2+3q+1
       119: 2q^2+3q+1
       120: 3q^2+3q+1
       121: 2q^2+3q+1
       122: q^3+3q^2+3q+1
       123: q^3+3q^2+3q+1
       124: 2q^2+3q+1
       125: 3q^2+3q+1
       126: 2q^2+3q+1
       127: q^3+3q^2+3q+1
       128: q^3+3q^2+3q+1
       129: q^3+4q^2+3q+1
       130: 3q^2+3q+1
       131: 2q^2+3q+1
       132: q^3+3q^2+3q+1
       133: q^3+3q^2+3q+1
       134: 3q^2+3q+1
       135: 3q^2+3q+1
       136: 3q^2+3q+1
       137: q^3+4q^2+3q+1
       138: q^3+4q^2+3q+1
       139: q^3+4q^2+3q+1
       140: 2q^3+4q^2+3q+1
       141: 3q^2+3q+1
       142: 3q^2+3q+1
       143: 3q^2+3q+1
       144: 2q^3+4q^2+3q+1
       145: 2q^3+4q^2+3q+1
       146: q^3+4q^2+3q+1
       147: 3q^2+3q+1
       148: q^3+3q^2+3q+1
       149: q^3+4q^2+3q+1
       150: 3q^2+3q+1
       151: q^3+3q^2+3q+1
       152: q^3+4q^2+3q+1
       153: 2q^3+4q^2+3q+1
       154: q^3+3q^2+3q+1
       155: 3q^2+3q+1
       156: 3q^2+3q+1
       157: 3q^2+3q+1
       158: q^3+4q^2+3q+1
       159: q^3+4q^2+3q+1
       160: q^3+4q^2+3q+1
       161: 2q^3+4q^2+3q+1
       162: 3q^2+3q+1
       163: 3q^2+3q+1
       164: 3q^2+3q+1
       165: 2q^3+4q^2+3q+1
       166: 2q^3+4q^2+3q+1
       167: q^3+4q^2+3q+1
       168: 3q^2+3q+1
       169: q^3+3q^2+3q+1
       170: q^3+4q^2+3q+1
       171: 3q^2+3q+1
       172: q^3+3q^2+3q+1
       173: q^3+4q^2+3q+1
       174: 2q^3+4q^2+3q+1
       175: q^3+3q^2+3q+1
       176: 3q^2+3q+1
       177: 2q^3+4q^2+3q+1
       178: q^3+4q^2+3q+1
       179: 2q^3+4q^2+3q+1
       180: 2q^3+4q^2+3q+1
       181: q^3+4q^2+3q+1
       182: 3q^2+3q+1
       183: 2q^3+4q^2+3q+1
       184: q^3+4q^2+3q+1
       185: 2q^3+4q^2+3q+1
       186: q^3+4q^2+3q+1
       187: 2q^3+4q^2+3q+1
       188: 2q^3+4q^2+3q+1
       189: q^2+2q+1
       190: 3q^2+3q+1
       191: 3q^2+3q+1
       192: 3q^2+3q+1
       193: 2q^2+3q+1
       194: 2q^2+3q+1
       195: q^3+4q^2+3q+1
       196: q^3+3q^2+3q+1
       197: q^3+3q^2+3q+1
       198: 3q^2+3q+1
       199: 2q^2+3q+1
       200: 2q^2+3q+1
       201: 2q^2+3q+1
       202: 3q^2+3q+1
       203: 3q^2+3q+1
       204: 3q^2+3q+1
       205: 2q^2+3q+1
       206: 2q^2+3q+1
       207: 2q^2+3q+1
       208: q^2+3q+1
       209: 2q^2+3q+1
       210: 2q^2+3q+1
       211: 2q^2+3q+1
       212: q^3+3q^2+3q+1
       213: 2q^2+3q+1
       214: 2q^2+3q+1
       215: q^2+3q+1
       216: 2q^2+3q+1
       217: 2q^2+3q+1
       218: 2q^2+3q+1
       219: q^3+3q^2+3q+1
       220: q^2+3q+1
       221: 3q^2+3q+1
       222: q^2+3q+1
       223: 2q^2+3q+1
       224: 2q^2+3q+1
       225: q^3+3q^2+3q+1
       226: q^2+2q+1
       227: 2q^2+3q+1
       228: 3q^2+3q+1
       229: 3q^2+3q+1
       230: 3q^2+3q+1
       231: 3q^2+3q+1
       232: q^3+4q^2+3q+1
       233: q^3+4q^2+3q+1
       234: q^3+4q^2+3q+1
       235: q^3+3q^2+3q+1
       236: 3q^2+3q+1
       237: 3q^2+3q+1
       238: 2q^2+3q+1
       239: 3q^2+3q+1
       240: 3q^2+3q+1
       241: 3q^2+3q+1
       242: 2q^3+4q^2+3q+1
       243: 2q^2+3q+1
       244: 3q^2+3q+1
       245: 2q^2+3q+1
       246: q^3+3q^2+3q+1
       247: q^3+3q^2+3q+1
       248: 2q^2+3q+1
       249: 3q^2+3q+1
       250: 2q^2+3q+1
       251: q^3+3q^2+3q+1
       252: q^3+3q^2+3q+1
       253: q^3+4q^2+3q+1
       254: 3q^2+3q+1
       255: 2q^2+3q+1
       256: q^3+3q^2+3q+1
       257: q^3+3q^2+3q+1
       258: 3q^2+3q+1
       259: 3q^2+3q+1
       260: 3q^2+3q+1
       261: 3q^2+3q+1
       262: q^3+4q^2+3q+1
       263: q^3+4q^2+3q+1
       264: q^3+4q^2+3q+1
       265: q^3+3q^2+3q+1
       266: 3q^2+3q+1
       267: 3q^2+3q+1
       268: 2q^2+3q+1
       269: 3q^2+3q+1
       270: 3q^2+3q+1
       271: 3q^2+3q+1
       272: 2q^3+4q^2+3q+1
       273: 2q^2+3q+1
       274: 3q^2+3q+1
       275: 2q^2+3q+1
       276: q^3+3q^2+3q+1
       277: q^3+3q^2+3q+1
       278: 2q^2+3q+1
       279: 3q^2+3q+1
       280: 2q^2+3q+1
       281: q^3+3q^2+3q+1
       282: q^3+3q^2+3q+1
       283: q^3+4q^2+3q+1
       284: 3q^2+3q+1
       285: 2q^2+3q+1
       286: q^3+3q^2+3q+1
       287: q^3+3q^2+3q+1
       288: 3q^2+3q+1
       289: 3q^2+3q+1
       290: 3q^2+3q+1
       291: q^3+4q^2+3q+1
       292: q^3+4q^2+3q+1
       293: q^3+4q^2+3q+1
       294: 2q^3+4q^2+3q+1
       295: 3q^2+3q+1
       296: 3q^2+3q+1
       297: 3q^2+3q+1
       298: 2q^3+4q^2+3q+1
       299: 2q^3+4q^2+3q+1
       300: q^3+4q^2+3q+1
       301: 3q^2+3q+1
       302: q^3+3q^2+3q+1
       303: q^3+4q^2+3q+1
       304: 3q^2+3q+1
       305: q^3+3q^2+3q+1
       306: q^3+4q^2+3q+1
       307: 2q^3+4q^2+3q+1
       308: q^3+3q^2+3q+1
       309: q^2+2q+1
       310: q^2+2q+1
       311: 3q^2+3q+1
       312: 2q^2+3q+1
       313: 2q^2+3q+1
       314: 2q^2+3q+1
       315: 2q^2+3q+1
       316: q^2+3q+1
       317: q^3+3q^2+3q+1
       318: q^2+2q+1
       319: 2q+1
       320: 2q^2+3q+1
       321: 2q^2+3q+1
       322: 2q^2+3q+1
       323: q^2+3q+1
       324: q^2+3q+1
       325: 3q^2+3q+1
       326: q^2+3q+1
       327: 2q^2+3q+1
       328: 2q^2+3q+1
       329: q^2+3q+1
       330: q^2+3q+1
       331: q^2+3q+1
       332: 2q^2+3q+1
       333: 2q^2+3q+1
       334: 2q^2+3q+1
       335: 2q^2+3q+1
       336: 2q^2+3q+1
       337: q^2+3q+1
       338: q^2+3q+1
       339: q^2+3q+1
       340: 2q^2+3q+1
       341: 2q^2+3q+1
       342: 2q^2+3q+1
       343: 2q^2+3q+1
       344: q^2+3q+1
       345: q^2+3q+1
       346: 3q+1
       347: q^2+3q+1
       348: q^2+3q+1
       349: q^2+3q+1
       350: 2q^2+3q+1
       351: q^2+3q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q^2+3q+1
       355: 2q^2+3q+1
       356: q^2+2q+1
       357: 3q^2+3q+1
       358: 3q^2+3q+1
       359: 3q^2+3q+1
       360: 2q^2+3q+1
       361: 2q^2+3q+1
       362: q^3+4q^2+3q+1
       363: q^3+3q^2+3q+1
       364: q^3+3q^2+3q+1
       365: 3q^2+3q+1
       366: 2q^2+3q+1
       367: 2q^2+3q+1
       368: 2q^2+3q+1
       369: 3q^2+3q+1
       370: 3q^2+3q+1
       371: 3q^2+3q+1
       372: 2q^2+3q+1
       373: 2q^2+3q+1
       374: 2q^2+3q+1
       375: q^2+3q+1
       376: 2q^2+3q+1
       377: 2q^2+3q+1
       378: 2q^2+3q+1
       379: q^3+3q^2+3q+1
       380: 2q^2+3q+1
       381: 2q^2+3q+1
       382: q^2+3q+1
       383: 2q^2+3q+1
       384: 2q^2+3q+1
       385: 2q^2+3q+1
       386: q^3+3q^2+3q+1
       387: q^2+3q+1
       388: 3q^2+3q+1
       389: q^2+3q+1
       390: 2q^2+3q+1
       391: 2q^2+3q+1
       392: q^3+3q^2+3q+1
       393: q^2+2q+1
       394: 2q^2+3q+1
       395: q^2+2q+1
       396: 3q^2+3q+1
       397: 3q^2+3q+1
       398: 3q^2+3q+1
       399: 2q^2+3q+1
       400: 2q^2+3q+1
       401: q^3+4q^2+3q+1
       402: q^3+3q^2+3q+1
       403: q^3+3q^2+3q+1
       404: 3q^2+3q+1
       405: 2q^2+3q+1
       406: 2q^2+3q+1
       407: 2q^2+3q+1
       408: 3q^2+3q+1
       409: 3q^2+3q+1
       410: 3q^2+3q+1
       411: 2q^2+3q+1
       412: 2q^2+3q+1
       413: 2q^2+3q+1
       414: q^2+3q+1
       415: 2q^2+3q+1
       416: 2q^2+3q+1
       417: 2q^2+3q+1
       418: q^3+3q^2+3q+1
       419: 2q^2+3q+1
       420: 2q^2+3q+1
       421: q^2+3q+1
       422: 2q^2+3q+1
       423: 2q^2+3q+1
       424: 2q^2+3q+1
       425: q^3+3q^2+3q+1
       426: q^2+3q+1
       427: 3q^2+3q+1
       428: q^2+3q+1
       429: 2q^2+3q+1
       430: 2q^2+3q+1
       431: q^3+3q^2+3q+1
       432: q^2+2q+1
       433: 2q^2+3q+1
       434: 3q^2+3q+1
       435: 3q^2+3q+1
       436: 3q^2+3q+1
       437: 3q^2+3q+1
       438: q^3+4q^2+3q+1
       439: q^3+4q^2+3q+1
       440: q^3+4q^2+3q+1
       441: q^3+3q^2+3q+1
       442: 3q^2+3q+1
       443: 3q^2+3q+1
       444: 2q^2+3q+1
       445: 3q^2+3q+1
       446: 3q^2+3q+1
       447: 3q^2+3q+1
       448: 2q^3+4q^2+3q+1
       449: 2q^2+3q+1
       450: 3q^2+3q+1
       451: 2q^2+3q+1
       452: q^3+3q^2+3q+1
       453: q^3+3q^2+3q+1
       454: 2q^2+3q+1
       455: 3q^2+3q+1
       456: 2q^2+3q+1
       457: q^3+3q^2+3q+1
       458: q^3+3q^2+3q+1
       459: q^3+4q^2+3q+1
       460: 3q^2+3q+1
       461: 2q^2+3q+1
       462: q^3+3q^2+3q+1
       463: q^3+3q^2+3q+1
       465: q^2+2q+1
       466: 2q+1
       467: 2q^2+3q+1
       468: 2q^2+3q+1
       469: q^2+3q+1
       470: q^2+3q+1
       471: q^2+3q+1
       472: q^2+2q+1
       473: 2q+1
       474: 2q+1
       475: 2q^2+3q+1
       476: q^2+3q+1
       477: q^2+3q+1
       478: q^2+3q+1
       479: q^2+3q+1
       480: 3q+1
       481: q^2+3q+1
       482: 2q+1
       483: 2q+1
       484: q^2+3q+1
       485: q^2+3q+1
       486: q^2+3q+1
       487: q^2+3q+1
       488: 2q+1
       489: 2q^2+3q+1
       490: q^2+3q+1
       491: 2q^2+3q+1
       492: 2q+1
       493: q^2+3q+1
       494: q^2+3q+1
       495: q^2+3q+1
       496: 2q+1
       497: q^2+3q+1
       498: 2q^2+3q+1
       499: q^2+3q+1
       500: 2q^2+3q+1
       501: q^2+3q+1
       502: 3q+1
       503: 3q+1
       504: 3q+1
       505: q^2+3q+1
       506: q^2+3q+1
       507: q^2+3q+1
       508: 2q^2+3q+1
       509: q^2+3q+1
       510: q^2+3q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: 2q+1
       515: 2q^2+3q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: 3q^2+3q+1
       519: 2q^2+3q+1
       520: 2q^2+3q+1
       521: 2q^2+3q+1
       522: 2q^2+3q+1
       523: q^2+3q+1
       524: q^3+3q^2+3q+1
       525: q^2+2q+1
       526: 2q+1
       527: 2q^2+3q+1
       528: 2q^2+3q+1
       529: 2q^2+3q+1
       530: q^2+3q+1
       531: q^2+3q+1
       532: 3q^2+3q+1
       533: q^2+3q+1
       534: 2q^2+3q+1
       535: 2q^2+3q+1
       536: q^2+3q+1
       537: q^2+3q+1
       538: q^2+3q+1
       539: 2q^2+3q+1
       540: 2q^2+3q+1
       541: 2q^2+3q+1
       542: 2q^2+3q+1
       543: 2q^2+3q+1
       544: q^2+3q+1
       545: q^2+3q+1
       546: q^2+3q+1
       547: 2q^2+3q+1
       548: 2q^2+3q+1
       549: 2q^2+3q+1
       550: 2q^2+3q+1
       551: q^2+3q+1
       552: q^2+3q+1
       553: 3q+1
       554: q^2+3q+1
       555: q^2+3q+1
       556: q^2+3q+1
       557: 2q^2+3q+1
       558: q^2+3q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q^2+3q+1
       562: 2q^2+3q+1
       563: q^2+2q+1
       564: q^2+2q+1
       565: 3q^2+3q+1
       566: 2q^2+3q+1
       567: 2q^2+3q+1
       568: 2q^2+3q+1
       569: 2q^2+3q+1
       570: q^2+3q+1
       571: q^3+3q^2+3q+1
       572: q^2+2q+1
       573: 2q+1
       574: 2q^2+3q+1
       575: 2q^2+3q+1
       576: 2q^2+3q+1
       577: q^2+3q+1
       578: q^2+3q+1
       579: 3q^2+3q+1
       580: q^2+3q+1
       581: 2q^2+3q+1
       582: 2q^2+3q+1
       583: q^2+3q+1
       584: q^2+3q+1
       585: q^2+3q+1
       586: 2q^2+3q+1
       587: 2q^2+3q+1
       588: 2q^2+3q+1
       589: 2q^2+3q+1
       590: 2q^2+3q+1
       591: q^2+3q+1
       592: q^2+3q+1
       593: q^2+3q+1
       594: 2q^2+3q+1
       595: 2q^2+3q+1
       596: 2q^2+3q+1
       597: 2q^2+3q+1
       598: q^2+3q+1
       599: q^2+3q+1
       600: 3q+1
       601: q^2+3q+1
       602: q^2+3q+1
       603: q^2+3q+1
       604: 2q^2+3q+1
       605: q^2+3q+1
       606: q^2+2q+1
       607: 2q+1
       608: 2q^2+3q+1
       609: 2q^2+3q+1
       610: q^2+2q+1
       611: 3q^2+3q+1
       612: 3q^2+3q+1
       613: 3q^2+3q+1
       614: 2q^2+3q+1
       615: 2q^2+3q+1
       616: q^3+4q^2+3q+1
       617: q^3+3q^2+3q+1
       618: q^3+3q^2+3q+1
       619: 3q^2+3q+1
       620: 2q^2+3q+1
       621: 2q^2+3q+1
       622: 2q^2+3q+1
       623: 3q^2+3q+1
       624: 3q^2+3q+1
       625: 3q^2+3q+1
       626: 2q^2+3q+1
       627: 2q^2+3q+1
       628: 2q^2+3q+1
       629: q^2+3q+1
       630: 2q^2+3q+1
       631: 2q^2+3q+1
       632: 2q^2+3q+1
       633: q^3+3q^2+3q+1
       634: 2q^2+3q+1
       635: 2q^2+3q+1
       636: q^2+3q+1
       637: 2q^2+3q+1
       638: 2q^2+3q+1
       639: 2q^2+3q+1
       640: q^3+3q^2+3q+1
       641: q^2+3q+1
       642: 3q^2+3q+1
       643: q^2+3q+1
       644: 2q^2+3q+1
       645: 2q^2+3q+1
       646: q^3+3q^2+3q+1
       647: q^2+2q+1
       648: 2q^2+3q+1
       650: 2q+1
       651: 2q+1
       652: 2q+1
       653: q^2+3q+1
       654: q^2+3q+1
       655: q^2+3q+1
       656: 2q+1
       658: 2q+1
       659: 2q+1
       660: q^2+3q+1
       661: q^2+3q+1
       662: 3q+1
       663: 3q+1
       664: 3q+1
       665: 2q+1
       666: 2q+1
       667: 2q+1
       668: q^2+3q+1
       669: q^2+3q+1
       670: q^2+3q+1
       671: 2q+1
       672: 2q+1
       673: 2q+1
       674: q^2+3q+1
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: q^2+3q+1
       679: 2q+1
       680: 2q+1
       681: q^2+3q+1
       682: q^2+3q+1
       683: 2q+1
       684: q^2+3q+1
       685: 2q+1
       686: 2q+1
       687: 3q+1
       688: 3q+1
       689: 3q+1
       690: 2q+1
       691: 2q+1
       692: q^2+3q+1
       693: q^2+3q+1
       694: 2q^2+3q+1
       695: q^2+3q+1
       696: 2q+1
       697: 2q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: 2q+1
       702: q^2+2q+1
       704: q^2+2q+1
       705: 2q+1
       706: 2q^2+3q+1
       707: 2q^2+3q+1
       708: q^2+3q+1
       709: q^2+3q+1
       710: q^2+3q+1
       711: q^2+2q+1
       712: 2q+1
       713: 2q+1
       714: 2q^2+3q+1
       715: q^2+3q+1
       716: q^2+3q+1
       717: q^2+3q+1
       718: q^2+3q+1
       719: 3q+1
       720: q^2+3q+1
       721: 2q+1
       722: 2q+1
       723: q^2+3q+1
       724: q^2+3q+1
       725: q^2+3q+1
       726: q^2+3q+1
       727: 2q+1
       728: 2q^2+3q+1
       729: q^2+3q+1
       730: 2q^2+3q+1
       731: 2q+1
       732: q^2+3q+1
       733: q^2+3q+1
       734: q^2+3q+1
       735: 2q+1
       736: q^2+3q+1
       737: 2q^2+3q+1
       738: q^2+3q+1
       739: 2q^2+3q+1
       740: q^2+3q+1
       741: 3q+1
       742: 3q+1
       743: 3q+1
       744: q^2+3q+1
       745: q^2+3q+1
       746: q^2+3q+1
       747: 2q^2+3q+1
       748: q^2+3q+1
       749: q^2+3q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: 2q+1
       754: 2q^2+3q+1
       756: q^2+2q+1
       757: 2q+1
       758: 2q^2+3q+1
       759: 2q^2+3q+1
       760: q^2+3q+1
       761: q^2+3q+1
       762: q^2+3q+1
       763: q^2+2q+1
       764: 2q+1
       765: 2q+1
       766: 2q^2+3q+1
       767: q^2+3q+1
       768: q^2+3q+1
       769: q^2+3q+1
       770: q^2+3q+1
       771: 3q+1
       772: q^2+3q+1
       773: 2q+1
       774: 2q+1
       775: q^2+3q+1
       776: q^2+3q+1
       777: q^2+3q+1
       778: q^2+3q+1
       779: 2q+1
       780: 2q^2+3q+1
       781: q^2+3q+1
       782: 2q^2+3q+1
       783: 2q+1
       784: q^2+3q+1
       785: q^2+3q+1
       786: q^2+3q+1
       787: 2q+1
       788: q^2+3q+1
       789: 2q^2+3q+1
       790: q^2+3q+1
       791: 2q^2+3q+1
       792: q^2+3q+1
       793: 3q+1
       794: 3q+1
       795: 3q+1
       796: q^2+3q+1
       797: q^2+3q+1
       798: q^2+3q+1
       799: 2q^2+3q+1
       800: q^2+3q+1
       801: q^2+3q+1
       802: 2q+1
       803: 2q+1
       804: 2q+1
       805: 2q+1
       806: 2q^2+3q+1
       807: q^2+2q+1
       808: q^2+2q+1
       809: 3q^2+3q+1
       810: 2q^2+3q+1
       811: 2q^2+3q+1
       812: 2q^2+3q+1
       813: 2q^2+3q+1
       814: q^2+3q+1
       815: q^3+3q^2+3q+1
       816: q^2+2q+1
       817: 2q+1
       818: 2q^2+3q+1
       819: 2q^2+3q+1
       820: 2q^2+3q+1
       821: q^2+3q+1
       822: q^2+3q+1
       823: 3q^2+3q+1
       824: q^2+3q+1
       825: 2q^2+3q+1
       826: 2q^2+3q+1
       827: q^2+3q+1
       828: q^2+3q+1
       829: q^2+3q+1
       830: 2q^2+3q+1
       831: 2q^2+3q+1
       832: 2q^2+3q+1
       833: 2q^2+3q+1
       834: 2q^2+3q+1
       835: q^2+3q+1
       836: q^2+3q+1
       837: q^2+3q+1
       838: 2q^2+3q+1
       839: 2q^2+3q+1
       840: 2q^2+3q+1
       841: 2q^2+3q+1
       842: q^2+3q+1
       843: q^2+3q+1
       844: 3q+1
       845: q^2+3q+1
       846: q^2+3q+1
       847: q^2+3q+1
       848: 2q^2+3q+1
       849: q^2+3q+1
       850: q^2+2q+1
       851: 2q+1
       852: 2q^2+3q+1
       853: 2q^2+3q+1
       855: 2q+1
       856: 2q+1
       857: 2q+1
       858: q^2+3q+1
       859: 2q+1
       860: 2q+1
       862: 2q+1
       863: 2q+1
       864: 2q+1
       865: 3q+1
       866: 3q+1
       867: 3q+1
       868: 2q+1
       870: 2q+1
       871: q+1
       872: q^2+3q+1
       873: 2q+1
       874: 2q+1
       875: 2q+1
       876: 2q+1
       877: 2q+1
       879: 2q+1
       880: q+1
       881: 2q+1
       882: q^2+3q+1
       883: 2q+1
       884: 2q+1
       885: 2q+1
       886: 2q+1
       887: 2q+1
       888: 2q+1
       889: 3q+1
       890: 2q+1
       891: 2q+1
       892: 2q+1
       893: 2q+1
       894: q+1
       895: q^2+3q+1
       896: 2q+1
       897: q+1
       898: 2q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: q+1
       905: q^2+2q+1
       907: 2q+1
       908: 2q+1
       909: 2q+1
       910: q^2+3q+1
       911: q^2+3q+1
       912: q^2+3q+1
       913: 2q+1
       915: 2q+1
       916: 2q+1
       917: q^2+3q+1
       918: q^2+3q+1
       919: 3q+1
       920: 3q+1
       921: 3q+1
       922: 2q+1
       923: 2q+1
       924: 2q+1
       925: q^2+3q+1
       926: q^2+3q+1
       927: q^2+3q+1
       928: 2q+1
       929: 2q+1
       930: 2q+1
       931: q^2+3q+1
       932: 2q+1
       933: 2q+1
       934: 2q+1
       935: q^2+3q+1
       936: 2q+1
       937: 2q+1
       938: q^2+3q+1
       939: q^2+3q+1
       940: 2q+1
       941: q^2+3q+1
       942: 2q+1
       943: 2q+1
       944: 3q+1
       945: 3q+1
       946: 3q+1
       947: 2q+1
       948: 2q+1
       949: q^2+3q+1
       950: q^2+3q+1
       951: 2q^2+3q+1
       952: q^2+3q+1
       953: 2q+1
       954: 2q+1
       955: 2q+1
       956: 2q+1
       957: 2q+1
       958: 2q+1
       959: q^2+2q+1
       961: 2q+1
       962: 2q+1
       963: 2q+1
       964: q^2+3q+1
       965: q^2+3q+1
       966: q^2+3q+1
       967: 2q+1
       969: 2q+1
       970: 2q+1
       971: q^2+3q+1
       972: q^2+3q+1
       973: 3q+1
       974: 3q+1
       975: 3q+1
       976: 2q+1
       977: 2q+1
       978: 2q+1
       979: q^2+3q+1
       980: q^2+3q+1
       981: q^2+3q+1
       982: 2q+1
       983: 2q+1
       984: 2q+1
       985: q^2+3q+1
       986: 2q+1
       987: 2q+1
       988: 2q+1
       989: q^2+3q+1
       990: 2q+1
       991: 2q+1
       992: q^2+3q+1
       993: q^2+3q+1
       994: 2q+1
       995: q^2+3q+1
       996: 2q+1
       997: 2q+1
       998: 3q+1
       999: 3q+1
      1000: 3q+1
      1001: 2q+1
      1002: 2q+1
      1003: q^2+3q+1
      1004: q^2+3q+1
      1005: 2q^2+3q+1
      1006: q^2+3q+1
      1007: 2q+1
      1008: 2q+1
      1009: 2q+1
      1010: 2q+1
      1011: 2q+1
      1012: 2q+1
      1013: q^2+2q+1
      1015: q^2+2q+1
      1016: 2q+1
      1017: 2q^2+3q+1
      1018: 2q^2+3q+1
      1019: q^2+3q+1
      1020: q^2+3q+1
      1021: q^2+3q+1
      1022: q^2+2q+1
      1023: 2q+1
      1024: 2q+1
      1025: 2q^2+3q+1
      1026: q^2+3q+1
      1027: q^2+3q+1
      1028: q^2+3q+1
      1029: q^2+3q+1
      1030: 3q+1
      1031: q^2+3q+1
      1032: 2q+1
      1033: 2q+1
      1034: q^2+3q+1
      1035: q^2+3q+1
      1036: q^2+3q+1
      1037: q^2+3q+1
      1038: 2q+1
      1039: 2q^2+3q+1
      1040: q^2+3q+1
      1041: 2q^2+3q+1
      1042: 2q+1
      1043: q^2+3q+1
      1044: q^2+3q+1
      1045: q^2+3q+1
      1046: 2q+1
      1047: q^2+3q+1
      1048: 2q^2+3q+1
      1049: q^2+3q+1
      1050: 2q^2+3q+1
      1051: q^2+3q+1
      1052: 3q+1
      1053: 3q+1
      1054: 3q+1
      1055: q^2+3q+1
      1056: q^2+3q+1
      1057: q^2+3q+1
      1058: 2q^2+3q+1
      1059: q^2+3q+1
      1060: q^2+3q+1
      1061: 2q+1
      1062: 2q+1
      1063: 2q+1
      1064: 2q+1
      1065: 2q^2+3q+1
      1068: 2q+1
      1069: q+1
      1070: 2q+1
      1072: 2q+1
      1073: 2q+1
      1074: 2q+1
      1075: 3q+1
      1076: 2q+1
      1077: 2q+1
      1079: q+1
      1080: q+1
      1081: q+1
      1082: 2q+1
      1083: 2q+1
      1084: 2q+1
      1085: q+1
      1087: q+1
      1088: q+1
      1089: q+1
      1090: 2q+1
      1091: 2q+1
      1092: 2q+1
      1093: q+1
      1095: 2q+1
      1096: 1
      1097: 2q+1
      1098: 2q+1
      1099: q+1
      1100: q+1
      1101: q+1
      1102: 2q+1
      1103: q+1
      1104: q+1
      1105: 2q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1111: q+1
      1112: q+1
      1114: 2q+1
      1115: 2q+1
      1116: 2q+1
      1117: q^2+3q+1
      1118: 2q+1
      1119: 2q+1
      1121: 2q+1
      1122: 2q+1
      1123: 2q+1
      1124: 3q+1
      1125: 3q+1
      1126: 3q+1
      1127: 2q+1
      1129: 2q+1
      1130: q+1
      1131: q^2+3q+1
      1132: 2q+1
      1133: 2q+1
      1134: 2q+1
      1135: 2q+1
      1136: 2q+1
      1138: 2q+1
      1139: q+1
      1140: 2q+1
      1141: q^2+3q+1
      1142: 2q+1
      1143: 2q+1
      1144: 2q+1
      1145: 2q+1
      1146: 2q+1
      1147: 2q+1
      1148: 3q+1
      1149: 2q+1
      1150: 2q+1
      1151: 2q+1
      1152: 2q+1
      1153: q+1
      1154: q^2+3q+1
      1155: 2q+1
      1156: q+1
      1157: 2q+1
      1158: 2q+1
      1159: 2q+1
      1160: q+1
      1161: q+1
      1162: 2q+1
      1163: q+1
      1164: q^2+2q+1
      1166: 2q+1
      1167: 2q+1
      1168: 2q+1
      1169: q^2+3q+1
      1170: 2q+1
      1171: 2q+1
      1173: 2q+1
      1174: 2q+1
      1175: 2q+1
      1176: 3q+1
      1177: 3q+1
      1178: 3q+1
      1179: 2q+1
      1181: 2q+1
      1182: q+1
      1183: q^2+3q+1
      1184: 2q+1
      1185: 2q+1
      1186: 2q+1
      1187: 2q+1
      1188: 2q+1
      1190: 2q+1
      1191: q+1
      1192: 2q+1
      1193: q^2+3q+1
      1194: 2q+1
      1195: 2q+1
      1196: 2q+1
      1197: 2q+1
      1198: 2q+1
      1199: 2q+1
      1200: 3q+1
      1201: 2q+1
      1202: 2q+1
      1203: 2q+1
      1204: 2q+1
      1205: q+1
      1206: q^2+3q+1
      1207: 2q+1
      1208: q+1
      1209: 2q+1
      1210: 2q+1
      1211: 2q+1
      1212: q+1
      1213: q+1
      1214: 2q+1
      1215: q+1
      1216: q^2+2q+1
      1218: 2q+1
      1219: 2q+1
      1220: 2q+1
      1221: q^2+3q+1
      1222: q^2+3q+1
      1223: q^2+3q+1
      1224: 2q+1
      1226: 2q+1
      1227: 2q+1
      1228: q^2+3q+1
      1229: q^2+3q+1
      1230: 3q+1
      1231: 3q+1
      1232: 3q+1
      1233: 2q+1
      1234: 2q+1
      1235: 2q+1
      1236: q^2+3q+1
      1237: q^2+3q+1
      1238: q^2+3q+1
      1239: 2q+1
      1240: 2q+1
      1241: 2q+1
      1242: q^2+3q+1
      1243: 2q+1
      1244: 2q+1
      1245: 2q+1
      1246: q^2+3q+1
      1247: 2q+1
      1248: 2q+1
      1249: q^2+3q+1
      1250: q^2+3q+1
      1251: 2q+1
      1252: q^2+3q+1
      1253: 2q+1
      1254: 2q+1
      1255: 3q+1
      1256: 3q+1
      1257: 3q+1
      1258: 2q+1
      1259: 2q+1
      1260: q^2+3q+1
      1261: q^2+3q+1
      1262: 2q^2+3q+1
      1263: q^2+3q+1
      1264: 2q+1
      1265: 2q+1
      1266: 2q+1
      1267: 2q+1
      1268: 2q+1
      1269: 2q+1
      1270: q^2+2q+1
      1272: q+1
      1273: q+1
      1276: 2q+1
      1277: 1
      1278: 2q+1
      1280: q+1
      1281: q+1
      1282: q+1
      1283: 2q+1
      1284: q+1
      1285: q+1
      1287: q+1
      1288: q+1
      1289: q+1
      1290: 2q+1
      1291: q+1
      1292: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: q+1
      1298: q+1
      1299: q+1
      1300: 1
      1302: q+1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1309: q+1
      1312: 2q+1
      1313: q+1
      1314: 2q+1
      1316: 2q+1
      1317: 2q+1
      1318: 2q+1
      1319: 3q+1
      1320: 2q+1
      1321: 2q+1
      1323: q+1
      1324: q+1
      1325: q+1
      1326: 2q+1
      1327: 2q+1
      1328: 2q+1
      1329: q+1
      1331: q+1
      1332: q+1
      1333: q+1
      1334: 2q+1
      1335: 2q+1
      1336: 2q+1
      1337: q+1
      1339: 2q+1
      1340: 1
      1341: 2q+1
      1342: 2q+1
      1343: q+1
      1344: q+1
      1345: q+1
      1346: 2q+1
      1347: q+1
      1348: q+1
      1349: 2q+1
      1350: q+1
      1351: q+1
      1352: q+1
      1353: q+1
      1354: 1
      1355: q+1
      1356: q+1
      1359: 2q+1
      1360: q+1
      1361: 2q+1
      1363: 2q+1
      1364: 2q+1
      1365: 2q+1
      1366: 3q+1
      1367: 2q+1
      1368: 2q+1
      1370: q+1
      1371: q+1
      1372: q+1
      1373: 2q+1
      1374: 2q+1
      1375: 2q+1
      1376: q+1
      1378: q+1
      1379: q+1
      1380: q+1
      1381: 2q+1
      1382: 2q+1
      1383: 2q+1
      1384: q+1
      1386: 2q+1
      1387: 1
      1388: 2q+1
      1389: 2q+1
      1390: q+1
      1391: q+1
      1392: q+1
      1393: 2q+1
      1394: q+1
      1395: q+1
      1396: 2q+1
      1397: q+1
      1398: q+1
      1399: q+1
      1400: q+1
      1401: 1
      1402: q+1
      1403: q+1
      1405: 2q+1
      1406: 2q+1
      1407: 2q+1
      1408: q^2+3q+1
      1409: 2q+1
      1410: 2q+1
      1412: 2q+1
      1413: 2q+1
      1414: 2q+1
      1415: 3q+1
      1416: 3q+1
      1417: 3q+1
      1418: 2q+1
      1420: 2q+1
      1421: q+1
      1422: q^2+3q+1
      1423: 2q+1
      1424: 2q+1
      1425: 2q+1
      1426: 2q+1
      1427: 2q+1
      1429: 2q+1
      1430: q+1
      1431: 2q+1
      1432: q^2+3q+1
      1433: 2q+1
      1434: 2q+1
      1435: 2q+1
      1436: 2q+1
      1437: 2q+1
      1438: 2q+1
      1439: 3q+1
      1440: 2q+1
      1441: 2q+1
      1442: 2q+1
      1443: 2q+1
      1444: q+1
      1445: q^2+3q+1
      1446: 2q+1
      1447: q+1
      1448: 2q+1
      1449: 2q+1
      1450: 2q+1
      1451: q+1
      1452: q+1
      1453: 2q+1
      1454: q+1
      1455: q^2+2q+1
      1457: q+1
      1459: 1
      1460: 1
      1463: q+1
      1464: 1
      1465: q+1
      1468: q+1
      1469: 1
      1470: q+1
      1472: 1
      1473: 1
      1474: 1
      1475: q+1
      1476: 1
      1477: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1487: q+1
      1488: q+1
      1491: 2q+1
      1492: 1
      1493: 2q+1
      1495: q+1
      1496: q+1
      1497: q+1
      1498: 2q+1
      1499: q+1
      1500: q+1
      1502: q+1
      1503: q+1
      1504: q+1
      1505: 2q+1
      1506: q+1
      1507: q+1
      1509: 1
      1510: 1
      1511: 1
      1512: q+1
      1513: q+1
      1514: q+1
      1515: 1
      1517: q+1
      1518: 1
      1519: q+1
      1520: q+1
      1521: 1
      1522: 1
      1523: 1
      1524: q+1
      1526: q+1
      1527: q+1
      1530: 2q+1
      1531: 1
      1532: 2q+1
      1534: q+1
      1535: q+1
      1536: q+1
      1537: 2q+1
      1538: q+1
      1539: q+1
      1541: q+1
      1542: q+1
      1543: q+1
      1544: 2q+1
      1545: q+1
      1546: q+1
      1548: 1
      1549: 1
      1550: 1
      1551: q+1
      1552: q+1
      1553: q+1
      1554: 1
      1556: q+1
      1557: 1
      1558: q+1
      1559: q+1
      1560: 1
      1561: 1
      1562: 1
      1563: q+1
      1566: 2q+1
      1567: q+1
      1568: 2q+1
      1570: 2q+1
      1571: 2q+1
      1572: 2q+1
      1573: 3q+1
      1574: 2q+1
      1575: 2q+1
      1577: q+1
      1578: q+1
      1579: q+1
      1580: 2q+1
      1581: 2q+1
      1582: 2q+1
      1583: q+1
      1585: q+1
      1586: q+1
      1587: q+1
      1588: 2q+1
      1589: 2q+1
      1590: 2q+1
      1591: q+1
      1593: 2q+1
      1594: 1
      1595: 2q+1
      1596: 2q+1
      1597: q+1
      1598: q+1
      1599: q+1
      1600: 2q+1
      1601: q+1
      1602: q+1
      1603: 2q+1
      1604: q+1
      1605: q+1
      1606: q+1
      1607: q+1
      1608: 1
      1609: q+1
      1610: q+1
      1613: 1
      1615: 1
      1616: 1
      1618: 1
      1619: 1
      1622: 1
      1623: 1
      1624: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1633: q+1
      1635: 1
      1636: 1
      1639: q+1
      1640: 1
      1641: q+1
      1644: q+1
      1645: 1
      1646: q+1
      1648: 1
      1649: 1
      1650: 1
      1651: q+1
      1652: 1
      1653: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1663: q+1
      1665: 1
      1666: 1
      1669: q+1
      1670: 1
      1671: q+1
      1674: q+1
      1675: 1
      1676: q+1
      1678: 1
      1679: 1
      1680: 1
      1681: q+1
      1682: 1
      1683: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1693: q+1
      1694: q+1
      1697: 2q+1
      1698: 1
      1699: 2q+1
      1701: q+1
      1702: q+1
      1703: q+1
      1704: 2q+1
      1705: q+1
      1706: q+1
      1708: q+1
      1709: q+1
      1710: q+1
      1711: 2q+1
      1712: q+1
      1713: q+1
      1715: 1
      1716: 1
      1717: 1
      1718: q+1
      1719: q+1
      1720: q+1
      1721: 1
      1723: q+1
      1724: 1
      1725: q+1
      1726: q+1
      1727: 1
      1728: 1
      1729: 1
      1730: q+1
      1733: 1
      1735: 1
      1737: 1
      1738: 1
      1741: 1
      1743: 1
      1746: 1
      1748: 1
      1749: 1
      1751: 1
      1752: 1
      1755: 1
      1756: 1
      1757: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1767: 1
      1769: 1
      1770: 1
      1772: 1
      1773: 1
      1776: 1
      1777: 1
      1778: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1787: q+1
      1789: 1
      1790: 1
      1793: q+1
      1794: 1
      1795: q+1
      1798: q+1
      1799: 1
      1800: q+1
      1802: 1
      1803: 1
      1804: 1
      1805: q+1
      1806: 1
      1807: 1
      1809: 1
      1810: 1
      1811: 1
      1812: 1
      1813: 1
      1814: 1
      1815: 1
      1819: 1
      1825: 1
      1827: 1
      1829: 1
      1830: 1
      1833: 1
      1835: 1
      1838: 1
      1840: 1
      1842: 1
      1843: 1
      1846: 1
      1848: 1
      1851: 1
      1853: 1
      1854: 1
      1856: 1
      1857: 1
      1860: 1
      1861: 1
      1862: 1
      1864: 1
      1865: 1
      1866: 1
      1867: 1
      1868: 1
      1869: 1
      1876: 1
      1883: 1
      1889: 1
      1891: 1
      1893: 1
      1894: 1
      1897: 1
      1899: 1
      1910: 1

1911:    0: q^2+2q+1
         1: q^2+2q+1
         2: q^2+2q+1
         3: q^2+2q+1
         4: q^2+2q+1
         5: q^2+2q+1
         6: q^2+2q+1
         7: q^2+2q+1
         8: 2q+1
         9: q^2+2q+1
        10: q^2+2q+1
        11: q^2+2q+1
        12: q^2+2q+1
        13: q^2+2q+1
        14: q^2+2q+1
        15: q^2+2q+1
        16: q^2+2q+1
        17: q^2+2q+1
        18: q^2+2q+1
        19: q^2+2q+1
        20: 2q+1
        21: q^2+2q+1
        22: 2q+1
        23: 2q+1
        24: 2q+1
        25: q^2+2q+1
        26: q^2+2q+1
        27: 2q+1
        28: q^2+2q+1
        29: q^2+2q+1
        30: q^2+2q+1
        31: q^2+2q+1
        32: q^2+2q+1
        33: q^2+2q+1
        34: q^2+2q+1
        35: 2q+1
        36: q^2+2q+1
        37: q^2+2q+1
        38: q^2+2q+1
        39: q^2+2q+1
        40: q^2+2q+1
        41: q^2+2q+1
        42: 2q+1
        43: q^2+2q+1
        44: q^2+2q+1
        45: q^2+2q+1
        46: q^2+2q+1
        47: q^2+2q+1
        48: q^2+2q+1
        49: q^2+2q+1
        50: 2q+1
        51: 2q+1
        52: 2q+1
        53: 2q+1
        54: 2q+1
        55: 2q+1
        56: 2q+1
        57: 2q+1
        58: q^2+2q+1
        59: 2q+1
        60: 2q+1
        61: 2q+1
        62: q^2+2q+1
        63: q^2+2q+1
        64: 2q+1
        65: q^2+2q+1
        66: q^2+2q+1
        67: 2q+1
        68: q^2+2q+1
        69: q^2+2q+1
        70: q^2+2q+1
        71: 2q+1
        72: q^2+2q+1
        73: 2q+1
        74: 2q+1
        75: 2q+1
        76: q^2+2q+1
        77: q^2+2q+1
        78: 2q+1
        79: q^2+2q+1
        80: q^2+2q+1
        81: q^2+2q+1
        82: q^2+2q+1
        83: q^2+2q+1
        84: 2q+1
        85: q^2+2q+1
        86: 2q+1
        87: 2q+1
        88: 2q+1
        89: q^2+2q+1
        90: q^2+2q+1
        91: 2q+1
        92: q^2+2q+1
        93: q^2+2q+1
        94: q^2+2q+1
        95: q^2+2q+1
        96: q^2+2q+1
        97: q^2+2q+1
        98: q^2+2q+1
        99: 2q+1
       100: q^2+2q+1
       101: q^2+2q+1
       102: q^2+2q+1
       103: q^2+2q+1
       104: 2q+1
       105: 2q+1
       106: 2q+1
       107: 2q+1
       108: 2q+1
       109: 2q+1
       110: 2q+1
       111: q+1
       112: 2q+1
       113: 2q+1
       114: 2q+1
       115: 2q+1
       116: 2q+1
       117: 2q+1
       118: 2q+1
       119: 2q+1
       120: q^2+2q+1
       121: 2q+1
       122: 2q+1
       123: 2q+1
       124: 2q+1
       125: q^2+2q+1
       126: 2q+1
       127: 2q+1
       128: 2q+1
       129: q^2+2q+1
       130: q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q+1
       135: 2q+1
       136: 2q+1
       137: 2q+1
       138: 2q+1
       139: 2q+1
       140: 2q+1
       141: 2q+1
       142: q^2+2q+1
       143: 2q+1
       144: 2q+1
       145: 2q+1
       146: q^2+2q+1
       147: q^2+2q+1
       148: 2q+1
       149: q^2+2q+1
       150: q^2+2q+1
       151: 2q+1
       152: q^2+2q+1
       153: q^2+2q+1
       154: q^2+2q+1
       155: 2q+1
       156: 2q+1
       157: 2q+1
       158: 2q+1
       159: 2q+1
       160: 2q+1
       161: 2q+1
       162: 2q+1
       163: q^2+2q+1
       164: 2q+1
       165: 2q+1
       166: 2q+1
       167: q^2+2q+1
       168: q^2+2q+1
       169: 2q+1
       170: q^2+2q+1
       171: q^2+2q+1
       172: 2q+1
       173: q^2+2q+1
       174: q^2+2q+1
       175: q^2+2q+1
       176: 2q+1
       177: q^2+2q+1
       178: 2q+1
       179: 2q+1
       180: 2q+1
       181: q^2+2q+1
       182: q^2+2q+1
       183: 2q+1
       184: q^2+2q+1
       185: q^2+2q+1
       186: q^2+2q+1
       187: q^2+2q+1
       188: q^2+2q+1
       189: q+1
       190: 2q+1
       191: 2q+1
       192: 2q+1
       193: q+1
       194: q+1
       195: 2q+1
       196: q+1
       197: q+1
       198: 2q+1
       199: 2q+1
       200: 2q+1
       201: 2q+1
       202: 2q+1
       203: 2q+1
       204: 2q+1
       205: q+1
       206: 2q+1
       207: 2q+1
       208: 2q+1
       209: 2q+1
       210: 2q+1
       211: 2q+1
       212: 2q+1
       213: 2q+1
       214: 2q+1
       215: 2q+1
       216: 2q+1
       217: 2q+1
       218: 2q+1
       219: 2q+1
       220: 2q+1
       221: q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 2q+1
       229: 2q+1
       230: 2q+1
       231: 2q+1
       232: 2q+1
       233: 2q+1
       234: 2q+1
       235: q+1
       236: 2q+1
       237: 2q+1
       238: 2q+1
       239: 2q+1
       240: 2q+1
       241: 2q+1
       242: 2q+1
       243: 2q+1
       244: q^2+2q+1
       245: 2q+1
       246: 2q+1
       247: 2q+1
       248: 2q+1
       249: q^2+2q+1
       250: 2q+1
       251: 2q+1
       252: 2q+1
       253: q^2+2q+1
       254: q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q+1
       259: 2q+1
       260: 2q+1
       261: 2q+1
       262: 2q+1
       263: 2q+1
       264: 2q+1
       265: q+1
       266: 2q+1
       267: 2q+1
       268: 2q+1
       269: 2q+1
       270: 2q+1
       271: 2q+1
       272: 2q+1
       273: 2q+1
       274: q^2+2q+1
       275: 2q+1
       276: 2q+1
       277: 2q+1
       278: 2q+1
       279: q^2+2q+1
       280: 2q+1
       281: 2q+1
       282: 2q+1
       283: q^2+2q+1
       284: q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q+1
       289: 2q+1
       290: 2q+1
       291: 2q+1
       292: 2q+1
       293: 2q+1
       294: 2q+1
       295: 2q+1
       296: q^2+2q+1
       297: 2q+1
       298: 2q+1
       299: 2q+1
       300: q^2+2q+1
       301: q^2+2q+1
       302: 2q+1
       303: q^2+2q+1
       304: q^2+2q+1
       305: 2q+1
       306: q^2+2q+1
       307: q^2+2q+1
       308: q^2+2q+1
       309: q+1
       310: q+1
       311: 2q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: 1
       317: q+1
       318: q+1
       319: q+1
       320: 2q+1
       321: 2q+1
       322: 2q+1
       323: q+1
       324: q+1
       325: 2q+1
       326: q+1
       327: q+1
       328: 2q+1
       329: 2q+1
       330: 2q+1
       331: 2q+1
       332: 2q+1
       333: 2q+1
       334: 2q+1
       335: q+1
       336: 2q+1
       337: 2q+1
       338: 2q+1
       339: 2q+1
       340: 2q+1
       341: 2q+1
       342: 2q+1
       343: q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       356: q+1
       357: 2q+1
       358: 2q+1
       359: 2q+1
       360: q+1
       361: q+1
       362: 2q+1
       363: q+1
       364: q+1
       365: 2q+1
       366: 2q+1
       367: 2q+1
       368: 2q+1
       369: 2q+1
       370: 2q+1
       371: 2q+1
       372: q+1
       373: 2q+1
       374: 2q+1
       375: 2q+1
       376: 2q+1
       377: 2q+1
       378: 2q+1
       379: 2q+1
       380: 2q+1
       381: 2q+1
       382: 2q+1
       383: 2q+1
       384: 2q+1
       385: 2q+1
       386: 2q+1
       387: 2q+1
       388: q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: 2q+1
       395: q+1
       396: 2q+1
       397: 2q+1
       398: 2q+1
       399: q+1
       400: q+1
       401: 2q+1
       402: q+1
       403: q+1
       404: 2q+1
       405: 2q+1
       406: 2q+1
       407: 2q+1
       408: 2q+1
       409: 2q+1
       410: 2q+1
       411: q+1
       412: 2q+1
       413: 2q+1
       414: 2q+1
       415: 2q+1
       416: 2q+1
       417: 2q+1
       418: 2q+1
       419: 2q+1
       420: 2q+1
       421: 2q+1
       422: 2q+1
       423: 2q+1
       424: 2q+1
       425: 2q+1
       426: 2q+1
       427: q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: 2q+1
       434: 2q+1
       435: 2q+1
       436: 2q+1
       437: 2q+1
       438: 2q+1
       439: 2q+1
       440: 2q+1
       441: q+1
       442: 2q+1
       443: 2q+1
       444: 2q+1
       445: 2q+1
       446: 2q+1
       447: 2q+1
       448: 2q+1
       449: 2q+1
       450: q^2+2q+1
       451: 2q+1
       452: 2q+1
       453: 2q+1
       454: 2q+1
       455: q^2+2q+1
       456: 2q+1
       457: 2q+1
       458: 2q+1
       459: q^2+2q+1
       460: q^2+2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q+1
       465: q+1
       466: 1
       467: q+1
       468: q+1
       469: 1
       470: 1
       471: 1
       472: q+1
       473: q+1
       474: q+1
       475: 2q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: 1
       481: q+1
       482: q+1
       483: q+1
       484: 2q+1
       485: 2q+1
       486: 2q+1
       487: q+1
       488: q+1
       489: 2q+1
       490: q+1
       491: q+1
       492: q+1
       493: 2q+1
       494: 2q+1
       495: 2q+1
       496: q+1
       497: q+1
       498: 2q+1
       499: q+1
       500: q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: q+1
       509: 2q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: q+1
       517: q+1
       518: 2q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: 1
       524: q+1
       525: q+1
       526: q+1
       527: 2q+1
       528: 2q+1
       529: 2q+1
       530: q+1
       531: q+1
       532: 2q+1
       533: q+1
       534: q+1
       535: 2q+1
       536: 2q+1
       537: 2q+1
       538: 2q+1
       539: 2q+1
       540: 2q+1
       541: 2q+1
       542: q+1
       543: 2q+1
       544: 2q+1
       545: 2q+1
       546: 2q+1
       547: 2q+1
       548: 2q+1
       549: 2q+1
       550: q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 2q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q+1
       562: 2q+1
       563: q+1
       564: q+1
       565: 2q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: 1
       571: q+1
       572: q+1
       573: q+1
       574: 2q+1
       575: 2q+1
       576: 2q+1
       577: q+1
       578: q+1
       579: 2q+1
       580: q+1
       581: q+1
       582: 2q+1
       583: 2q+1
       584: 2q+1
       585: 2q+1
       586: 2q+1
       587: 2q+1
       588: 2q+1
       589: q+1
       590: 2q+1
       591: 2q+1
       592: 2q+1
       593: 2q+1
       594: 2q+1
       595: 2q+1
       596: 2q+1
       597: q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 2q+1
       606: q^2+2q+1
       607: 2q+1
       608: 2q+1
       609: 2q+1
       610: q+1
       611: 2q+1
       612: 2q+1
       613: 2q+1
       614: q+1
       615: q+1
       616: 2q+1
       617: q+1
       618: q+1
       619: 2q+1
       620: 2q+1
       621: 2q+1
       622: 2q+1
       623: 2q+1
       624: 2q+1
       625: 2q+1
       626: q+1
       627: 2q+1
       628: 2q+1
       629: 2q+1
       630: 2q+1
       631: 2q+1
       632: 2q+1
       633: 2q+1
       634: 2q+1
       635: 2q+1
       636: 2q+1
       637: 2q+1
       638: 2q+1
       639: 2q+1
       640: 2q+1
       641: 2q+1
       642: q^2+2q+1
       643: 2q+1
       644: 2q+1
       645: 2q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: 2q+1
       649: q+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       657: q+1
       658: q+1
       659: 1
       660: q+1
       661: q+1
       662: 1
       663: 1
       664: 1
       665: q+1
       666: q+1
       667: q+1
       668: 2q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: 1
       674: q+1
       675: q+1
       676: q+1
       677: q+1
       678: 2q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: 1
       684: q+1
       685: q+1
       686: q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: q+1
       694: q+1
       695: 2q+1
       696: 2q+1
       697: 2q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: 2q+1
       702: q+1
       703: q+1
       704: q+1
       705: 1
       706: q+1
       707: q+1
       708: 1
       709: 1
       710: 1
       711: q+1
       712: q+1
       713: q+1
       714: 2q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: 1
       720: q+1
       721: q+1
       722: q+1
       723: 2q+1
       724: 2q+1
       725: 2q+1
       726: q+1
       727: q+1
       728: 2q+1
       729: q+1
       730: q+1
       731: q+1
       732: 2q+1
       733: 2q+1
       734: 2q+1
       735: q+1
       736: q+1
       737: 2q+1
       738: q+1
       739: q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: q+1
       748: 2q+1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: 2q+1
       754: 2q+1
       755: q+1
       756: q+1
       757: 1
       758: q+1
       759: q+1
       760: 1
       761: 1
       762: 1
       763: q+1
       764: q+1
       765: q+1
       766: 2q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: 1
       772: q+1
       773: q+1
       774: q+1
       775: 2q+1
       776: 2q+1
       777: 2q+1
       778: q+1
       779: q+1
       780: 2q+1
       781: q+1
       782: q+1
       783: q+1
       784: 2q+1
       785: 2q+1
       786: 2q+1
       787: q+1
       788: q+1
       789: 2q+1
       790: q+1
       791: q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: q+1
       800: 2q+1
       801: 2q+1
       802: 2q+1
       803: 2q+1
       804: 2q+1
       805: 2q+1
       806: 2q+1
       807: q+1
       808: q+1
       809: 2q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: 1
       815: q+1
       816: q+1
       817: q+1
       818: 2q+1
       819: 2q+1
       820: 2q+1
       821: q+1
       822: q+1
       823: 2q+1
       824: q+1
       825: q+1
       826: 2q+1
       827: 2q+1
       828: 2q+1
       829: 2q+1
       830: 2q+1
       831: 2q+1
       832: 2q+1
       833: q+1
       834: 2q+1
       835: 2q+1
       836: 2q+1
       837: 2q+1
       838: 2q+1
       839: 2q+1
       840: 2q+1
       841: q+1
       842: 2q+1
       843: 2q+1
       844: 2q+1
       845: 2q+1
       846: 2q+1
       847: 2q+1
       848: 2q+1
       849: 2q+1
       850: q^2+2q+1
       851: 2q+1
       852: 2q+1
       853: 2q+1
       854: 1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       861: q+1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       869: q+1
       870: q+1
       871: 1
       872: q+1
       873: q+1
       874: 1
       875: 1
       876: 1
       877: q+1
       878: q+1
       879: q+1
       880: 1
       881: q+1
       882: q+1
       883: 1
       884: 1
       885: 1
       886: q+1
       887: q+1
       888: q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: q+1
       896: q+1
       897: q+1
       898: 2q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: q+1
       905: q+1
       906: q+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: q+1
       915: q+1
       916: 1
       917: q+1
       918: q+1
       919: 1
       920: 1
       921: 1
       922: q+1
       923: q+1
       924: q+1
       925: 2q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: 1
       931: q+1
       932: q+1
       933: q+1
       934: q+1
       935: 2q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: 1
       941: q+1
       942: q+1
       943: q+1
       944: 2q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: q+1
       951: q+1
       952: 2q+1
       953: 2q+1
       954: 2q+1
       955: 2q+1
       956: 2q+1
       957: 2q+1
       958: 2q+1
       959: q+1
       960: q+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: q+1
       969: q+1
       970: 1
       971: q+1
       972: q+1
       973: 1
       974: 1
       975: 1
       976: q+1
       977: q+1
       978: q+1
       979: 2q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: 1
       985: q+1
       986: q+1
       987: q+1
       988: q+1
       989: 2q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: 1
       995: q+1
       996: q+1
       997: q+1
       998: 2q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: q+1
      1005: q+1
      1006: 2q+1
      1007: 2q+1
      1008: 2q+1
      1009: 2q+1
      1010: 2q+1
      1011: 2q+1
      1012: 2q+1
      1013: q+1
      1014: q+1
      1015: q+1
      1016: 1
      1017: q+1
      1018: q+1
      1019: 1
      1020: 1
      1021: 1
      1022: q+1
      1023: q+1
      1024: q+1
      1025: 2q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: 1
      1031: q+1
      1032: q+1
      1033: q+1
      1034: 2q+1
      1035: 2q+1
      1036: 2q+1
      1037: q+1
      1038: q+1
      1039: 2q+1
      1040: q+1
      1041: q+1
      1042: q+1
      1043: 2q+1
      1044: 2q+1
      1045: 2q+1
      1046: q+1
      1047: q+1
      1048: 2q+1
      1049: q+1
      1050: q+1
      1051: 2q+1
      1052: 2q+1
      1053: 2q+1
      1054: 2q+1
      1055: 2q+1
      1056: 2q+1
      1057: 2q+1
      1058: q+1
      1059: 2q+1
      1060: 2q+1
      1061: 2q+1
      1062: 2q+1
      1063: 2q+1
      1064: 2q+1
      1065: 2q+1
      1066: 1
      1067: 1
      1068: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1078: q+1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q+1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: q+1
      1095: q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1102: q+1
      1103: q+1
      1104: q+1
      1105: 2q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1111: q+1
      1112: q+1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: q+1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: q+1
      1129: q+1
      1130: 1
      1131: q+1
      1132: q+1
      1133: 1
      1134: 1
      1135: 1
      1136: q+1
      1137: q+1
      1138: q+1
      1139: 1
      1140: q+1
      1141: q+1
      1142: 1
      1143: 1
      1144: 1
      1145: q+1
      1146: q+1
      1147: q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: q+1
      1155: q+1
      1156: q+1
      1157: 2q+1
      1158: 2q+1
      1159: 2q+1
      1160: q+1
      1161: q+1
      1162: 2q+1
      1163: q+1
      1164: q+1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: q+1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: q+1
      1181: q+1
      1182: 1
      1183: q+1
      1184: q+1
      1185: 1
      1186: 1
      1187: 1
      1188: q+1
      1189: q+1
      1190: q+1
      1191: 1
      1192: q+1
      1193: q+1
      1194: 1
      1195: 1
      1196: 1
      1197: q+1
      1198: q+1
      1199: q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1203: q+1
      1204: q+1
      1205: 1
      1206: q+1
      1207: q+1
      1208: q+1
      1209: 2q+1
      1210: 2q+1
      1211: 2q+1
      1212: q+1
      1213: q+1
      1214: 2q+1
      1215: q+1
      1216: q+1
      1217: q+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: q+1
      1226: q+1
      1227: 1
      1228: q+1
      1229: q+1
      1230: 1
      1231: 1
      1232: 1
      1233: q+1
      1234: q+1
      1235: q+1
      1236: 2q+1
      1237: q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: 1
      1242: q+1
      1243: q+1
      1244: q+1
      1245: q+1
      1246: 2q+1
      1247: q+1
      1248: q+1
      1249: q+1
      1250: q+1
      1251: 1
      1252: q+1
      1253: q+1
      1254: q+1
      1255: 2q+1
      1256: 2q+1
      1257: 2q+1
      1258: q+1
      1259: q+1
      1260: 2q+1
      1261: q+1
      1262: q+1
      1263: 2q+1
      1264: 2q+1
      1265: 2q+1
      1266: 2q+1
      1267: 2q+1
      1268: 2q+1
      1269: 2q+1
      1270: q+1
      1271: 1
      1274: 1
      1275: 1
      1276: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: q+1
      1302: q+1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1309: q+1
      1310: 1
      1311: 1
      1312: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: q+1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: q+1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: q+1
      1339: q+1
      1340: 1
      1341: q+1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1346: q+1
      1347: q+1
      1348: q+1
      1349: 2q+1
      1350: q+1
      1351: q+1
      1352: q+1
      1353: q+1
      1354: 1
      1355: q+1
      1356: q+1
      1357: 1
      1358: 1
      1359: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: q+1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: q+1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: q+1
      1386: q+1
      1387: 1
      1388: q+1
      1389: q+1
      1390: 1
      1391: 1
      1392: 1
      1393: q+1
      1394: q+1
      1395: q+1
      1396: 2q+1
      1397: q+1
      1398: q+1
      1399: q+1
      1400: q+1
      1401: 1
      1402: q+1
      1403: q+1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: q+1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: q+1
      1420: q+1
      1421: 1
      1422: q+1
      1423: q+1
      1424: 1
      1425: 1
      1426: 1
      1427: q+1
      1428: q+1
      1429: q+1
      1430: 1
      1431: q+1
      1432: q+1
      1433: 1
      1434: 1
      1435: 1
      1436: q+1
      1437: q+1
      1438: q+1
      1439: 2q+1
      1440: q+1
      1441: q+1
      1442: q+1
      1443: q+1
      1444: 1
      1445: q+1
      1446: q+1
      1447: q+1
      1448: 2q+1
      1449: 2q+1
      1450: 2q+1
      1451: q+1
      1452: q+1
      1453: 2q+1
      1454: q+1
      1455: q+1
      1458: 1
      1461: 1
      1462: 1
      1463: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: q+1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1489: 1
      1490: 1
      1491: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: q+1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: q+1
      1517: q+1
      1518: 1
      1519: q+1
      1520: q+1
      1521: 1
      1522: 1
      1523: 1
      1524: q+1
      1525: 1
      1528: 1
      1529: 1
      1530: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: q+1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: q+1
      1556: q+1
      1557: 1
      1558: q+1
      1559: q+1
      1560: 1
      1561: 1
      1562: 1
      1563: q+1
      1564: 1
      1565: 1
      1566: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: q+1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1584: q+1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1592: q+1
      1593: q+1
      1594: 1
      1595: q+1
      1596: q+1
      1597: 1
      1598: 1
      1599: 1
      1600: q+1
      1601: q+1
      1602: q+1
      1603: 2q+1
      1604: q+1
      1605: q+1
      1606: q+1
      1607: q+1
      1608: 1
      1609: q+1
      1610: q+1
      1614: 1
      1617: 1
      1620: 1
      1621: 1
      1622: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1634: 1
      1637: 1
      1638: 1
      1639: 1
      1641: 1
      1642: 1
      1643: 1
      1644: 1
      1646: 1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1654: q+1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1664: 1
      1667: 1
      1668: 1
      1669: 1
      1671: 1
      1672: 1
      1673: 1
      1674: 1
      1676: 1
      1677: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1684: q+1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1692: 1
      1695: 1
      1696: 1
      1697: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1707: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1714: q+1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1722: q+1
      1723: q+1
      1724: 1
      1725: q+1
      1726: q+1
      1727: 1
      1728: 1
      1729: 1
      1730: q+1
      1736: 1
      1739: 1
      1740: 1
      1741: 1
      1743: 1
      1747: 1
      1750: 1
      1753: 1
      1754: 1
      1755: 1
      1757: 1
      1758: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1768: 1
      1771: 1
      1774: 1
      1775: 1
      1776: 1
      1778: 1
      1779: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1788: 1
      1791: 1
      1792: 1
      1793: 1
      1795: 1
      1796: 1
      1797: 1
      1798: 1
      1800: 1
      1801: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1806: 1
      1807: 1
      1808: q+1
      1809: 1
      1810: 1
      1811: 1
      1812: 1
      1813: 1
      1814: 1
      1815: 1
      1820: 1
      1828: 1
      1831: 1
      1832: 1
      1833: 1
      1835: 1
      1841: 1
      1844: 1
      1845: 1
      1846: 1
      1848: 1
      1852: 1
      1855: 1
      1858: 1
      1859: 1
      1860: 1
      1862: 1
      1863: 1
      1864: 1
      1865: 1
      1866: 1
      1867: 1
      1868: 1
      1869: 1
      1877: 1
      1884: 1
      1892: 1
      1895: 1
      1896: 1
      1897: 1
      1899: 1
      1911: 1

1912:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: q^2+1
         7: 1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: q^2+1
        21: 1
        22: 1
        23: q^2+1
        24: q^2+1
        25: q^2+1
        26: 1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: q^2+1
        31: q^2+1
        32: q^2+1
        33: q^2+1
        34: 1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: q^2+1
        39: q^2+1
        40: q^2+1
        41: 1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: q^2+1
        51: q^2+1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q^2+1
        57: q^2+1
        58: 1
        59: 1
        60: q^2+1
        61: q^2+1
        62: q^2+1
        63: 1
        64: q^2+1
        65: q^2+1
        66: 1
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: q^2+1
        72: 1
        73: 1
        74: q^2+1
        75: q^2+1
        76: q^2+1
        77: 1
        78: q^2+1
        79: q^2+1
        80: q^2+1
        81: q^2+1
        82: q^2+1
        83: q^2+1
        84: q^2+1
        85: 1
        86: 1
        87: q^2+1
        88: q^2+1
        89: q^2+1
        90: 1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: q^2+1
        98: 1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: q^2+1
       103: q^2+1
       104: q^2+1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q^2+1
       112: q^2+1
       113: q^2+1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q^2+1
       119: q^2+1
       120: 1
       121: 1
       122: q^2+1
       123: q^2+1
       124: q^2+1
       125: 1
       126: 1
       127: q^2+1
       128: q^2+1
       129: q^2+1
       130: 1
       131: q^2+1
       132: q^2+1
       133: q^2+1
       134: q^2+1
       135: q^2+1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q^2+1
       141: q^2+1
       142: 1
       143: 1
       144: q^2+1
       145: q^2+1
       146: q^2+1
       147: 1
       148: q^2+1
       149: q^2+1
       150: 1
       151: q^2+1
       152: q^2+1
       153: q^2+1
       154: q^2+1
       155: q^2+1
       156: q^2+1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q^2+1
       162: q^2+1
       163: 1
       164: 1
       165: q^2+1
       166: q^2+1
       167: q^2+1
       168: 1
       169: q^2+1
       170: q^2+1
       171: 1
       172: q^2+1
       173: q^2+1
       174: q^2+1
       175: q^2+1
       176: q^2+1
       177: 1
       178: 1
       179: q^2+1
       180: q^2+1
       181: q^2+1
       182: 1
       183: q^2+1
       184: q^2+1
       185: q^2+1
       186: q^2+1
       187: q^2+1
       188: q^2+1
       189: q^2+1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q^2+1
       198: q^2+1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q^2+1
       206: q^2+1
       207: q^2+1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q^2+1
       213: q^2+1
       214: q^2+1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q^2+1
       220: q^2+1
       221: 1
       222: 1
       223: q^2+1
       224: q^2+1
       225: q^2+1
       226: 1
       227: q^2+1
       228: q^2+1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q^2+1
       236: q^2+1
       237: q^2+1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q^2+1
       243: q^2+1
       244: 1
       245: 1
       246: q^2+1
       247: q^2+1
       248: q^2+1
       249: 1
       250: 1
       251: q^2+1
       252: q^2+1
       253: q^2+1
       254: 1
       255: q^2+1
       256: q^2+1
       257: q^2+1
       258: q^2+1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q^2+1
       266: q^2+1
       267: q^2+1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q^2+1
       273: q^2+1
       274: 1
       275: 1
       276: q^2+1
       277: q^2+1
       278: q^2+1
       279: 1
       280: 1
       281: q^2+1
       282: q^2+1
       283: q^2+1
       284: 1
       285: q^2+1
       286: q^2+1
       287: q^2+1
       288: q^2+1
       289: q^2+1
       290: 1
       291: 1
       292: 1
       293: 1
       294: q^2+1
       295: q^2+1
       296: 1
       297: 1
       298: q^2+1
       299: q^2+1
       300: q^2+1
       301: 1
       302: q^2+1
       303: q^2+1
       304: 1
       305: q^2+1
       306: q^2+1
       307: q^2+1
       308: q^2+1
       309: q^2+1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       319: q^2+1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q^2+1
       328: q^2+1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q^2+1
       336: q^2+1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q^2+1
       344: q^2+1
       345: q^2+1
       346: 1
       347: 1
       348: 1
       349: 1
       350: q^2+1
       351: q^2+1
       352: 1
       353: 1
       354: q^2+1
       355: q^2+1
       356: q^2+1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: q^2+1
       365: q^2+1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q^2+1
       373: q^2+1
       374: q^2+1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q^2+1
       380: q^2+1
       381: q^2+1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q^2+1
       387: q^2+1
       388: 1
       389: 1
       390: q^2+1
       391: q^2+1
       392: q^2+1
       393: 1
       394: q^2+1
       395: q^2+1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: q^2+1
       404: q^2+1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q^2+1
       412: q^2+1
       413: q^2+1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q^2+1
       419: q^2+1
       420: q^2+1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q^2+1
       426: q^2+1
       427: 1
       428: 1
       429: q^2+1
       430: q^2+1
       431: q^2+1
       432: 1
       433: q^2+1
       434: q^2+1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: q^2+1
       442: q^2+1
       443: q^2+1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q^2+1
       449: q^2+1
       450: 1
       451: 1
       452: q^2+1
       453: q^2+1
       454: q^2+1
       455: 1
       456: 1
       457: q^2+1
       458: q^2+1
       459: q^2+1
       460: 1
       461: q^2+1
       462: q^2+1
       463: q^2+1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       473: q^2+1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       483: q^2+1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q^2+1
       492: q^2+1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q^2+1
       501: q^2+1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: q^2+1
       509: q^2+1
       510: q^2+1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q^2+1
       516: q^2+1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       526: q^2+1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q^2+1
       535: q^2+1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q^2+1
       543: q^2+1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q^2+1
       551: q^2+1
       552: q^2+1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q^2+1
       558: q^2+1
       559: 1
       560: 1
       561: q^2+1
       562: q^2+1
       563: q^2+1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       573: q^2+1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q^2+1
       582: q^2+1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q^2+1
       590: q^2+1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q^2+1
       598: q^2+1
       599: q^2+1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q^2+1
       605: q^2+1
       606: 1
       607: 1
       608: q^2+1
       609: q^2+1
       610: q^2+1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: q^2+1
       619: q^2+1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q^2+1
       627: q^2+1
       628: q^2+1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q^2+1
       634: q^2+1
       635: q^2+1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q^2+1
       641: q^2+1
       642: 1
       643: 1
       644: q^2+1
       645: q^2+1
       646: q^2+1
       647: 1
       648: q^2+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       666: q^2+1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       676: q^2+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       686: q^2+1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: q^2+1
       695: q^2+1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: q^2+1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       712: q^2+1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       722: q^2+1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: q^2+1
       731: q^2+1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q^2+1
       740: q^2+1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: q^2+1
       748: q^2+1
       749: q^2+1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q^2+1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       764: q^2+1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       774: q^2+1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q^2+1
       783: q^2+1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: q^2+1
       792: q^2+1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: q^2+1
       800: q^2+1
       801: q^2+1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q^2+1
       807: q^2+1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       817: q^2+1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: q^2+1
       826: q^2+1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q^2+1
       834: q^2+1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q^2+1
       842: q^2+1
       843: q^2+1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q^2+1
       849: q^2+1
       850: 1
       851: 1
       852: q^2+1
       853: q^2+1
       855: 1
       856: 1
       857: 1
       858: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       887: q^2+1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       897: q^2+1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: q^2+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       923: q^2+1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       933: q^2+1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       943: q^2+1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: q^2+1
       952: q^2+1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q^2+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       977: q^2+1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       987: q^2+1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       997: q^2+1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: q^2+1
      1006: q^2+1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q^2+1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1023: q^2+1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1033: q^2+1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q^2+1
      1042: q^2+1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q^2+1
      1051: q^2+1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q^2+1
      1059: q^2+1
      1060: q^2+1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q^2+1
      1068: 1
      1069: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1103: q^2+1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1146: q^2+1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1156: q^2+1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: q^2+1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1198: q^2+1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1208: q^2+1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q^2+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1234: q^2+1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1244: q^2+1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1254: q^2+1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q^2+1
      1263: q^2+1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q^2+1
      1272: 1
      1276: 1
      1277: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1312: 1
      1313: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1339: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1347: q^2+1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1359: 1
      1360: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1386: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1394: q^2+1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1420: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1429: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1437: q^2+1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1447: q^2+1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q^2+1
      1459: 1
      1463: 1
      1464: 1
      1468: 1
      1469: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1487: 1
      1491: 1
      1492: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1517: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1526: 1
      1530: 1
      1531: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1556: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1566: 1
      1567: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1593: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1601: q^2+1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1615: 1
      1618: 1
      1622: 1
      1623: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1635: 1
      1639: 1
      1640: 1
      1644: 1
      1645: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1665: 1
      1669: 1
      1670: 1
      1674: 1
      1675: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1693: 1
      1697: 1
      1698: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1723: 1
      1724: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1729: 1
      1737: 1
      1741: 1
      1742: 1
      1748: 1
      1751: 1
      1755: 1
      1756: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1769: 1
      1772: 1
      1776: 1
      1777: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1789: 1
      1793: 1
      1794: 1
      1798: 1
      1799: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1809: 1
      1810: 1
      1811: 1
      1812: 1
      1813: 1
      1814: 1
      1821: 1
      1829: 1
      1833: 1
      1834: 1
      1842: 1
      1846: 1
      1847: 1
      1853: 1
      1856: 1
      1860: 1
      1861: 1
      1864: 1
      1865: 1
      1866: 1
      1867: 1
      1878: 1
      1885: 1
      1893: 1
      1897: 1
      1898: 1
      1912: 1

1913:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: 1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: 1
        21: 1
        22: q^2+1
        23: q^2+1
        24: q^2+1
        25: 1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: q^2+1
        31: q^2+1
        32: q^2+1
        33: 1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: q^2+1
        39: q^2+1
        40: 1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: q^2+1
        55: q^2+1
        56: q^2+1
        57: 1
        58: 1
        59: q^2+1
        60: q^2+1
        61: q^2+1
        62: 1
        63: q^2+1
        64: q^2+1
        65: 1
        66: q^2+1
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: 1
        72: 1
        73: q^2+1
        74: q^2+1
        75: q^2+1
        76: 1
        77: q^2+1
        78: q^2+1
        79: q^2+1
        80: q^2+1
        81: q^2+1
        82: q^2+1
        83: q^2+1
        84: 1
        85: 1
        86: q^2+1
        87: q^2+1
        88: q^2+1
        89: 1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: 1
        98: q^2+1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: q^2+1
       103: q^2+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: q^2+1
       111: q^2+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: q^2+1
       117: q^2+1
       118: q^2+1
       119: 1
       120: 1
       121: q^2+1
       122: q^2+1
       123: q^2+1
       124: 1
       125: 1
       126: q^2+1
       127: q^2+1
       128: q^2+1
       129: 1
       130: q^2+1
       131: q^2+1
       132: q^2+1
       133: q^2+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: q^2+1
       139: q^2+1
       140: q^2+1
       141: 1
       142: 1
       143: q^2+1
       144: q^2+1
       145: q^2+1
       146: 1
       147: q^2+1
       148: q^2+1
       149: 1
       150: q^2+1
       151: q^2+1
       152: q^2+1
       153: q^2+1
       154: q^2+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: q^2+1
       160: q^2+1
       161: q^2+1
       162: 1
       163: 1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: 1
       168: q^2+1
       169: q^2+1
       170: 1
       171: q^2+1
       172: q^2+1
       173: q^2+1
       174: q^2+1
       175: q^2+1
       176: 1
       177: 1
       178: q^2+1
       179: q^2+1
       180: q^2+1
       181: 1
       182: q^2+1
       183: q^2+1
       184: q^2+1
       185: q^2+1
       186: q^2+1
       187: q^2+1
       188: q^2+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: q^2+1
       197: q^2+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: q^2+1
       205: q^2+1
       206: 1
       207: 1
       208: 1
       209: 1
       210: q^2+1
       211: q^2+1
       212: q^2+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: q^2+1
       218: q^2+1
       219: q^2+1
       220: 1
       221: 1
       222: q^2+1
       223: q^2+1
       224: q^2+1
       225: 1
       226: q^2+1
       227: q^2+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: q^2+1
       235: q^2+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: q^2+1
       241: q^2+1
       242: q^2+1
       243: 1
       244: 1
       245: q^2+1
       246: q^2+1
       247: q^2+1
       248: 1
       249: 1
       250: q^2+1
       251: q^2+1
       252: q^2+1
       253: 1
       254: q^2+1
       255: q^2+1
       256: q^2+1
       257: q^2+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: q^2+1
       265: q^2+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: q^2+1
       271: q^2+1
       272: q^2+1
       273: 1
       274: 1
       275: q^2+1
       276: q^2+1
       277: q^2+1
       278: 1
       279: 1
       280: q^2+1
       281: q^2+1
       282: q^2+1
       283: 1
       284: q^2+1
       285: q^2+1
       286: q^2+1
       287: q^2+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: q^2+1
       293: q^2+1
       294: q^2+1
       295: 1
       296: 1
       297: q^2+1
       298: q^2+1
       299: q^2+1
       300: 1
       301: q^2+1
       302: q^2+1
       303: 1
       304: q^2+1
       305: q^2+1
       306: q^2+1
       307: q^2+1
       308: q^2+1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: q^2+1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: q^2+1
       327: q^2+1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: q^2+1
       335: q^2+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: q^2+1
       343: q^2+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: q^2+1
       349: q^2+1
       350: q^2+1
       351: 1
       352: 1
       353: q^2+1
       354: q^2+1
       355: q^2+1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: q^2+1
       364: q^2+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: q^2+1
       372: q^2+1
       373: 1
       374: 1
       375: 1
       376: 1
       377: q^2+1
       378: q^2+1
       379: q^2+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: q^2+1
       385: q^2+1
       386: q^2+1
       387: 1
       388: 1
       389: q^2+1
       390: q^2+1
       391: q^2+1
       392: 1
       393: q^2+1
       394: q^2+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: q^2+1
       403: q^2+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: q^2+1
       411: q^2+1
       412: 1
       413: 1
       414: 1
       415: 1
       416: q^2+1
       417: q^2+1
       418: q^2+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: q^2+1
       424: q^2+1
       425: q^2+1
       426: 1
       427: 1
       428: q^2+1
       429: q^2+1
       430: q^2+1
       431: 1
       432: q^2+1
       433: q^2+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: q^2+1
       441: q^2+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: q^2+1
       447: q^2+1
       448: q^2+1
       449: 1
       450: 1
       451: q^2+1
       452: q^2+1
       453: q^2+1
       454: 1
       455: 1
       456: q^2+1
       457: q^2+1
       458: q^2+1
       459: 1
       460: q^2+1
       461: q^2+1
       462: q^2+1
       463: q^2+1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: q^2+1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: q^2+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: q^2+1
       500: q^2+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: q^2+1
       508: q^2+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: q^2+1
       514: q^2+1
       515: q^2+1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: q^2+1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: q^2+1
       534: q^2+1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: q^2+1
       542: q^2+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: q^2+1
       550: q^2+1
       551: 1
       552: 1
       553: 1
       554: 1
       555: q^2+1
       556: q^2+1
       557: q^2+1
       558: 1
       559: 1
       560: q^2+1
       561: q^2+1
       562: q^2+1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: q^2+1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: q^2+1
       581: q^2+1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: q^2+1
       589: q^2+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: q^2+1
       597: q^2+1
       598: 1
       599: 1
       600: 1
       601: 1
       602: q^2+1
       603: q^2+1
       604: q^2+1
       605: 1
       606: 1
       607: q^2+1
       608: q^2+1
       609: q^2+1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: q^2+1
       618: q^2+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: q^2+1
       626: q^2+1
       627: 1
       628: 1
       629: 1
       630: 1
       631: q^2+1
       632: q^2+1
       633: q^2+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: q^2+1
       639: q^2+1
       640: q^2+1
       641: 1
       642: 1
       643: q^2+1
       644: q^2+1
       645: q^2+1
       646: 1
       647: q^2+1
       648: q^2+1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: q^2+1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: q^2+1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: q^2+1
       694: q^2+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: q^2+1
       702: q^2+1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: q^2+1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: q^2+1
       730: q^2+1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: q^2+1
       739: q^2+1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: q^2+1
       747: q^2+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: q^2+1
       753: q^2+1
       754: q^2+1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: q^2+1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: q^2+1
       782: q^2+1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: q^2+1
       791: q^2+1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: q^2+1
       799: q^2+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: q^2+1
       805: q^2+1
       806: q^2+1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: q^2+1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: q^2+1
       825: q^2+1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: q^2+1
       833: q^2+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: q^2+1
       841: q^2+1
       842: 1
       843: 1
       844: 1
       845: 1
       846: q^2+1
       847: q^2+1
       848: q^2+1
       849: 1
       850: 1
       851: q^2+1
       852: q^2+1
       853: q^2+1
       857: 1
       858: 1
       859: 1
       860: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: q^2+1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: q^2+1
       905: q^2+1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       932: q^2+1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       942: q^2+1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: q^2+1
       951: q^2+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: q^2+1
       959: q^2+1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       986: q^2+1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: q^2+1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: q^2+1
      1005: q^2+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: q^2+1
      1013: q^2+1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: q^2+1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: q^2+1
      1041: q^2+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: q^2+1
      1050: q^2+1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: q^2+1
      1058: q^2+1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: q^2+1
      1064: q^2+1
      1065: q^2+1
      1069: 1
      1070: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: q^2+1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: q^2+1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: q^2+1
      1164: q^2+1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: q^2+1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: q^2+1
      1216: q^2+1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: q^2+1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: q^2+1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: q^2+1
      1262: q^2+1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: q^2+1
      1270: q^2+1
      1273: 1
      1277: 1
      1278: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1313: 1
      1314: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: q^2+1
      1360: 1
      1361: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: q^2+1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: q^2+1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: q^2+1
      1455: q^2+1
      1460: 1
      1464: 1
      1465: 1
      1469: 1
      1470: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1488: 1
      1492: 1
      1493: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1524: 1
      1527: 1
      1531: 1
      1532: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1563: 1
      1567: 1
      1568: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1600: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1610: q^2+1
      1616: 1
      1619: 1
      1623: 1
      1624: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1636: 1
      1640: 1
      1641: 1
      1645: 1
      1646: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1666: 1
      1670: 1
      1671: 1
      1675: 1
      1676: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1694: 1
      1698: 1
      1699: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1724: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1729: 1
      1730: 1
      1738: 1
      1742: 1
      1743: 1
      1749: 1
      1752: 1
      1756: 1
      1757: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1770: 1
      1773: 1
      1777: 1
      1778: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1790: 1
      1794: 1
      1795: 1
      1799: 1
      1800: 1
      1804: 1
      1805: 1
      1806: 1
      1807: 1
      1810: 1
      1811: 1
      1812: 1
      1813: 1
      1814: 1
      1815: 1
      1822: 1
      1830: 1
      1834: 1
      1835: 1
      1843: 1
      1847: 1
      1848: 1
      1854: 1
      1857: 1
      1861: 1
      1862: 1
      1866: 1
      1867: 1
      1868: 1
      1869: 1
      1879: 1
      1886: 1
      1894: 1
      1898: 1
      1899: 1
      1913: 1

1914:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: q^2+1
        31: q^2+1
        32: q^2+1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: q^2+1
        39: q^2+1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: 1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: q^2+1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: q^2+1
        56: q^2+1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: q^2+1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: q^2+1
        72: q^2+1
        73: q^2+1
        74: q^2+1
        75: q^2+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: q^2+1
        80: q^2+1
        81: q^2+1
        82: q^2+1
        83: q^2+1
        84: q^2+1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: 1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: 1
        95: 1
        96: 1
        97: q^2+1
        98: q^2+1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: q^2+1
       103: 1
       104: q^2+1
       105: q^2+1
       106: q^2+1
       107: q^2+1
       108: q^2+1
       109: q^2+1
       110: q^2+1
       111: q^2+1
       112: q^2+1
       113: q^2+1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: q^2+1
       118: q^2+1
       119: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: 1
       124: q^2+1
       125: q^2+1
       126: q^2+1
       127: q^2+1
       128: q^2+1
       129: q^2+1
       130: q^2+1
       131: q^2+1
       132: q^2+1
       133: q^2+1
       134: q^2+1
       135: q^2+1
       136: q^2+1
       137: q^2+1
       138: q^2+1
       139: q^2+1
       140: q^2+1
       141: q^2+1
       142: q^2+1
       143: q^2+1
       144: q^2+1
       145: q^2+1
       146: q^2+1
       147: q^2+1
       148: q^2+1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: q^2+1
       153: q^2+1
       154: q^2+1
       155: q^2+1
       156: 1
       157: q^2+1
       158: q^2+1
       159: q^2+1
       160: 1
       161: 1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: 1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: 1
       171: 1
       172: 1
       173: 1
       174: 1
       175: 1
       176: q^2+1
       177: q^2+1
       178: q^2+1
       179: q^2+1
       180: 1
       181: q^2+1
       182: q^2+1
       183: q^2+1
       184: q^2+1
       185: q^2+1
       186: 1
       187: 1
       188: 1
       189: q^2+1
       190: q^2+1
       191: q^2+1
       192: q^2+1
       193: q^2+1
       194: q^2+1
       195: q^2+1
       196: q^2+1
       197: q^2+1
       198: q^2+1
       199: q^2+1
       200: q^2+1
       201: q^2+1
       202: q^2+1
       203: q^2+1
       204: q^2+1
       205: q^2+1
       206: q^2+1
       207: 1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: 1
       212: 1
       213: q^2+1
       214: q^2+1
       215: q^2+1
       216: q^2+1
       217: q^2+1
       218: q^2+1
       219: q^2+1
       220: q^2+1
       221: q^2+1
       222: q^2+1
       223: q^2+1
       224: 1
       225: q^2+1
       226: q^2+1
       227: q^2+1
       228: q^2+1
       229: q^2+1
       230: q^2+1
       231: q^2+1
       232: q^2+1
       233: q^2+1
       234: q^2+1
       235: q^2+1
       236: q^2+1
       237: q^2+1
       238: q^2+1
       239: q^2+1
       240: q^2+1
       241: q^2+1
       242: q^2+1
       243: q^2+1
       244: q^2+1
       245: q^2+1
       246: q^2+1
       247: 1
       248: q^2+1
       249: q^2+1
       250: q^2+1
       251: q^2+1
       252: q^2+1
       253: q^2+1
       254: q^2+1
       255: q^2+1
       256: q^2+1
       257: q^2+1
       258: 1
       259: q^2+1
       260: 1
       261: q^2+1
       262: q^2+1
       263: 1
       264: 1
       265: 1
       266: q^2+1
       267: 1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: 1
       272: 1
       273: q^2+1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: 1
       278: 1
       279: 1
       280: 1
       281: 1
       282: 1
       283: 1
       284: 1
       285: 1
       286: 1
       287: 1
       288: q^2+1
       289: 1
       290: q^2+1
       291: q^2+1
       292: q^2+1
       293: 1
       294: 1
       295: q^2+1
       296: q^2+1
       297: q^2+1
       298: q^2+1
       299: 1
       300: q^2+1
       301: q^2+1
       302: q^2+1
       303: 1
       304: 1
       305: 1
       306: 1
       307: 1
       308: 1
       309: q^2+1
       310: q^2+1
       311: q^2+1
       312: q^2+1
       313: 1
       314: q^2+1
       315: q^2+1
       316: q^2+1
       317: q^2+1
       318: q^2+1
       319: q^2+1
       320: q^2+1
       321: q^2+1
       322: q^2+1
       323: q^2+1
       324: q^2+1
       325: q^2+1
       326: q^2+1
       327: q^2+1
       328: 1
       329: q^2+1
       330: 1
       331: q^2+1
       332: q^2+1
       333: 1
       334: 1
       335: 1
       336: q^2+1
       337: q^2+1
       338: q^2+1
       339: q^2+1
       340: q^2+1
       341: q^2+1
       342: q^2+1
       343: q^2+1
       344: q^2+1
       345: 1
       346: q^2+1
       347: q^2+1
       348: q^2+1
       349: 1
       350: 1
       351: q^2+1
       352: q^2+1
       353: q^2+1
       354: q^2+1
       355: 1
       356: q^2+1
       357: q^2+1
       358: q^2+1
       359: q^2+1
       360: q^2+1
       361: q^2+1
       362: q^2+1
       363: q^2+1
       364: q^2+1
       365: q^2+1
       366: q^2+1
       367: q^2+1
       368: q^2+1
       369: q^2+1
       370: q^2+1
       371: q^2+1
       372: q^2+1
       373: q^2+1
       374: 1
       375: q^2+1
       376: q^2+1
       377: q^2+1
       378: 1
       379: 1
       380: q^2+1
       381: q^2+1
       382: q^2+1
       383: q^2+1
       384: q^2+1
       385: q^2+1
       386: q^2+1
       387: q^2+1
       388: q^2+1
       389: q^2+1
       390: q^2+1
       391: 1
       392: q^2+1
       393: q^2+1
       394: q^2+1
       395: 1
       396: 1
       397: q^2+1
       398: 1
       399: q^2+1
       400: 1
       401: 1
       402: 1
       403: 1
       404: 1
       405: q^2+1
       406: 1
       407: q^2+1
       408: q^2+1
       409: 1
       410: 1
       411: 1
       412: q^2+1
       413: 1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: 1
       418: 1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: 1
       426: 1
       427: 1
       428: 1
       429: 1
       430: 1
       431: 1
       432: 1
       433: 1
       434: 1
       435: q^2+1
       436: 1
       437: q^2+1
       438: q^2+1
       439: 1
       440: 1
       441: 1
       442: q^2+1
       443: 1
       444: q^2+1
       445: q^2+1
       446: q^2+1
       447: 1
       448: 1
       449: q^2+1
       450: q^2+1
       451: q^2+1
       452: q^2+1
       453: 1
       454: 1
       455: 1
       456: 1
       457: 1
       458: 1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       464: q^2+1
       465: q^2+1
       466: q^2+1
       467: 1
       468: q^2+1
       469: q^2+1
       470: 1
       471: q^2+1
       472: q^2+1
       473: q^2+1
       474: q^2+1
       475: q^2+1
       476: q^2+1
       477: 1
       478: q^2+1
       479: q^2+1
       480: q^2+1
       481: q^2+1
       482: q^2+1
       483: 1
       484: 1
       485: q^2+1
       486: 1
       487: q^2+1
       488: 1
       489: 1
       490: 1
       491: 1
       492: q^2+1
       493: q^2+1
       494: q^2+1
       495: q^2+1
       496: q^2+1
       497: q^2+1
       498: q^2+1
       499: q^2+1
       500: q^2+1
       501: 1
       502: q^2+1
       503: 1
       504: q^2+1
       505: q^2+1
       506: 1
       507: 1
       508: 1
       509: q^2+1
       510: 1
       511: q^2+1
       512: q^2+1
       513: q^2+1
       514: 1
       515: 1
       516: q^2+1
       517: q^2+1
       518: q^2+1
       519: q^2+1
       520: 1
       521: q^2+1
       522: q^2+1
       523: q^2+1
       524: q^2+1
       525: q^2+1
       526: q^2+1
       527: q^2+1
       528: q^2+1
       529: q^2+1
       530: q^2+1
       531: q^2+1
       532: q^2+1
       533: q^2+1
       534: q^2+1
       535: 1
       536: q^2+1
       537: 1
       538: q^2+1
       539: q^2+1
       540: 1
       541: 1
       542: 1
       543: q^2+1
       544: q^2+1
       545: q^2+1
       546: q^2+1
       547: q^2+1
       548: q^2+1
       549: q^2+1
       550: q^2+1
       551: q^2+1
       552: 1
       553: q^2+1
       554: q^2+1
       555: q^2+1
       556: 1
       557: 1
       558: q^2+1
       559: q^2+1
       560: q^2+1
       561: q^2+1
       562: 1
       563: 1
       564: 1
       565: 1
       566: q^2+1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: q^2+1
       576: 1
       577: q^2+1
       578: 1
       579: 1
       580: 1
       581: 1
       582: 1
       583: q^2+1
       584: 1
       585: q^2+1
       586: q^2+1
       587: 1
       588: 1
       589: 1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: 1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: 1
       605: 1
       606: 1
       607: 1
       608: 1
       609: 1
       610: 1
       611: 1
       612: q^2+1
       613: 1
       614: q^2+1
       615: 1
       616: 1
       617: 1
       618: 1
       619: 1
       620: q^2+1
       621: 1
       622: q^2+1
       623: q^2+1
       624: 1
       625: 1
       626: 1
       627: q^2+1
       628: 1
       629: q^2+1
       630: q^2+1
       631: q^2+1
       632: 1
       633: 1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: q^2+1
       650: q^2+1
       651: 1
       652: q^2+1
       653: 1
       654: q^2+1
       655: 1
       656: q^2+1
       657: q^2+1
       658: q^2+1
       659: q^2+1
       660: 1
       661: q^2+1
       662: q^2+1
       663: 1
       664: q^2+1
       665: q^2+1
       666: 1
       667: 1
       668: 1
       669: q^2+1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: q^2+1
       677: q^2+1
       678: q^2+1
       679: q^2+1
       680: 1
       681: q^2+1
       682: q^2+1
       683: q^2+1
       684: q^2+1
       685: q^2+1
       686: 1
       687: 1
       688: q^2+1
       689: 1
       690: q^2+1
       691: 1
       692: 1
       693: 1
       694: 1
       695: 1
       696: q^2+1
       697: 1
       698: q^2+1
       699: q^2+1
       700: 1
       701: 1
       702: 1
       703: q^2+1
       704: q^2+1
       705: q^2+1
       706: 1
       707: q^2+1
       708: q^2+1
       709: 1
       710: q^2+1
       711: q^2+1
       712: q^2+1
       713: q^2+1
       714: q^2+1
       715: q^2+1
       716: 1
       717: q^2+1
       718: q^2+1
       719: q^2+1
       720: q^2+1
       721: q^2+1
       722: 1
       723: 1
       724: q^2+1
       725: 1
       726: q^2+1
       727: 1
       728: 1
       729: 1
       730: 1
       731: q^2+1
       732: q^2+1
       733: q^2+1
       734: q^2+1
       735: q^2+1
       736: q^2+1
       737: q^2+1
       738: q^2+1
       739: q^2+1
       740: 1
       741: q^2+1
       742: 1
       743: q^2+1
       744: q^2+1
       745: 1
       746: 1
       747: 1
       748: q^2+1
       749: 1
       750: q^2+1
       751: q^2+1
       752: q^2+1
       753: 1
       754: 1
       755: 1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: q^2+1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: q^2+1
       777: 1
       778: q^2+1
       779: 1
       780: 1
       781: 1
       782: 1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: 1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: 1
       807: 1
       808: 1
       809: 1
       810: q^2+1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: q^2+1
       820: 1
       821: q^2+1
       822: 1
       823: 1
       824: 1
       825: 1
       826: 1
       827: q^2+1
       828: 1
       829: q^2+1
       830: q^2+1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       854: q^2+1
       855: 1
       856: q^2+1
       857: 1
       858: 1
       859: q^2+1
       860: 1
       861: q^2+1
       862: q^2+1
       863: 1
       864: q^2+1
       865: 1
       866: q^2+1
       867: 1
       868: q^2+1
       869: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       878: q^2+1
       879: q^2+1
       880: q^2+1
       881: 1
       882: q^2+1
       883: q^2+1
       884: 1
       885: q^2+1
       886: q^2+1
       887: 1
       888: 1
       889: 1
       890: q^2+1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: q^2+1
       900: 1
       901: q^2+1
       902: 1
       903: 1
       904: 1
       905: 1
       906: q^2+1
       907: q^2+1
       908: 1
       909: q^2+1
       910: 1
       911: q^2+1
       912: 1
       913: q^2+1
       914: q^2+1
       915: q^2+1
       916: q^2+1
       917: 1
       918: q^2+1
       919: q^2+1
       920: 1
       921: q^2+1
       922: q^2+1
       923: 1
       924: 1
       925: 1
       926: q^2+1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: q^2+1
       934: q^2+1
       935: q^2+1
       936: q^2+1
       937: 1
       938: q^2+1
       939: q^2+1
       940: q^2+1
       941: q^2+1
       942: q^2+1
       943: 1
       944: 1
       945: q^2+1
       946: 1
       947: q^2+1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: q^2+1
       954: 1
       955: q^2+1
       956: q^2+1
       957: 1
       958: 1
       959: 1
       960: 1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       968: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: q^2+1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: q^2+1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: q^2+1
      1036: 1
      1037: q^2+1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1066: 1
      1067: q^2+1
      1068: 1
      1069: 1
      1070: 1
      1071: q^2+1
      1072: 1
      1073: q^2+1
      1074: 1
      1075: 1
      1076: q^2+1
      1077: 1
      1078: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1086: q^2+1
      1087: q^2+1
      1088: 1
      1089: q^2+1
      1090: 1
      1091: q^2+1
      1092: 1
      1093: q^2+1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: q^2+1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1113: q^2+1
      1114: 1
      1115: q^2+1
      1116: 1
      1117: 1
      1118: q^2+1
      1119: 1
      1120: q^2+1
      1121: q^2+1
      1122: 1
      1123: q^2+1
      1124: 1
      1125: q^2+1
      1126: 1
      1127: q^2+1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1137: q^2+1
      1138: q^2+1
      1139: q^2+1
      1140: 1
      1141: q^2+1
      1142: q^2+1
      1143: 1
      1144: q^2+1
      1145: q^2+1
      1146: 1
      1147: 1
      1148: 1
      1149: q^2+1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: q^2+1
      1159: 1
      1160: q^2+1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: 1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1180: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1189: 1
      1190: 1
      1191: 1
      1193: 1
      1194: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: q^2+1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: q^2+1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1286: q^2+1
      1287: 1
      1288: q^2+1
      1289: 1
      1290: 1
      1291: q^2+1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1311: q^2+1
      1312: 1
      1313: 1
      1314: 1
      1315: q^2+1
      1316: 1
      1317: q^2+1
      1318: 1
      1319: 1
      1320: q^2+1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1330: q^2+1
      1331: q^2+1
      1332: 1
      1333: q^2+1
      1334: 1
      1335: q^2+1
      1336: 1
      1337: q^2+1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: q^2+1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1380: 1
      1382: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1389: 1
      1390: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1432: 1
      1433: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: q^2+1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: q^2+1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: q^2+1
      1502: 1
      1503: q^2+1
      1504: 1
      1505: 1
      1506: q^2+1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1542: 1
      1545: 1
      1547: 1
      1548: 1
      1550: 1
      1552: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1559: 1
      1560: 1
      1562: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1587: 1
      1589: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1596: 1
      1597: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1642: 1
      1643: q^2+1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1662: 1
      1663: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1673: 1
      1677: 1
      1679: 1
      1682: 1
      1684: 1
      1685: 1
      1687: 1
      1689: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1707: 1
      1709: 1
      1712: 1
      1714: 1
      1715: 1
      1717: 1
      1719: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1726: 1
      1727: 1
      1729: 1
      1730: 1
      1731: 1
      1732: 1
      1733: 1
      1734: 1
      1735: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1742: 1
      1743: 1
      1744: 1
      1745: 1
      1746: 1
      1747: 1
      1748: 1
      1749: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1754: 1
      1755: 1
      1756: 1
      1757: 1
      1758: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1765: 1
      1766: 1
      1767: 1
      1768: 1
      1769: 1
      1770: 1
      1775: 1
      1779: 1
      1781: 1
      1784: 1
      1786: 1
      1787: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1792: 1
      1793: 1
      1794: 1
      1795: 1
      1797: 1
      1801: 1
      1803: 1
      1806: 1
      1808: 1
      1809: 1
      1811: 1
      1813: 1
      1815: 1
      1816: 1
      1817: 1
      1818: 1
      1819: 1
      1820: 1
      1821: 1
      1822: 1
      1823: 1
      1824: 1
      1825: 1
      1826: 1
      1827: 1
      1828: 1
      1829: 1
      1830: 1
      1831: 1
      1832: 1
      1833: 1
      1834: 1
      1835: 1
      1836: 1
      1837: 1
      1838: 1
      1845: 1
      1849: 1
      1850: 1
      1851: 1
      1852: 1
      1853: 1
      1854: 1
      1859: 1
      1863: 1
      1865: 1
      1868: 1
      1870: 1
      1871: 1
      1872: 1
      1873: 1
      1874: 1
      1875: 1
      1876: 1
      1877: 1
      1878: 1
      1879: 1
      1880: 1
      1887: 1
      1888: 1
      1889: 1
      1896: 1
      1900: 1
      1901: 1
      1902: 1
      1903: 1
      1907: 1
      1914: 1

1915:    0: q^2+1
         1: q^2+1
         2: q^2+1
         3: q^2+1
         4: q^2+1
         5: q^2+1
         6: q^2+1
         7: q^2+1
         8: q^2+1
         9: q^2+1
        10: q^2+1
        11: q^2+1
        12: q^2+1
        13: q^2+1
        14: q^2+1
        15: q^2+1
        16: q^2+1
        17: q^2+1
        18: q^2+1
        19: q^2+1
        20: q^2+1
        21: q^2+1
        22: q^2+1
        23: q^2+1
        24: q^2+1
        25: q^2+1
        26: q^2+1
        27: q^2+1
        28: q^2+1
        29: q^2+1
        30: q^2+1
        31: q^2+1
        32: q^2+1
        33: q^2+1
        34: q^2+1
        35: q^2+1
        36: q^2+1
        37: q^2+1
        38: 1
        39: q^2+1
        40: q^2+1
        41: q^2+1
        42: q^2+1
        43: q^2+1
        44: q^2+1
        45: q^2+1
        46: q^2+1
        47: q^2+1
        48: q^2+1
        49: q^2+1
        50: q^2+1
        51: q^2+1
        52: q^2+1
        53: q^2+1
        54: q^2+1
        55: q^2+1
        56: q^2+1
        57: q^2+1
        58: q^2+1
        59: q^2+1
        60: q^2+1
        61: q^2+1
        62: q^2+1
        63: q^2+1
        64: q^2+1
        65: q^2+1
        66: q^2+1
        67: q^2+1
        68: q^2+1
        69: q^2+1
        70: q^2+1
        71: q^2+1
        72: q^2+1
        73: q^2+1
        74: 1
        75: q^2+1
        76: q^2+1
        77: q^2+1
        78: q^2+1
        79: 1
        80: 1
        81: q^2+1
        82: q^2+1
        83: 1
        84: q^2+1
        85: q^2+1
        86: q^2+1
        87: q^2+1
        88: q^2+1
        89: q^2+1
        90: q^2+1
        91: q^2+1
        92: q^2+1
        93: q^2+1
        94: q^2+1
        95: q^2+1
        96: q^2+1
        97: q^2+1
        98: q^2+1
        99: q^2+1
       100: q^2+1
       101: q^2+1
       102: 1
       103: q^2+1
       104: q^2+1
       105: q^2+1
       106: q^2+1
       107: q^2+1
       108: q^2+1
       109: q^2+1
       110: q^2+1
       111: q^2+1
       112: q^2+1
       113: q^2+1
       114: q^2+1
       115: q^2+1
       116: q^2+1
       117: q^2+1
       118: q^2+1
       119: q^2+1
       120: q^2+1
       121: q^2+1
       122: q^2+1
       123: q^2+1
       124: q^2+1
       125: q^2+1
       126: q^2+1
       127: 1
       128: q^2+1
       129: q^2+1
       130: q^2+1
       131: q^2+1
       132: q^2+1
       133: q^2+1
       134: 1
       135: q^2+1
       136: q^2+1
       137: q^2+1
       138: 1
       139: q^2+1
       140: 1
       141: q^2+1
       142: q^2+1
       143: q^2+1
       144: 1
       145: q^2+1
       146: 1
       147: 1
       148: 1
       149: q^2+1
       150: q^2+1
       151: q^2+1
       152: 1
       153: 1
       154: 1
       155: q^2+1
       156: q^2+1
       157: q^2+1
       158: q^2+1
       159: q^2+1
       160: q^2+1
       161: q^2+1
       162: q^2+1
       163: q^2+1
       164: q^2+1
       165: q^2+1
       166: q^2+1
       167: q^2+1
       168: q^2+1
       169: q^2+1
       170: q^2+1
       171: q^2+1
       172: q^2+1
       173: q^2+1
       174: q^2+1
       175: q^2+1
       176: q^2+1
       177: q^2+1
       178: q^2+1
       179: 1
       180: q^2+1
       181: q^2+1
       182: q^2+1
       183: q^2+1
       184: 1
       185: 1
       186: q^2+1
       187: q^2+1
       188: 1
       189: q^2+1
       190: q^2+1
       191: q^2+1
       192: q^2+1
       193: q^2+1
       194: q^2+1
       195: q^2+1
       196: q^2+1
       197: q^2+1
       198: q^2+1
       199: q^2+1
       200: q^2+1
       201: q^2+1
       202: q^2+1
       203: q^2+1
       204: q^2+1
       205: q^2+1
       206: q^2+1
       207: q^2+1
       208: q^2+1
       209: q^2+1
       210: q^2+1
       211: q^2+1
       212: q^2+1
       213: 1
       214: q^2+1
       215: q^2+1
       216: q^2+1
       217: 1
       218: q^2+1
       219: 1
       220: q^2+1
       221: q^2+1
       222: q^2+1
       223: 1
       224: q^2+1
       225: q^2+1
       226: q^2+1
       227: q^2+1
       228: 1
       229: 1
       230: q^2+1
       231: q^2+1
       232: 1
       233: q^2+1
       234: 1
       235: 1
       236: 1
       237: q^2+1
       238: q^2+1
       239: q^2+1
       240: 1
       241: q^2+1
       242: 1
       243: 1
       244: 1
       245: 1
       246: 1
       247: 1
       248: q^2+1
       249: q^2+1
       250: q^2+1
       251: 1
       252: q^2+1
       253: 1
       254: 1
       255: 1
       256: 1
       257: 1
       258: q^2+1
       259: q^2+1
       260: q^2+1
       261: q^2+1
       262: q^2+1
       263: q^2+1
       264: q^2+1
       265: q^2+1
       266: q^2+1
       267: q^2+1
       268: q^2+1
       269: q^2+1
       270: q^2+1
       271: q^2+1
       272: q^2+1
       273: q^2+1
       274: q^2+1
       275: q^2+1
       276: q^2+1
       277: q^2+1
       278: q^2+1
       279: q^2+1
       280: q^2+1
       281: 1
       282: q^2+1
       283: q^2+1
       284: q^2+1
       285: q^2+1
       286: q^2+1
       287: q^2+1
       288: 1
       289: q^2+1
       290: q^2+1
       291: q^2+1
       292: 1
       293: q^2+1
       294: 1
       295: q^2+1
       296: q^2+1
       297: q^2+1
       298: 1
       299: q^2+1
       300: 1
       301: 1
       302: 1
       303: q^2+1
       304: q^2+1
       305: q^2+1
       306: 1
       307: 1
       308: 1
       309: q^2+1
       310: q^2+1
       311: q^2+1
       312: q^2+1
       313: q^2+1
       314: 1
       315: q^2+1
       316: q^2+1
       317: q^2+1
       318: q^2+1
       319: q^2+1
       320: q^2+1
       321: q^2+1
       322: q^2+1
       323: q^2+1
       324: q^2+1
       325: q^2+1
       326: q^2+1
       327: q^2+1
       328: q^2+1
       329: q^2+1
       330: q^2+1
       331: q^2+1
       332: q^2+1
       333: q^2+1
       334: q^2+1
       335: q^2+1
       336: 1
       337: 1
       338: q^2+1
       339: q^2+1
       340: 1
       341: q^2+1
       342: 1
       343: 1
       344: 1
       345: q^2+1
       346: q^2+1
       347: q^2+1
       348: 1
       349: q^2+1
       350: 1
       351: q^2+1
       352: q^2+1
       353: q^2+1
       354: 1
       355: q^2+1
       356: 1
       357: 1
       358: 1
       359: q^2+1
       360: 1
       361: q^2+1
       362: 1
       363: 1
       364: 1
       365: 1
       366: 1
       367: q^2+1
       368: q^2+1
       369: 1
       370: q^2+1
       371: 1
       372: 1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: 1
       380: 1
       381: q^2+1
       382: q^2+1
       383: q^2+1
       384: 1
       385: q^2+1
       386: 1
       387: 1
       388: 1
       389: 1
       390: 1
       391: 1
       392: 1
       393: 1
       394: 1
       395: q^2+1
       396: q^2+1
       397: q^2+1
       398: q^2+1
       399: q^2+1
       400: q^2+1
       401: q^2+1
       402: q^2+1
       403: q^2+1
       404: q^2+1
       405: q^2+1
       406: q^2+1
       407: q^2+1
       408: q^2+1
       409: q^2+1
       410: q^2+1
       411: q^2+1
       412: q^2+1
       413: q^2+1
       414: q^2+1
       415: q^2+1
       416: q^2+1
       417: q^2+1
       418: q^2+1
       419: 1
       420: q^2+1
       421: q^2+1
       422: q^2+1
       423: 1
       424: q^2+1
       425: 1
       426: q^2+1
       427: q^2+1
       428: q^2+1
       429: 1
       430: q^2+1
       431: q^2+1
       432: q^2+1
       433: q^2+1
       434: 1
       435: 1
       436: q^2+1
       437: q^2+1
       438: 1
       439: q^2+1
       440: 1
       441: 1
       442: 1
       443: q^2+1
       444: q^2+1
       445: q^2+1
       446: 1
       447: q^2+1
       448: 1
       449: 1
       450: 1
       451: 1
       452: 1
       453: 1
       454: q^2+1
       455: q^2+1
       456: q^2+1
       457: 1
       458: q^2+1
       459: 1
       460: 1
       461: 1
       462: 1
       463: 1
       464: q^2+1
       465: q^2+1
       466: q^2+1
       467: q^2+1
       468: 1
       469: 1
       470: q^2+1
       471: q^2+1
       472: q^2+1
       473: q^2+1
       474: q^2+1
       475: q^2+1
       476: q^2+1
       477: q^2+1
       478: 1
       479: q^2+1
       480: q^2+1
       481: q^2+1
       482: q^2+1
       483: q^2+1
       484: q^2+1
       485: q^2+1
       486: q^2+1
       487: q^2+1
       488: q^2+1
       489: q^2+1
       490: q^2+1
       491: q^2+1
       492: 1
       493: 1
       494: 1
       495: q^2+1
       496: 1
       497: q^2+1
       498: 1
       499: 1
       500: 1
       501: 1
       502: 1
       503: q^2+1
       504: q^2+1
       505: 1
       506: q^2+1
       507: 1
       508: 1
       509: 1
       510: q^2+1
       511: q^2+1
       512: q^2+1
       513: 1
       514: q^2+1
       515: 1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: q^2+1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: q^2+1
       530: 1
       531: q^2+1
       532: 1
       533: 1
       534: 1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: 1
       543: 1
       544: 1
       545: q^2+1
       546: q^2+1
       547: 1
       548: q^2+1
       549: 1
       550: 1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: 1
       558: 1
       559: 1
       560: 1
       561: 1
       562: 1
       563: q^2+1
       564: q^2+1
       565: q^2+1
       566: q^2+1
       567: q^2+1
       568: 1
       569: q^2+1
       570: q^2+1
       571: q^2+1
       572: q^2+1
       573: q^2+1
       574: q^2+1
       575: q^2+1
       576: q^2+1
       577: q^2+1
       578: q^2+1
       579: q^2+1
       580: q^2+1
       581: q^2+1
       582: q^2+1
       583: q^2+1
       584: q^2+1
       585: q^2+1
       586: q^2+1
       587: q^2+1
       588: q^2+1
       589: q^2+1
       590: 1
       591: 1
       592: q^2+1
       593: q^2+1
       594: 1
       595: q^2+1
       596: 1
       597: 1
       598: 1
       599: q^2+1
       600: q^2+1
       601: q^2+1
       602: 1
       603: q^2+1
       604: 1
       605: q^2+1
       606: q^2+1
       607: q^2+1
       608: 1
       609: q^2+1
       610: 1
       611: 1
       612: 1
       613: q^2+1
       614: 1
       615: q^2+1
       616: 1
       617: 1
       618: 1
       619: 1
       620: 1
       621: q^2+1
       622: q^2+1
       623: 1
       624: q^2+1
       625: 1
       626: 1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: 1
       634: 1
       635: q^2+1
       636: q^2+1
       637: q^2+1
       638: 1
       639: q^2+1
       640: 1
       641: 1
       642: 1
       643: 1
       644: 1
       645: 1
       646: 1
       647: 1
       648: 1
       649: q^2+1
       650: q^2+1
       651: q^2+1
       652: 1
       653: 1
       654: 1
       655: q^2+1
       656: q^2+1
       657: q^2+1
       658: q^2+1
       659: q^2+1
       660: q^2+1
       661: 1
       662: 1
       663: q^2+1
       664: q^2+1
       665: q^2+1
       666: q^2+1
       667: q^2+1
       668: q^2+1
       669: q^2+1
       670: q^2+1
       671: 1
       672: q^2+1
       673: q^2+1
       674: q^2+1
       675: q^2+1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: q^2+1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: q^2+1
       690: 1
       691: q^2+1
       692: 1
       693: 1
       694: 1
       695: 1
       696: 1
       697: q^2+1
       698: q^2+1
       699: 1
       700: q^2+1
       701: 1
       702: 1
       703: 1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: q^2+1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: 1
       731: 1
       732: 1
       733: 1
       734: q^2+1
       735: 1
       736: q^2+1
       737: 1
       738: 1
       739: 1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: 1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: 1
       755: q^2+1
       756: q^2+1
       757: q^2+1
       758: q^2+1
       759: 1
       760: 1
       761: q^2+1
       762: q^2+1
       763: q^2+1
       764: q^2+1
       765: q^2+1
       766: q^2+1
       767: q^2+1
       768: q^2+1
       769: 1
       770: q^2+1
       771: q^2+1
       772: q^2+1
       773: q^2+1
       774: q^2+1
       775: q^2+1
       776: q^2+1
       777: q^2+1
       778: q^2+1
       779: q^2+1
       780: q^2+1
       781: q^2+1
       782: q^2+1
       783: 1
       784: 1
       785: 1
       786: q^2+1
       787: 1
       788: q^2+1
       789: 1
       790: 1
       791: 1
       792: 1
       793: 1
       794: q^2+1
       795: q^2+1
       796: 1
       797: q^2+1
       798: 1
       799: 1
       800: 1
       801: q^2+1
       802: q^2+1
       803: q^2+1
       804: 1
       805: q^2+1
       806: 1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: q^2+1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: q^2+1
       821: 1
       822: q^2+1
       823: 1
       824: 1
       825: 1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: 1
       834: 1
       835: 1
       836: q^2+1
       837: q^2+1
       838: 1
       839: q^2+1
       840: 1
       841: 1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: 1
       849: 1
       850: 1
       851: 1
       852: 1
       853: 1
       854: q^2+1
       855: q^2+1
       856: 1
       857: 1
       858: 1
       859: 1
       860: q^2+1
       861: q^2+1
       862: q^2+1
       863: q^2+1
       864: 1
       865: 1
       866: 1
       867: q^2+1
       868: q^2+1
       869: q^2+1
       870: q^2+1
       871: q^2+1
       872: q^2+1
       873: 1
       874: 1
       875: q^2+1
       876: q^2+1
       877: q^2+1
       878: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: q^2+1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: q^2+1
       901: 1
       902: q^2+1
       903: 1
       904: 1
       905: 1
       906: 1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       914: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: q^2+1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: 1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: 1
       960: q^2+1
       961: q^2+1
       962: q^2+1
       963: 1
       964: 1
       965: 1
       966: q^2+1
       967: q^2+1
       968: q^2+1
       969: q^2+1
       970: q^2+1
       971: q^2+1
       972: 1
       973: 1
       974: q^2+1
       975: q^2+1
       976: q^2+1
       977: q^2+1
       978: q^2+1
       979: q^2+1
       980: q^2+1
       981: q^2+1
       982: 1
       983: q^2+1
       984: q^2+1
       985: q^2+1
       986: q^2+1
       987: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: q^2+1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: q^2+1
      1001: 1
      1002: q^2+1
      1003: 1
      1004: 1
      1005: 1
      1006: 1
      1007: 1
      1008: q^2+1
      1009: q^2+1
      1010: 1
      1011: q^2+1
      1012: 1
      1013: 1
      1014: 1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: q^2+1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: 1
      1042: 1
      1043: 1
      1044: 1
      1045: q^2+1
      1046: 1
      1047: q^2+1
      1048: 1
      1049: 1
      1050: 1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: 1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: 1
      1066: q^2+1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: q^2+1
      1072: q^2+1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: q^2+1
      1078: q^2+1
      1079: q^2+1
      1080: q^2+1
      1081: 1
      1082: 1
      1083: 1
      1084: q^2+1
      1085: q^2+1
      1086: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1094: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: q^2+1
      1110: 1
      1111: 1
      1112: 1
      1113: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1128: 1
      1129: 1
      1130: 1
      1131: 1
      1134: 1
      1135: 1
      1136: 1
      1137: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: 1
      1165: q^2+1
      1166: q^2+1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: q^2+1
      1172: q^2+1
      1173: q^2+1
      1174: q^2+1
      1175: 1
      1176: 1
      1177: 1
      1178: q^2+1
      1179: q^2+1
      1180: q^2+1
      1181: q^2+1
      1182: q^2+1
      1183: q^2+1
      1184: 1
      1185: 1
      1186: q^2+1
      1187: q^2+1
      1188: q^2+1
      1189: 1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: q^2+1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: q^2+1
      1212: 1
      1213: q^2+1
      1214: 1
      1215: 1
      1216: 1
      1217: 1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1225: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: q^2+1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: 1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: 1
      1271: 1
      1272: 1
      1273: 1
      1274: q^2+1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: q^2+1
      1280: q^2+1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: q^2+1
      1286: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1338: 1
      1339: 1
      1340: 1
      1341: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1357: q^2+1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: q^2+1
      1363: q^2+1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: q^2+1
      1369: q^2+1
      1370: q^2+1
      1371: q^2+1
      1372: 1
      1373: 1
      1374: 1
      1375: q^2+1
      1376: q^2+1
      1377: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1385: 1
      1386: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: q^2+1
      1401: 1
      1402: 1
      1403: 1
      1404: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1419: 1
      1420: 1
      1421: 1
      1422: 1
      1425: 1
      1426: 1
      1427: 1
      1428: 1
      1429: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: q^2+1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: 1
      1522: 1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: q^2+1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: q^2+1
      1534: q^2+1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: q^2+1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1595: 1
      1598: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1660: 1
      1661: 1
      1662: 1
      1663: 1
      1664: 1
      1665: 1
      1666: 1
      1667: q^2+1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1684: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1706: 1
      1707: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1715: 1
      1716: 1
      1720: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1725: 1
      1728: 1
      1729: 1
      1730: 1
      1731: 1
      1732: 1
      1733: 1
      1734: 1
      1735: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1742: 1
      1743: 1
      1744: 1
      1745: 1
      1746: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1758: 1
      1759: 1
      1764: 1
      1765: 1
      1766: 1
      1767: 1
      1768: 1
      1769: 1
      1770: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1775: 1
      1776: 1
      1777: 1
      1778: 1
      1779: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1786: 1
      1787: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1796: 1
      1797: 1
      1798: 1
      1799: 1
      1800: 1
      1801: 1
      1802: 1
      1807: 1
      1808: 1
      1809: 1
      1810: 1
      1814: 1
      1815: 1
      1816: 1
      1817: 1
      1818: 1
      1819: 1
      1820: 1
      1821: 1
      1822: 1
      1823: 1
      1826: 1
      1827: 1
      1831: 1
      1836: 1
      1837: 1
      1838: 1
      1839: 1
      1840: 1
      1841: 1
      1842: 1
      1843: 1
      1844: 1
      1845: 1
      1846: 1
      1847: 1
      1848: 1
      1849: 1
      1850: 1
      1851: 1
      1855: 1
      1856: 1
      1857: 1
      1858: 1
      1863: 1
      1864: 1
      1869: 1
      1870: 1
      1871: 1
      1872: 1
      1874: 1
      1880: 1
      1881: 1
      1882: 1
      1883: 1
      1884: 1
      1885: 1
      1886: 1
      1887: 1
      1890: 1
      1891: 1
      1895: 1
      1900: 1
      1904: 1
      1905: 1
      1906: 1
      1908: 1
      1915: 1

1916:    0: q^3+2q^2+2q+1
         1: q^3+2q^2+2q+1
         2: q^3+2q^2+2q+1
         3: 2q^2+2q+1
         4: q^3+2q^2+2q+1
         5: q^3+2q^2+2q+1
         6: q^3+2q^2+2q+1
         7: q^3+2q^2+2q+1
         8: 2q^2+2q+1
         9: 2q^2+2q+1
        10: 2q^2+2q+1
        11: 2q^2+2q+1
        12: 2q^2+2q+1
        13: q^3+2q^2+2q+1
        14: q^3+2q^2+2q+1
        15: 2q^2+2q+1
        16: q^3+2q^2+2q+1
        17: q^3+2q^2+2q+1
        18: 2q^2+2q+1
        19: q^3+2q^2+2q+1
        20: 2q^2+2q+1
        21: q^3+2q^2+2q+1
        22: 2q^2+2q+1
        23: 2q^2+2q+1
        24: 2q^2+2q+1
        25: 2q^2+2q+1
        26: 2q^2+2q+1
        27: 2q^2+2q+1
        28: 2q^2+2q+1
        29: 2q^2+2q+1
        30: 2q^2+2q+1
        31: 2q^2+2q+1
        32: 2q^2+2q+1
        33: q^3+2q^2+2q+1
        34: q^3+2q^2+2q+1
        35: 2q^2+2q+1
        36: 2q^2+2q+1
        37: 2q^2+2q+1
        38: 2q^2+2q+1
        39: 2q^2+2q+1
        40: q^3+2q^2+2q+1
        41: q^3+2q^2+2q+1
        42: 2q^2+2q+1
        43: 2q^2+2q+1
        44: 2q^2+2q+1
        45: 2q^2+2q+1
        46: 2q^2+2q+1
        47: q^3+2q^2+2q+1
        48: q^3+2q^2+2q+1
        49: 2q^2+2q+1
        50: 2q^2+2q+1
        51: 2q^2+2q+1
        52: 2q^2+2q+1
        53: 2q^2+2q+1
        54: 2q^2+2q+1
        55: 2q^2+2q+1
        56: 2q^2+2q+1
        57: 2q^2+2q+1
        58: 2q^2+2q+1
        59: 2q^2+2q+1
        60: 2q^2+2q+1
        61: 2q^2+2q+1
        62: 2q^2+2q+1
        63: 2q^2+2q+1
        64: q^2+2q+1
        65: 2q^2+2q+1
        66: 2q^2+2q+1
        67: q^2+2q+1
        68: 2q^2+2q+1
        69: 2q^2+2q+1
        70: q^2+2q+1
        71: 2q^2+2q+1
        72: q^3+2q^2+2q+1
        73: 2q^2+2q+1
        74: 2q^2+2q+1
        75: 2q^2+2q+1
        76: 2q^2+2q+1
        77: 2q^2+2q+1
        78: 2q^2+2q+1
        79: 2q^2+2q+1
        80: 2q^2+2q+1
        81: 2q^2+2q+1
        82: 2q^2+2q+1
        83: 2q^2+2q+1
        84: 2q^2+2q+1
        85: q^3+2q^2+2q+1
        86: 2q^2+2q+1
        87: 2q^2+2q+1
        88: 2q^2+2q+1
        89: 2q^2+2q+1
        90: 2q^2+2q+1
        91: 2q^2+2q+1
        92: 2q^2+2q+1
        93: 2q^2+2q+1
        94: 2q^2+2q+1
        95: 2q^2+2q+1
        96: 2q^2+2q+1
        97: q^3+2q^2+2q+1
        98: q^3+2q^2+2q+1
        99: 2q^2+2q+1
       100: 2q^2+2q+1
       101: 2q^2+2q+1
       102: 2q^2+2q+1
       103: 2q^2+2q+1
       104: 2q^2+2q+1
       105: 2q^2+2q+1
       106: 2q^2+2q+1
       107: 2q^2+2q+1
       108: 2q^2+2q+1
       109: 2q^2+2q+1
       110: 2q^2+2q+1
       111: q^2+2q+1
       112: 2q^2+2q+1
       113: 2q^2+2q+1
       114: 2q^2+2q+1
       115: 2q^2+2q+1
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       118: 2q^2+2q+1
       119: q^2+2q+1
       120: 2q^2+2q+1
       121: q^2+2q+1
       122: q^2+2q+1
       123: q^2+2q+1
       124: q^2+2q+1
       125: 2q^2+2q+1
       126: q^2+2q+1
       127: q^2+2q+1
       128: q^2+2q+1
       129: 2q^2+2q+1
       130: 2q^2+2q+1
       131: 2q+1
       132: q^2+2q+1
       133: q^2+2q+1
       134: 2q^2+2q+1
       135: 2q^2+2q+1
       136: 2q^2+2q+1
       137: 2q^2+2q+1
       138: 2q^2+2q+1
       139: 2q^2+2q+1
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       146: 2q^2+2q+1
       147: 2q^2+2q+1
       148: q^2+2q+1
       149: 2q^2+2q+1
       150: 2q^2+2q+1
       151: q^2+2q+1
       152: 2q^2+2q+1
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       154: q^2+2q+1
       155: 2q^2+2q+1
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       168: 2q^2+2q+1
       169: q^2+2q+1
       170: 2q^2+2q+1
       171: 2q^2+2q+1
       172: q^2+2q+1
       173: 2q^2+2q+1
       174: 2q^2+2q+1
       175: q^2+2q+1
       176: 2q^2+2q+1
       177: q^3+2q^2+2q+1
       178: 2q^2+2q+1
       179: 2q^2+2q+1
       180: 2q^2+2q+1
       181: 2q^2+2q+1
       182: 2q^2+2q+1
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       189: q^2+2q+1
       190: 2q^2+2q+1
       191: 2q^2+2q+1
       192: 2q^2+2q+1
       193: q^2+2q+1
       194: q^2+2q+1
       195: 2q^2+2q+1
       196: q^2+2q+1
       197: q^2+2q+1
       198: 2q^2+2q+1
       199: 2q^2+2q+1
       200: 2q^2+2q+1
       201: 2q^2+2q+1
       202: 2q^2+2q+1
       203: 2q^2+2q+1
       204: 2q^2+2q+1
       205: 2q+1
       206: q^2+2q+1
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       208: q^2+2q+1
       209: q^2+2q+1
       210: q^2+2q+1
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       218: q^2+2q+1
       219: q^2+2q+1
       220: 2q+1
       221: 2q^2+2q+1
       222: 2q+1
       223: 2q+1
       224: 2q+1
       225: q^2+2q+1
       226: q^2+2q+1
       227: 2q+1
       228: 2q^2+2q+1
       229: 2q^2+2q+1
       230: 2q^2+2q+1
       231: 2q^2+2q+1
       232: 2q^2+2q+1
       233: 2q^2+2q+1
       234: 2q^2+2q+1
       235: q^2+2q+1
       236: 2q^2+2q+1
       237: 2q^2+2q+1
       238: 2q^2+2q+1
       239: 2q^2+2q+1
       240: 2q^2+2q+1
       241: 2q^2+2q+1
       242: 2q^2+2q+1
       243: q^2+2q+1
       244: 2q^2+2q+1
       245: q^2+2q+1
       246: q^2+2q+1
       247: q^2+2q+1
       248: q^2+2q+1
       249: 2q^2+2q+1
       250: q^2+2q+1
       251: q^2+2q+1
       252: q^2+2q+1
       253: 2q^2+2q+1
       254: 2q^2+2q+1
       255: 2q+1
       256: q^2+2q+1
       257: q^2+2q+1
       258: 2q^2+2q+1
       259: 2q^2+2q+1
       260: 2q^2+2q+1
       261: 2q^2+2q+1
       262: 2q^2+2q+1
       263: 2q^2+2q+1
       264: 2q^2+2q+1
       265: q^2+2q+1
       266: 2q^2+2q+1
       267: 2q^2+2q+1
       268: 2q^2+2q+1
       269: 2q^2+2q+1
       270: 2q^2+2q+1
       271: 2q^2+2q+1
       272: 2q^2+2q+1
       273: q^2+2q+1
       274: 2q^2+2q+1
       275: q^2+2q+1
       276: q^2+2q+1
       277: q^2+2q+1
       278: q^2+2q+1
       279: 2q^2+2q+1
       280: q^2+2q+1
       281: q^2+2q+1
       282: q^2+2q+1
       283: 2q^2+2q+1
       284: 2q^2+2q+1
       285: 2q+1
       286: q^2+2q+1
       287: q^2+2q+1
       288: 2q^2+2q+1
       289: 2q^2+2q+1
       290: 2q^2+2q+1
       291: 2q^2+2q+1
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       293: 2q^2+2q+1
       294: 2q^2+2q+1
       295: 2q^2+2q+1
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       298: 2q^2+2q+1
       299: 2q^2+2q+1
       300: 2q^2+2q+1
       301: 2q^2+2q+1
       302: q^2+2q+1
       303: 2q^2+2q+1
       304: 2q^2+2q+1
       305: q^2+2q+1
       306: 2q^2+2q+1
       307: 2q^2+2q+1
       308: q^2+2q+1
       309: q^2+2q+1
       310: q^2+2q+1
       311: 2q^2+2q+1
       312: q^2+2q+1
       313: q^2+2q+1
       314: q^2+2q+1
       315: q^2+2q+1
       316: 2q+1
       317: q^2+2q+1
       318: q^2+2q+1
       319: 2q+1
       320: 2q^2+2q+1
       321: 2q^2+2q+1
       322: 2q^2+2q+1
       323: q^2+2q+1
       324: q^2+2q+1
       325: 2q^2+2q+1
       326: 2q+1
       327: 2q+1
       328: q^2+2q+1
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       330: q^2+2q+1
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       333: q^2+2q+1
       334: q^2+2q+1
       335: 2q+1
       336: q^2+2q+1
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       338: q^2+2q+1
       339: q^2+2q+1
       340: q^2+2q+1
       341: q^2+2q+1
       342: q^2+2q+1
       343: 2q+1
       344: 2q+1
       345: 2q+1
       346: 2q+1
       347: 2q+1
       348: 2q+1
       349: 2q+1
       350: 2q+1
       351: 2q+1
       352: q^2+2q+1
       353: 2q+1
       354: 2q+1
       355: 2q+1
       356: q^2+2q+1
       357: 2q^2+2q+1
       358: 2q^2+2q+1
       359: 2q^2+2q+1
       360: q^2+2q+1
       361: q^2+2q+1
       362: 2q^2+2q+1
       363: q^2+2q+1
       364: q^2+2q+1
       365: 2q^2+2q+1
       366: 2q^2+2q+1
       367: 2q^2+2q+1
       368: 2q^2+2q+1
       369: 2q^2+2q+1
       370: 2q^2+2q+1
       371: 2q^2+2q+1
       372: 2q+1
       373: q^2+2q+1
       374: q^2+2q+1
       375: q^2+2q+1
       376: q^2+2q+1
       377: q^2+2q+1
       378: q^2+2q+1
       379: q^2+2q+1
       380: q^2+2q+1
       381: q^2+2q+1
       382: q^2+2q+1
       383: q^2+2q+1
       384: q^2+2q+1
       385: q^2+2q+1
       386: q^2+2q+1
       387: 2q+1
       388: 2q^2+2q+1
       389: 2q+1
       390: 2q+1
       391: 2q+1
       392: q^2+2q+1
       393: q^2+2q+1
       394: 2q+1
       395: q^2+2q+1
       396: 2q^2+2q+1
       397: 2q^2+2q+1
       398: 2q^2+2q+1
       399: q^2+2q+1
       400: q^2+2q+1
       401: 2q^2+2q+1
       402: q^2+2q+1
       403: q^2+2q+1
       404: 2q^2+2q+1
       405: 2q^2+2q+1
       406: 2q^2+2q+1
       407: 2q^2+2q+1
       408: 2q^2+2q+1
       409: 2q^2+2q+1
       410: 2q^2+2q+1
       411: 2q+1
       412: q^2+2q+1
       413: q^2+2q+1
       414: q^2+2q+1
       415: q^2+2q+1
       416: q^2+2q+1
       417: q^2+2q+1
       418: q^2+2q+1
       419: q^2+2q+1
       420: q^2+2q+1
       421: q^2+2q+1
       422: q^2+2q+1
       423: q^2+2q+1
       424: q^2+2q+1
       425: q^2+2q+1
       426: 2q+1
       427: 2q^2+2q+1
       428: 2q+1
       429: 2q+1
       430: 2q+1
       431: q^2+2q+1
       432: q^2+2q+1
       433: 2q+1
       434: 2q^2+2q+1
       435: 2q^2+2q+1
       436: 2q^2+2q+1
       437: 2q^2+2q+1
       438: 2q^2+2q+1
       439: 2q^2+2q+1
       440: 2q^2+2q+1
       441: q^2+2q+1
       442: 2q^2+2q+1
       443: 2q^2+2q+1
       444: 2q^2+2q+1
       445: 2q^2+2q+1
       446: 2q^2+2q+1
       447: 2q^2+2q+1
       448: 2q^2+2q+1
       449: q^2+2q+1
       450: 2q^2+2q+1
       451: q^2+2q+1
       452: q^2+2q+1
       453: q^2+2q+1
       454: q^2+2q+1
       455: 2q^2+2q+1
       456: q^2+2q+1
       457: q^2+2q+1
       458: q^2+2q+1
       459: 2q^2+2q+1
       460: 2q^2+2q+1
       461: 2q+1
       462: q^2+2q+1
       463: q^2+2q+1
       464: q^2+2q+1
       465: q^2+2q+1
       466: 2q+1
       467: q^2+2q+1
       468: q^2+2q+1
       469: 2q+1
       470: 2q+1
       471: 2q+1
       472: q^2+2q+1
       473: 2q+1
       474: 2q+1
       475: 2q^2+2q+1
       476: q^2+2q+1
       477: q^2+2q+1
       478: q^2+2q+1
       479: q^2+2q+1
       480: 2q+1
       481: 2q+1
       482: 2q+1
       483: 2q+1
       484: q^2+2q+1
       485: q^2+2q+1
       486: q^2+2q+1
       487: q^2+2q+1
       488: q+1
       489: q^2+2q+1
       490: 2q+1
       491: 2q+1
       492: 2q+1
       493: q^2+2q+1
       494: q^2+2q+1
       495: q^2+2q+1
       496: q+1
       497: q^2+2q+1
       498: q^2+2q+1
       499: 2q+1
       500: 2q+1
       501: 2q+1
       502: 2q+1
       503: 2q+1
       504: 2q+1
       505: 2q+1
       506: 2q+1
       507: 2q+1
       508: 2q+1
       509: 2q+1
       510: 2q+1
       511: 2q+1
       512: 2q+1
       513: 2q+1
       514: 2q+1
       515: 2q+1
       516: q^2+2q+1
       517: q^2+2q+1
       518: 2q^2+2q+1
       519: q^2+2q+1
       520: q^2+2q+1
       521: q^2+2q+1
       522: q^2+2q+1
       523: 2q+1
       524: q^2+2q+1
       525: q^2+2q+1
       526: 2q+1
       527: 2q^2+2q+1
       528: 2q^2+2q+1
       529: 2q^2+2q+1
       530: q^2+2q+1
       531: q^2+2q+1
       532: 2q^2+2q+1
       533: 2q+1
       534: 2q+1
       535: q^2+2q+1
       536: q^2+2q+1
       537: q^2+2q+1
       538: q^2+2q+1
       539: q^2+2q+1
       540: q^2+2q+1
       541: q^2+2q+1
       542: 2q+1
       543: q^2+2q+1
       544: q^2+2q+1
       545: q^2+2q+1
       546: q^2+2q+1
       547: q^2+2q+1
       548: q^2+2q+1
       549: q^2+2q+1
       550: 2q+1
       551: 2q+1
       552: 2q+1
       553: 2q+1
       554: 2q+1
       555: 2q+1
       556: 2q+1
       557: 2q+1
       558: 2q+1
       559: q^2+2q+1
       560: 2q+1
       561: 2q+1
       562: 2q+1
       563: q^2+2q+1
       564: q^2+2q+1
       565: 2q^2+2q+1
       566: q^2+2q+1
       567: q^2+2q+1
       568: q^2+2q+1
       569: q^2+2q+1
       570: 2q+1
       571: q^2+2q+1
       572: q^2+2q+1
       573: 2q+1
       574: 2q^2+2q+1
       575: 2q^2+2q+1
       576: 2q^2+2q+1
       577: q^2+2q+1
       578: q^2+2q+1
       579: 2q^2+2q+1
       580: 2q+1
       581: 2q+1
       582: q^2+2q+1
       583: q^2+2q+1
       584: q^2+2q+1
       585: q^2+2q+1
       586: q^2+2q+1
       587: q^2+2q+1
       588: q^2+2q+1
       589: 2q+1
       590: q^2+2q+1
       591: q^2+2q+1
       592: q^2+2q+1
       593: q^2+2q+1
       594: q^2+2q+1
       595: q^2+2q+1
       596: q^2+2q+1
       597: 2q+1
       598: 2q+1
       599: 2q+1
       600: 2q+1
       601: 2q+1
       602: 2q+1
       603: 2q+1
       604: 2q+1
       605: 2q+1
       606: q^2+2q+1
       607: 2q+1
       608: 2q+1
       609: 2q+1
       610: q^2+2q+1
       611: 2q^2+2q+1
       612: 2q^2+2q+1
       613: 2q^2+2q+1
       614: q^2+2q+1
       615: q^2+2q+1
       616: 2q^2+2q+1
       617: q^2+2q+1
       618: q^2+2q+1
       619: 2q^2+2q+1
       620: 2q^2+2q+1
       621: 2q^2+2q+1
       622: 2q^2+2q+1
       623: 2q^2+2q+1
       624: 2q^2+2q+1
       625: 2q^2+2q+1
       626: 2q+1
       627: q^2+2q+1
       628: q^2+2q+1
       629: q^2+2q+1
       630: q^2+2q+1
       631: q^2+2q+1
       632: q^2+2q+1
       633: q^2+2q+1
       634: q^2+2q+1
       635: q^2+2q+1
       636: q^2+2q+1
       637: q^2+2q+1
       638: q^2+2q+1
       639: q^2+2q+1
       640: q^2+2q+1
       641: 2q+1
       642: 2q^2+2q+1
       643: 2q+1
       644: 2q+1
       645: 2q+1
       646: q^2+2q+1
       647: q^2+2q+1
       648: 2q+1
       649: q^2+2q+1
       650: 2q+1
       651: 2q+1
       652: 2q+1
       653: 2q+1
       654: 2q+1
       655: 2q+1
       656: 2q+1
       657: 2q+1
       658: 2q+1
       659: 2q+1
       660: q^2+2q+1
       661: q^2+2q+1
       662: 2q+1
       663: 2q+1
       664: 2q+1
       665: 2q+1
       666: 2q+1
       667: 2q+1
       668: q^2+2q+1
       669: q^2+2q+1
       670: q^2+2q+1
       671: q+1
       672: q+1
       673: q+1
       674: 2q+1
       675: 2q+1
       676: 2q+1
       677: 2q+1
       678: q^2+2q+1
       679: q+1
       680: q+1
       681: q^2+2q+1
       682: q^2+2q+1
       683: q+1
       684: 2q+1
       685: 2q+1
       686: 2q+1
       687: 2q+1
       688: 2q+1
       689: 2q+1
       690: q+1
       691: q+1
       692: 2q+1
       693: 2q+1
       694: 2q+1
       695: 2q+1
       696: 2q+1
       697: 2q+1
       698: 2q+1
       699: 2q+1
       700: 2q+1
       701: 2q+1
       702: q+1
       703: q^2+2q+1
       704: q^2+2q+1
       705: 2q+1
       706: q^2+2q+1
       707: q^2+2q+1
       708: 2q+1
       709: 2q+1
       710: 2q+1
       711: q^2+2q+1
       712: 2q+1
       713: 2q+1
       714: 2q^2+2q+1
       715: q^2+2q+1
       716: q^2+2q+1
       717: q^2+2q+1
       718: q^2+2q+1
       719: 2q+1
       720: 2q+1
       721: 2q+1
       722: 2q+1
       723: q^2+2q+1
       724: q^2+2q+1
       725: q^2+2q+1
       726: q^2+2q+1
       727: q+1
       728: q^2+2q+1
       729: 2q+1
       730: 2q+1
       731: 2q+1
       732: q^2+2q+1
       733: q^2+2q+1
       734: q^2+2q+1
       735: q+1
       736: q^2+2q+1
       737: q^2+2q+1
       738: 2q+1
       739: 2q+1
       740: 2q+1
       741: 2q+1
       742: 2q+1
       743: 2q+1
       744: 2q+1
       745: 2q+1
       746: 2q+1
       747: 2q+1
       748: 2q+1
       749: 2q+1
       750: 2q+1
       751: 2q+1
       752: 2q+1
       753: 2q+1
       754: 2q+1
       755: q^2+2q+1
       756: q^2+2q+1
       757: 2q+1
       758: q^2+2q+1
       759: q^2+2q+1
       760: 2q+1
       761: 2q+1
       762: 2q+1
       763: q^2+2q+1
       764: 2q+1
       765: 2q+1
       766: 2q^2+2q+1
       767: q^2+2q+1
       768: q^2+2q+1
       769: q^2+2q+1
       770: q^2+2q+1
       771: 2q+1
       772: 2q+1
       773: 2q+1
       774: 2q+1
       775: q^2+2q+1
       776: q^2+2q+1
       777: q^2+2q+1
       778: q^2+2q+1
       779: q+1
       780: q^2+2q+1
       781: 2q+1
       782: 2q+1
       783: 2q+1
       784: q^2+2q+1
       785: q^2+2q+1
       786: q^2+2q+1
       787: q+1
       788: q^2+2q+1
       789: q^2+2q+1
       790: 2q+1
       791: 2q+1
       792: 2q+1
       793: 2q+1
       794: 2q+1
       795: 2q+1
       796: 2q+1
       797: 2q+1
       798: 2q+1
       799: 2q+1
       800: 2q+1
       801: 2q+1
       802: 2q+1
       803: 2q+1
       804: 2q+1
       805: 2q+1
       806: 2q+1
       807: q^2+2q+1
       808: q^2+2q+1
       809: 2q^2+2q+1
       810: q^2+2q+1
       811: q^2+2q+1
       812: q^2+2q+1
       813: q^2+2q+1
       814: 2q+1
       815: q^2+2q+1
       816: q^2+2q+1
       817: 2q+1
       818: 2q^2+2q+1
       819: 2q^2+2q+1
       820: 2q^2+2q+1
       821: q^2+2q+1
       822: q^2+2q+1
       823: 2q^2+2q+1
       824: 2q+1
       825: 2q+1
       826: q^2+2q+1
       827: q^2+2q+1
       828: q^2+2q+1
       829: q^2+2q+1
       830: q^2+2q+1
       831: q^2+2q+1
       832: q^2+2q+1
       833: 2q+1
       834: q^2+2q+1
       835: q^2+2q+1
       836: q^2+2q+1
       837: q^2+2q+1
       838: q^2+2q+1
       839: q^2+2q+1
       840: q^2+2q+1
       841: 2q+1
       842: 2q+1
       843: 2q+1
       844: 2q+1
       845: 2q+1
       846: 2q+1
       847: 2q+1
       848: 2q+1
       849: 2q+1
       850: q^2+2q+1
       851: 2q+1
       852: 2q+1
       853: 2q+1
       854: 2q+1
       855: 2q+1
       856: 2q+1
       857: 2q+1
       858: 2q+1
       859: 2q+1
       860: 2q+1
       861: 2q+1
       862: 2q+1
       863: 2q+1
       864: 2q+1
       865: 2q+1
       866: 2q+1
       867: 2q+1
       868: 2q+1
       869: 2q+1
       870: 2q+1
       871: q+1
       872: q^2+2q+1
       873: q+1
       874: q+1
       875: q+1
       876: q+1
       877: 2q+1
       878: 2q+1
       879: 2q+1
       880: q+1
       881: q+1
       882: q^2+2q+1
       883: q+1
       884: q+1
       885: q+1
       886: 2q+1
       887: 2q+1
       888: 2q+1
       889: 2q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: 1
       895: 2q+1
       896: 2q+1
       897: q+1
       898: 2q+1
       899: 2q+1
       900: 2q+1
       901: q+1
       902: q+1
       903: 2q+1
       904: q+1
       905: q+1
       906: q^2+2q+1
       907: 2q+1
       908: 2q+1
       909: 2q+1
       910: 2q+1
       911: 2q+1
       912: 2q+1
       913: 2q+1
       914: 2q+1
       915: 2q+1
       916: 2q+1
       917: q^2+2q+1
       918: q^2+2q+1
       919: 2q+1
       920: 2q+1
       921: 2q+1
       922: 2q+1
       923: 2q+1
       924: 2q+1
       925: q^2+2q+1
       926: q^2+2q+1
       927: q^2+2q+1
       928: q+1
       929: q+1
       930: q+1
       931: 2q+1
       932: 2q+1
       933: 2q+1
       934: 2q+1
       935: q^2+2q+1
       936: q+1
       937: q+1
       938: q^2+2q+1
       939: q^2+2q+1
       940: q+1
       941: 2q+1
       942: 2q+1
       943: 2q+1
       944: 2q+1
       945: 2q+1
       946: 2q+1
       947: q+1
       948: q+1
       949: 2q+1
       950: 2q+1
       951: 2q+1
       952: 2q+1
       953: 2q+1
       954: 2q+1
       955: 2q+1
       956: 2q+1
       957: 2q+1
       958: 2q+1
       959: q+1
       960: q^2+2q+1
       961: 2q+1
       962: 2q+1
       963: 2q+1
       964: 2q+1
       965: 2q+1
       966: 2q+1
       967: 2q+1
       968: 2q+1
       969: 2q+1
       970: 2q+1
       971: q^2+2q+1
       972: q^2+2q+1
       973: 2q+1
       974: 2q+1
       975: 2q+1
       976: 2q+1
       977: 2q+1
       978: 2q+1
       979: q^2+2q+1
       980: q^2+2q+1
       981: q^2+2q+1
       982: q+1
       983: q+1
       984: q+1
       985: 2q+1
       986: 2q+1
       987: 2q+1
       988: 2q+1
       989: q^2+2q+1
       990: q+1
       991: q+1
       992: q^2+2q+1
       993: q^2+2q+1
       994: q+1
       995: 2q+1
       996: 2q+1
       997: 2q+1
       998: 2q+1
       999: 2q+1
      1000: 2q+1
      1001: q+1
      1002: q+1
      1003: 2q+1
      1004: 2q+1
      1005: 2q+1
      1006: 2q+1
      1007: 2q+1
      1008: 2q+1
      1009: 2q+1
      1010: 2q+1
      1011: 2q+1
      1012: 2q+1
      1013: q+1
      1014: q^2+2q+1
      1015: q^2+2q+1
      1016: 2q+1
      1017: q^2+2q+1
      1018: q^2+2q+1
      1019: 2q+1
      1020: 2q+1
      1021: 2q+1
      1022: q^2+2q+1
      1023: 2q+1
      1024: 2q+1
      1025: 2q^2+2q+1
      1026: q^2+2q+1
      1027: q^2+2q+1
      1028: q^2+2q+1
      1029: q^2+2q+1
      1030: 2q+1
      1031: 2q+1
      1032: 2q+1
      1033: 2q+1
      1034: q^2+2q+1
      1035: q^2+2q+1
      1036: q^2+2q+1
      1037: q^2+2q+1
      1038: q+1
      1039: q^2+2q+1
      1040: 2q+1
      1041: 2q+1
      1042: 2q+1
      1043: q^2+2q+1
      1044: q^2+2q+1
      1045: q^2+2q+1
      1046: q+1
      1047: q^2+2q+1
      1048: q^2+2q+1
      1049: 2q+1
      1050: 2q+1
      1051: 2q+1
      1052: 2q+1
      1053: 2q+1
      1054: 2q+1
      1055: 2q+1
      1056: 2q+1
      1057: 2q+1
      1058: 2q+1
      1059: 2q+1
      1060: 2q+1
      1061: 2q+1
      1062: 2q+1
      1063: 2q+1
      1064: 2q+1
      1065: 2q+1
      1066: 2q+1
      1067: 2q+1
      1068: 2q+1
      1069: q+1
      1070: 2q+1
      1071: 2q+1
      1072: 2q+1
      1073: 2q+1
      1074: 2q+1
      1075: 2q+1
      1076: 2q+1
      1077: 2q+1
      1078: 2q+1
      1079: q+1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: q+1
      1084: q+1
      1085: q+1
      1086: 2q+1
      1087: q+1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: q+1
      1092: q+1
      1093: q+1
      1094: 2q+1
      1095: 2q+1
      1096: 1
      1097: q+1
      1098: q+1
      1099: 1
      1100: 1
      1101: 1
      1102: 2q+1
      1103: q+1
      1104: q+1
      1105: 2q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: 1
      1111: q+1
      1112: q+1
      1113: 2q+1
      1114: 2q+1
      1115: 2q+1
      1116: 2q+1
      1117: 2q+1
      1118: 2q+1
      1119: 2q+1
      1120: 2q+1
      1121: 2q+1
      1122: 2q+1
      1123: 2q+1
      1124: 2q+1
      1125: 2q+1
      1126: 2q+1
      1127: 2q+1
      1128: 2q+1
      1129: 2q+1
      1130: q+1
      1131: q^2+2q+1
      1132: q+1
      1133: q+1
      1134: q+1
      1135: q+1
      1136: 2q+1
      1137: 2q+1
      1138: 2q+1
      1139: q+1
      1140: q+1
      1141: q^2+2q+1
      1142: q+1
      1143: q+1
      1144: q+1
      1145: 2q+1
      1146: 2q+1
      1147: 2q+1
      1148: 2q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: 1
      1154: 2q+1
      1155: 2q+1
      1156: q+1
      1157: 2q+1
      1158: 2q+1
      1159: 2q+1
      1160: q+1
      1161: q+1
      1162: 2q+1
      1163: q+1
      1164: q+1
      1165: 2q+1
      1166: 2q+1
      1167: 2q+1
      1168: 2q+1
      1169: 2q+1
      1170: 2q+1
      1171: 2q+1
      1172: 2q+1
      1173: 2q+1
      1174: 2q+1
      1175: 2q+1
      1176: 2q+1
      1177: 2q+1
      1178: 2q+1
      1179: 2q+1
      1180: 2q+1
      1181: 2q+1
      1182: q+1
      1183: q^2+2q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: q+1
      1188: 2q+1
      1189: 2q+1
      1190: 2q+1
      1191: q+1
      1192: q+1
      1193: q^2+2q+1
      1194: q+1
      1195: q+1
      1196: q+1
      1197: 2q+1
      1198: 2q+1
      1199: 2q+1
      1200: 2q+1
      1201: q+1
      1202: q+1
      1203: q+1
      1204: q+1
      1205: 1
      1206: 2q+1
      1207: 2q+1
      1208: q+1
      1209: 2q+1
      1210: 2q+1
      1211: 2q+1
      1212: q+1
      1213: q+1
      1214: 2q+1
      1215: q+1
      1216: q+1
      1217: q^2+2q+1
      1218: 2q+1
      1219: 2q+1
      1220: 2q+1
      1221: 2q+1
      1222: 2q+1
      1223: 2q+1
      1224: 2q+1
      1225: 2q+1
      1226: 2q+1
      1227: 2q+1
      1228: q^2+2q+1
      1229: q^2+2q+1
      1230: 2q+1
      1231: 2q+1
      1232: 2q+1
      1233: 2q+1
      1234: 2q+1
      1235: 2q+1
      1236: q^2+2q+1
      1237: q^2+2q+1
      1238: q^2+2q+1
      1239: q+1
      1240: q+1
      1241: q+1
      1242: 2q+1
      1243: 2q+1
      1244: 2q+1
      1245: 2q+1
      1246: q^2+2q+1
      1247: q+1
      1248: q+1
      1249: q^2+2q+1
      1250: q^2+2q+1
      1251: q+1
      1252: 2q+1
      1253: 2q+1
      1254: 2q+1
      1255: 2q+1
      1256: 2q+1
      1257: 2q+1
      1258: q+1
      1259: q+1
      1260: 2q+1
      1261: 2q+1
      1262: 2q+1
      1263: 2q+1
      1264: 2q+1
      1265: 2q+1
      1266: 2q+1
      1267: 2q+1
      1268: 2q+1
      1269: 2q+1
      1270: q+1
      1271: 2q+1
      1272: q+1
      1273: q+1
      1274: 2q+1
      1275: 2q+1
      1276: 2q+1
      1277: 1
      1278: 2q+1
      1279: q+1
      1280: q+1
      1281: q+1
      1282: q+1
      1283: q+1
      1284: q+1
      1285: q+1
      1286: q+1
      1287: q+1
      1288: q+1
      1289: q+1
      1290: q+1
      1291: q+1
      1292: q+1
      1293: 2q+1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1301: q+1
      1302: q+1
      1303: 1
      1304: q+1
      1305: q+1
      1306: 1
      1307: 1
      1308: 1
      1309: q+1
      1310: 2q+1
      1311: 2q+1
      1312: 2q+1
      1313: q+1
      1314: 2q+1
      1315: 2q+1
      1316: 2q+1
      1317: 2q+1
      1318: 2q+1
      1319: 2q+1
      1320: 2q+1
      1321: 2q+1
      1322: 2q+1
      1323: q+1
      1324: q+1
      1325: q+1
      1326: q+1
      1327: q+1
      1328: q+1
      1329: q+1
      1330: 2q+1
      1331: q+1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: q+1
      1336: q+1
      1337: q+1
      1338: 2q+1
      1339: 2q+1
      1340: 1
      1341: q+1
      1342: q+1
      1343: 1
      1344: 1
      1345: 1
      1346: 2q+1
      1347: q+1
      1348: q+1
      1349: 2q+1
      1350: q+1
      1351: q+1
      1352: q+1
      1353: q+1
      1354: 1
      1355: q+1
      1356: q+1
      1357: 2q+1
      1358: 2q+1
      1359: 2q+1
      1360: q+1
      1361: 2q+1
      1362: 2q+1
      1363: 2q+1
      1364: 2q+1
      1365: 2q+1
      1366: 2q+1
      1367: 2q+1
      1368: 2q+1
      1369: 2q+1
      1370: q+1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: q+1
      1375: q+1
      1376: q+1
      1377: 2q+1
      1378: q+1
      1379: q+1
      1380: q+1
      1381: q+1
      1382: q+1
      1383: q+1
      1384: q+1
      1385: 2q+1
      1386: 2q+1
      1387: 1
      1388: q+1
      1389: q+1
      1390: 1
      1391: 1
      1392: 1
      1393: 2q+1
      1394: q+1
      1395: q+1
      1396: 2q+1
      1397: q+1
      1398: q+1
      1399: q+1
      1400: q+1
      1401: 1
      1402: q+1
      1403: q+1
      1404: 2q+1
      1405: 2q+1
      1406: 2q+1
      1407: 2q+1
      1408: 2q+1
      1409: 2q+1
      1410: 2q+1
      1411: 2q+1
      1412: 2q+1
      1413: 2q+1
      1414: 2q+1
      1415: 2q+1
      1416: 2q+1
      1417: 2q+1
      1418: 2q+1
      1419: 2q+1
      1420: 2q+1
      1421: q+1
      1422: q^2+2q+1
      1423: q+1
      1424: q+1
      1425: q+1
      1426: q+1
      1427: 2q+1
      1428: 2q+1
      1429: 2q+1
      1430: q+1
      1431: q+1
      1432: q^2+2q+1
      1433: q+1
      1434: q+1
      1435: q+1
      1436: 2q+1
      1437: 2q+1
      1438: 2q+1
      1439: 2q+1
      1440: q+1
      1441: q+1
      1442: q+1
      1443: q+1
      1444: 1
      1445: 2q+1
      1446: 2q+1
      1447: q+1
      1448: 2q+1
      1449: 2q+1
      1450: 2q+1
      1451: q+1
      1452: q+1
      1453: 2q+1
      1454: q+1
      1455: q+1
      1456: q+1
      1457: q+1
      1458: 2q+1
      1459: 1
      1460: 1
      1461: q+1
      1462: q+1
      1463: q+1
      1464: 1
      1465: q+1
      1466: q+1
      1467: q+1
      1468: q+1
      1469: 1
      1470: q+1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: q+1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 2q+1
      1487: q+1
      1488: q+1
      1489: 2q+1
      1490: 2q+1
      1491: 2q+1
      1492: 1
      1493: 2q+1
      1494: q+1
      1495: q+1
      1496: q+1
      1497: q+1
      1498: q+1
      1499: q+1
      1500: q+1
      1501: q+1
      1502: q+1
      1503: q+1
      1504: q+1
      1505: q+1
      1506: q+1
      1507: q+1
      1508: 2q+1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: q+1
      1517: q+1
      1518: 1
      1519: q+1
      1520: q+1
      1521: 1
      1522: 1
      1523: 1
      1524: q+1
      1525: 2q+1
      1526: q+1
      1527: q+1
      1528: 2q+1
      1529: 2q+1
      1530: 2q+1
      1531: 1
      1532: 2q+1
      1533: q+1
      1534: q+1
      1535: q+1
      1536: q+1
      1537: q+1
      1538: q+1
      1539: q+1
      1540: q+1
      1541: q+1
      1542: q+1
      1543: q+1
      1544: q+1
      1545: q+1
      1546: q+1
      1547: 2q+1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: q+1
      1556: q+1
      1557: 1
      1558: q+1
      1559: q+1
      1560: 1
      1561: 1
      1562: 1
      1563: q+1
      1564: 2q+1
      1565: 2q+1
      1566: 2q+1
      1567: q+1
      1568: 2q+1
      1569: 2q+1
      1570: 2q+1
      1571: 2q+1
      1572: 2q+1
      1573: 2q+1
      1574: 2q+1
      1575: 2q+1
      1576: 2q+1
      1577: q+1
      1578: q+1
      1579: q+1
      1580: q+1
      1581: q+1
      1582: q+1
      1583: q+1
      1584: 2q+1
      1585: q+1
      1586: q+1
      1587: q+1
      1588: q+1
      1589: q+1
      1590: q+1
      1591: q+1
      1592: 2q+1
      1593: 2q+1
      1594: 1
      1595: q+1
      1596: q+1
      1597: 1
      1598: 1
      1599: 1
      1600: 2q+1
      1601: q+1
      1602: q+1
      1603: 2q+1
      1604: q+1
      1605: q+1
      1606: q+1
      1607: q+1
      1608: 1
      1609: q+1
      1610: q+1
      1611: q+1
      1612: 1
      1613: 1
      1614: q+1
      1615: 1
      1616: 1
      1617: q+1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1632: q+1
      1633: q+1
      1634: 2q+1
      1635: 1
      1636: 1
      1637: q+1
      1638: q+1
      1639: q+1
      1640: 1
      1641: q+1
      1642: q+1
      1643: q+1
      1644: q+1
      1645: 1
      1646: q+1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1654: q+1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1662: q+1
      1663: q+1
      1664: 2q+1
      1665: 1
      1666: 1
      1667: q+1
      1668: q+1
      1669: q+1
      1670: 1
      1671: q+1
      1672: q+1
      1673: q+1
      1674: q+1
      1675: 1
      1676: q+1
      1677: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1684: q+1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1692: 2q+1
      1693: q+1
      1694: q+1
      1695: 2q+1
      1696: 2q+1
      1697: 2q+1
      1698: 1
      1699: 2q+1
      1700: q+1
      1701: q+1
      1702: q+1
      1703: q+1
      1704: q+1
      1705: q+1
      1706: q+1
      1707: q+1
      1708: q+1
      1709: q+1
      1710: q+1
      1711: q+1
      1712: q+1
      1713: q+1
      1714: 2q+1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1722: q+1
      1723: q+1
      1724: 1
      1725: q+1
      1726: q+1
      1727: 1
      1728: 1
      1729: 1
      1730: q+1
      1731: 1
      1732: 1
      1733: 1
      1734: 1
      1735: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1743: 1
      1744: q+1
      1745: 1
      1746: 1
      1747: q+1
      1748: 1
      1749: 1
      1750: q+1
      1751: 1
      1752: 1
      1753: 1
      1754: 1
      1755: 1
      1756: 1
      1757: 1
      1758: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1765: q+1
      1766: 1
      1767: 1
      1768: q+1
      1769: 1
      1770: 1
      1771: q+1
      1772: 1
      1773: 1
      1774: 1
      1775: 1
      1776: 1
      1777: 1
      1778: 1
      1779: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1786: q+1
      1787: q+1
      1788: 2q+1
      1789: 1
      1790: 1
      1791: q+1
      1792: q+1
      1793: q+1
      1794: 1
      1795: q+1
      1796: q+1
      1797: q+1
      1798: q+1
      1799: 1
      1800: q+1
      1801: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1806: 1
      1807: 1
      1808: q+1
      1809: 1
      1810: 1
      1811: 1
      1812: 1
      1813: 1
      1814: 1
      1815: 1
      1816: 1
      1817: 1
      1818: 1
      1819: 1
      1820: 1
      1823: 1
      1824: 1
      1825: 1
      1826: 1
      1827: 1
      1828: 1
      1829: 1
      1830: 1
      1831: 1
      1832: 1
      1833: 1
      1835: 1
      1836: 1
      1837: 1
      1838: 1
      1839: 1
      1840: 1
      1841: 1
      1842: 1
      1843: 1
      1844: 1
      1845: 1
      1846: 1
      1848: 1
      1849: q+1
      1850: 1
      1851: 1
      1852: q+1
      1853: 1
      1854: 1
      1855: q+1
      1856: 1
      1857: 1
      1858: 1
      1859: 1
      1860: 1
      1861: 1
      1862: 1
      1863: 1
      1864: 1
      1865: 1
      1866: 1
      1867: 1
      1868: 1
      1869: 1
      1870: 1
      1873: 1
      1874: 1
      1875: 1
      1876: 1
      1877: 1
      1880: 1
      1881: 1
      1882: 1
      1883: 1
      1884: 1
      1887: 1
      1888: 1
      1889: 1
      1890: 1
      1891: 1
      1892: 1
      1893: 1
      1894: 1
      1895: 1
      1896: 1
      1897: 1
      1899: 1
      1901: 1
      1904: 1
      1907: 1
      1908: 1
      1909: 1
      1910: 1
      1911: 1
      1916: 1

1917:    0: q^3+q^2+q+1
         1: q^3+q^2+q+1
         2: q^2+q+1
         3: q^3+q^2+q+1
         4: q^3+q^2+q+1
         5: q^3+q^2+q+1
         6: q^2+q+1
         7: q^2+q+1
         8: q^2+q+1
         9: q^3+q^2+q+1
        10: q^2+q+1
        11: q^3+q^2+q+1
        12: q^3+q^2+q+1
        13: q^3+q^2+q+1
        14: q^2+q+1
        15: q^3+q^2+q+1
        16: q^3+q^2+q+1
        17: q^2+q+1
        18: q^3+q^2+q+1
        19: q^3+q^2+q+1
        20: q^2+q+1
        21: q^2+q+1
        22: q^2+q+1
        23: q^2+q+1
        24: q^2+q+1
        25: q^2+q+1
        26: q^2+q+1
        27: q^2+q+1
        28: q^3+q^2+q+1
        29: q^2+q+1
        30: q^3+q^2+q+1
        31: q^2+q+1
        32: q^3+q^2+q+1
        33: q^2+q+1
        34: q^2+q+1
        35: q^2+q+1
        36: q^3+q^2+q+1
        37: q^2+q+1
        38: q^3+q^2+q+1
        39: q^3+q^2+q+1
        40: q^2+q+1
        41: q^2+q+1
        42: q^2+q+1
        43: q^3+q^2+q+1
        44: q^2+q+1
        45: q^3+q^2+q+1
        46: q^3+q^2+q+1
        47: q^3+q^2+q+1
        48: q^2+q+1
        49: q^3+q^2+q+1
        50: q^2+q+1
        51: q^2+q+1
        52: q^2+q+1
        53: q+1
        54: q^2+q+1
        55: q^2+q+1
        56: q^2+q+1
        57: q^2+q+1
        58: q^2+q+1
        59: q^2+q+1
        60: q^2+q+1
        61: q^2+q+1
        62: q^2+q+1
        63: q^2+q+1
        64: q^2+q+1
        65: q^2+q+1
        66: q^2+q+1
        67: q^2+q+1
        68: q^3+q^2+q+1
        69: q^2+q+1
        70: q^3+q^2+q+1
        71: q^2+q+1
        72: q^2+q+1
        73: q^2+q+1
        74: q^2+q+1
        75: q^2+q+1
        76: q^2+q+1
        77: q^2+q+1
        78: q^2+q+1
        79: q^3+q^2+q+1
        80: q^2+q+1
        81: q^3+q^2+q+1
        82: q^2+q+1
        83: q^3+q^2+q+1
        84: q^2+q+1
        85: q^2+q+1
        86: q^2+q+1
        87: q^2+q+1
        88: q^2+q+1
        89: q^2+q+1
        90: q^2+q+1
        91: q^2+q+1
        92: q^3+q^2+q+1
        93: q^2+q+1
        94: q^3+q^2+q+1
        95: q^2+q+1
        96: q^3+q^2+q+1
        97: q^2+q+1
        98: q^2+q+1
        99: q^2+q+1
       100: q^3+q^2+q+1
       101: q^2+q+1
       102: q^3+q^2+q+1
       103: q^3+q^2+q+1
       104: q^2+q+1
       105: q^2+q+1
       106: q^2+q+1
       107: q+1
       108: q+1
       109: q+1
       110: q^2+q+1
       111: q^2+q+1
       112: q^2+q+1
       113: q^2+q+1
       114: q^2+q+1
       115: q+1
       116: q^2+q+1
       117: q^2+q+1
       118: q^2+q+1
       119: q^2+q+1
       120: q^2+q+1
       121: q^2+q+1
       122: q^2+q+1
       123: q^2+q+1
       124: q^2+q+1
       125: q^2+q+1
       126: q^2+q+1
       127: q^2+q+1
       128: q^2+q+1
       129: q^2+q+1
       130: q^2+q+1
       131: q^2+q+1
       132: q^3+q^2+q+1
       133: q^2+q+1
       134: q^2+q+1
       135: q^2+q+1
       136: q^2+q+1
       137: q+1
       138: q^2+q+1
       139: q^2+q+1
       140: q^2+q+1
       141: q^2+q+1
       142: q^2+q+1
       143: q^2+q+1
       144: q^2+q+1
       145: q^2+q+1
       146: q^2+q+1
       147: q^2+q+1
       148: q^2+q+1
       149: q^2+q+1
       150: q^2+q+1
       151: q^2+q+1
       152: q^3+q^2+q+1
       153: q^2+q+1
       154: q^3+q^2+q+1
       155: q^2+q+1
       156: q^2+q+1
       157: q^2+q+1
       158: q+1
       159: q^2+q+1
       160: q^2+q+1
       161: q^2+q+1
       162: q^2+q+1
       163: q^2+q+1
       164: q^2+q+1
       165: q^2+q+1
       166: q^2+q+1
       167: q^2+q+1
       168: q^2+q+1
       169: q^2+q+1
       170: q^2+q+1
       171: q^2+q+1
       172: q^2+q+1
       173: q^3+q^2+q+1
       174: q^2+q+1
       175: q^3+q^2+q+1
       176: q^2+q+1
       177: q^2+q+1
       178: q^2+q+1
       179: q^2+q+1
       180: q^2+q+1
       181: q^2+q+1
       182: q^2+q+1
       183: q^2+q+1
       184: q^3+q^2+q+1
       185: q^2+q+1
       186: q^3+q^2+q+1
       187: q^2+q+1
       188: q^3+q^2+q+1
       189: q^2+q+1
       190: q^2+q+1
       191: q+1
       192: q+1
       193: q+1
       194: q+1
       195: q+1
       196: q^2+q+1
       197: q^2+1
       198: q^2+q+1
       199: q^2+q+1
       200: q^2+q+1
       201: q+1
       202: q+1
       203: q+1
       204: q^2+q+1
       205: q^2+q+1
       206: q^2+q+1
       207: q^2+q+1
       208: q^2+q+1
       209: q+1
       210: q^2+q+1
       211: q^2+q+1
       212: q^2+q+1
       213: q^2+q+1
       214: q^2+q+1
       215: q^2+q+1
       216: q+1
       217: q^2+q+1
       218: q^2+q+1
       219: q^2+q+1
       220: q^2+q+1
       221: q^2+q+1
       222: q^2+q+1
       223: q^2+q+1
       224: q^2+q+1
       225: q^2+q+1
       226: q^2+q+1
       227: q^2+q+1
       228: q^2+q+1
       229: q^2+q+1
       230: q^2+q+1
       231: q+1
       232: q+1
       233: q+1
       234: q^2+q+1
       235: q^2+q+1
       236: q^2+q+1
       237: q^2+q+1
       238: q^2+q+1
       239: q+1
       240: q^2+q+1
       241: q^2+q+1
       242: q^2+q+1
       243: q^2+q+1
       244: q^2+q+1
       245: q^2+q+1
       246: q^2+q+1
       247: q^2+q+1
       248: q^2+q+1
       249: q^2+q+1
       250: q^2+q+1
       251: q^2+q+1
       252: q^2+q+1
       253: q^2+q+1
       254: q^2+q+1
       255: q^2+q+1
       256: q^3+q^2+q+1
       257: q^2+q+1
       258: q^2+q+1
       259: q^2+q+1
       260: q^2+q+1
       261: q+1
       262: q+1
       263: q+1
       264: q^2+q+1
       265: q^2+q+1
       266: q^2+q+1
       267: q^2+q+1
       268: q^2+q+1
       269: q+1
       270: q^2+q+1
       271: q^2+q+1
       272: q^2+q+1
       273: q^2+q+1
       274: q^2+q+1
       275: q^2+q+1
       276: q^2+q+1
       277: q^2+q+1
       278: q^2+q+1
       279: q^2+q+1
       280: q^2+q+1
       281: q^2+q+1
       282: q^2+q+1
       283: q^2+q+1
       284: q^2+q+1
       285: q^2+q+1
       286: q^3+q^2+q+1
       287: q^2+q+1
       288: q^2+q+1
       289: q^2+q+1
       290: q^2+q+1
       291: q+1
       292: q^2+q+1
       293: q^2+q+1
       294: q^2+q+1
       295: q^2+q+1
       296: q^2+q+1
       297: q^2+q+1
       298: q^2+q+1
       299: q^2+q+1
       300: q^2+q+1
       301: q^2+q+1
       302: q^2+q+1
       303: q^2+q+1
       304: q^2+q+1
       305: q^2+q+1
       306: q^3+q^2+q+1
       307: q^2+q+1
       308: q^3+q^2+q+1
       309: q^2+1
       310: q^2+q+1
       311: q+1
       312: q+1
       313: q+1
       314: q+1
       315: q+1
       316: q+1
       317: 1
       318: q^2+1
       319: q^2+q+1
       320: q^2+q+1
       321: q+1
       322: q+1
       323: q+1
       324: q+1
       325: q+1
       326: q^2+q+1
       327: q^2+1
       328: q^2+q+1
       329: q^2+q+1
       330: q^2+q+1
       331: q+1
       332: q+1
       333: q+1
       334: q^2+q+1
       335: q^2+q+1
       336: q^2+q+1
       337: q^2+q+1
       338: q^2+q+1
       339: q+1
       340: q+1
       341: q+1
       342: q^2+q+1
       343: q^2+q+1
       344: q^2+q+1
       345: q^2+q+1
       346: q^2+q+1
       347: q+1
       348: q^2+q+1
       349: q^2+q+1
       350: q^2+q+1
       351: q^2+q+1
       352: q^2+q+1
       353: q^2+q+1
       354: q^2+q+1
       355: q^2+q+1
       356: q^2+q+1
       357: q^2+q+1
       358: q+1
       359: q+1
       360: q+1
       361: q+1
       362: q+1
       363: q^2+q+1
       364: q^2+1
       365: q^2+q+1
       366: q^2+q+1
       367: q^2+q+1
       368: q+1
       369: q+1
       370: q+1
       371: q^2+q+1
       372: q^2+q+1
       373: q^2+q+1
       374: q^2+q+1
       375: q^2+q+1
       376: q+1
       377: q^2+q+1
       378: q^2+q+1
       379: q^2+q+1
       380: q^2+q+1
       381: q^2+q+1
       382: q^2+q+1
       383: q+1
       384: q^2+q+1
       385: q^2+q+1
       386: q^2+q+1
       387: q^2+q+1
       388: q^2+q+1
       389: q^2+q+1
       390: q^2+q+1
       391: q^2+q+1
       392: q^2+q+1
       393: q^2+q+1
       394: q^2+q+1
       395: q^2+q+1
       396: q^2+q+1
       397: q+1
       398: q+1
       399: q+1
       400: q+1
       401: q+1
       402: q^2+q+1
       403: q^2+1
       404: q^2+q+1
       405: q^2+q+1
       406: q^2+q+1
       407: q+1
       408: q+1
       409: q+1
       410: q^2+q+1
       411: q^2+q+1
       412: q^2+q+1
       413: q^2+q+1
       414: q^2+q+1
       415: q+1
       416: q^2+q+1
       417: q^2+q+1
       418: q^2+q+1
       419: q^2+q+1
       420: q^2+q+1
       421: q^2+q+1
       422: q+1
       423: q^2+q+1
       424: q^2+q+1
       425: q^2+q+1
       426: q^2+q+1
       427: q^2+q+1
       428: q^2+q+1
       429: q^2+q+1
       430: q^2+q+1
       431: q^2+q+1
       432: q^2+q+1
       433: q^2+q+1
       434: q^2+q+1
       435: q^2+q+1
       436: q^2+q+1
       437: q+1
       438: q+1
       439: q+1
       440: q^2+q+1
       441: q^2+q+1
       442: q^2+q+1
       443: q^2+q+1
       444: q^2+q+1
       445: q+1
       446: q^2+q+1
       447: q^2+q+1
       448: q^2+q+1
       449: q^2+q+1
       450: q^2+q+1
       451: q^2+q+1
       452: q^2+q+1
       453: q^2+q+1
       454: q^2+q+1
       455: q^2+q+1
       456: q^2+q+1
       457: q^2+q+1
       458: q^2+q+1
       459: q^2+q+1
       460: q^2+q+1
       461: q^2+q+1
       462: q^3+q^2+q+1
       463: q^2+q+1
       464: q^2+1
       465: 1
       466: q+1
       467: q+1
       468: q+1
       469: q+1
       470: q+1
       471: 1
       472: 1
       473: q^2+1
       474: q^2+q+1
       475: q+1
       476: q+1
       477: q+1
       478: q+1
       479: q+1
       480: q+1
       481: 1
       482: q^2+1
       483: q^2+q+1
       484: q^2+q+1
       485: q+1
       486: q+1
       487: q+1
       488: q+1
       489: q+1
       490: q^2+q+1
       491: q^2+1
       492: q^2+q+1
       493: q^2+q+1
       494: q+1
       495: q+1
       496: q+1
       497: q+1
       498: q+1
       499: q^2+q+1
       500: q^2+1
       501: q^2+q+1
       502: q^2+q+1
       503: q^2+q+1
       504: q+1
       505: q+1
       506: q+1
       507: q^2+q+1
       508: q^2+q+1
       509: q^2+q+1
       510: q^2+q+1
       511: q^2+q+1
       512: q+1
       513: q^2+q+1
       514: q^2+q+1
       515: q^2+q+1
       516: q^2+1
       517: q^2+q+1
       518: q+1
       519: q+1
       520: q+1
       521: q+1
       522: q+1
       523: q+1
       524: 1
       525: q^2+1
       526: q^2+q+1
       527: q^2+q+1
       528: q+1
       529: q+1
       530: q+1
       531: q+1
       532: q+1
       533: q^2+q+1
       534: q^2+1
       535: q^2+q+1
       536: q^2+q+1
       537: q^2+q+1
       538: q+1
       539: q+1
       540: q+1
       541: q^2+q+1
       542: q^2+q+1
       543: q^2+q+1
       544: q^2+q+1
       545: q^2+q+1
       546: q+1
       547: q+1
       548: q+1
       549: q^2+q+1
       550: q^2+q+1
       551: q^2+q+1
       552: q^2+q+1
       553: q^2+q+1
       554: q+1
       555: q^2+q+1
       556: q^2+q+1
       557: q^2+q+1
       558: q^2+q+1
       559: q^2+q+1
       560: q^2+q+1
       561: q^2+q+1
       562: q^2+q+1
       563: q^2+1
       564: q^2+q+1
       565: q+1
       566: q+1
       567: q+1
       568: q+1
       569: q+1
       570: q+1
       571: 1
       572: q^2+1
       573: q^2+q+1
       574: q^2+q+1
       575: q+1
       576: q+1
       577: q+1
       578: q+1
       579: q+1
       580: q^2+q+1
       581: q^2+1
       582: q^2+q+1
       583: q^2+q+1
       584: q^2+q+1
       585: q+1
       586: q+1
       587: q+1
       588: q^2+q+1
       589: q^2+q+1
       590: q^2+q+1
       591: q^2+q+1
       592: q^2+q+1
       593: q+1
       594: q+1
       595: q+1
       596: q^2+q+1
       597: q^2+q+1
       598: q^2+q+1
       599: q^2+q+1
       600: q^2+q+1
       601: q+1
       602: q^2+q+1
       603: q^2+q+1
       604: q^2+q+1
       605: q^2+q+1
       606: q^2+q+1
       607: q^2+q+1
       608: q^2+q+1
       609: q^2+q+1
       610: q^2+q+1
       611: q^2+q+1
       612: q+1
       613: q+1
       614: q+1
       615: q+1
       616: q+1
       617: q^2+q+1
       618: q^2+1
       619: q^2+q+1
       620: q^2+q+1
       621: q^2+q+1
       622: q+1
       623: q+1
       624: q+1
       625: q^2+q+1
       626: q^2+q+1
       627: q^2+q+1
       628: q^2+q+1
       629: q^2+q+1
       630: q+1
       631: q^2+q+1
       632: q^2+q+1
       633: q^2+q+1
       634: q^2+q+1
       635: q^2+q+1
       636: q^2+q+1
       637: q+1
       638: q^2+q+1
       639: q^2+q+1
       640: q^2+q+1
       641: q^2+q+1
       642: q^2+q+1
       643: q^2+q+1
       644: q^2+q+1
       645: q^2+q+1
       646: q^2+q+1
       647: q^2+q+1
       648: q^2+q+1
       649: 1
       650: 1
       651: q+1
       652: q+1
       653: q+1
       654: 1
       655: 1
       656: 1
       657: q^2+1
       658: 1
       659: q+1
       660: q+1
       661: q+1
       662: q+1
       663: q+1
       664: 1
       665: 1
       666: q^2+1
       667: q^2+q+1
       668: q+1
       669: q+1
       670: q+1
       671: q+1
       672: q+1
       673: q+1
       674: 1
       675: q^2+1
       676: q^2+1
       677: q^2+q+1
       678: q+1
       679: q+1
       680: q+1
       681: q+1
       682: q+1
       683: q+1
       684: 1
       685: q^2+1
       686: q^2+q+1
       687: q^2+q+1
       688: q+1
       689: q+1
       690: q+1
       691: q+1
       692: q+1
       693: q^2+q+1
       694: q^2+1
       695: q^2+q+1
       696: q^2+q+1
       697: q^2+q+1
       698: q+1
       699: q+1
       700: q+1
       701: q^2+q+1
       702: q^2+q+1
       703: q^2+1
       704: 1
       705: q+1
       706: q+1
       707: q+1
       708: q+1
       709: q+1
       710: 1
       711: 1
       712: q^2+1
       713: q^2+q+1
       714: q+1
       715: q+1
       716: q+1
       717: q+1
       718: q+1
       719: q+1
       720: 1
       721: q^2+1
       722: q^2+q+1
       723: q^2+q+1
       724: q+1
       725: q+1
       726: q+1
       727: q+1
       728: q+1
       729: q^2+q+1
       730: q^2+1
       731: q^2+q+1
       732: q^2+q+1
       733: q+1
       734: q+1
       735: q+1
       736: q+1
       737: q+1
       738: q^2+q+1
       739: q^2+1
       740: q^2+q+1
       741: q^2+q+1
       742: q^2+q+1
       743: q+1
       744: q+1
       745: q+1
       746: q^2+q+1
       747: q^2+q+1
       748: q^2+q+1
       749: q^2+q+1
       750: q^2+q+1
       751: q+1
       752: q^2+q+1
       753: q^2+q+1
       754: q^2+q+1
       755: q^2+1
       756: 1
       757: q+1
       758: q+1
       759: q+1
       760: q+1
       761: q+1
       762: 1
       763: 1
       764: q^2+1
       765: q^2+q+1
       766: q+1
       767: q+1
       768: q+1
       769: q+1
       770: q+1
       771: q+1
       772: 1
       773: q^2+1
       774: q^2+q+1
       775: q^2+q+1
       776: q+1
       777: q+1
       778: q+1
       779: q+1
       780: q+1
       781: q^2+q+1
       782: q^2+1
       783: q^2+q+1
       784: q^2+q+1
       785: q+1
       786: q+1
       787: q+1
       788: q+1
       789: q+1
       790: q^2+q+1
       791: q^2+1
       792: q^2+q+1
       793: q^2+q+1
       794: q^2+q+1
       795: q+1
       796: q+1
       797: q+1
       798: q^2+q+1
       799: q^2+q+1
       800: q^2+q+1
       801: q^2+q+1
       802: q^2+q+1
       803: q+1
       804: q^2+q+1
       805: q^2+q+1
       806: q^2+q+1
       807: q^2+1
       808: q^2+q+1
       809: q+1
       810: q+1
       811: q+1
       812: q+1
       813: q+1
       814: q+1
       815: 1
       816: q^2+1
       817: q^2+q+1
       818: q^2+q+1
       819: q+1
       820: q+1
       821: q+1
       822: q+1
       823: q+1
       824: q^2+q+1
       825: q^2+1
       826: q^2+q+1
       827: q^2+q+1
       828: q^2+q+1
       829: q+1
       830: q+1
       831: q+1
       832: q^2+q+1
       833: q^2+q+1
       834: q^2+q+1
       835: q^2+q+1
       836: q^2+q+1
       837: q+1
       838: q+1
       839: q+1
       840: q^2+q+1
       841: q^2+q+1
       842: q^2+q+1
       843: q^2+q+1
       844: q^2+q+1
       845: q+1
       846: q^2+q+1
       847: q^2+q+1
       848: q^2+q+1
       849: q^2+q+1
       850: q^2+q+1
       851: q^2+q+1
       852: q^2+q+1
       853: q^2+q+1
       854: 1
       855: 1
       856: 1
       857: q+1
       858: 1
       859: 1
       860: 1
       861: 1
       862: 1
       863: q+1
       864: q+1
       865: q+1
       866: 1
       867: 1
       868: 1
       869: q^2+1
       870: 1
       871: q+1
       872: q+1
       873: q+1
       874: q+1
       875: q+1
       876: 1
       877: 1
       878: q^2+1
       879: 1
       880: q+1
       881: q+1
       882: q+1
       883: q+1
       884: q+1
       885: 1
       886: 1
       887: q^2+1
       888: q^2+q+1
       889: q+1
       890: q+1
       891: q+1
       892: q+1
       893: q+1
       894: q+1
       895: 1
       896: q^2+1
       897: q^2+q+1
       898: q^2+q+1
       899: q+1
       900: q+1
       901: q+1
       902: q+1
       903: q+1
       904: q^2+q+1
       905: q^2+1
       906: 1
       907: 1
       908: q+1
       909: q+1
       910: q+1
       911: 1
       912: 1
       913: 1
       914: q^2+1
       915: 1
       916: q+1
       917: q+1
       918: q+1
       919: q+1
       920: q+1
       921: 1
       922: 1
       923: q^2+1
       924: q^2+q+1
       925: q+1
       926: q+1
       927: q+1
       928: q+1
       929: q+1
       930: q+1
       931: 1
       932: q^2+1
       933: q^2+1
       934: q^2+q+1
       935: q+1
       936: q+1
       937: q+1
       938: q+1
       939: q+1
       940: q+1
       941: 1
       942: q^2+1
       943: q^2+q+1
       944: q^2+q+1
       945: q+1
       946: q+1
       947: q+1
       948: q+1
       949: q+1
       950: q^2+q+1
       951: q^2+1
       952: q^2+q+1
       953: q^2+q+1
       954: q^2+q+1
       955: q+1
       956: q+1
       957: q+1
       958: q^2+q+1
       959: q^2+q+1
       960: 1
       961: 1
       962: q+1
       963: q+1
       964: q+1
       965: 1
       966: 1
       967: 1
       968: q^2+1
       969: 1
       970: q+1
       971: q+1
       972: q+1
       973: q+1
       974: q+1
       975: 1
       976: 1
       977: q^2+1
       978: q^2+q+1
       979: q+1
       980: q+1
       981: q+1
       982: q+1
       983: q+1
       984: q+1
       985: 1
       986: q^2+1
       987: q^2+1
       988: q^2+q+1
       989: q+1
       990: q+1
       991: q+1
       992: q+1
       993: q+1
       994: q+1
       995: 1
       996: q^2+1
       997: q^2+q+1
       998: q^2+q+1
       999: q+1
      1000: q+1
      1001: q+1
      1002: q+1
      1003: q+1
      1004: q^2+q+1
      1005: q^2+1
      1006: q^2+q+1
      1007: q^2+q+1
      1008: q^2+q+1
      1009: q+1
      1010: q+1
      1011: q+1
      1012: q^2+q+1
      1013: q^2+q+1
      1014: q^2+1
      1015: 1
      1016: q+1
      1017: q+1
      1018: q+1
      1019: q+1
      1020: q+1
      1021: 1
      1022: 1
      1023: q^2+1
      1024: q^2+q+1
      1025: q+1
      1026: q+1
      1027: q+1
      1028: q+1
      1029: q+1
      1030: q+1
      1031: 1
      1032: q^2+1
      1033: q^2+q+1
      1034: q^2+q+1
      1035: q+1
      1036: q+1
      1037: q+1
      1038: q+1
      1039: q+1
      1040: q^2+q+1
      1041: q^2+1
      1042: q^2+q+1
      1043: q^2+q+1
      1044: q+1
      1045: q+1
      1046: q+1
      1047: q+1
      1048: q+1
      1049: q^2+q+1
      1050: q^2+1
      1051: q^2+q+1
      1052: q^2+q+1
      1053: q^2+q+1
      1054: q+1
      1055: q+1
      1056: q+1
      1057: q^2+q+1
      1058: q^2+q+1
      1059: q^2+q+1
      1060: q^2+q+1
      1061: q^2+q+1
      1062: q+1
      1063: q^2+q+1
      1064: q^2+q+1
      1065: q^2+q+1
      1066: 1
      1067: 1
      1068: 1
      1069: 1
      1070: 1
      1071: 1
      1072: 1
      1073: 1
      1074: q+1
      1075: 1
      1076: 1
      1077: 1
      1078: 1
      1079: 1
      1080: q+1
      1081: q+1
      1082: q+1
      1083: 1
      1084: 1
      1085: 1
      1086: 1
      1087: 1
      1088: q+1
      1089: q+1
      1090: q+1
      1091: 1
      1092: 1
      1093: 1
      1094: q^2+1
      1095: 1
      1096: q+1
      1097: q+1
      1098: q+1
      1099: q+1
      1100: q+1
      1101: 1
      1102: 1
      1103: q^2+1
      1104: q^2+q+1
      1105: q+1
      1106: q+1
      1107: q+1
      1108: q+1
      1109: q+1
      1110: q+1
      1111: 1
      1112: q^2+1
      1113: 1
      1114: 1
      1115: 1
      1116: q+1
      1117: 1
      1118: 1
      1119: 1
      1120: 1
      1121: 1
      1122: q+1
      1123: q+1
      1124: q+1
      1125: 1
      1126: 1
      1127: 1
      1128: q^2+1
      1129: 1
      1130: q+1
      1131: q+1
      1132: q+1
      1133: q+1
      1134: q+1
      1135: 1
      1136: 1
      1137: q^2+1
      1138: 1
      1139: q+1
      1140: q+1
      1141: q+1
      1142: q+1
      1143: q+1
      1144: 1
      1145: 1
      1146: q^2+1
      1147: q^2+q+1
      1148: q+1
      1149: q+1
      1150: q+1
      1151: q+1
      1152: q+1
      1153: q+1
      1154: 1
      1155: q^2+1
      1156: q^2+q+1
      1157: q^2+q+1
      1158: q+1
      1159: q+1
      1160: q+1
      1161: q+1
      1162: q+1
      1163: q^2+q+1
      1164: q^2+1
      1165: 1
      1166: 1
      1167: 1
      1168: q+1
      1169: 1
      1170: 1
      1171: 1
      1172: 1
      1173: 1
      1174: q+1
      1175: q+1
      1176: q+1
      1177: 1
      1178: 1
      1179: 1
      1180: q^2+1
      1181: 1
      1182: q+1
      1183: q+1
      1184: q+1
      1185: q+1
      1186: q+1
      1187: 1
      1188: 1
      1189: q^2+1
      1190: 1
      1191: q+1
      1192: q+1
      1193: q+1
      1194: q+1
      1195: q+1
      1196: 1
      1197: 1
      1198: q^2+1
      1199: q^2+q+1
      1200: q+1
      1201: q+1
      1202: q+1
      1203: q+1
      1204: q+1
      1205: q+1
      1206: 1
      1207: q^2+1
      1208: q^2+q+1
      1209: q^2+q+1
      1210: q+1
      1211: q+1
      1212: q+1
      1213: q+1
      1214: q+1
      1215: q^2+q+1
      1216: q^2+1
      1217: 1
      1218: 1
      1219: q+1
      1220: q+1
      1221: q+1
      1222: 1
      1223: 1
      1224: 1
      1225: q^2+1
      1226: 1
      1227: q+1
      1228: q+1
      1229: q+1
      1230: q+1
      1231: q+1
      1232: 1
      1233: 1
      1234: q^2+1
      1235: q^2+q+1
      1236: q+1
      1237: q+1
      1238: q+1
      1239: q+1
      1240: q+1
      1241: q+1
      1242: 1
      1243: q^2+1
      1244: q^2+1
      1245: q^2+q+1
      1246: q+1
      1247: q+1
      1248: q+1
      1249: q+1
      1250: q+1
      1251: q+1
      1252: 1
      1253: q^2+1
      1254: q^2+q+1
      1255: q^2+q+1
      1256: q+1
      1257: q+1
      1258: q+1
      1259: q+1
      1260: q+1
      1261: q^2+q+1
      1262: q^2+1
      1263: q^2+q+1
      1264: q^2+q+1
      1265: q^2+q+1
      1266: q+1
      1267: q+1
      1268: q+1
      1269: q^2+q+1
      1270: q^2+q+1
      1271: 1
      1272: 1
      1273: 1
      1274: 1
      1275: 1
      1276: 1
      1277: 1
      1278: 1
      1279: 1
      1280: 1
      1281: 1
      1282: q+1
      1283: 1
      1284: 1
      1285: 1
      1286: 1
      1287: 1
      1288: 1
      1289: q+1
      1290: 1
      1291: 1
      1292: 1
      1293: 1
      1294: 1
      1295: q+1
      1296: q+1
      1297: q+1
      1298: 1
      1299: 1
      1300: 1
      1301: q^2+1
      1302: 1
      1303: q+1
      1304: q+1
      1305: q+1
      1306: q+1
      1307: q+1
      1308: 1
      1309: 1
      1310: 1
      1311: 1
      1312: 1
      1313: 1
      1314: 1
      1315: 1
      1316: 1
      1317: 1
      1318: q+1
      1319: 1
      1320: 1
      1321: 1
      1322: 1
      1323: 1
      1324: q+1
      1325: q+1
      1326: q+1
      1327: 1
      1328: 1
      1329: 1
      1330: 1
      1331: 1
      1332: q+1
      1333: q+1
      1334: q+1
      1335: 1
      1336: 1
      1337: 1
      1338: q^2+1
      1339: 1
      1340: q+1
      1341: q+1
      1342: q+1
      1343: q+1
      1344: q+1
      1345: 1
      1346: 1
      1347: q^2+1
      1348: q^2+q+1
      1349: q+1
      1350: q+1
      1351: q+1
      1352: q+1
      1353: q+1
      1354: q+1
      1355: 1
      1356: q^2+1
      1357: 1
      1358: 1
      1359: 1
      1360: 1
      1361: 1
      1362: 1
      1363: 1
      1364: 1
      1365: q+1
      1366: 1
      1367: 1
      1368: 1
      1369: 1
      1370: 1
      1371: q+1
      1372: q+1
      1373: q+1
      1374: 1
      1375: 1
      1376: 1
      1377: 1
      1378: 1
      1379: q+1
      1380: q+1
      1381: q+1
      1382: 1
      1383: 1
      1384: 1
      1385: q^2+1
      1386: 1
      1387: q+1
      1388: q+1
      1389: q+1
      1390: q+1
      1391: q+1
      1392: 1
      1393: 1
      1394: q^2+1
      1395: q^2+q+1
      1396: q+1
      1397: q+1
      1398: q+1
      1399: q+1
      1400: q+1
      1401: q+1
      1402: 1
      1403: q^2+1
      1404: 1
      1405: 1
      1406: 1
      1407: q+1
      1408: 1
      1409: 1
      1410: 1
      1411: 1
      1412: 1
      1413: q+1
      1414: q+1
      1415: q+1
      1416: 1
      1417: 1
      1418: 1
      1419: q^2+1
      1420: 1
      1421: q+1
      1422: q+1
      1423: q+1
      1424: q+1
      1425: q+1
      1426: 1
      1427: 1
      1428: q^2+1
      1429: 1
      1430: q+1
      1431: q+1
      1432: q+1
      1433: q+1
      1434: q+1
      1435: 1
      1436: 1
      1437: q^2+1
      1438: q^2+q+1
      1439: q+1
      1440: q+1
      1441: q+1
      1442: q+1
      1443: q+1
      1444: q+1
      1445: 1
      1446: q^2+1
      1447: q^2+q+1
      1448: q^2+q+1
      1449: q+1
      1450: q+1
      1451: q+1
      1452: q+1
      1453: q+1
      1454: q^2+q+1
      1455: q^2+1
      1456: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: q+1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: q+1
      1481: q+1
      1482: q+1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: q+1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: q+1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: q+1
      1511: q+1
      1512: q+1
      1513: 1
      1514: 1
      1515: 1
      1516: q^2+1
      1517: 1
      1518: q+1
      1519: q+1
      1520: q+1
      1521: q+1
      1522: q+1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: q+1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1541: 1
      1542: 1
      1543: q+1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1548: 1
      1549: q+1
      1550: q+1
      1551: q+1
      1552: 1
      1553: 1
      1554: 1
      1555: q^2+1
      1556: 1
      1557: q+1
      1558: q+1
      1559: q+1
      1560: q+1
      1561: q+1
      1562: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: q+1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: q+1
      1579: q+1
      1580: q+1
      1581: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1586: q+1
      1587: q+1
      1588: q+1
      1589: 1
      1590: 1
      1591: 1
      1592: q^2+1
      1593: 1
      1594: q+1
      1595: q+1
      1596: q+1
      1597: q+1
      1598: q+1
      1599: 1
      1600: 1
      1601: q^2+1
      1602: q^2+q+1
      1603: q+1
      1604: q+1
      1605: q+1
      1606: q+1
      1607: q+1
      1608: q+1
      1609: 1
      1610: q^2+1
      1612: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: q+1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1649: 1
      1650: q+1
      1651: 1
      1652: 1
      1653: 1
      1654: 1
      1655: 1
      1656: q+1
      1657: q+1
      1658: q+1
      1659: 1
      1660: 1
      1661: 1
      1662: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1679: 1
      1680: q+1
      1681: 1
      1682: 1
      1683: 1
      1684: 1
      1685: 1
      1686: q+1
      1687: q+1
      1688: q+1
      1689: 1
      1690: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: q+1
      1704: 1
      1705: 1
      1706: 1
      1707: 1
      1708: 1
      1709: 1
      1710: q+1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1715: 1
      1716: q+1
      1717: q+1
      1718: q+1
      1719: 1
      1720: 1
      1721: 1
      1722: q^2+1
      1723: 1
      1724: q+1
      1725: q+1
      1726: q+1
      1727: q+1
      1728: q+1
      1729: 1
      1730: 1
      1732: 1
      1734: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1742: 1
      1743: 1
      1745: 1
      1747: 1
      1748: 1
      1749: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1754: 1
      1755: 1
      1756: 1
      1757: 1
      1758: 1
      1759: 1
      1760: 1
      1761: q+1
      1762: 1
      1763: 1
      1764: 1
      1766: 1
      1768: 1
      1769: 1
      1770: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1775: 1
      1776: 1
      1777: 1
      1778: 1
      1779: 1
      1780: 1
      1781: 1
      1782: q+1
      1783: 1
      1784: 1
      1785: 1
      1786: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1792: 1
      1793: 1
      1794: 1
      1795: 1
      1796: 1
      1797: 1
      1798: 1
      1799: 1
      1800: 1
      1801: 1
      1802: 1
      1803: 1
      1804: q+1
      1805: 1
      1806: 1
      1807: 1
      1808: 1
      1809: 1
      1810: q+1
      1811: q+1
      1812: q+1
      1813: 1
      1814: 1
      1815: 1
      1818: 1
      1820: 1
      1821: 1
      1822: 1
      1824: 1
      1826: 1
      1828: 1
      1829: 1
      1830: 1
      1831: 1
      1832: 1
      1833: 1
      1834: 1
      1835: 1
      1837: 1
      1839: 1
      1841: 1
      1842: 1
      1843: 1
      1844: 1
      1845: 1
      1846: 1
      1847: 1
      1848: 1
      1850: 1
      1852: 1
      1853: 1
      1854: 1
      1855: 1
      1856: 1
      1857: 1
      1858: 1
      1859: 1
      1860: 1
      1861: 1
      1862: 1
      1863: 1
      1864: 1
      1865: 1
      1866: q+1
      1867: 1
      1868: 1
      1869: 1
      1871: 1
      1875: 1
      1877: 1
      1878: 1
      1879: 1
      1882: 1
      1884: 1
      1885: 1
      1886: 1
      1888: 1
      1890: 1
      1892: 1
      1893: 1
      1894: 1
      1895: 1
      1896: 1
      1897: 1
      1898: 1
      1899: 1
      1902: 1
      1905: 1
      1909: 1
      1911: 1
      1912: 1
      1913: 1
      1917: 1

1918:    0: q^3+1
         1: 1
         2: q^3+1
         3: q^3+1
         4: q^3+1
         5: q^3+1
         6: 1
         7: 1
         8: q^3+1
         9: 1
        10: q^3+1
        11: q^3+1
        12: q^3+1
        13: 1
        14: q^3+1
        15: q^3+1
        16: 1
        17: q^3+1
        18: q^3+1
        19: q^3+1
        20: 1
        21: 1
        22: 1
        23: q^3+1
        24: q^3+1
        25: 1
        26: 1
        27: q^3+1
        28: 1
        29: q^3+1
        30: 1
        31: q^3+1
        32: q^3+1
        33: 1
        34: 1
        35: q^3+1
        36: 1
        37: q^3+1
        38: q^3+1
        39: q^3+1
        40: 1
        41: 1
        42: q^3+1
        43: 1
        44: q^3+1
        45: q^3+1
        46: q^3+1
        47: 1
        48: q^3+1
        49: q^3+1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: q^3+1
        57: 1
        58: 1
        59: 1
        60: q^3+1
        61: q^3+1
        62: 1
        63: 1
        64: q^3+1
        65: 1
        66: 1
        67: q^3+1
        68: 1
        69: q^3+1
        70: q^3+1
        71: 1
        72: 1
        73: 1
        74: q^3+1
        75: q^3+1
        76: 1
        77: 1
        78: q^3+1
        79: 1
        80: q^3+1
        81: 1
        82: q^3+1
        83: q^3+1
        84: 1
        85: 1
        86: 1
        87: q^3+1
        88: q^3+1
        89: 1
        90: 1
        91: q^3+1
        92: 1
        93: q^3+1
        94: 1
        95: q^3+1
        96: q^3+1
        97: 1
        98: 1
        99: q^3+1
       100: 1
       101: q^3+1
       102: q^3+1
       103: q^3+1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: q^3+1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: q^3+1
       119: 1
       120: 1
       121: 1
       122: q^3+1
       123: q^3+1
       124: 1
       125: 1
       126: 1
       127: q^3+1
       128: q^3+1
       129: 1
       130: 1
       131: q^3+1
       132: 1
       133: q^3+1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: q^3+1
       141: 1
       142: 1
       143: 1
       144: q^3+1
       145: q^3+1
       146: 1
       147: 1
       148: q^3+1
       149: 1
       150: 1
       151: q^3+1
       152: 1
       153: q^3+1
       154: q^3+1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: q^3+1
       162: 1
       163: 1
       164: 1
       165: q^3+1
       166: q^3+1
       167: 1
       168: 1
       169: q^3+1
       170: 1
       171: 1
       172: q^3+1
       173: 1
       174: q^3+1
       175: q^3+1
       176: 1
       177: 1
       178: 1
       179: q^3+1
       180: q^3+1
       181: 1
       182: 1
       183: q^3+1
       184: 1
       185: q^3+1
       186: 1
       187: q^3+1
       188: q^3+1
       189: 1
       190: 1
       191: 1
       192: 1
       193: 1
       194: 1
       195: 1
       196: 1
       197: q^3+1
       198: 1
       199: 1
       200: 1
       201: 1
       202: 1
       203: 1
       204: 1
       205: q^3+1
       206: 1
       207: 1
       208: 1
       209: 1
       210: 1
       211: 1
       212: q^3+1
       213: 1
       214: 1
       215: 1
       216: 1
       217: 1
       218: 1
       219: q^3+1
       220: 1
       221: 1
       222: 1
       223: q^3+1
       224: q^3+1
       225: 1
       226: 1
       227: q^3+1
       228: 1
       229: 1
       230: 1
       231: 1
       232: 1
       233: 1
       234: 1
       235: q^3+1
       236: 1
       237: 1
       238: 1
       239: 1
       240: 1
       241: 1
       242: q^3+1
       243: 1
       244: 1
       245: 1
       246: q^3+1
       247: q^3+1
       248: 1
       249: 1
       250: 1
       251: q^3+1
       252: q^3+1
       253: 1
       254: 1
       255: q^3+1
       256: 1
       257: q^3+1
       258: 1
       259: 1
       260: 1
       261: 1
       262: 1
       263: 1
       264: 1
       265: q^3+1
       266: 1
       267: 1
       268: 1
       269: 1
       270: 1
       271: 1
       272: q^3+1
       273: 1
       274: 1
       275: 1
       276: q^3+1
       277: q^3+1
       278: 1
       279: 1
       280: 1
       281: q^3+1
       282: q^3+1
       283: 1
       284: 1
       285: q^3+1
       286: 1
       287: q^3+1
       288: 1
       289: 1
       290: 1
       291: 1
       292: 1
       293: 1
       294: q^3+1
       295: 1
       296: 1
       297: 1
       298: q^3+1
       299: q^3+1
       300: 1
       301: 1
       302: q^3+1
       303: 1
       304: 1
       305: q^3+1
       306: 1
       307: q^3+1
       308: q^3+1
       309: 1
       310: 1
       311: 1
       312: 1
       313: 1
       314: 1
       315: 1
       316: 1
       317: 1
       318: 1
       319: 1
       320: 1
       321: 1
       322: 1
       323: 1
       324: 1
       325: 1
       326: 1
       327: q^3+1
       328: 1
       329: 1
       330: 1
       331: 1
       332: 1
       333: 1
       334: 1
       335: q^3+1
       336: 1
       337: 1
       338: 1
       339: 1
       340: 1
       341: 1
       342: 1
       343: q^3+1
       344: 1
       345: 1
       346: 1
       347: 1
       348: 1
       349: 1
       350: q^3+1
       351: 1
       352: 1
       353: 1
       354: q^3+1
       355: q^3+1
       356: 1
       357: 1
       358: 1
       359: 1
       360: 1
       361: 1
       362: 1
       363: 1
       364: q^3+1
       365: 1
       366: 1
       367: 1
       368: 1
       369: 1
       370: 1
       371: 1
       372: q^3+1
       373: 1
       374: 1
       375: 1
       376: 1
       377: 1
       378: 1
       379: q^3+1
       380: 1
       381: 1
       382: 1
       383: 1
       384: 1
       385: 1
       386: q^3+1
       387: 1
       388: 1
       389: 1
       390: q^3+1
       391: q^3+1
       392: 1
       393: 1
       394: q^3+1
       395: 1
       396: 1
       397: 1
       398: 1
       399: 1
       400: 1
       401: 1
       402: 1
       403: q^3+1
       404: 1
       405: 1
       406: 1
       407: 1
       408: 1
       409: 1
       410: 1
       411: q^3+1
       412: 1
       413: 1
       414: 1
       415: 1
       416: 1
       417: 1
       418: q^3+1
       419: 1
       420: 1
       421: 1
       422: 1
       423: 1
       424: 1
       425: q^3+1
       426: 1
       427: 1
       428: 1
       429: q^3+1
       430: q^3+1
       431: 1
       432: 1
       433: q^3+1
       434: 1
       435: 1
       436: 1
       437: 1
       438: 1
       439: 1
       440: 1
       441: q^3+1
       442: 1
       443: 1
       444: 1
       445: 1
       446: 1
       447: 1
       448: q^3+1
       449: 1
       450: 1
       451: 1
       452: q^3+1
       453: q^3+1
       454: 1
       455: 1
       456: 1
       457: q^3+1
       458: q^3+1
       459: 1
       460: 1
       461: q^3+1
       462: 1
       463: q^3+1
       465: 1
       466: 1
       467: 1
       468: 1
       469: 1
       470: 1
       471: 1
       472: 1
       473: 1
       474: 1
       475: 1
       476: 1
       477: 1
       478: 1
       479: 1
       480: 1
       481: 1
       482: 1
       483: 1
       484: 1
       485: 1
       486: 1
       487: 1
       488: 1
       489: 1
       490: 1
       491: q^3+1
       492: 1
       493: 1
       494: 1
       495: 1
       496: 1
       497: 1
       498: 1
       499: 1
       500: q^3+1
       501: 1
       502: 1
       503: 1
       504: 1
       505: 1
       506: 1
       507: 1
       508: q^3+1
       509: 1
       510: 1
       511: 1
       512: 1
       513: 1
       514: 1
       515: q^3+1
       516: 1
       517: 1
       518: 1
       519: 1
       520: 1
       521: 1
       522: 1
       523: 1
       524: 1
       525: 1
       526: 1
       527: 1
       528: 1
       529: 1
       530: 1
       531: 1
       532: 1
       533: 1
       534: q^3+1
       535: 1
       536: 1
       537: 1
       538: 1
       539: 1
       540: 1
       541: 1
       542: q^3+1
       543: 1
       544: 1
       545: 1
       546: 1
       547: 1
       548: 1
       549: 1
       550: q^3+1
       551: 1
       552: 1
       553: 1
       554: 1
       555: 1
       556: 1
       557: q^3+1
       558: 1
       559: 1
       560: 1
       561: q^3+1
       562: q^3+1
       563: 1
       564: 1
       565: 1
       566: 1
       567: 1
       568: 1
       569: 1
       570: 1
       571: 1
       572: 1
       573: 1
       574: 1
       575: 1
       576: 1
       577: 1
       578: 1
       579: 1
       580: 1
       581: q^3+1
       582: 1
       583: 1
       584: 1
       585: 1
       586: 1
       587: 1
       588: 1
       589: q^3+1
       590: 1
       591: 1
       592: 1
       593: 1
       594: 1
       595: 1
       596: 1
       597: q^3+1
       598: 1
       599: 1
       600: 1
       601: 1
       602: 1
       603: 1
       604: q^3+1
       605: 1
       606: 1
       607: 1
       608: q^3+1
       609: q^3+1
       610: 1
       611: 1
       612: 1
       613: 1
       614: 1
       615: 1
       616: 1
       617: 1
       618: q^3+1
       619: 1
       620: 1
       621: 1
       622: 1
       623: 1
       624: 1
       625: 1
       626: q^3+1
       627: 1
       628: 1
       629: 1
       630: 1
       631: 1
       632: 1
       633: q^3+1
       634: 1
       635: 1
       636: 1
       637: 1
       638: 1
       639: 1
       640: q^3+1
       641: 1
       642: 1
       643: 1
       644: q^3+1
       645: q^3+1
       646: 1
       647: 1
       648: q^3+1
       650: 1
       651: 1
       652: 1
       653: 1
       654: 1
       655: 1
       656: 1
       658: 1
       659: 1
       660: 1
       661: 1
       662: 1
       663: 1
       664: 1
       665: 1
       666: 1
       667: 1
       668: 1
       669: 1
       670: 1
       671: 1
       672: 1
       673: 1
       674: 1
       675: 1
       676: 1
       677: 1
       678: 1
       679: 1
       680: 1
       681: 1
       682: 1
       683: 1
       684: 1
       685: 1
       686: 1
       687: 1
       688: 1
       689: 1
       690: 1
       691: 1
       692: 1
       693: 1
       694: q^3+1
       695: 1
       696: 1
       697: 1
       698: 1
       699: 1
       700: 1
       701: 1
       702: q^3+1
       704: 1
       705: 1
       706: 1
       707: 1
       708: 1
       709: 1
       710: 1
       711: 1
       712: 1
       713: 1
       714: 1
       715: 1
       716: 1
       717: 1
       718: 1
       719: 1
       720: 1
       721: 1
       722: 1
       723: 1
       724: 1
       725: 1
       726: 1
       727: 1
       728: 1
       729: 1
       730: q^3+1
       731: 1
       732: 1
       733: 1
       734: 1
       735: 1
       736: 1
       737: 1
       738: 1
       739: q^3+1
       740: 1
       741: 1
       742: 1
       743: 1
       744: 1
       745: 1
       746: 1
       747: q^3+1
       748: 1
       749: 1
       750: 1
       751: 1
       752: 1
       753: 1
       754: q^3+1
       756: 1
       757: 1
       758: 1
       759: 1
       760: 1
       761: 1
       762: 1
       763: 1
       764: 1
       765: 1
       766: 1
       767: 1
       768: 1
       769: 1
       770: 1
       771: 1
       772: 1
       773: 1
       774: 1
       775: 1
       776: 1
       777: 1
       778: 1
       779: 1
       780: 1
       781: 1
       782: q^3+1
       783: 1
       784: 1
       785: 1
       786: 1
       787: 1
       788: 1
       789: 1
       790: 1
       791: q^3+1
       792: 1
       793: 1
       794: 1
       795: 1
       796: 1
       797: 1
       798: 1
       799: q^3+1
       800: 1
       801: 1
       802: 1
       803: 1
       804: 1
       805: 1
       806: q^3+1
       807: 1
       808: 1
       809: 1
       810: 1
       811: 1
       812: 1
       813: 1
       814: 1
       815: 1
       816: 1
       817: 1
       818: 1
       819: 1
       820: 1
       821: 1
       822: 1
       823: 1
       824: 1
       825: q^3+1
       826: 1
       827: 1
       828: 1
       829: 1
       830: 1
       831: 1
       832: 1
       833: q^3+1
       834: 1
       835: 1
       836: 1
       837: 1
       838: 1
       839: 1
       840: 1
       841: q^3+1
       842: 1
       843: 1
       844: 1
       845: 1
       846: 1
       847: 1
       848: q^3+1
       849: 1
       850: 1
       851: 1
       852: q^3+1
       853: q^3+1
       855: 1
       856: 1
       857: 1
       858: 1
       859: 1
       860: 1
       862: 1
       863: 1
       864: 1
       865: 1
       866: 1
       867: 1
       868: 1
       870: 1
       871: 1
       872: 1
       873: 1
       874: 1
       875: 1
       876: 1
       877: 1
       879: 1
       880: 1
       881: 1
       882: 1
       883: 1
       884: 1
       885: 1
       886: 1
       887: 1
       888: 1
       889: 1
       890: 1
       891: 1
       892: 1
       893: 1
       894: 1
       895: 1
       896: 1
       897: 1
       898: 1
       899: 1
       900: 1
       901: 1
       902: 1
       903: 1
       904: 1
       905: q^3+1
       907: 1
       908: 1
       909: 1
       910: 1
       911: 1
       912: 1
       913: 1
       915: 1
       916: 1
       917: 1
       918: 1
       919: 1
       920: 1
       921: 1
       922: 1
       923: 1
       924: 1
       925: 1
       926: 1
       927: 1
       928: 1
       929: 1
       930: 1
       931: 1
       932: 1
       933: 1
       934: 1
       935: 1
       936: 1
       937: 1
       938: 1
       939: 1
       940: 1
       941: 1
       942: 1
       943: 1
       944: 1
       945: 1
       946: 1
       947: 1
       948: 1
       949: 1
       950: 1
       951: q^3+1
       952: 1
       953: 1
       954: 1
       955: 1
       956: 1
       957: 1
       958: 1
       959: q^3+1
       961: 1
       962: 1
       963: 1
       964: 1
       965: 1
       966: 1
       967: 1
       969: 1
       970: 1
       971: 1
       972: 1
       973: 1
       974: 1
       975: 1
       976: 1
       977: 1
       978: 1
       979: 1
       980: 1
       981: 1
       982: 1
       983: 1
       984: 1
       985: 1
       986: 1
       987: 1
       988: 1
       989: 1
       990: 1
       991: 1
       992: 1
       993: 1
       994: 1
       995: 1
       996: 1
       997: 1
       998: 1
       999: 1
      1000: 1
      1001: 1
      1002: 1
      1003: 1
      1004: 1
      1005: q^3+1
      1006: 1
      1007: 1
      1008: 1
      1009: 1
      1010: 1
      1011: 1
      1012: 1
      1013: q^3+1
      1015: 1
      1016: 1
      1017: 1
      1018: 1
      1019: 1
      1020: 1
      1021: 1
      1022: 1
      1023: 1
      1024: 1
      1025: 1
      1026: 1
      1027: 1
      1028: 1
      1029: 1
      1030: 1
      1031: 1
      1032: 1
      1033: 1
      1034: 1
      1035: 1
      1036: 1
      1037: 1
      1038: 1
      1039: 1
      1040: 1
      1041: q^3+1
      1042: 1
      1043: 1
      1044: 1
      1045: 1
      1046: 1
      1047: 1
      1048: 1
      1049: 1
      1050: q^3+1
      1051: 1
      1052: 1
      1053: 1
      1054: 1
      1055: 1
      1056: 1
      1057: 1
      1058: q^3+1
      1059: 1
      1060: 1
      1061: 1
      1062: 1
      1063: 1
      1064: 1
      1065: q^3+1
      1068: 1
      1069: 1
      1070: 1
      1072: 1
      1073: 1
      1074: 1
      1075: 1
      1076: 1
      1077: 1
      1079: 1
      1080: 1
      1081: 1
      1082: 1
      1083: 1
      1084: 1
      1085: 1
      1087: 1
      1088: 1
      1089: 1
      1090: 1
      1091: 1
      1092: 1
      1093: 1
      1095: 1
      1096: 1
      1097: 1
      1098: 1
      1099: 1
      1100: 1
      1101: 1
      1102: 1
      1103: 1
      1104: 1
      1105: 1
      1106: 1
      1107: 1
      1108: 1
      1109: 1
      1110: 1
      1111: 1
      1112: 1
      1114: 1
      1115: 1
      1116: 1
      1117: 1
      1118: 1
      1119: 1
      1121: 1
      1122: 1
      1123: 1
      1124: 1
      1125: 1
      1126: 1
      1127: 1
      1129: 1
      1130: 1
      1131: 1
      1132: 1
      1133: 1
      1134: 1
      1135: 1
      1136: 1
      1138: 1
      1139: 1
      1140: 1
      1141: 1
      1142: 1
      1143: 1
      1144: 1
      1145: 1
      1146: 1
      1147: 1
      1148: 1
      1149: 1
      1150: 1
      1151: 1
      1152: 1
      1153: 1
      1154: 1
      1155: 1
      1156: 1
      1157: 1
      1158: 1
      1159: 1
      1160: 1
      1161: 1
      1162: 1
      1163: 1
      1164: q^3+1
      1166: 1
      1167: 1
      1168: 1
      1169: 1
      1170: 1
      1171: 1
      1173: 1
      1174: 1
      1175: 1
      1176: 1
      1177: 1
      1178: 1
      1179: 1
      1181: 1
      1182: 1
      1183: 1
      1184: 1
      1185: 1
      1186: 1
      1187: 1
      1188: 1
      1190: 1
      1191: 1
      1192: 1
      1193: 1
      1194: 1
      1195: 1
      1196: 1
      1197: 1
      1198: 1
      1199: 1
      1200: 1
      1201: 1
      1202: 1
      1203: 1
      1204: 1
      1205: 1
      1206: 1
      1207: 1
      1208: 1
      1209: 1
      1210: 1
      1211: 1
      1212: 1
      1213: 1
      1214: 1
      1215: 1
      1216: q^3+1
      1218: 1
      1219: 1
      1220: 1
      1221: 1
      1222: 1
      1223: 1
      1224: 1
      1226: 1
      1227: 1
      1228: 1
      1229: 1
      1230: 1
      1231: 1
      1232: 1
      1233: 1
      1234: 1
      1235: 1
      1236: 1
      1237: 1
      1238: 1
      1239: 1
      1240: 1
      1241: 1
      1242: 1
      1243: 1
      1244: 1
      1245: 1
      1246: 1
      1247: 1
      1248: 1
      1249: 1
      1250: 1
      1251: 1
      1252: 1
      1253: 1
      1254: 1
      1255: 1
      1256: 1
      1257: 1
      1258: 1
      1259: 1
      1260: 1
      1261: 1
      1262: q^3+1
      1263: 1
      1264: 1
      1265: 1
      1266: 1
      1267: 1
      1268: 1
      1269: 1
      1270: q^3+1
      1272: 1
      1273: 1
      1276: 1
      1277: 1
      1278: 1
      1280: 1
      1281: 1
      1282: 1
      1283: 1
      1284: 1
      1285: 1
      1287: 1
      1288: 1
      1289: 1
      1290: 1
      1291: 1
      1292: 1
      1294: 1
      1295: 1
      1296: 1
      1297: 1
      1298: 1
      1299: 1
      1300: 1
      1302: 1
      1303: 1
      1304: 1
      1305: 1
      1306: 1
      1307: 1
      1308: 1
      1309: 1
      1312: 1
      1313: 1
      1314: 1
      1316: 1
      1317: 1
      1318: 1
      1319: 1
      1320: 1
      1321: 1
      1323: 1
      1324: 1
      1325: 1
      1326: 1
      1327: 1
      1328: 1
      1329: 1
      1331: 1
      1332: 1
      1333: 1
      1334: 1
      1335: 1
      1336: 1
      1337: 1
      1339: 1
      1340: 1
      1341: 1
      1342: 1
      1343: 1
      1344: 1
      1345: 1
      1346: 1
      1347: 1
      1348: 1
      1349: 1
      1350: 1
      1351: 1
      1352: 1
      1353: 1
      1354: 1
      1355: 1
      1356: 1
      1359: 1
      1360: 1
      1361: 1
      1363: 1
      1364: 1
      1365: 1
      1366: 1
      1367: 1
      1368: 1
      1370: 1
      1371: 1
      1372: 1
      1373: 1
      1374: 1
      1375: 1
      1376: 1
      1378: 1
      1379: 1
      1380: 1
      1381: 1
      1382: 1
      1383: 1
      1384: 1
      1386: 1
      1387: 1
      1388: 1
      1389: 1
      1390: 1
      1391: 1
      1392: 1
      1393: 1
      1394: 1
      1395: 1
      1396: 1
      1397: 1
      1398: 1
      1399: 1
      1400: 1
      1401: 1
      1402: 1
      1403: 1
      1405: 1
      1406: 1
      1407: 1
      1408: 1
      1409: 1
      1410: 1
      1412: 1
      1413: 1
      1414: 1
      1415: 1
      1416: 1
      1417: 1
      1418: 1
      1420: 1
      1421: 1
      1422: 1
      1423: 1
      1424: 1
      1425: 1
      1426: 1
      1427: 1
      1429: 1
      1430: 1
      1431: 1
      1432: 1
      1433: 1
      1434: 1
      1435: 1
      1436: 1
      1437: 1
      1438: 1
      1439: 1
      1440: 1
      1441: 1
      1442: 1
      1443: 1
      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: q^3+1
      1457: 1
      1459: 1
      1460: 1
      1463: 1
      1464: 1
      1465: 1
      1468: 1
      1469: 1
      1470: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1487: 1
      1488: 1
      1491: 1
      1492: 1
      1493: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1517: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1524: 1
      1526: 1
      1527: 1
      1530: 1
      1531: 1
      1532: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1556: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1563: 1
      1566: 1
      1567: 1
      1568: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1593: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1613: 1
      1615: 1
      1616: 1
      1618: 1
      1619: 1
      1622: 1
      1623: 1
      1624: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1633: 1
      1635: 1
      1636: 1
      1639: 1
      1640: 1
      1641: 1
      1644: 1
      1645: 1
      1646: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1663: 1
      1665: 1
      1666: 1
      1669: 1
      1670: 1
      1671: 1
      1674: 1
      1675: 1
      1676: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1693: 1
      1694: 1
      1697: 1
      1698: 1
      1699: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1723: 1
      1724: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1729: 1
      1730: 1
      1733: 1
      1735: 1
      1737: 1
      1738: 1
      1741: 1
      1742: 1
      1743: 1
      1746: 1
      1748: 1
      1749: 1
      1751: 1
      1752: 1
      1755: 1
      1756: 1
      1757: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1767: 1
      1769: 1
      1770: 1
      1772: 1
      1773: 1
      1776: 1
      1777: 1
      1778: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1787: 1
      1789: 1
      1790: 1
      1793: 1
      1794: 1
      1795: 1
      1798: 1
      1799: 1
      1800: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1806: 1
      1807: 1
      1809: 1
      1810: 1
      1811: 1
      1812: 1
      1813: 1
      1814: 1
      1815: 1
      1819: 1
      1821: 1
      1822: 1
      1825: 1
      1827: 1
      1829: 1
      1830: 1
      1833: 1
      1834: 1
      1835: 1
      1838: 1
      1840: 1
      1842: 1
      1843: 1
      1846: 1
      1847: 1
      1848: 1
      1851: 1
      1853: 1
      1854: 1
      1856: 1
      1857: 1
      1860: 1
      1861: 1
      1862: 1
      1864: 1
      1865: 1
      1866: 1
      1867: 1
      1868: 1
      1869: 1
      1872: 1
      1876: 1
      1878: 1
      1879: 1
      1883: 1
      1885: 1
      1886: 1
      1889: 1
      1891: 1
      1893: 1
      1894: 1
      1897: 1
      1898: 1
      1899: 1
      1903: 1
      1906: 1
      1910: 1
      1912: 1
      1913: 1
      1918: 1

1919:    0: 1
         1: 1
         2: 1
         3: 1
         4: 1
         5: 1
         6: 1
         7: 1
         8: 1
         9: 1
        10: 1
        11: 1
        12: 1
        13: 1
        14: 1
        15: 1
        16: 1
        17: 1
        18: 1
        19: 1
        20: 1
        21: 1
        22: 1
        23: 1
        24: 1
        25: 1
        26: 1
        27: 1
        28: 1
        29: 1
        30: 1
        31: 1
        32: 1
        33: 1
        34: 1
        35: 1
        36: 1
        37: 1
        38: 1
        39: 1
        40: 1
        41: 1
        42: 1
        43: 1
        44: 1
        45: 1
        46: 1
        47: 1
        48: 1
        49: 1
        50: 1
        51: 1
        52: 1
        53: 1
        54: 1
        55: 1
        56: 1
        57: 1
        58: 1
        59: 1
        60: 1
        61: 1
        62: 1
        63: 1
        64: 1
        65: 1
        66: 1
        67: 1
        68: 1
        69: 1
        70: 1
        71: 1
        72: 1
        73: 1
        74: 1
        75: 1
        76: 1
        77: 1
        78: 1
        79: 1
        80: 1
        81: 1
        82: 1
        83: 1
        84: 1
        85: 1
        86: 1
        87: 1
        88: 1
        89: 1
        90: 1
        91: 1
        92: 1
        93: 1
        94: 1
        95: 1
        96: 1
        97: 1
        98: 1
        99: 1
       100: 1
       101: 1
       102: 1
       103: 1
       104: 1
       105: 1
       106: 1
       107: 1
       108: 1
       109: 1
       110: 1
       111: 1
       112: 1
       113: 1
       114: 1
       115: 1
       116: 1
       117: 1
       118: 1
       119: 1
       120: 1
       121: 1
       122: 1
       123: 1
       124: 1
       125: 1
       126: 1
       127: 1
       128: 1
       129: 1
       130: 1
       131: 1
       132: 1
       133: 1
       134: 1
       135: 1
       136: 1
       137: 1
       138: 1
       139: 1
       140: 1
       141: 1
       142: 1
       143: 1
       144: 1
       145: 1
       146: 1
       147: 1
       148: 1
       149: 1
       150: 1
       151: 1
       152: 1
       153: 1
       154: 1
       155: 1
       156: 1
       157: 1
       158: 1
       159: 1
       160: 1
       161: 1
       162: 1
       163: 1
       164: 1
       165: 1
       166: 1
       167: 1
       168: 1
       169: 1
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      1444: 1
      1445: 1
      1446: 1
      1447: 1
      1448: 1
      1449: 1
      1450: 1
      1451: 1
      1452: 1
      1453: 1
      1454: 1
      1455: 1
      1456: 1
      1457: 1
      1458: 1
      1459: 1
      1460: 1
      1461: 1
      1462: 1
      1463: 1
      1464: 1
      1465: 1
      1466: 1
      1467: 1
      1468: 1
      1469: 1
      1470: 1
      1471: 1
      1472: 1
      1473: 1
      1474: 1
      1475: 1
      1476: 1
      1477: 1
      1478: 1
      1479: 1
      1480: 1
      1481: 1
      1482: 1
      1483: 1
      1484: 1
      1485: 1
      1486: 1
      1487: 1
      1488: 1
      1489: 1
      1490: 1
      1491: 1
      1492: 1
      1493: 1
      1494: 1
      1495: 1
      1496: 1
      1497: 1
      1498: 1
      1499: 1
      1500: 1
      1501: 1
      1502: 1
      1503: 1
      1504: 1
      1505: 1
      1506: 1
      1507: 1
      1508: 1
      1509: 1
      1510: 1
      1511: 1
      1512: 1
      1513: 1
      1514: 1
      1515: 1
      1516: 1
      1517: 1
      1518: 1
      1519: 1
      1520: 1
      1521: 1
      1522: 1
      1523: 1
      1524: 1
      1525: 1
      1526: 1
      1527: 1
      1528: 1
      1529: 1
      1530: 1
      1531: 1
      1532: 1
      1533: 1
      1534: 1
      1535: 1
      1536: 1
      1537: 1
      1538: 1
      1539: 1
      1540: 1
      1541: 1
      1542: 1
      1543: 1
      1544: 1
      1545: 1
      1546: 1
      1547: 1
      1548: 1
      1549: 1
      1550: 1
      1551: 1
      1552: 1
      1553: 1
      1554: 1
      1555: 1
      1556: 1
      1557: 1
      1558: 1
      1559: 1
      1560: 1
      1561: 1
      1562: 1
      1563: 1
      1564: 1
      1565: 1
      1566: 1
      1567: 1
      1568: 1
      1569: 1
      1570: 1
      1571: 1
      1572: 1
      1573: 1
      1574: 1
      1575: 1
      1576: 1
      1577: 1
      1578: 1
      1579: 1
      1580: 1
      1581: 1
      1582: 1
      1583: 1
      1584: 1
      1585: 1
      1586: 1
      1587: 1
      1588: 1
      1589: 1
      1590: 1
      1591: 1
      1592: 1
      1593: 1
      1594: 1
      1595: 1
      1596: 1
      1597: 1
      1598: 1
      1599: 1
      1600: 1
      1601: 1
      1602: 1
      1603: 1
      1604: 1
      1605: 1
      1606: 1
      1607: 1
      1608: 1
      1609: 1
      1610: 1
      1611: 1
      1612: 1
      1613: 1
      1614: 1
      1615: 1
      1616: 1
      1617: 1
      1618: 1
      1619: 1
      1620: 1
      1621: 1
      1622: 1
      1623: 1
      1624: 1
      1625: 1
      1626: 1
      1627: 1
      1628: 1
      1629: 1
      1630: 1
      1631: 1
      1632: 1
      1633: 1
      1634: 1
      1635: 1
      1636: 1
      1637: 1
      1638: 1
      1639: 1
      1640: 1
      1641: 1
      1642: 1
      1643: 1
      1644: 1
      1645: 1
      1646: 1
      1647: 1
      1648: 1
      1649: 1
      1650: 1
      1651: 1
      1652: 1
      1653: 1
      1654: 1
      1655: 1
      1656: 1
      1657: 1
      1658: 1
      1659: 1
      1660: 1
      1661: 1
      1662: 1
      1663: 1
      1664: 1
      1665: 1
      1666: 1
      1667: 1
      1668: 1
      1669: 1
      1670: 1
      1671: 1
      1672: 1
      1673: 1
      1674: 1
      1675: 1
      1676: 1
      1677: 1
      1678: 1
      1679: 1
      1680: 1
      1681: 1
      1682: 1
      1683: 1
      1684: 1
      1685: 1
      1686: 1
      1687: 1
      1688: 1
      1689: 1
      1690: 1
      1691: 1
      1692: 1
      1693: 1
      1694: 1
      1695: 1
      1696: 1
      1697: 1
      1698: 1
      1699: 1
      1700: 1
      1701: 1
      1702: 1
      1703: 1
      1704: 1
      1705: 1
      1706: 1
      1707: 1
      1708: 1
      1709: 1
      1710: 1
      1711: 1
      1712: 1
      1713: 1
      1714: 1
      1715: 1
      1716: 1
      1717: 1
      1718: 1
      1719: 1
      1720: 1
      1721: 1
      1722: 1
      1723: 1
      1724: 1
      1725: 1
      1726: 1
      1727: 1
      1728: 1
      1729: 1
      1730: 1
      1731: 1
      1732: 1
      1733: 1
      1734: 1
      1735: 1
      1736: 1
      1737: 1
      1738: 1
      1739: 1
      1740: 1
      1741: 1
      1742: 1
      1743: 1
      1744: 1
      1745: 1
      1746: 1
      1747: 1
      1748: 1
      1749: 1
      1750: 1
      1751: 1
      1752: 1
      1753: 1
      1754: 1
      1755: 1
      1756: 1
      1757: 1
      1758: 1
      1759: 1
      1760: 1
      1761: 1
      1762: 1
      1763: 1
      1764: 1
      1765: 1
      1766: 1
      1767: 1
      1768: 1
      1769: 1
      1770: 1
      1771: 1
      1772: 1
      1773: 1
      1774: 1
      1775: 1
      1776: 1
      1777: 1
      1778: 1
      1779: 1
      1780: 1
      1781: 1
      1782: 1
      1783: 1
      1784: 1
      1785: 1
      1786: 1
      1787: 1
      1788: 1
      1789: 1
      1790: 1
      1791: 1
      1792: 1
      1793: 1
      1794: 1
      1795: 1
      1796: 1
      1797: 1
      1798: 1
      1799: 1
      1800: 1
      1801: 1
      1802: 1
      1803: 1
      1804: 1
      1805: 1
      1806: 1
      1807: 1
      1808: 1
      1809: 1
      1810: 1
      1811: 1
      1812: 1
      1813: 1
      1814: 1
      1815: 1
      1816: 1
      1817: 1
      1818: 1
      1819: 1
      1820: 1
      1821: 1
      1822: 1
      1823: 1
      1824: 1
      1825: 1
      1826: 1
      1827: 1
      1828: 1
      1829: 1
      1830: 1
      1831: 1
      1832: 1
      1833: 1
      1834: 1
      1835: 1
      1836: 1
      1837: 1
      1838: 1
      1839: 1
      1840: 1
      1841: 1
      1842: 1
      1843: 1
      1844: 1
      1845: 1
      1846: 1
      1847: 1
      1848: 1
      1849: 1
      1850: 1
      1851: 1
      1852: 1
      1853: 1
      1854: 1
      1855: 1
      1856: 1
      1857: 1
      1858: 1
      1859: 1
      1860: 1
      1861: 1
      1862: 1
      1863: 1
      1864: 1
      1865: 1
      1866: 1
      1867: 1
      1868: 1
      1869: 1
      1870: 1
      1871: 1
      1872: 1
      1873: 1
      1874: 1
      1875: 1
      1876: 1
      1877: 1
      1878: 1
      1879: 1
      1880: 1
      1881: 1
      1882: 1
      1883: 1
      1884: 1
      1885: 1
      1886: 1
      1887: 1
      1888: 1
      1889: 1
      1890: 1
      1891: 1
      1892: 1
      1893: 1
      1894: 1
      1895: 1
      1896: 1
      1897: 1
      1898: 1
      1899: 1
      1900: 1
      1901: 1
      1902: 1
      1903: 1
      1904: 1
      1905: 1
      1906: 1
      1907: 1
      1908: 1
      1909: 1
      1910: 1
      1911: 1
      1912: 1
      1913: 1
      1914: 1
      1915: 1
      1916: 1
      1917: 1
      1918: 1
      1919: 1

745377 nonzero polynomials, and 0 zero polynomials,
 at 745377 Bruhat-comparable pairs.